tag:theconversation.com,2011:/uk/topics/maths-skills-16361/articlesMaths skills – The Conversation2023-12-13T13:31:09Ztag:theconversation.com,2011:article/2196462023-12-13T13:31:09Z2023-12-13T13:31:09ZWales’s Pisa school test results have declined – but it’s not a true reflection of an education system<p>Every three years, an early Christmas gift arrives for the global education community from the Organisation for Economic Co-operation and Development (OECD). The Programme for International Student Assessments (<a href="https://www.oecd.org/pisa/">Pisa</a>) is an international test in which 15 year olds are tested on their knowledge and skills. </p>
<p>It relegates those far below the Pisa top ten as poor performers in desperate need of improvement, which this time includes Wales.</p>
<p>The Pisa scores for participating education systems around the world are unquestionably significant. But since its inception in 2000, Pisa has sparked much debate, especially among experts and policymakers, with many viewing it as a <a href="https://ffteducationdatalab.org.uk/2019/11/is-pisa-fundamentally-flawed-because-of-the-scaling-methodology-used/">flawed</a> assessment of educational outcomes. In <a href="https://www.oecd.org/pisa/Combined_Executive_Summaries_PISA_2018.pdf">2018</a>, around 600,000 students took part in the standardised Pisa tests, which measured their performance in maths, science and reading, and also looked at wellbeing.</p>
<p>Predictably, the 2023 Pisa results captured the negative impact of COVID on learners and learning, with some downward trends in performance visible across the data set. </p>
<p>The results signalled mixed fortunes for the <a href="https://www.education.ox.ac.uk/pisa-results-reveal-students-in-the-uk-have-higher-than-average-levels-of-maths-reading-and-science/">UK</a>. The <a href="https://www.bbc.co.uk/news/uk-wales-67616536">BBC headline</a>, reporting the results starkly stated: “Wales slumps to worst school test results.” Such sweeping statements are by now an anticipated byproduct of Pisa that ignore how the tests are often highly contested and <a href="https://revisesociology.com/2020/05/15/the-pisa-global-education-tests-arguments-for-and-against/">controversial</a>. </p>
<h2>Pisa in Wales</h2>
<p>Every three years, Pisa measures the ability of 15 year olds to use their reading, mathematics and science knowledge and skills to meet real-life challenges. In Wales, 2,568 pupils from 89 schools took a two-hour computer-based exercise. To put this in context, there are <a href="https://statswales.gov.wales/Catalogue/Education-and-Skills/Schools-and-Teachers/Schools-Census/Pupil-Level-Annual-School-Census/Pupils/pupils-by-yeargroup-sex">approximately</a> 33,000 pupils in Year 11 in 178 secondary schools and 27 middle schools in Wales.</p>
<p>The subsequent OECD report <a href="https://www.gov.wales/achievement-15-year-olds-program-international-student-assessment-pisa-national-report-2022">acknowledges</a> that “the sample for Wales, and for many other countries, did not meet some of the Pisa standards”. It is important to reflect on how a test taken by a sample of 15-year-old students, every three years for two hours, can possibly be a valid and reliable measure of a system’s performance even in a relative sense. </p>
<p>Pisa’s statistics show that Wales’s average score for mathematics in 2022 was significantly lower than the average across OECD countries. Wales’s average scores for mathematics, reading and science have all declined significantly since 2018. This was also the case, on average, across OECD countries for mathematics and reading. Although for science, the difference between the OECD average in 2022 was not significantly different to that in 2018. </p>
<p>It also noted that the gap in performance between pupils from the most disadvantaged backgrounds and the least disadvantaged backgrounds was smaller in Wales than it was on average across OECD countries for all subjects. </p>
<p>The important thing to observe is that Pisa deals in averages. In the latest results, those averages are derived from the 81 countries that took part, which is a huge range. The report notes a relative fall in Welsh performance against an aggregated average of OECD countries. </p>
<p>It then highlights that this decline was also the case on average across OECD countries for mathematics and reading. In other words, this is a trend. It also suggests that Wales has been more successful in closing the achievement gap between the most disadvantaged and least disadvantaged pupils than most other OECD countries. Yet this important indicator of success has been overshadowed by the blanket headlines of abject educational failure.</p>
<p>If all countries participating in Pisa now recover fully after COVID and improve their educational performance across the board, it is highly likely that Wales will “underperform” on Pisa yet again, whatever it does. If all countries in Pisa continue a steady trajectory of improvement, the country differentials will remain largely the same. Some countries may move up or down, but that movement will be marginal. </p>
<h2>A game of relatives</h2>
<p>There were no real surprises in the latest results. Countries like Singapore, Taiwan and Japan have retained their comparative advantage and will probably continue to do so, because Pisa is a game of relatives. The complexity and dynamic of any education system cannot (and should not) be at the mercy of a single measure of assessment however compelling or lucrative. </p>
<p>But what does that mean for Wales? First, it should encourage us to look at Pisa as one data set only and to not be obsessed by its findings. It is important to put Pisa in perspective by looking far beyond the simple headlines and delving into the detail of the report. </p>
<p>Second, it should be a reminder that Pisa is a snapshot of performance at a particular moment in time. It takes no account of the possibilities and potential of ongoing reform – deep contextual detail is not on its global radar. Hence, the danger is that every three years, Pisa fuels doubt, dissent and concern, when education systems need certainty, confidence and consensus about the reforms they are putting in place.</p>
<p>Third, no education system is perfect. Getting great Pisa scores is certainly no guarantee that the wellbeing and mental health of children and young people is not compromised or sidestepped along the way. The potential of human collateral damage in achieving high Pisa performance over two decades, unsurprisingly, does not feature in the OECD reports. </p>
<p>Wales has a choice, to either let this global compass direct its educational pathway, accepting that every three years it will derail and disrupt the reform agenda, or to hold its nerve. We cannot ignore Pisa, but we can put it in perspective and continue to focus on the learning and wellbeing of all children and young people in Wales. This is what matters most.</p><img src="https://counter.theconversation.com/content/219646/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Alma Harris does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.</span></em></p>Pisa measures 15-year-olds in reading, maths and science every three years - but is that the best way to test an education system?Alma Harris, Professor of Leadership in Education, Cardiff Metropolitan UniversityLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/2093262023-07-20T02:28:56Z2023-07-20T02:28:56ZCurriculum changes must tackle the lifelong consequences of NZ’s alarming literacy and numeracy declines<figure><img src="https://images.theconversation.com/files/538176/original/file-20230719-21-rrwrbn.jpg?ixlib=rb-1.1.0&rect=37%2C61%2C8206%2C5425&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">
</span> <span class="attribution"><span class="source">Getty Images</span></span></figcaption></figure><p>Literacy and numeracy are under the spotlight as Aotearoa New Zealand grapples with how to improve student performance in these basic skills. </p>
<p>At the beginning of 2023, the government rolled out its <a href="https://www.newsroom.co.nz/ideasroom/nz-schools-move-away-from-goodies-and-baddies-history">new history curriculum</a>. But further <a href="https://www.newshub.co.nz/home/politics/2023/04/education-government-makes-changes-to-new-ncea-curriculum-timeline-as-jan-tinetti-puts-focus-on-maths-literacy.html">changes to the curriculum</a> were deferred to put the focus on maths and literacy.</p>
<p>This decision followed a <a href="https://www.newshub.co.nz/home/new-zealand/2022/03/damning-new-report-finds-two-in-five-new-zealand-children-failing-or-only-just-meeting-literacy-standards.html">damning report</a> revealed that by the age of 15, two out of five children are either only just meeting or failing to meet literacy standards. </p>
<p>It is clear the warning bells are ringing over student learning – maybe just not loud or urgently enough.</p>
<p><a href="https://workresearch.aut.ac.nz/__data/assets/pdf_file/0007/689938/PISA-trajectories-Nov-2022.pdf">Our research</a> shows just how essential it is that education policy addresses these basic skills now. If we don’t, struggling students – particularly in already disadvantaged groups – face lifelong consequences that reach well beyond educational success.</p>
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<h2>The state of New Zealand education</h2>
<p>There is a growing sense something is wrong with New Zealand’s education system. </p>
<p>Level 1 National Certificates of Educational Achievement (NCEA) results have been <a href="https://www2.nzqa.govt.nz/about-us/news/ncea-and-ue-2022-attainment-data-now-available/">steadily decreasing since 2017</a>. A 2022 trial of new NCEA literacy and numeracy tests – due to become compulsory in 2024 – produced abysmal results and caused <a href="https://www.rnz.co.nz/news/national/474261/low-pass-rates-in-trial-of-ncea-literacy-and-numeracy-tests-alarm-principals">alarm for a number of principals</a>.</p>
<p>Against international benchmarks, New Zealand’s trends in literacy and numeracy paint a gloomy picture.</p>
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Read more:
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<p>A <a href="https://www.oecd.org/education/pisa-2018-results-volume-i-5f07c754-en.htm">global study</a> found a sharp decline in New Zealand students’ proficiency in reading and mathematics. </p>
<p>In 2009, 14% of students fell below the baseline threshold for literacy proficiency and 15% fell below in maths. In 2018, those falling below the baseline climbed to 19% and 22% respectively. </p>
<p>The OECD considers the baseline level to be one that <a href="https://doi.org/10.1787/9789264091450-en">enables students</a> “to participate effectively and productively in life”. </p>
<p><a href="https://www.educationcounts.govt.nz/__data/assets/pdf_file/0006/196629/PISA-2018-NZ-Summary-Report.pdf">For Māori students</a>, the decline in basic literacy and numeracy is even more significant. In 2009, 24% of Māori students fell below the literacy baseline. This increased to 30% in 2018. Over the decade, the number of Māori students who fell below the baseline in maths went from 27% to 37%. </p>
<p>The decline was smaller for Pacific students, although their starting point was less favourable. More than a third fell below the literacy baseline in 2009, with this share increasing only slightly to 36% in 2018. For maths, 40% of Pacific students fell below the baseline in 2009, increasing to 44% in 2018.</p>
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<h2>Why literacy and numeracy matter</h2>
<p><a href="https://workresearch.aut.ac.nz/__data/assets/pdf_file/0007/689938/PISA-trajectories-Nov-2022.pdf">Our research</a> found literacy and numeracy skills correlate to the wellbeing of individuals. As such, they significantly influence life choices and outcomes. </p>
<p>Our ten-year study followed a cohort of rangatahi (young people) who were 15 years old in 2009. We found those with low reading and maths skills have poorer outcomes across a range of wellbeing measures including education, employment, income, and health and justice.</p>
<p>That those with low literacy and numeracy skills have poorer educational outcomes, particularly in attaining bachelor’s degrees and tertiary qualifications, is unsurprising. They are also less likely to be employed and have lower earnings. The difference is particularly stark among women.</p>
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Read more:
<a href="https://theconversation.com/to-lift-literacy-levels-among-indigenous-children-their-parents-literacy-skills-must-be-improved-first-78827">To lift literacy levels among Indigenous children, their parents' literacy skills must be improved first</a>
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<p>But the impact of these low skills goes beyond education and employment – it also affects wider areas of wellbeing such as health and justice. </p>
<p>For example, those with lower literacy and numeracy skills have higher hospitalisation rates – 59% had at least one hospitalisation between the ages of 15 and 25, compared to 46% of those with higher core competencies. </p>
<p>They were also more likely to engage in criminal activity: just over a quarter of this group had a conviction by time they were 25, compared to just 8% of the group with above-baseline skills.</p>
<p>Importantly, while life outcomes are influenced by literacy and numeracy skills, we also found that higher core skills alone do not necessarily lead to positive wellbeing outcomes. </p>
<p>Ethnicity also plays a powerful role. For example, we found that at age 25, Māori with above-baseline literacy and numeracy skills have about the same average earnings as Pākehā with low skill levels.</p>
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<img alt="" src="https://images.theconversation.com/files/537572/original/file-20230715-26-gzw5vq.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/537572/original/file-20230715-26-gzw5vq.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=392&fit=crop&dpr=1 600w, https://images.theconversation.com/files/537572/original/file-20230715-26-gzw5vq.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=392&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/537572/original/file-20230715-26-gzw5vq.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=392&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/537572/original/file-20230715-26-gzw5vq.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=492&fit=crop&dpr=1 754w, https://images.theconversation.com/files/537572/original/file-20230715-26-gzw5vq.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=492&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/537572/original/file-20230715-26-gzw5vq.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=492&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
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<span class="caption">Average annual earnings at age 25.</span>
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<h2>Using education to address systematic inequalities</h2>
<p>There are myriad reasons why New Zealand needs a curriculum that ensures our future generations are equipped with the skills necessary to succeed and thrive in our fast-changing global economy. </p>
<p>Future generations need and deserve tools that will help them navigate the complexities of life within and beyond our shores. Failure to deliver on the government’s literacy and numeracy goals for the new curriculum will merely perpetuate the existing inequities.</p>
<p>Most of all, failure will undermine the yet-to-be-realised potential in our individual rangatahi and across our collective communities of Aotearoa.</p><img src="https://counter.theconversation.com/content/209326/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>This research was funded by a Ministry of Business, Innovation & Employment Endeavour grant.</span></em></p>The effect of NZ’s abysmal literacy and numeracy rates can be seen in employment, health and justice outcomes. Education policy must address improving in these basic skills.Gail Pacheco, Professor of Economics, Director of the NZ Work Research Institute, Auckland University of TechnologyLisa Meehan, Associate Director (Economics & Research), NZ Work Research Institute, Auckland University of TechnologyThomas Schober, Senior Research Fellow, NZ Work Research Institute, Auckland University of TechnologyLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1980412023-02-08T06:05:56Z2023-02-08T06:05:56ZMaths that will help you as an adult: from baking a cake to asking for a pay rise<figure><img src="https://images.theconversation.com/files/507614/original/file-20230201-10139-vyv5pl.jpg?ixlib=rb-1.1.0&rect=0%2C8%2C6000%2C3979&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">
</span> <span class="attribution"><a class="source" href="https://www.shutterstock.com/image-photo/young-african-man-baking-homemade-cake-2122875098">DimaBerlin/Shutterstock</a></span></figcaption></figure><p>The prime minister, Rishi Sunak, has proposed that school pupils should continue learning <a href="https://www.gov.uk/government/news/prime-minister-sets-ambition-of-maths-to-18-in-speech">maths until 18</a> in order to obtain the numeracy skills needed in careers and everyday adult life. This proposal may be useful to current teenagers – but what about those of us who have already started grappling with adult life, and may feel anxious every time we encounter numbers? </p>
<p><a href="https://www.nationalnumeracy.org.uk/sites/default/files/documents/National_Numeracy_publishes_2019_Impact_Report/nn180_2019_impact_report.pdf">Millions of adults</a> in the UK <a href="https://business-school.open.ac.uk/news/one-five-parents-suffer-arithmophobia">struggle with basic arithmetic</a>. Many suffer from a real phobia – <a href="https://www.nationalnumeracy.org.uk/what-issue/about-maths-anxiety">mathematics anxiety</a> – of numbers, calculations, and even the word “maths”.</p>
<p>Buy there are many times in our daily life where knowing some maths can be helpful to make good decisions. Here are just a few examples to get you started using maths more confidently. </p>
<h2>1. Use ratios to adapt a recipe</h2>
<p>You’ve found a great recipe in a cookbook that you want to try – but the recipe serves four, and you’re only cooking for three and don’t want to use extra ingredients. Ratios can help you work it out. This means dividing something up into parts. Where the recipe calls for four parts of something, you only need three. Mathematically, you can say that what you need compared to the recipe is on a 3:4 ratio. Or, you could use the fraction ¾; the mathematics to solve it is the same. </p>
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<img alt="Quarter life, a series by The Conversation" src="https://images.theconversation.com/files/451343/original/file-20220310-13-1bj6csd.png?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/451343/original/file-20220310-13-1bj6csd.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=600&fit=crop&dpr=1 600w, https://images.theconversation.com/files/451343/original/file-20220310-13-1bj6csd.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=600&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/451343/original/file-20220310-13-1bj6csd.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=600&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/451343/original/file-20220310-13-1bj6csd.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=754&fit=crop&dpr=1 754w, https://images.theconversation.com/files/451343/original/file-20220310-13-1bj6csd.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=754&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/451343/original/file-20220310-13-1bj6csd.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=754&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
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<p><em><strong><a href="https://theconversation.com/uk/topics/quarter-life-117947?utm_source=TCUK&utm_medium=linkback&utm_campaign=UK+YP2022&utm_content=InArticleTop">This article is part of Quarter Life</a></strong>, a series about issues affecting those of us in our twenties and thirties. From the challenges of beginning a career and taking care of our mental health, to the excitement of starting a family, adopting a pet or just making friends as an adult. The articles in this series explore the questions and bring answers as we navigate this turbulent period of life.</em></p>
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<p>If the recipe calls for 120g of flour, you know that that’s to serve four. To find one part, divide 120 by four. Use a calculator – no problem. One part is 30g of flour. Then multiply by the three people you’re cooking for. This gives you 90g of flour for your recipe. </p>
<p>If the recipe said six teaspoons of oil, how much oil would you need? Divide it by four, which gives you one and a half. </p>
<p>You then need three lots of one and a half teaspoons – that’s four and a half teaspoons of oil for your recipe. </p>
<h2>2. Understand averages to see if you need a payrise</h2>
<p>In 2021, the average yearly earnings of people working full time in the UK was <a href="https://www.avtrinity.com/uk-average-salary">£38,131</a>. How do we make sense of this number? </p>
<p>There are different ways of working out an average. In this case, this figure is a type of average known as the mean. It was calculated by adding up all the earnings of all the people working full time, and then dividing that vast number by the number of people. But it doesn’t actually tell us how common it is to earn this amount. </p>
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<img alt="Woman looking at bills anxiously" src="https://images.theconversation.com/files/507605/original/file-20230201-9701-bz77s1.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/507605/original/file-20230201-9701-bz77s1.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/507605/original/file-20230201-9701-bz77s1.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/507605/original/file-20230201-9701-bz77s1.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/507605/original/file-20230201-9701-bz77s1.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/507605/original/file-20230201-9701-bz77s1.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/507605/original/file-20230201-9701-bz77s1.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=503&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
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<span class="caption">Many people find that numbers make them anxious.</span>
<span class="attribution"><a class="source" href="https://www.shutterstock.com/image-photo/portrait-worried-young-single-mother-feeling-696059800">Cast Of Thousands/Shutterstock</a></span>
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<p>This number could be reached if most people earn around £38,131. But it could also be reached if just a few people earned huge amounts and the rest earned very little. The mean could be the same.</p>
<p>Another way of understanding averages is to use the median. This essentially means ordering all the people in a line from the one that earns the least to the one that earns most, and picking the one in the middle. Their earnings would be the median. This is more meaningful, because it means that just a few people earning much more than others don’t skew the average. It is the notion used by the Office of National Statistics to talk about <a href="https://www.ons.gov.uk/employmentandlabourmarket/peopleinwork/earningsandworkinghours/bulletins/annualsurveyofhoursandearnings/2022">“average earnings”</a>.</p>
<p>The median earning for full-time workers in 2021 in the UK was £31,285. If you earn much less than the mean salary for your industry, this doesn’t necessarily tell you a huge deal, because it could also include the earnings of CEOs. But if you earn a lot less than the median, it could be worth figuring out why. </p>
<h2>3. Use mental division at a restaurant</h2>
<p>Having calculators on our phones can make splitting the bill at a restaurant easy, and there’s no shame in using one. But there may be times when your phone is lost at the bottom of a bag, or out of battery. Being able to do the maths in your head is a great skill to have. </p>
<p>The best way to do quick division is to develop your own methods to make it easier. This could involve rounding the figure up or down to a number that is easy to split by the number of people at your table. </p>
<p>Imagine you have to split a £92 bill between four people: 92 is nearly 100, and we know that 100 divided by four is 25. But 92 is eight less than 100, so we need to take that eight off the bill. £8 divided by four people is £2 each less per person. So the bill for each person is £25 minus £2 – £23 each. </p>
<figure class="align-center ">
<img alt="Friends clinking beers at restaurant" src="https://images.theconversation.com/files/507612/original/file-20230201-10196-xvmqx2.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/507612/original/file-20230201-10196-xvmqx2.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=381&fit=crop&dpr=1 600w, https://images.theconversation.com/files/507612/original/file-20230201-10196-xvmqx2.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=381&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/507612/original/file-20230201-10196-xvmqx2.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=381&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/507612/original/file-20230201-10196-xvmqx2.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=478&fit=crop&dpr=1 754w, https://images.theconversation.com/files/507612/original/file-20230201-10196-xvmqx2.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=478&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/507612/original/file-20230201-10196-xvmqx2.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=478&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Maths can help you split the bill.</span>
<span class="attribution"><a class="source" href="https://www.shutterstock.com/image-photo/happy-friends-toasting-bio-organic-beer-691181062">DisobeyArt/Shutterstock</a></span>
</figcaption>
</figure>
<p>Someone else might prefer to round the £92 down to another number that is easy to divide by four: £80. This makes £20 each. There’s then £12 left on the total to divide up between four. This means an extra £3 each, so £23 for each to pay. </p>
<h2>Work out a route for a hike</h2>
<p>Perhaps you’re planning a trip with some friends, and it involves a sightseeing walk through a city or a countryside hike. You want to plan a route that suits everybody and won’t leave you stranded and far from your destination when it gets dark. Maths can help you. </p>
<p>More than a century ago, a Scottish mountaineer devised a formula called <a href="https://www.ordnancesurvey.co.uk/newsroom/blog/why-were-adjusting-naismiths-rule">Naismith’s rule</a>. It says that when planning a route, allow one hour for each 5km (three miles) you will walk, and, if you’re going uphill, add ten minutes for each 100m (300 feet) you climb. So if your planned route is a 15km hike with 600m of climbing, this would take you three hours plus one extra hour: four hours in total. </p>
<p>Once you’ve worked that out, another mathematical skill can come in useful: estimation. Perhaps your walk will be more of an amble – so add on a bit of time. You’re going to stop for lunch, so an hour to eat. You might end up giving yourself about six hours to complete your walk, and now can figure out what might be a good time to set off. </p>
<p>Mathematics is there to help you. With the right mindset, <a href="http://www.mathematicalresilience.org/">everybody can learn mathematics</a>.</p><img src="https://counter.theconversation.com/content/198041/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Davide Penazzi does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.</span></em></p>Many people suffer from maths anxiety, which can make using numbers difficult.Davide Penazzi, Senior Lecturer in Mathematics, University of Central LancashireLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1972362023-01-05T20:05:54Z2023-01-05T20:05:54ZRishi Sunak is right about a lack of maths skills in England: here’s how plans to extend teaching could work<figure><img src="https://images.theconversation.com/files/503277/original/file-20230105-24-sxz5c4.jpg?ixlib=rb-1.1.0&rect=0%2C8%2C5799%2C3845&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">
</span> <span class="attribution"><a class="source" href="https://www.shutterstock.com/image-photo/young-african-man-solving-mathematics-problem-1894312696">Ground Picture/Shutterstock</a></span></figcaption></figure><p>UK prime minister Rishi Sunak has proposed making <a href="https://www.gov.uk/government/news/prime-minister-sets-ambition-of-maths-to-18-in-speech">the study of mathematics compulsory</a> for all students in England up to the age of 18, to help young people “in a world where data is everywhere and statistics underpin every job”.</p>
<p>Extending compulsory maths education past 16 is not a new idea. It has been suggested by <a href="https://www.gov.uk/government/speeches/michael-gove-speaks-to-the-royal-society-on-maths-and-science">other ministers</a> and has failed to materialise. What is clear, though, is that the prime minister’s reasoning is grounded in fact. There is a mathematical skills shortage in the UK.</p>
<p>The government’s <a href="https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/630488/AS_review_report.pdf">2017 Smith Review</a> found that only around 20% of students on non-STEM degrees in higher education have studied mathematics after the age of 16. A <a href="https://www.nuffieldfoundation.org/wp-content/uploads/2019/12/Is-the-UK-an-Outlier_Nuffield-Foundation_v_FINAL.pdf">Nuffield Foundation report</a>, which compared England, Scotland, Northern Ireland and Wales to 20 other developed nations (including Estonia, Spain, Japan, Korea and Russia) found that they were four of only six countries that did not require any mathematics study after 16. </p>
<p>What’s more, around half of adults in the UK are reported to have the same level of numeracy as is expected of a child <a href="https://www.nationalnumeracy.org.uk/sites/default/files/documents/National_Numeracy_publishes_2019_Impact_Report/nn180_2019_impact_report.pdf">at primary school</a>. This lack of maths skills has been estimated to cost the UK <a href="https://www.nationalnumeracy.org.uk/sites/default/files/documents/nn124_essentials_numeracyreport_for_web.pdf">£20 billion per year</a>. </p>
<h2>Limited resources</h2>
<p>However, Sunak’s plan has been met with criticism. A hurdle to the idea to extend maths teaching is the <a href="https://www.tes.com/magazine/news/secondary/teacher-shortage-schools-recruitment-non-specialist-maths-lessons">widespread shortage</a> of maths teachers. This shortage is compounded by teachers leaving the profession. Approximately a third of all teachers have left <a href="https://epi.org.uk/wp-content/uploads/2021/05/EPI-Local-teacher-labour-markets-2021.pdf">five years after qualifying</a>. </p>
<p>There are also <a href="https://www.naht.org.uk/News/Latest-comments/News/ArtMID/556/ArticleID/1223/A-failure-to-invest-the-state-of-school-funding-2021">issues of funding</a>. Schools have had to make budget cuts, meaning that they are struggling to offer the necessary provisions to their staff and students.</p>
<p><div data-react-class="Tweet" data-react-props="{"tweetId":"1610699904791285761"}"></div></p>
<p>While the government has not as yet specified what form post-16 compulsory maths would take, Sunak made it clear that he was not intending that all pupils should take A-level maths. Instead, the government is <a href="https://www.gov.uk/government/news/prime-minister-sets-ambition-of-maths-to-18-in-speech">exploring options</a> which include existing qualifications, such as <a href="https://www.gov.uk/government/publications/core-maths-qualifications-technical-guidance">core maths</a>. </p>
<p>The subject was <a href="https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/266717/Policy_statement_on_16-18_Core_Maths_qualifications_-_final__3_.pdf">introduced in 2013</a> and has been taught since 2015. It differs from A-level maths by focusing on topics such as finance, modelling, optimisation, statistics, probability and risk in a way which favours the application of these ideas rather than the theory behind them. Most of the background mathematical skills needed are at a similar difficulty to GCSE maths. </p>
<h2>Expanding core maths</h2>
<p>If the government is committed to extending post-16 maths, making core maths compulsory (for those who do not take A-level maths) may well be <a href="https://royalsociety.org/blog/2022/01/core-maths-qualifications/">the best option</a>. </p>
<p>The added advantage of core maths is that it does not strictly require teachers to be subject specialists, though teachers must have a competent level of mathematics knowledge. </p>
<p>It is intended for A-level students who have passed their GCSE maths but who are not taking A-levels in maths. It can be taught alongside existing A-level qualifications, carrying the same number of UCAS points as an AS-level (roughly equivalent to half an A-level). It can be taught in one year or spread over two.</p>
<p><a href="https://mei.org.uk/summary-of-core-maths-entries-and-results-august-2022-uk/">The number of students</a> taking core maths has grown, if slowly: from just under 3,000 in 2015 to just over 12,000 students in 2022. </p>
<p>A limited number of further education colleges <a href="https://coremathsproject.leeds.ac.uk/wp-content/uploads/sites/32/2020/09/Core-Maths-Final-Report-Sept-2020.pdf">have made the qualification available</a>. Universities have also been slow to recognise the qualification, as core maths does not count as one of the three required A-level qualifications which universities traditionally base offers on. However, <a href="https://amsp.org.uk/the-universities-of-sheffield-and-york-add-their-support-for-level-3-maths-including-core-maths/">some universities</a> have started recognising core maths in their offers to students. </p>
<p>Some post-16 educational pathways which are not based on A-levels already have some form of compulsory mathematics. These include the <a href="https://www.ibo.org/">International Baccalaureate</a> and some vocational qualifications such as <a href="https://www.ncetm.org.uk/features/t-levels-what-maths-teachers-need-to-know/">T-Levels</a>. In addition, students in post-16 education who have failed to reach a level 4 or grade C in GCSE mathematics must resit this qualification until they <a href="https://www.cambridgeassessment.org.uk/Images/476535-which-students-benefit-from-retaking-mathematics-and-english-gcses-post-16-.pdf">achieve a pass</a>.</p>
<p>However, if Sunak’s statements are correct in that there is such an obvious need for mathematics to be made compulsory until the age of 18, this may suggest that GCSE mathematics is not adequately meeting the needs of students. The reasons for the low uptake of mathematics after the age of 16 often stem from issues which learners face at a much younger age. </p>
<p>Many young people feel <a href="https://theconversation.com/what-a-fear-of-maths-does-to-children-new-research-150108">high anxiety</a> about maths and even a strong dislike towards the subject. It may be that the existing mathematics curriculum should be carefully considered before post-16 mathematics is made compulsory.</p><img src="https://counter.theconversation.com/content/197236/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>The authors do not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and have disclosed no relevant affiliations beyond their academic appointment.</span></em></p>Extending the existing core maths qualification could help improve numeracy.Alexei Vernitski, Senior Lecturer in Mathematics, University of EssexAlexander Partner, Lecturer and PhD researcher in mathematics education, University of EssexLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1890952022-09-02T15:14:31Z2022-09-02T15:14:31ZCost of living: four ways to stop banks and companies using complex maths against you<figure><img src="https://images.theconversation.com/files/482022/original/file-20220831-21-29fb0n.jpg?ixlib=rb-1.1.0&rect=125%2C83%2C9198%2C6094&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">You can do it.</span> <span class="attribution"><a class="source" href="https://www.shutterstock.com/image-photo/young-african-american-girl-accountant-working-1947491656">Krakenimages.com/Shutterstock</a></span></figcaption></figure><p>The cost of living crisis is dominating headlines at the moment. With so much conflicting information flying around, it can be hard to work out what is the best way to look after your household finances. </p>
<p>Banks, energy providers and shops will often try to blind you with big numbers and confusing mathematical terms – often preying on people’s fear of mathematics. However, even if you count yourself as a numberphobe, there are a few very simple steps you can take to use maths in your favour and save some money.</p>
<h2>The trouble with averages</h2>
<p>For most people, the biggest impact on the cost of living will come from hikes in gas and electricity costs. This is tied to the price cap, which is set by Ofgem. But much of the reporting around this cap is somewhat misleading. </p>
<p>Last week, the October price cap <a href="https://www.ofgem.gov.uk/publications/ofgem-updates-price-cap-level-and-tightens-rules-suppliers">was announced</a> as being £3,549. But that price is based on an average household. The very nature of an average is that roughly half of households will use more energy than this, and roughly half will use less.</p>
<p>Therefore, it is very useful to have an idea of how much energy your own household actually uses in a year. If you have lived in the same house for a few years, you can look at your usage over previous years as a guide. If you’re in a new home, you can make an estimate by factoring in the size of house, number of people who live there and other information using an <a href="https://great-home.co.uk/average-energy-consumption-calculator/">energy consumption calculator</a>.</p>
<p>Your energy bill for each type of fuel is based on two values – a daily standing charge (SC), which you pay every day regardless of usage, and a cost per unit of energy (CPU). Once you know how many units (u) of that fuel you use per year, you can easily calculate your expected bill for a given year by computing (365 x SC) + (u x CPU).</p>
<h2>Know your percentages</h2>
<p>Another huge contributor to the cost of living crisis is the rocketing inflation rate, which currently sits at 8.8%. In response to this, the Bank of England has raised its base rate to 1.75%, which has a knock-on effect on interest rates on both savings and loans.</p>
<p>The impact of this change in the short term depends on whether you are in net debt. If you have more money in savings than in loans (including your mortgage, student loans etc), then it’s possible the increased interest rate will give you an opportunity to address some of the impacts of inflation. However, if the opposite is true, and especially if you are coming to the end of the fixed-rate period of a mortgage, then you will most likely be a lot worse off than you are now.</p>
<p>The simplest way to review the impact is to look at the interest rates associated with each of your accounts. For a savings account, a 2% interest rate on a balance of £100 will leave you with £102 at the end of the year. If it’s a loan, you’ll owe £2 more. If you have both but the savings account has a lower interest rate, then it may be in your interest to use at least some of those savings to pay off your loan.</p>
<p>However, most loans – including most mortgages – are repayment loans, which means you borrow a certain amount and then pay it off over a pre-agreed period, <a href="https://www.zoopla.co.uk/discover/buying/how-to-work-out-your-mortgage-repayment/">according to a certain formula</a>. The way such loans are structured means the first few payments will see the majority of your money going towards the interest, with the overall balance being reduced by only a small amount. For a £150,000 loan at a 4% interest rate over 25 years, your monthly payment would be £791.76 – and in the first month, £500 of that would be interest.</p>
<p>Therefore in many cases, if you are in the early stages of a mortgage and have the ability to overpay, you may save yourself a lot more money in the long run. You can use <a href="http://mortgagecalculator.co.uk/">mortgage calculators</a> to look at how much of your monthly payment actually goes towards paying off your debt.</p>
<h2>Divide and conquer</h2>
<p>The aisles of large supermarkets can be confusing places, with different versions and sizes of the same product available at a wide range of prices designed to bamboozle you. For example, the soft drinks aisle of my local shop often includes 2-litre, 1.5-litre, 1.25-litre, 1-litre, 600ml and 500ml bottles, plus 330ml and 150ml cans sold individually and in multi-packs. </p>
<figure class="align-center ">
<img alt="Image of a supermarket aisle." src="https://images.theconversation.com/files/482021/original/file-20220831-16-p9q0dr.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/482021/original/file-20220831-16-p9q0dr.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=450&fit=crop&dpr=1 600w, https://images.theconversation.com/files/482021/original/file-20220831-16-p9q0dr.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=450&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/482021/original/file-20220831-16-p9q0dr.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=450&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/482021/original/file-20220831-16-p9q0dr.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=566&fit=crop&dpr=1 754w, https://images.theconversation.com/files/482021/original/file-20220831-16-p9q0dr.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=566&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/482021/original/file-20220831-16-p9q0dr.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=566&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
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<span class="caption">Do some maths in the supermarket.</span>
<span class="attribution"><span class="source">Simon Shek/Flickr</span>, <a class="license" href="http://creativecommons.org/licenses/by-sa/4.0/">CC BY-SA</a></span>
</figcaption>
</figure>
<p>Although it’s typically true that the larger sizes are better value (and better for the environment since they use less packaging), this isn’t always the case once you factor in special offers. A simple tip that will work for any non-perishable product is to calculate the price per unit so you have a direct comparison. </p>
<p>For example, if a 2-litre (2000ml) bottle of cola costs £1.75, that means the cost per 100ml is 175/20 = 8.75p. The equivalent for a 1.25-litre bottle on offer at £1 would be 100/12.5 = 8p per litre, meaning the smaller bottle would be better value in this case.</p>
<p>In many cases, supermarkets include these costs on the price label to help you out. Even when they don’t, it might be worth calculating the unit costs of more expensive products to save yourself a few quid each week. </p>
<h2>Don’t expect the unexpected</h2>
<p>It can be tempting to think about the potential riches of winning big in a lottery or hitting the casino, but these are surefire ways to lose money on average. That’s because of the statistical concept of <a href="https://www.statisticshowto.com/probability-and-statistics/expected-value/">expected value</a> – the average outcome you would expect if you could theoretically repeat an activity over and over again.</p>
<p>Suppose I suggested a game where we rolled a die, and if it was a number from one to five you had to give me £1, but if it was a six you’d get £2. Clearly that wouldn’t seem like a good idea since I would win most of the time, so your “prize” for getting lucky isn’t high enough. But how do we know what prize would be high enough? That’s where our expected value comes in.</p>
<p>Think about the first example. All six outcomes from throwing a die are equally likely. In one of the six outcomes your profit is £2, but in five of the six outcomes you lose £1 (i.e. have a profit of -£1). We can use some simple probability to calculate your expected profit from this game:</p>
<blockquote>
<p>E(profit) = (-£1 * 5/6) + (£2 * 1/6) = -£1/2 (or -50p).</p>
</blockquote>
<p>On average, every time we play, you will lose 50p. But using the same equation, if the “prize” for rolling a 6 is increased to £5, then E(profit) = 0. On average, you will now break even from this game. A prize of £8 gives E(profit) = 50p, meaning that on average you would win 50p each time you played.</p>
<p>We can apply a similar concept to the National Lottery, where the odds of matching six numbers can be calculated using some slightly more complicated probability. Based on this, the expected value of a £2 lottery ticket on August 27 was 95p – if this draw was repeated over and over again, you’d lose over £1 each time. Therefore, the lottery should not be considered anything more than a bit of fun, <a href="https://www.theguardian.com/science/2016/jan/09/national-lottery-lotto-drawing-odds-of-winning-maths">except perhaps on the rare exceptions</a> where there is a large rollover prize. </p>
<p>Similar concepts apply to a casino, where the house introduces measures specifically designed to weight the odds in its favour. For example, the presence of the 0 on a roulette wheel means the expected value from a £1 bet on a particular number is 97.3p – in other words, you lose over 2p per spin on average. </p>
<p>Ultimately, it is going to be a very challenging winter for most of us. The main way the country can overcome this crisis is with more large-scale help. But while we wait to see if that actually arrives, all we can really do as individuals is make small changes, and of course help out others less fortunate than ourselves.</p><img src="https://counter.theconversation.com/content/189095/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Craig Anderson does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.</span></em></p>A few mathematical tools can help you save cash during the cost of living crisis.Craig Anderson, Lecturer in Statistics, University of GlasgowLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1686252021-09-29T13:50:23Z2021-09-29T13:50:23ZBeing good at maths might help you become great at sports – Emma Raducanu showed us why<p>Following her triumph in the recent US Open tennis tournament, Emma Raducanu was interviewed by Chinese media outlet <a href="https://www.youtube.com/watch?v=ryBaGnweihc&ab_channel=CGTNSportsScene">CGTN</a> and revealed that maths was her favourite subject at school. Raducanu told the interviewer she was “a numbers person” and really enjoyed the problem-solving aspect. The tennis player, who recently received an A* at A-level, said she loved working on maths puzzles which, she said, gave her a thrill to solve.</p>
<p>Her passion for maths follows in the footsteps of Britain’s last US Open winner in the women’s singles, Virginia Wade. Wade is also a keen mathematician, picking up a maths <a href="http://news.bbc.co.uk/sport1/hi/tv_and_radio/sports_personality_of_the_year/7689413.stm">degree</a> from the University of Sussex in 1966. This coincidence may spark questions about whether mathematical ability is useful for elite sportspeople, especially in tennis.</p>
<p>Sport and maths are very different activities, but some aspects of the mindset required to be successful in maths or sport can certainly help you to achieve success in the other. </p>
<p>Let’s consider the hard skills that we may associate with both maths and tennis. <a href="https://www.sciencedirect.com/science/article/pii/S0306261921007194?casa_token=WkgNf7SO6JwAAAAA:wJtfmu-3oo7cr7TKZrJrWIsbFS-5_qv6IWMO6FATeyo_PJnVybn7JNG-odXqWB7K-hgHL2Sfrs4">Hard skills</a> can be thought of as the technical, physical, or knowledge expertise that we bring to a given task. In this case we may think of mathematicians (as well as physicists) as being good with angles or able to understand how <a href="https://www.sciencedirect.com/science/article/pii/S1877705814006134">spin</a> may affect a tennis ball. </p>
<figure>
<iframe width="440" height="260" src="https://www.youtube.com/embed/ryBaGnweihc?wmode=transparent&start=0" frameborder="0" allowfullscreen=""></iframe>
<figcaption><span class="caption">Emma Radacanu talks about maths being her favourite subject.</span></figcaption>
</figure>
<p>This often is the case, but calculating angles or how a tennis ball may spin or bounce on different <a href="https://link.springer.com/content/pdf/10.1007/BF02903531.pdf">court types</a> while in the comfort of a classroom or office is quite a different beast to the split-second decisions that tennis players have to make about angle and spin as the ball comes hurtling towards them at speeds of over 100mph. </p>
<p>There are certainly interesting aspects in a game of tennis for mathematicians to study and it is important for players to understand how spin and bounce may be affected in different conditions. But the way in which the mathematician and tennis player go about their work here is very different and the crossover of skills seems minimal in this sense.</p>
<p>Instead, we may wish to think about the soft skills that studying maths may provide us with. Soft skills are <a href="https://muse.jhu.edu/article/609811/summary?casa_token=Z68FLM4UyoIAAAAA:NHYpkVRA3XQMkTa6zVpFQe4P-fVmhTMkBSsXRkJa7CJt0sIsW12DLXiMcp4k1XplHEOk-SLN0i8">harder to define</a> but loosely relate to personality traits such as creativity, communication, leadership, and mentality that contribute to our success. They are also an increasingly important part of the <a href="https://eric.ed.gov/?id=EJ764824">higher education curriculum</a>, in mathematics and beyond, as educators try to prepare students for the job market after their degree. Two soft skills in particular stand out as connecting mathematicians to elite athletes, especially tennis players.</p>
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Read more:
<a href="https://theconversation.com/tennis-a-smashing-history-of-how-rackets-shaped-the-game-127784">Tennis: a smashing history of how rackets shaped the game</a>
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</em>
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<hr>
<h2>Problem Solving</h2>
<p>Problem solving is listed in almost every list of soft skills, be that from the job market or in <a href="https://ir.nust.na/handle/10628/39">education literature</a>, and is the most obvious connection between maths and tennis. Maths is essentially a series of problems that mathematicians try to solve, and this can help with our problem solving skills in life. This could be simple arithmetic at a young age, going all the way up to the <a href="https://www.claymath.org/millennium-problems">Millennium Prize Problems</a> that the very best modern mathematicians are desperately trying to solve in order to claim a $1 million prize. </p>
<p>In tennis, problem solving truly is a buzz phrase and there are countless interviews with players, such as <a href="https://www.wtatennis.com/news/2243992/swiatek-overcomes-kontaveit-sakkari-pliskova-advance-to-us-open-round-of-16">this example</a> from the recent US Open, in which players discuss their efforts in trying to solve the problem or puzzle set by their opponent. Raducanu even mentions it herself in the <a href="https://www.youtube.com/watch?v=ryBaGnweihc&ab_channel=CGTNSportsScene">CGTN</a> interview. This is not just limited to tennis though, almost all sports contain a problem-solving aspect, as shown in <a href="https://opensportssciencesjournal.com/VOLUME/5/PAGE/26/ABSTRACT/">this research</a> highlighting examples in combat sports and rugby. </p>
<figure class="align-center ">
<img alt="Girl doing maths at school" src="https://images.theconversation.com/files/423818/original/file-20210929-19363-ozlmo5.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/423818/original/file-20210929-19363-ozlmo5.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/423818/original/file-20210929-19363-ozlmo5.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/423818/original/file-20210929-19363-ozlmo5.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/423818/original/file-20210929-19363-ozlmo5.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/423818/original/file-20210929-19363-ozlmo5.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/423818/original/file-20210929-19363-ozlmo5.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=503&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Learning maths can help with problem solving skills in sport.</span>
<span class="attribution"><span class="source">Kiselev Andrey Valerevich/Shutterstock</span></span>
</figcaption>
</figure>
<h2>Resilience</h2>
<p>This is the big one. In maths this has been <a href="https://www.researchgate.net/publication/48989695_Developing_mathematical_resilience">defined</a> as a stance “that enables pupils to continue learning despite finding setbacks”. At almost any level in maths, we will eventually come across a problem that we struggle to solve or get wrong first time. The ability to persevere and try new techniques and to not simply give up is fundamental in becoming a successful mathematician. </p>
<p>This is a huge issue on a global scale, with studies on <a href="https://academic.oup.com/teamat/advance-article/doi/10.1093/teamat/hrab005/6228273?login=true">Welsh A-Level students</a> and <a href="https://iopscience.iop.org/article/10.1088/1742-6596/1806/1/012060/meta">Indonesian high school students</a> providing just two of many examples from 2021 alone of research looking to further understand how to develop resilience among maths students. From a sporting perspective, <a href="https://www.tandfonline.com/doi/full/10.1080/21520704.2016.1236050?casa_token=I0NIu6RJW14AAAAA%3AUyQ9NJd5_aU2iV9kQ-nxf0pzS0xdwiMF2CWymdVcJekSyS_9fl7n2yrsGwY-zKWXSsqyGy2YKQ6LBQ">developing resilience</a> and <a href="https://www.tandfonline.com/doi/full/10.1080/02640414.2014.901551?casa_token=MBqz6klu0gUAAAAA%3A5JcipDpVOypdUMw7_MVTGZn0vP_Q5bvTLNWQ8k3Zg2B7kq85FqRyB7U-NVzpr74ih0tyfcCCBnIImQ">understanding what affects</a> resilience among athletes is also a major area of current research interest.</p>
<p>In this sense, Radacanu has truly excelled. Winning the US Open in the aftermath of her early <a href="https://www.bbc.co.uk/sport/tennis/57724076">exit in her first Wimbledon tournament</a> and the subsequent <a href="https://news.sky.com/story/andy-murray-hits-back-at-piers-morgans-very-harsh-take-on-british-tennis-star-emma-raducanu-12350136">criticism that came her way</a> showed a level of resilience that is far beyond the capabilities of almost all of us.</p>
<h2>Crossover skills</h2>
<p>Previous research has suggested that early achievements in physical activity and mathematics are related at a <a href="https://www.sciencedirect.com/science/article/pii/S1440244019312149?casa_token=weObnwoeikcAAAAA:vhnQwPqSvKMYWAP01aVWMcKk-VuovEag2Vy8WJV3sfULuL2t0wwxHpOh0-RuTcW2xavwozIdN5U">young age</a>. The evidence given above of how problem solving and resilience are vital to both higher level mathematics and professional sport indicates that this relationship continues to some extent as we get older.</p>
<p>These crossover skills have brought Raducanu success in both fields. She does not just possess the ability to problem solve and the resilience to overcome adversity, she has honed those skills to an incredibly high level. Raducanu may have the ingredients needed to become a great mathematician (although we may never know), but she also has so much more than that. </p>
<p>Physical fitness, a strong work ethic, and the ability to make decisions within a second or two of her opponent making their play put her skill set on a completely different level to a mere mathematician like this author. Being good at maths has not made her a great tennis player, but it’s possible that some of the skills she has learned through maths have helped her along, in small ways.</p><img src="https://counter.theconversation.com/content/168625/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Laurence Shaw does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.</span></em></p>A love of mathematics could help sports stars solve problems on court.Laurence Shaw, Lecturer in Mathematics, Nottingham Trent UniversityLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1631102021-07-06T20:09:27Z2021-07-06T20:09:27ZAussie kids’ financial knowledge is on the decline. The proposed national curriculum has downgraded it even further<figure><img src="https://images.theconversation.com/files/409659/original/file-20210705-19-18k5p6l.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">
</span> <span class="attribution"><a class="source" href="https://www.shutterstock.com/image-photo/little-boy-putting-pocket-money-piggy-1100944310">Shutterstock</a></span></figcaption></figure><p>Financial literacy means <a href="https://www.oecd-ilibrary.org/sites/a1fad77c-en/index.html?itemId=/content/component/a1fad77c-en">having an understanding of financial concepts</a> and risks, and the skills, motivation and confidence to make effective decisions across a range of financial contexts. </p>
<p>In Australia, many young people have trouble with financial literacy, <a href="https://journal.spera.asn.au/index.php/AIJRE/article/view/6">especially young people</a> in lower socioeconomic groups, who live in rural areas or who have a language background other than English. </p>
<p>According to Scott Pape — author of the Barefoot Investor and whose program Money Movement is screening on <a href="https://www.dailytelegraph.com.au/education-new-south-wales/barefoot-investor-scott-pape-brings-financial-literacy-into-nsw-schools/news-story/bc848d9915d93233ca76b7b239a5aa77">Foxtel’s Lifestyle Channel</a> — most children don’t learn the necessary financial skills they need at school. More than 100,000 people have signed his <a href="https://www.change.org/p/australian-state-governments-it-s-time-to-kick-the-banks-out-of-schools-and-teach-kids-real-money-skills?recruiter=1210900675&recruited_by_id=fffc3ee0-cbc1-11eb-9c44-8d2b44c61d46&utm_source=share_petition&utm_medium=copylink&utm_campaign=petition_dashboard">recently launched petition</a> to bring a “financial revolution” to schools.</p>
<p>There is no independent financial literacy strand in the Australian Curriculum, but a sub-strand exists within maths. This is clearly not enough. The <a href="https://research.acer.edu.au/cgi/viewcontent.cgi?article=1049&context=ozpisa">financial literacy performance of Australian 15 year olds’</a> in the OECD’s 2018 Programme for International Student Assessment (PISA) financial literacy assessment fell by by 15 points (or half a year of schooling) since 2012.</p>
<p><div data-react-class="Tweet" data-react-props="{"tweetId":"1285391520481153024"}"></div></p>
<p>And yet, the draft of the revised Australian Curriculum downgrades financial literacy even further.</p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/teaching-kids-about-maths-using-money-can-set-them-up-for-financial-security-85327">Teaching kids about maths using money can set them up for financial security</a>
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<h2>What’s changed?</h2>
<p>The current maths curriculum includes some content providing teachers with explicit direction to teach fundamental financial concepts. These include representing monetary values, rounding up to the nearest five cents, or solving simple and compound interest problems. </p>
<p>For example, in the <a href="https://www.australiancurriculum.edu.au/media/7046/mathematics_comparative_information_7-10.pdf">current year 10 curriculum</a>, students are required to</p>
<blockquote>
<p>Connect the compound interest formula to repeated applications of simple interest using appropriate digital technologies.</p>
</blockquote>
<p>This is a clear description of the need for teachers to help develop essential financial maths knowledge and skills. </p>
<p>The Australian Curriculum, Assessment and Reporting Authority in April released a draft of the <a href="https://www.australiancurriculum.edu.au/consultation/">proposed revised curriculum</a> for consultation. The above <a href="https://www.australiancurriculum.edu.au/media/7046/mathematics_comparative_information_7-10.pdf">year 10 content has changed</a> to students having to:</p>
<blockquote>
<p>use formulas involving exponents and real numbers to solve practical problems (including financial contexts) involving growth and decay and solve using digital tools as appropriate.</p>
</blockquote>
<p>This wording no longer ensures students are taught about social aspects of, as well as how to calculate, compound interest. Previously it was the teacher’s discretion as to how they taught exponential growth and decay. Currently teachers are likely using transmission of COVID as the context to teach these concepts. </p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/409818/original/file-20210706-21-xq88fw.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="Four stacks of coins of various heights in front of a clock." src="https://images.theconversation.com/files/409818/original/file-20210706-21-xq88fw.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/409818/original/file-20210706-21-xq88fw.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/409818/original/file-20210706-21-xq88fw.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/409818/original/file-20210706-21-xq88fw.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/409818/original/file-20210706-21-xq88fw.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/409818/original/file-20210706-21-xq88fw.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/409818/original/file-20210706-21-xq88fw.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=503&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">The current curriculum explicitly says year 10 students must learn about compound interest but the new curriculum doesn’t.</span>
<span class="attribution"><a class="source" href="https://www.shutterstock.com/image-photo/time-saveing-value-money-coin-clock-1012303318">Shutterstock</a></span>
</figcaption>
</figure>
<p>In terms of what students should achieve by the end of each year, the proposed curriculum has also removed explicit mentions to financial literacy. For instance, in the current curriculum, by the end of year 7 students will</p>
<blockquote>
<p>[…] solve problems involving percentages and […] operations with fractions and decimals. They compare the cost of items to make financial decisions. Students represent numbers using variables. </p>
</blockquote>
<p>In the proposed curriculum, students by the end of year 7</p>
<blockquote>
<p>[…] solve problems involving rational numbers, percentages and ratios and explain their choice of representation of rational numbers and results when they model situations, including those in financial contexts.</p>
</blockquote>
<p>Again, this doesn’t mean they will learn about financial matters — they might.</p>
<h2>Why does this matter?</h2>
<p>One <a href="https://www.australiancurriculum.edu.au/consultation">aim of the curriculum review </a> is to declutter content. This may be why applications of maths have been relegated to optional status. </p>
<p>By making financial concepts mere examples, the number of content descriptions decreases. This might provide the appearance the quantity of maths has decreased. But teachers still need to provide students with a context in which to apply their maths skills.</p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/a-crowded-curriculum-sure-it-may-be-complex-but-so-is-the-world-kids-must-engage-with-157690">A 'crowded curriculum'? Sure, it may be complex, but so is the world kids must engage with</a>
</strong>
</em>
</p>
<hr>
<p>Systematically teaching financial concepts in a maths course can <a href="https://connect.springerpub.com/content/sgrjfcp/30/2/313">improve the financial outcomes</a> of more disadvantaged students. But research <a href="https://ro.ecu.edu.au/ajte/vol42/iss5/4/">shows there is a diversity</a> in practising teachers’ ability to identify and interpret opportunities for teaching financial literacy in curriculum. </p>
<p>If financial literacy is left as an example, not all teachers will see the same opportunities for teaching it and financial teaching will be haphazard across schools, and classrooms.</p>
<p><div data-react-class="Tweet" data-react-props="{"tweetId":"1034687007941746688"}"></div></p>
<p>The issue is further complicated by the fact 38% of maths teachers in years 7-10 are <a href="https://research.acer.edu.au/policyinsights/6/">not qualified in maths</a> or maths teaching. Teaching financial maths for these teachers will be much more difficult if there are no explicit guidelines in the curriculum.</p>
<p>After Scott Pape’s lobbying <a href="https://education.nsw.gov.au/news/latest-news/-treasurer-s-new-financial-literacy-challenge">New South Wales</a> announced from term 3 all school children could participate in a “financial literacy challenge” to encourage them to develop positive money habits and increase their financial literacy. </p>
<p>But teachers will still need time to teach these programs. So the elements that have been removed from the curriculum to declutter it will then reappear in the form of additional teaching programs.</p>
<p>The Australian Curriculum provides the content all teachers are required to teach. While many states and territories then reflect this in their own syllabuses or curriculum documents, they all use the national curriculum as the basis.</p>
<p>If the Australian Curriculum doesn’t value financial maths, then other states and territories can choose not to include it. </p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/proposed-new-curriculum-acknowledges-first-nations-view-of-british-invasion-and-a-multicultural-australia-160011">Proposed new curriculum acknowledges First Nations' view of British 'invasion' and a multicultural Australia</a>
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<p>Once the revised Australian Curriculum is released, other states and territories will begin their processes of redeveloping their own curricula. A structured financial literacy program may need to be created, even more so in Queensland where the national curriculum is adopted as it is written.</p>
<p>We need to ensure the Australian Curriculum keeps the explicit language to embed financial literacy concepts into maths lessons. This way, kids will grow up with the financial knowledge they need to make important decisions and participate meaningfully in society and the economy.</p><img src="https://counter.theconversation.com/content/163110/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>The authors do not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and have disclosed no relevant affiliations beyond their academic appointment.</span></em></p>The national curriculum expects teachers to teach some maths concepts through a financial lens. The revised curriculum includes the financial lens as an example teachers can use, if they choose to.Emily Ross, Lecturer, Curriculum and Pedagogy, University of the Sunshine CoastMargaret Marshman, Senior lecturer mathematics and physics education, University of the Sunshine CoastLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1611002021-05-24T21:16:33Z2021-05-24T21:16:33Z1 in 4 Australian year 8s have teachers unqualified in maths — this hits disadvantaged schools even harder<figure><img src="https://images.theconversation.com/files/402276/original/file-20210524-19-10vv69l.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">
</span> <span class="attribution"><a class="source" href="https://www.shutterstock.com/image-photo/close-students-writing-reading-exam-answer-1062306728">Shutterstock</a></span></figcaption></figure><p>Almost one in four (23%) Australian year 8 students were being taught maths in 2018 by teachers whose major qualification was in a field other than maths, <a href="https://research.acer.edu.au/timss_2019/4/">new analysis</a> reveals. </p>
<p>Internationally, on average, just one in ten year 8 equivalent students are taught maths by such teachers. </p>
<p>The analysis of Australia’s participation in the 2019 Trends in International Mathematics and Science Study (TIMSS) — an international assessment — was released today by the Australian Council for Educational Research (ACER). </p>
<p>The above figures have remained much the same since the 2015 <a href="https://research.acer.edu.au/timss_2015/2/">TIMSS data</a> collection.</p>
<p>When qualified teachers are assigned to teach subjects and year levels they have not studied at a tertiary level, this is known as out-of-field teaching. TIMSS also shows a large achievement difference between students taught by expert teachers and students taught by out-of-field teachers. </p>
<p>However, socioeconomic status has a large impact on student achievement, and TIMSS also shows more disadvantaged students are being taught by non-expert teachers.So, there may be a cumulative effect — with both teacher expertise and disadvantage playing a role in results.</p>
<h2>Students with expert maths teachers score higher</h2>
<p>TIMSS summarises achievement on the test on a scale with a mean of 500 and standard deviation of 100. In TIMSS 2019, Australian students achieved an overall average of 516 points in maths. </p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/australia-lifts-to-be-among-top-ten-countries-in-maths-and-science-150275">Australia lifts to be among top ten countries in maths and science</a>
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<p>Students with expert teachers in maths, with specialist teacher training, scored significantly higher in maths in the TIMSS test than any other group. </p>
<p>Those taught by teachers with strong subject matter knowledge and pedagogical training in subjects other than maths scored next highest. </p>
<p>They all performed at a higher level than students taught by teachers with neither the subject-matter knowledge nor the pedagogical knowledge in maths. </p>
<hr>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/402024/original/file-20210520-13-29wjao.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="Chart showing percentages of students and their average maths score corresponding to type of major of their teacher" src="https://images.theconversation.com/files/402024/original/file-20210520-13-29wjao.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/402024/original/file-20210520-13-29wjao.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/402024/original/file-20210520-13-29wjao.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/402024/original/file-20210520-13-29wjao.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/402024/original/file-20210520-13-29wjao.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/402024/original/file-20210520-13-29wjao.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/402024/original/file-20210520-13-29wjao.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=503&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Percentages of Australian students (Year 8) by the type of major of mathematics teachers and corresponding average mathematics scores.</span>
<span class="attribution"><a class="source" href="https://research.acer.edu.au/timss_2019/4/">Data: ACER</a>, <a class="license" href="http://creativecommons.org/licenses/by/4.0/">CC BY</a></span>
</figcaption>
</figure>
<p>–</p>
<p>It’s important to note, however, the scores of students in this point-of-time assessment are not the simple result of the one teacher surveyed for TIMSS. They are a cumulative result of eight years of schooling. </p>
<p>One of the <a href="https://theconversation.com/educational-disadvantage-is-a-huge-problem-in-australia-we-cant-just-carry-on-the-same-74530">largest effects on student achievement</a> is socioeconomic advantage and disadvantage.</p>
<h2>Disadvantaged students bearing the brunt</h2>
<p>Overall, 46% of year 8 students were taught maths by teachers with a major in both maths and maths education, while 23% were taught by out-of-field teachers. </p>
<p>However, while there is a general shortage of qualified maths teachers, it affects some students more than others. </p>
<p>Principals of the schools selected for TIMSS also reported on the socioeconomic composition of their schools. They were asked to indicate the percentages of students who came from economically affluent homes and from economically disadvantaged homes. </p>
<p>These responses were used to create three categories of school socioeconomic composition: more affluent, more disadvantaged and neither. </p>
<p>The TIMSS data show disadvantaged students are bearing the brunt of maths teacher shortages.</p>
<p>In more affluent schools, out-of-field teachers taught just 16% of students. More qualified maths teachers taught 54% of these students. </p>
<p>In contrast, in more disadvantaged schools, out-of-field teachers taught 28% of students. More qualified maths teachers taught just 31% of students.</p>
<hr>
<figure class="align-center ">
<img alt="Chart showing percentages of maths teachers by type of major in affluent and disadvantaged schools" src="https://images.theconversation.com/files/402029/original/file-20210520-19-1jaw42v.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/402029/original/file-20210520-19-1jaw42v.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/402029/original/file-20210520-19-1jaw42v.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/402029/original/file-20210520-19-1jaw42v.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/402029/original/file-20210520-19-1jaw42v.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/402029/original/file-20210520-19-1jaw42v.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/402029/original/file-20210520-19-1jaw42v.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=503&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption"></span>
<span class="attribution"><a class="source" href="https://research.acer.edu.au/timss_2019/4/">Data: ACER</a>, <a class="license" href="http://creativecommons.org/licenses/by/4.0/">CC BY</a></span>
</figcaption>
</figure>
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<p>The average maths score for more affluent schools was 558 points, compared to 474 points for more disadvantaged schools. </p>
<p>A proportion of the achievement gap between students taught by out-of-field teachers and those taught by more qualified maths teachers must therefore be related to disadvantage. </p>
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<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/australian-schools-are-becoming-more-segregated-this-threatens-student-outcomes-155455">Australian schools are becoming more segregated. This threatens student outcomes</a>
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</em>
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<p>Many students in the disadvantaged secondary schools also would have attended disadvantaged primary schools, so may have had many years of more poorly resourced teaching.</p>
<h2>Out-of-field teachers in Australia</h2>
<p>According to the <a href="https://www.aph.gov.au/%7E/media/Estimates/Live/eet_ctte/estimates/sup_1213/answers/EW0743_13_Attachment_A.ashx">National School Improvement Tool</a> (among many other documents on effective teachers and schools), highly effective schools have “teachers … [who] are experts in the fields in which they teach, [and] have high levels of confidence in teaching in those fields”. </p>
<p>Yet <a href="https://amsi.org.au/media/AMSI-Occasional-Paper-Out-of-Field-Maths-Teaching.pdf">analysis</a> from the Australian Mathematical Sciences Institute (AMSI) has warned that 76% of students will be taught by an out-of-field maths teacher at least once, and 35% of students twice, in the first four years of high school. Worryingly, 8% will be taught by out-of-field teachers for all four years.</p>
<p>Many out-of-field teachers have been teaching in that subject area for several years. <a href="https://research.acer.edu.au/policyinsights/6/">Analysis</a> of the 2013 Staff in Australia’s Schools survey showed out-of-field maths teachers had been teaching the subject to years 7-10 for an average total of 7.4 years. </p>
<p>While TIMSS data on years of teaching were not specific to maths teaching, it did show out-of-field teachers tended to have fewer years of teaching overall under their belt. Out-of-field teachers had 10.9 years on average compared to 16.3 years for the most qualified maths teachers.</p>
<h2>How can we support out-of-field teachers?</h2>
<p>The <a href="https://amsi.org.au/media/AMSI-Occasional-Paper-Out-of-Field-Maths-Teaching.pdf">AMSI analysis</a> suggests Australia will not be able to train enough new maths teachers in the short to medium term. So we need other alternatives. </p>
<p>One of these is to support out-of-field teachers by providing targeted forms of professional development. To do this requires an understanding of where weaknesses lie. </p>
<p>Some teachers might have the maths skills required but not enough understanding of maths teaching methods and practices. Other teachers might have the pedagogical background but weaker maths skills. Each group requires different professional development opportunities. </p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/fixing-the-shortage-of-specialist-science-and-maths-teachers-will-be-hard-not-impossible-99651">Fixing the shortage of specialist science and maths teachers will be hard, not impossible</a>
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</em>
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<p>The TIMSS data show three-quarters of Australia’s out-of-field teachers reported needing professional development in maths content, compared to around half of the more qualified teachers. </p>
<p>And around 70% of all teachers said they need professional development in maths pedagogy and instruction, as well as assessment. </p>
<p>Initiatives like the federal government’s <a href="https://ministers.dese.gov.au/tehan/strengthening-maths-teaching-australian-schools">$9.5 million investment</a> in high-quality mathematics and numeracy professional learning and resources is an important step in supporting out-of-field and in-field maths teachers alike to improve mathematics education, but it must be targeted.</p><img src="https://counter.theconversation.com/content/161100/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Sue Thomson does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.</span></em></p>Students with expert maths teachers scored significantly higher on an international maths test than any other group. But a student’s level of advantage also affects assessment scores.Sue Thomson, Deputy CEO (Research), Australian Council for Educational ResearchLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1543962021-02-02T11:27:54Z2021-02-02T11:27:54ZHow to help your children with maths you don’t understand<figure><img src="https://images.theconversation.com/files/381727/original/file-20210201-17-1bdyjod.jpg?ixlib=rb-1.1.0&rect=0%2C0%2C7014%2C4084&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">
</span> <span class="attribution"><a class="source" href="https://www.shutterstock.com/image-photo/mother-learning-her-daughter-calculate-elementary-383236585">Flamingo Images/Shutterstock</a></span></figcaption></figure><p>School closures have left many parents in charge of overseeing their children’s education at home. If you are one of them, you might be struggling with maths in particular – not least due to having to grapple with topics and techniques you are unfamiliar with, such as <a href="https://www.splashlearn.com/math-vocabulary/number-sense/number-bonds">number bonds</a>, <a href="https://nrich.maths.org/1011">abundant numbers</a>, <a href="https://www.theschoolrun.com/what-is-chunking">chunking</a> and more. </p>
<p>But this is where a positive mindset, and the ability to accept that you are also on a learning path, can help. Here are some tips on the best way to tackle teaching maths you don’t know.</p>
<h2>Work together</h2>
<p>Think of yourself as accompanying your child towards understanding a new concept, rather than explaining it to them. As a parent, there is a natural desire to provide for and support your child with your experience, but this is impossible when you do not know what you want to explain. </p>
<p>What you are able to do is to tap into is your past experiences of having solved problems and managed challenges. So simply be honest and say to your child that this method is new to you, too, but that you will work to understand it together.</p>
<h2>Start small and use props</h2>
<p>New concepts can be overwhelming. Start as small as you can, and play around with something concrete – such as buttons or pennies or pieces of Lego – to help you both understand. For instance, your child might be working on number bonds: learning the pairs of numbers that add together to make a particular total. </p>
<figure class="align-center ">
<img alt="Child writing diagrams with pencil on paper" src="https://images.theconversation.com/files/381657/original/file-20210201-23-16a360q.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/381657/original/file-20210201-23-16a360q.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/381657/original/file-20210201-23-16a360q.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/381657/original/file-20210201-23-16a360q.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/381657/original/file-20210201-23-16a360q.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/381657/original/file-20210201-23-16a360q.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/381657/original/file-20210201-23-16a360q.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=503&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
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<span class="caption">A child working on number bonds for 10.</span>
<span class="attribution"><a class="source" href="https://www.shutterstock.com/image-photo/boy-writing-number-bond-another-way-651914917">Phil's Mommy/Shutterstock</a></span>
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</figure>
<p>To give an example, the number bonds of seven are two plus five and three plus four. Physically laying out seven buttons and splitting them into two and five, and then three and four, can help both you and your child familiarise yourselves with the concept and then understand how it works.</p>
<h2>Think about why it’s useful</h2>
<p>Learning maths may seem pointless, and this can lead to frustration. After all, there is not much need to know how to divide 155,252,188 by 19,838 when the calculator on your phone will do it for you. </p>
<p>But this does not mean that you don’t need to do any mental computation at all in life. Perhaps you have a budget of £50 and want to know quickly if buying three items priced £13, £20 and £17 will push you over this total. Your knowledge of number bonds tells you that three plus seven is ten – so 13 plus 17 is 30, which plus the additional 20 puts you perfectly at your budget. </p>
<p>Since the 1980s, theories about the best methods of education have moved away from rote learning, which can cause pupils to <a href="https://bera-journals.onlinelibrary.wiley.com/doi/abs/10.1080/01411920301852">disengage from maths</a>. Instead, education experts have championed more engaging methods, based on learning through experience. The maths national curriculum was lagging behind these ideas until the <a href="https://www.oxfordreference.com/view/10.1093/oi/authority.20110803100224411">national numeracy strategy</a> was launched in 1999. A further revamp of the national curriculum followed in 2013.</p>
<p>The focus is now on teaching pupils to become problem solvers: fluent in maths with the ability to reason and apply what they have learned. In teaching number bonds, you are helping your child develop a numerical tool that can allow them to effectively process simple computations, which in turn make them more capable of dealing with problems in life or at work.</p>
<h2>Avoid the fear factor</h2>
<p>It is easy, especially if you have had bad experiences with maths in your past, to give way to panic. Teaching unknown concepts could make what is known as <a href="https://theconversation.com/how-to-overcome-a-fear-of-maths-115646">maths anxiety</a> – the irrational fear of anything mathematical – resurface. </p>
<figure class="align-center ">
<img alt="Father and son looking stressed doing homework" src="https://images.theconversation.com/files/381731/original/file-20210201-21-1ya2icu.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/381731/original/file-20210201-21-1ya2icu.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/381731/original/file-20210201-21-1ya2icu.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/381731/original/file-20210201-21-1ya2icu.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/381731/original/file-20210201-21-1ya2icu.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/381731/original/file-20210201-21-1ya2icu.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/381731/original/file-20210201-21-1ya2icu.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=503&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
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<span class="caption">Many people suffer from maths anxiety.</span>
<span class="attribution"><a class="source" href="https://www.shutterstock.com/image-photo/sad-father-tired-about-sons-failure-782571799">sakkmesterke/Shutterstock</a></span>
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<p>The risk is that this fear can be <a href="https://journals.sagepub.com/doi/full/10.1177/0956797615592630?casa_token=RKpThwKXXi0AAAAA%3ADcJ0zS9017k-nCdNDm6opwCcCeduPCd5omhQUYXJIJEVWPNruVBskzUvOVZNElmOXWoxyneddwa0">passed to your child</a>. This can have consequences for their enjoyment of school – and even for the decisions <a href="https://behavioralandbrainfunctions.biomedcentral.com/articles/10.1186/1744-9081-10-31">they make in life</a>.</p>
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<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/what-a-fear-of-maths-does-to-children-new-research-150108">What a fear of maths does to children – new research</a>
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<p>A simple trick is to not think that you are doing maths, but that you helping your child to learn useful life tools. Giving maths a more friendly name, such as “problem-solving tricks” or “calculation tools” – that better reflects your own abilities – can boost confidence and keep <a href="https://www.magonlinelibrary.com/doi/abs/10.12968/jprp.2020.2.5.226">maths anxiety at bay</a>.</p>
<h2>Keep it real</h2>
<p>Once you and your child have learned a mathematical concept, try to make it more real and use it in everyday life. Make number bonds with biscuits or pieces of fruit. Add up prices of supermarket items. Be creative and make colourful number bond patterns with building blocks or objects such as sticks and leaves you find on a stroll.</p>
<p>Finally, don’t be discouraged if you sometimes struggle. And allow yourself and your child plenty of time to learn a new idea. Some mathematical concepts can be counter-intuitive or hard, and it is fine to sometimes let go, do something else, and come back to it at another time. Try to reward yourself for your successes, and remember that learning in a more positive, playful way will help make homeschooling a positive experience.</p><img src="https://counter.theconversation.com/content/154396/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Davide Penazzi does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.</span></em></p>Think of yourself as learning alongside your child.Davide Penazzi, Senior Lecturer in Mathematics, University of Central LancashireLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1502622020-12-16T03:32:42Z2020-12-16T03:32:42ZJump, split or make to the next 10: strategies to teach maths have changed since you were at school<figure><img src="https://images.theconversation.com/files/375248/original/file-20201215-15-1lh0rut.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">
</span> <span class="attribution"><a class="source" href="https://www.shutterstock.com/image-photo/portrait-african-girl-writing-solution-sums-1078335890">Shutterstock</a></span></figcaption></figure><p>I’m sure most people can remember trying to master a certain maths rule or procedure in primary or secondary school.</p>
<p>My elderly mother has a story about a time her father was helping her with arithmetic homework. She remembers getting upset because her father did not do it “the school way”. I suspect her father was able to do the calculation mentally rather than the school way, which was to use the vertical algorithm.</p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/375289/original/file-20201216-19-1saklzv.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/375289/original/file-20201216-19-1saklzv.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=166&fit=crop&dpr=1 600w, https://images.theconversation.com/files/375289/original/file-20201216-19-1saklzv.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=166&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/375289/original/file-20201216-19-1saklzv.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=166&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/375289/original/file-20201216-19-1saklzv.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=208&fit=crop&dpr=1 754w, https://images.theconversation.com/files/375289/original/file-20201216-19-1saklzv.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=208&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/375289/original/file-20201216-19-1saklzv.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=208&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
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<span class="attribution"><a class="license" href="http://creativecommons.org/licenses/by-nd/4.0/">CC BY-ND</a></span>
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<p>Students are expected to add the numbers in the ones (right) column first, before adding the numbers in the tens (left) column. The task becomes more difficult when the total of the ones column is more than 10 — as you then have to “trade” ten ones for one ten.</p>
<p>Students who give the answer as 713 rather than the correct answer of 83 may well have started with the tens column first. Or they may have written 13 in the ones column rather than trading ten ones for one ten.</p>
<p>The formal school algorithms are still used for larger numbers and decimals but we encourage students to use whichever strategy they prefer for two-digit addition. </p>
<p>The trouble with teaching rules is many students then struggle to remember when to apply the rule because they don’t understand how or why the rule works. </p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/weapons-of-maths-destruction-are-calculators-killing-our-ability-to-work-it-out-in-our-head-44900">Weapons of maths destruction: are calculators killing our ability to work it out in our head?</a>
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<p>The <a href="https://australiancurriculum.edu.au/f-10-curriculum/mathematics/">Australian Curriculum: Mathematics</a> states that by the end of year 2, students will “perform simple addition and subtraction calculations using a range of strategies”. By the end of year 4, they will “identify and explain strategies for finding unknown quantities in number sentences”. </p>
<p><div data-react-class="Tweet" data-react-props="{"tweetId":"1143666051793788928"}"></div></p>
<p>We want children to remember how to do these equations in their head, rather than relying on writing down the process. Here are three strategies schools use to teach children how to add and subtract two-digit numbers.</p>
<h2>1. Split strategy</h2>
<p>This is sometimes called the decomposition, partitioning or partial-sums strategy. </p>
<p>You can add or subtract the tens separately to the ones (or units). For example, using the split strategy to add 46 + 23, you would:</p>
<ul>
<li><p>split each number (decompose) into tens and ones: 46 + 23 = 40 + 6 + 20 + 3</p></li>
<li><p>rearrange the tens and ones: 40 + 20 + 6 + 3</p></li>
<li><p>add the tens and then the ones 60 + 9 = 69</p></li>
</ul>
<p>Using the split strategy for addition such as 37 + 65 would be similar, but there would be an extra step:</p>
<ul>
<li><p>split or decompose the numbers into tens and ones: 30 + 7 + 60 + 5</p></li>
<li><p>rearrange the tens and ones: 30 + 60 + 7 + 5</p></li>
<li><p>add the tens and then the ones: 90 + 12 </p></li>
<li><p>split 12 (10 + 2) to give: 90 + 10 + 2 = 100 + 2 = 102</p></li>
</ul>
<p>Many students find the split strategy more difficult for subtraction than addition. This is because there are more steps if performing this strategy mentally. </p>
<p>For a subtraction such as 69 – 46, you would:</p>
<ul>
<li><p>split or decompose each number into tens and ones: 60 + 9 – (40 + 6)</p></li>
<li><p>remove bracket: 60 + 9 – 40 – 6</p></li>
<li><p>rearrange tens and ones: (60 – 40) + (9 – 6)</p></li>
<li><p>subtract the tens, then the ones: 20 + 3 = 23</p></li>
</ul>
<p>Students often make mistakes in the third step. Successful students may say: “I take 40 from 60, then 6 from 9”. Unsuccessful students will say “I take 40 from 60 then add 6 and 9”. </p>
<p>Students who use this strategy successfully are showing they understand place value (the value of each digit in a number) and their knowledge of maths rules needed for algebra. </p>
<h2>2. Jump strategy</h2>
<p>This is sometimes called the sequencing or cumulative sums strategy. The actual steps taken depend on the confidence and ability of the students. </p>
<p>Some students add increments of tens or ones, while others add or subtract multiples of tens then ones. </p>
<p>For example, adding 46 + 23 using the jump strategy might look like this:</p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/375290/original/file-20201216-13-1odomar.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/375290/original/file-20201216-13-1odomar.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=158&fit=crop&dpr=1 600w, https://images.theconversation.com/files/375290/original/file-20201216-13-1odomar.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=158&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/375290/original/file-20201216-13-1odomar.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=158&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/375290/original/file-20201216-13-1odomar.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=199&fit=crop&dpr=1 754w, https://images.theconversation.com/files/375290/original/file-20201216-13-1odomar.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=199&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/375290/original/file-20201216-13-1odomar.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=199&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
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<span class="attribution"><a class="license" href="http://creativecommons.org/licenses/by-nd/4.0/">CC BY-ND</a></span>
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<ul>
<li><p>add two lots of ten to 46: 46 + 10 = 56, then 56 + 10 = 66</p></li>
<li><p>add the remaining 3: 66 + 3 = 69 </p></li>
</ul>
<p>or </p>
<ul>
<li><p>add 20 to 46 which becomes 66</p></li>
<li><p>add the remaining 3: 66 + 3 = 69</p></li>
</ul>
<p>The two versions of this strategy can be shown using an empty number line. Using a blank or empty number line allows student to record their thinking and for teachers to analyse their thinking and determine the strategy they have attempted to use.</p>
<p>Subtracting 69 – 46 with the jump strategy could be done by:</p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/375291/original/file-20201216-19-n4muyw.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/375291/original/file-20201216-19-n4muyw.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=149&fit=crop&dpr=1 600w, https://images.theconversation.com/files/375291/original/file-20201216-19-n4muyw.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=149&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/375291/original/file-20201216-19-n4muyw.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=149&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/375291/original/file-20201216-19-n4muyw.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=187&fit=crop&dpr=1 754w, https://images.theconversation.com/files/375291/original/file-20201216-19-n4muyw.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=187&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/375291/original/file-20201216-19-n4muyw.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=187&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
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<span class="attribution"><a class="license" href="http://creativecommons.org/licenses/by-nd/4.0/">CC BY-ND</a></span>
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</figure>
<ul>
<li><p>subtracting four lots of ten (40) from 69: 69 – 10 = 59; 59 – 10 = 49; 49 – 10 = 39; 39 – 10 = 29 </p></li>
<li><p>then finally subtracting the remaining 6: 29 – 6 = 23 </p></li>
</ul>
<p>or</p>
<ul>
<li><p>subtract 40: 69 – 40 = 29 </p></li>
<li><p>then subtract 6: 29 – 6 = 23</p></li>
</ul>
<h2>3. ‘Make to the next ten’ strategy</h2>
<p>This is sometimes called the compensation or shortcut strategy. It involves adjusting one number to make the task easier to solve. </p>
<p>The “make to the next ten” strategy builds on the “friends of ten” strategy. </p>
<p>Many students in the first years of primary school create all the combinations of two single digit numbers that give a total of ten. </p>
<blockquote>
<p>9 + 1, 8 + 2, 7 + 3, 6 + 4, 5 + 5 … </p>
</blockquote>
<p>These are sometimes called the rainbow facts as the children create rainbows as they connect two numbers together. For instance, 9 may be on one end of a rainbow colour and 1 on the other. </p>
<p>By combining the numbers in this way teachers hope students will realise the answer for 9 + 1 is the same as 1 + 9.</p>
<p>In the “make to the next ten” strategy, you add or subtract a number larger than the number given (such as the next multiple of ten) and then readjust the number by subtracting what was added or adding what was subtracted.</p>
<p>In the diagrams the relationships are indicated by the use of arrows. </p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/375301/original/file-20201216-21-1lvy5ai.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/375301/original/file-20201216-21-1lvy5ai.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=156&fit=crop&dpr=1 600w, https://images.theconversation.com/files/375301/original/file-20201216-21-1lvy5ai.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=156&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/375301/original/file-20201216-21-1lvy5ai.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=156&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/375301/original/file-20201216-21-1lvy5ai.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=196&fit=crop&dpr=1 754w, https://images.theconversation.com/files/375301/original/file-20201216-21-1lvy5ai.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=196&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/375301/original/file-20201216-21-1lvy5ai.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=196&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
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<span class="attribution"><a class="license" href="http://creativecommons.org/licenses/by-nd/4.0/">CC BY-ND</a></span>
</figcaption>
</figure>
<p>So, to add 37 + 65, you would</p>
<ul>
<li><p>add 3 to 37 to give 40. </p></li>
<li><p>subtract 3 from 65 to get 62</p></li>
<li><p>this becomes: 40 + 62 = 102.</p></li>
</ul>
<p>If subtracting 102 – 65, you would:</p>
<ul>
<li><p>subtract 2 from 102 to make 100</p></li>
<li><p>subtract 2 from 65 to maintain the balance</p></li>
<li><p>this becomes 100 – 63 = 37.</p></li>
</ul>
<p>Many students using this strategy incorrectly add 2 to 65 instead of subtracting 2.</p>
<h2>Why these strategies?</h2>
<p>Students would have been using all these strategies, or some forms of them, in their head for generations. But for many years, the expectation was that students use the formal written algorithm rather than their own mental strategies. </p>
<p>The introduction of the empty or blank number line allowed students to record their mental strategies, which allowed teachers and parents to see them. Naming these strategies has allowed teachers and students to discuss possible strategies using a common vocabulary.</p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/kids-prefer-maths-when-you-let-them-figure-out-the-answer-for-themselves-44016">Kids prefer maths when you let them figure out the answer for themselves</a>
</strong>
</em>
</p>
<hr>
<p>Rather than teach rules and procedures, we now need to encourage students to explain their strategies using both concrete materials and diagrams to demonstrate their knowledge of addition and subtraction.</p><img src="https://counter.theconversation.com/content/150262/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Cath Pearn is affiliated with both the Australian Council for Educational Research and the Melbourne Graduate School of Education, The University of Melbourne. </span></em></p>For years you may have been adding and subtracting numbers in your head in a certain way, but these strategies were never formally taught at school. Now they are, and they all have names.Cath Pearn, Senior Research Fellow, Australian Council for Educational ResearchLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1502752020-12-08T09:02:34Z2020-12-08T09:02:34ZAustralia lifts to be among top ten countries in maths and science<figure><img src="https://images.theconversation.com/files/373484/original/file-20201208-19-t5es3d.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">
</span> <span class="attribution"><a class="source" href="https://www.shutterstock.com/image-photo/genius-girl-red-glasses-near-blackboard-178739876">Shutterstock</a></span></figcaption></figure><p>Results from the longest running large-scale international assessment of maths and science show <a href="https://research.acer.edu.au/timss_2019/1/">Australia has significantly improved</a> in Year 8 maths and science, and Year 4 science.</p>
<p>More than 580,000 students from 64 countries participated in the latest Trends in International Mathematics and Science Study (<a href="https://timssandpirls.bc.edu/timss2019/index.html">TIMSS</a>). This includes 14,950 Australian students from 571 Australian schools. </p>
<p><strong>In Year 8 maths</strong>, Australia came in equal seventh place in the 2019 assessment cycle (up from equal 13th in 2015), along with a number of countries including Ireland, the United States and England. We came behind Chinese Taipei (Taiwan), Korea, Japan, Hong Kong and Ireland. </p>
<p><strong>In Year 8 science</strong>, Australia also came in equal seventh (up from equal 15th in 2015) along with countries such as Lithuania, Ireland and the US. We were behind Singapore, Chinese Taipei, Japan, Korea, Russia and Finland. </p>
<p><strong>In Year 4 science</strong>, Australia came equal ninth (up from equal 18th in 2015) along with countries including the US, England, Hong Kong and Ireland. Australia was behind Singapore, Korea, Russia, Japan, Chinese Taipei, Finland, Latvia and Norway.</p>
<p><strong>In Year 4 maths</strong>, however, achievement has not changed since 2007. Australia was outperformed by 22 countries in 2019, similar to 2015. It came equal 23rd along with countries such as Germany, Poland and Canada; and behind Singapore, the US, England and Ireland.</p>
<hr>
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<hr>
<h2>Not just the rankings</h2>
<p>This is the seventh time the TIMSS test has been administered. Along with completing tests in maths and science, Year 4 and 8 students involved in TIMSS answer questionnaires on their background and experiences in learning maths and science at school.</p>
<p>Participating in TIMSS allows Australia to measure its progress towards national educational goals, which in 2019 included the Melbourne Declaration on Educational Goals for Young Australians (now the Mparntwe Education Declaration). </p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/australia-hasnt-performed-well-at-maths-and-science-recently-were-about-to-find-out-if-weve-improved-150274">Australia hasn't performed well at maths and science recently. We're about to find out if we've improved</a>
</strong>
</em>
</p>
<hr>
<p>In Year 4 maths, Australian students achieved an average score of 516 points. Singapore’s students scored the highest with 625 points, while England achieved 556, Canada 512 and New Zealand 487 points.</p>
<p>Australia’s average score in Year 8 maths was 517 points. This was compared to the highest score of 616 points for Singapore. Australia’s score was not significantly different to that of the US and England, which both achieved 515 points.</p>
<p>Australia not only improved in Year 8 maths and science, and Year 4 science relative to other countries, but also in an absolute sense. Compared to 2015, Australia’s mean score increased by 12 points in Year 8 maths; 16 points in Year 8 science and nine points in Year 4 science. </p>
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<hr>
<p>The TIMSS intermediate international benchmark is the nationally agreed proficient standard for maths and science achievement, which is 475 score points. In 2019 between 68% and 78% of Australian students achieved the required proficiency benchmark in maths and science at both year levels. In Singapore, more than 90% of students achieved this benchmark in both subject areas at both year levels. </p>
<p>Since 2015, the proportion of Australian students achieving this standard improved by five percentage points in Year 8 science. It did not change significantly in Year 4 maths and science, or Year 8 maths.</p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/aussie-students-are-a-year-behind-students-10-years-ago-in-science-maths-and-reading-127013">Aussie students are a year behind students 10 years ago in science, maths and reading</a>
</strong>
</em>
</p>
<hr>
<p>TIMSS results also provide a measure of Australia’s progress towards the United Nations 2030 Sustainable Development Goal for universal quality education. The TIMSS low international benchmark is an agreed global indicator of minimum proficiency in maths at the end of lower secondary schooling. </p>
<p>In the 2019 study, 90% of Australian Year 8 students achieved this benchmark, which was similar to 2015 and slightly higher than the 2019 international median of 87%. Meanwhile, 98% of students in Singapore and Chinese Taipei, and 99% of students in Japan achieved minimum proficiency in Year 8 maths.</p>
<h2>Differences between groups</h2>
<p>While of course these findings are positive, there are cautions evident when making comparisons among demographic groups.</p>
<p>There was no significant difference between the average performance of Australian girls and boys in Year 8 maths, Year 4 science or Year 8 science. </p>
<p>But boys outperformed girls in Year 4 maths in 27 of the 58 participating countries, including Australia. </p>
<p>The proportion of students who attained the national proficient standard was about the same for boys and girls (69% for girls, 70% for boys). But the proportion of boys who achieved the advanced benchmark (12%) was significantly higher than the proportion of girls (8%) who achieved at this level.</p>
<hr>
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<hr>
<p>While the achievement of First Nations Australian students and other Australian students has converged slightly in Year 4 and Year 8 science since 1995, the gaps are glaringly wide in both subject areas, but particularly in maths. </p>
<p>At Year 4 level in maths, 42% of First Nations students achieved the national proficient standard, compared to 72% of other Australian students. And 25% of First Nations students did not achieve the low benchmark, compared to 8% of other Australian students. </p>
<p>In Year 8 maths, 39% of First Nations students compared to 70% of other Australian students achieved the National Proficient standard, while 29% of First Nations students compared to 8% of other Australian students did not achieve the Low benchmark.</p>
<h2>Student socioeconomic background</h2>
<p>The largest gaps in achievement at school are often those defined by a students’ socioeconomic background. In TIMSS, several measures are used to define socioeconomic background, but the common method for Year 4 and Year 8 is simple but effective. Students are asked to estimate the number of books in their home within five categories. These are then collapsed into three:</p>
<ul>
<li><p>0-10: few books</p></li>
<li><p>11-200: average number of books</p></li>
<li><p>more than 200: many books. </p></li>
</ul>
<p><a href="https://kathyhirshpasek.com/wp-content/uploads/sites/9/2018/04/Pace-et-al.-2017.pdf">Analysis</a> has shown living in a home with many books influences academic achievement (or by implication, having a home environment that values literacy, the acquisition of knowledge and general academic support) in a positive manner.</p>
<p>In Year 4, 17% of students identified as living in a home with many books, and 28% with few books. In Year 8, 20% of students said their home had many books and 31% few books.</p>
<p>The differences between students with many books and those with few books is large at both year levels and for both subject areas. For example:</p>
<ul>
<li><p>in Year 8 maths, 83% of students living in a home with many books achieved the national proficient standard, compared to 48% of those from homes with few books </p></li>
<li><p>in Year 8 science, 90% of students from homes with many books achieved the standard, compared to 52% of those from homes with few books</p></li>
<li><p>in Year 8 maths and science, around 3% of students from homes with many books compared to around 20% of students from homes with few books did not achieve the low benchmark.</p></li>
</ul>
<p>Acknowledging the primary underlying factor behind poor achievement is socioeconomic background, and finding ways of redressing the imbalance in opportunities and resources available to these students, will help lift achievement for all Australian students.</p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/one-quarter-of-australian-11-12-year-olds-dont-have-the-literacy-and-numeracy-skills-they-need-148912">One quarter of Australian 11-12 year olds don't have the literacy and numeracy skills they need</a>
</strong>
</em>
</p>
<hr>
<img src="https://counter.theconversation.com/content/150275/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Sue Thomson does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.</span></em></p>Results from the world’s longest running large-scale international assessment of maths and science show Australia has significantly improved in Year 8 maths and science, and Year 4 science.Sue Thomson, Deputy CEO (Research), Australian Council for Educational ResearchLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1315632020-06-18T05:35:42Z2020-06-18T05:35:42ZGirls score the same in maths and science as boys, but higher in arts – this may be why they are less likely to pick STEM careers<figure><img src="https://images.theconversation.com/files/341773/original/file-20200615-65956-kg1kuo.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">
</span> <span class="attribution"><a class="source" href="https://www.shutterstock.com/image-vector/female-scientist-lab-coat-checking-artificial-1266139540">Shutterstock</a></span></figcaption></figure><p>Last month, the Australian Academy of Science <a href="https://www.science.org.au/sites/default/files/rrif-covid19-women-stem-workforce.pdf">published a report</a> showing the COVID-19 pandemic would disproportionately affect women in the STEM (science, technology, engineering and maths) disciplines. </p>
<p>The <a href="https://www.science.org.au/sites/default/files/rrif-covid19-women-stem-workforce.pdf">report noted</a> before COVID-19, around 7,500 women were employed
in STEM research fields in Australia in 2017, compared to around 18,400 men. The authors wrote:</p>
<blockquote>
<p>The pandemic appears to be compounding pre-existing gender disparity; women are under-represented across the STEM workforce, and weighted in roles that are typically less senior and less secure. Job loss at a greater rate than for men is now an immediate threat for many women in Australia’s STEM workforce, potentially reversing equity gains of recent years.</p>
</blockquote>
<p>Women are less likely to enrol in science and maths degrees than men. In Australia, only <a href="https://www.industry.gov.au/data-and-publications/stem-equity-monitor/higher-education/university-enrolment-and-completion-data">35% of STEM university degrees are awarded to women</a>. This figure has been stable over the past five years.</p>
<p>Some <a href="https://www.jstor.org/stable/2535301?seq=1#metadata_info_tab_contents">research in the 1990s</a> suggested girls don’t study maths and science because they might not do as well as boys. But <a href="https://www.nbcnews.com/health/health-news/girls-get-better-grades-boys-even-stem-subjects-study-finds-n912891">recent research</a> shows girls score similarly or slightly higher than boys in maths and science.</p>
<p>So why don’t they choose these careers as often as men?</p>
<p>Our <a href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3620627">recently published study</a> found while women perform at the same or higher level in maths and science as men, their performance in the humanities is markedly better. This may be the reason they’re choosing not to pursue STEM careers.</p>
<h2>Girls just as good at maths and science</h2>
<p>We wanted to see if there were gender differences in school performance when it came to science and maths and whether these affected students’ university applications. </p>
<p>Our study used data of more than 70,000 secondary school students in Greece over ten years. </p>
<p>We found girls’ scores in maths and science were around 4% higher than boys. But their scores in humanities subjects were around 13% higher. </p>
<p>We also found girls were 34% less likely to chose a STEM-related specialisation in their last years of high school. </p>
<p>These findings can be translated to Australia. According to the <a href="https://www.oecd.org/pisa/publications/PISA2018_CN_AUS.pdf">latest results</a> from the OECD’s Programme for International Student Assessment (PISA), girls in Australia perform on a similar level to boys in maths and science, but at a much higher level in reading. </p>
<p>The difference between girls’ and boys’ performance in reading is <a href="https://gpseducation.oecd.org/CountryProfile?primaryCountry=AUS&treshold=10&topic=PI">6% in Australia and 9% in Greece</a>.</p>
<p>But when it comes to maths and science, there is not much of a difference between girls’ and boys’ performance in either country.</p>
<h2>Female comparative advantage in STEM</h2>
<p>Our study showed students decided which fields they want to specialise in by comparing their academic strengths and weaknesses between subjects and with their classmates. </p>
<p>Using our data, we compared the students’ grades in STEM and humanities subjects. If a student had a higher grade in STEM than reading and writing subjects, we defined this student as having a <em>STEM advantage</em>. If this STEM advantage was greater than one of the students’ classmates, this student had STEM as an <em>academic strength</em>. </p>
<p>Because boys were generally better in science and maths than humanities, they had a higher <em>STEM advantage</em>. As girls were only slightly better in science and maths than humanities, their <em>STEM advantage</em> was lower than that of boys. </p>
<p>In our data, we considered pairs of girls with identical grades in STEM and humanities subjects at the beginning of secondary schools, who were randomly assigned to different classrooms. We then observed their enrolment decisions one to three years later. </p>
<p>For instance, two girls with a similar performance in STEM and humanities (with same <em>STEM advantage</em>) were assigned to different classrooms. </p>
<p>One girl was assigned to a classroom where her classmates had a high STEM advantage (higher scores in STEM than humanities). The other girl was assigned to a classroom where her classmates had a similar performance in STEM and humanities subject (no <em>STEM advantage</em>). </p>
<p>Our findings showed these two girls, on average, even if they had identical grades in STEM and humanities, chose different fields of study at the end of secondary school. The former (whose peers had a STEM advantage) was less likely to choose a STEM-related field. </p>
<p>Our study showed these two girls with identical performance ended up choosing a different educational career, based on which classmates they sat with. </p>
<p>This explained up to 12% of the gender gap in STEM enrolment in tertiary education.</p>
<p>We did the same for boys. Analysing pairs of boys with identical grades but different classmates, we did not observe any difference in their enrolment decisions. </p>
<h2>What can be done?</h2>
<p>Our research indicates girls are more influenced by their success relative to their peers, whereas this does not hold for boys. </p>
<p>Our findings are in line with <a href="https://www.sciencedirect.com/science/article/pii/S0272775707001185?casa_token=Qw06nnvWDxgAAAAA:QgPOT_7HomsDqiY08HbCnSMKuhtDEEafTovPclymU2LMRY3h-A0rQ5SBZcIztR_NPs2ci1VtX2Jg">previous research</a> that suggests girls are more influenced by negative grades than boys, especially in STEM, when making decisions about their future. </p>
<p>Our research suggests the teacher has an important role to play in recognising and encouraging individual academic strengths, independently of classmates or gender. </p>
<p><a href="https://academic.oup.com/qje/article/134/3/1163/5368349">Previous research</a> has shown teacher gender stereotypes regarding girls’ ability in STEM negatively affects the way girls see themselves. </p>
<p>Teachers can and must foster confidence in girls when it comes to science and maths subjects, even if they may be better at reading and writing.</p>
<p>Maths and science studies lead to occupations such as engineering, physics, data science and computer programming, which are in great <a href="https://www.abs.gov.au/ausstats/abs@.nsf/Lookup/4250.0.55.005main+features72010%E2%80%9311">demand and generally pay a high salary</a>. So turning away from STEM may have a long lasting impact on girls’ life earnings.</p><img src="https://counter.theconversation.com/content/131563/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Silvia Griselda receives funding from University of Melbourne. </span></em></p><p class="fine-print"><em><span>Rigissa Megalokonomou does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.</span></em></p>Findings from a study that followed more than 70,000 high school students in Greece suggest why girls may be less likely to pick careers in science and maths than boys.Silvia Griselda, PhD student, The University of MelbourneRigissa Megalokonomou, Lecturer in Economics, The University of QueenslandLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1300772020-01-23T13:51:06Z2020-01-23T13:51:06ZHow to fix the gap between school and work in South Africa<figure><img src="https://images.theconversation.com/files/310937/original/file-20200120-69555-9zr7pp.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">
</span> <span class="attribution"><span class="source">Shutterstock</span></span></figcaption></figure><p>The world of work is changing constantly, profoundly, and faster. This is <a href="https://www.workfront.com/blog/2017-trends-7-biggest-changes-coming-to-the-workplace">clear from</a> the outsourcing of work, waves of technological advances, increasing automation in business, and big data analysis driving the growth of industries. </p>
<p>The needs of industry are shifting constantly and the education system should be responding to provide needs-based support. </p>
<p>Education theorists, researchers, practitioners, and policy makers have to remember that the occupational situation differs from country to country. They also need to remember that changing work contexts are influencing employees and job-seekers in distinct ways. Work is becoming increasingly more complex. This means that there’s a growing need for lifelong learning, teamwork, and networking as well as an increased emphasis on digital skills to promote career <a href="https://www.wbdg.org/resources/changing-nature-organizations-work-and-workplace">adaptability and employability</a>.</p>
<p>They also have to bear in mind that the industrial sector is <a href="https://www.fxstreet.com/analysis/what-is-behind-shrinking-manufacturing-201911291511">shrinking</a>. Accordingly, work-seekers in the Global South have been turning to the service sector as well as to the informal economy with a fair amount of success. This trend is likely to <a href="http://www.scielo.org.za/scielo.php?script=sci_arttext&pid=S2222-34362019000100006">continue</a>. </p>
<p>The issue is whether education systems are keeping pace with the changes.</p>
<h2>Gateway subjects</h2>
<p>To understand whether young South Africans have the skills required by the current world of work after 12 years in school I use the lens of the so-called gateway subjects. These are maths and physical sciences and, to an extent, accounting. These form the <a href="https://www.iol.co.za/news/south-africa/concern-over-gateway-subjects-1447965">foundation</a> for scientific, economic, and industrial development and research. </p>
<p>Multiple <a href="https://www.itweb.co.za/content/DZQ58MVJZXoMzXy2">educationists and researchers</a> have contended that learners who’ve passed maths and physical sciences and have acquired the basic aspects of information communication skills and robotics have a competitive advantage in the occupational world over those that have not. South Africa simply cannot afford the unacceptably low percentage of school learners who pass Grade 12 with mathematics and physical sciences. </p>
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Read more:
<a href="https://theconversation.com/why-south-africas-declining-maths-performance-is-a-worry-129563">Why South Africa's declining maths performance is a worry</a>
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<p>Why the emphasis on maths and physical sciences? </p>
<p>Having passed Grade 12 with maths and physical sciences helps because these subjects contribute at least <a href="https://www.fin24.com/Economy/breaking-sas-economic-growth-shrinks-by-06-in-third-quarter-20191203">22% to the economy</a>. Likewise, having passed either information communication technology or even computer-assisted technology helps to <a href="https://borgenproject.org/how-technology-is-helping-economies/">advance</a> the economy by reducing production costs, boosting the growth of new businesses, and improving communication. </p>
<p>It also helps to acquire <a href="https://www.chieflearningofficer.com/2017/01/31/6-critical-skills-tomorrows-workplace/">“soft skills”</a> such as career adaptability, emotional-social intelligence, career resilience, creativity, innovation, and the ability to collaborate and to network, among other things. These skills are increasingly being seen as <a href="https://www.forbes.com/sites/anantagarwal/2018/10/02/data-reveals-why-the-soft-in-soft-skills-is-a-major-misnomer/#6b612da06f7b">“hard skills”</a> in the 21st century workplace because they’re strongly <a href="https://www.pnas.org/content/115/50/12630">aligned</a> with market needs.</p>
<p>Unfortunately, they aren’t being taught and learned adequately at school.</p>
<h2>South Africa’s overly academic school system</h2>
<p>A number of problems afflict South Africa’s education system.</p>
<p>Black learners continue to feel the effects of apartheid’s education system which <a href="https://newlearningonline.com/new-learning/chapter-5/supproting-materials/apartheid-education">spent</a> more on education for white learners. This means that the vast majority of black learners in the neediest environments get inadequate teaching and learning. </p>
<p>Unless the disparity between rich children and poor children is addressed, the gap between the achievements of learners in well-resourced schools and disadvantaged learners in resource-scarce schools will persist.</p>
<p>The effects of this disparity are felt for the rest of the pupils’ lives. One consequence is that they they struggle to succeed in university studies. </p>
<p>An added difficulty is that the country’s overly academic school system sends the message to learners and their parents that learners should strive to study at a university and that it is ‘better’ to study at a university than, for instance, at a TVET (Technical and Vocational Education and Training) College. </p>
<p>I’m <a href="https://www.springer.com/gp/book/9783030227982">in favour</a> of introducing a system that facilitates differentiated training from an early stage. </p>
<p>At the end of grade nine – at about 15 years old – most learners are already able decide whether they want to pursue academic or more vocational studies. This is the point where the system should start channelling them in career-related directions that will give them their best chance of eventually pursuing careers that “fit” their personalities – including their interests and aptitudes and enable them to enact their central life themes. </p>
<p>Another key factor that needs to be addressed is the matter of inadequate career counselling for pupils – black learners especially. During apartheid, the disadvantaged black majority of students were <a href="https://link.springer.com/chapter/10.1007/978-94-6300-154-0_1">denied access</a> to career counselling in schools. Even today, the <a href="http://www.scielo.org.za/scielo.php?script=sci_arttext&pid=S0256-01002017000400011">vast majority</a> of black learners still receive little career counselling at school and cannot afford to pay a career counsellor. </p>
<p>Funding should be <a href="https://sastudy.co.za/article/what-is-a-seta/">made available</a> by the government and employers to enable learners to consult career counsellors. Group-based career counselling is a viable solution to the challenge of providing career counselling in schools with large numbers of pupils. </p>
<h2>Solutions</h2>
<p>I maintain that there are solutions for these challenges. What’s needed is the will to use resources that are available and to move forward expeditiously.</p>
<p>To help narrow the disparity gap I’ve <a href="https://www.pressreader.com/south-africa/pretoria-news/20200108/281569472661080">argued</a> in favour of making it compulsory for graduating teachers and educational psychologists to do community service in rural areas and <a href="https://www.worldbank.org/en/country/southafrica/publication/the-economics-of-south-african-townships-special-focus-on-diepsloot">townships</a>. These professionals must be given incentives, their safety must be ensured, and they must be paid a decent salary. </p>
<p>Another step that could be taken is to rehire <a href="https://repository.up.ac.za/bitstream/handle/2263/16042/Maree_Critical(2010).pdf?sequence=1">the many</a> teachers who have been retrenched or who have taken severance package deals.</p><img src="https://counter.theconversation.com/content/130077/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Kobus Maree does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.</span></em></p>There are a few things South Africa needs to do to close the gap between what the education system produces and what the job market needs.Kobus Maree, Professor of Educational Psychology, University of PretoriaLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1295632020-01-09T17:08:57Z2020-01-09T17:08:57ZWhy South Africa’s declining maths performance is a worry<figure><img src="https://images.theconversation.com/files/309280/original/file-20200109-80107-18meh2w.jpg?ixlib=rb-1.1.0&rect=1015%2C134%2C2726%2C2345&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Basic Education Minister Angie Motshekga announces South Africa's 2019 matric results and congratulates top achievers.</span> <span class="attribution"><a class="source" href="https://flickr.com/photos/governmentza/49349311572/in/dateposted/">Flickr/GCIS</a></span></figcaption></figure><p>South Africa’s Department of Basic Education recently released the country’s National Senior Certificate results for the <a href="https://www.education.gov.za/Portals/0/Documents/Reports/2019%20NSC%20Examination%20Report.pdf?ver=2020-01-07-155811-230">class of 2019</a>. These are commonly known as the “matric results” and they determine school-leavers’ admission and placement into tertiary level study. About 81.3% of those who wrote the matriculation exams passed. There has been much well-deserved celebration of this achievement of the highest post-apartheid national matric pass rate. </p>
<p>What the country is not hearing about from the Minister of Basic Education, Angie Motshekga, is the drop in performance in mathematics. It is one of the <a href="https://www.iol.co.za/mercury/news/schools-warned-against-scrapping-hard-subjects-to-achieve-100-pass-marks-30974367">“gateway” subjects</a>, subjects which are considered critical for the country’s economic growth and development.</p>
<p>This decline can be measured in two ways. There is a reduction in the number of students writing mathematics from 270,516 in 2018 to 222,034 <a href="https://www.education.gov.za/Resources/Reports.aspx">in 2019</a>. The second measure is the performance: only 54% of the pupils who wrote the exam passed it. This pass rate is down from 58% in 2018. The minimum score for a pass is 30%. This means only 54% of mathematics exam candidates achieved a mark of at least 30%. Of all the maths candidates only 2% (4,415) <a href="https://www.education.gov.za/Resources/Reports.aspx">achieved distinctions</a>. A distinction is a score of 80%-100%. This is down from 2.5% in 2018.</p>
<h2>Why does this matter?</h2>
<p>The drop in numbers of pupils writing the grade 12 mathematics exam should be of great concern. Performance in mathematics matters for university entrance. Without it, school leavers are not eligible for programmes at university in science or engineering or some in commerce. A decline signals the closing of the doors of opportunity in these fields to a growing number of students. This will only increase inequality. Economics researcher Nic Spaull’s <a href="https://link.springer.com/chapter/10.1007%2F978-3-030-18811-5_1">research</a> has shown that the top 200 high schools in the country produce 97% of the mathematics distinctions. The majority of these schools charge significant fees. </p>
<p>The deterioration in performance is also of great concern. Getting a pass (30%) may secure a diploma or university entrance but these low pass marks will not prepare students to succeed at mathematics at university level. </p>
<p>This development runs contrary to the needs of the <a href="https://www.britannica.com/topic/The-Fourth-Industrial-Revolution-2119734">fourth industrial revolution</a>, which requires highly competent graduates in the science, technology, engineering and maths areas. Strong performance in mathematics is essential for careers in computing, programming, finance and machine learning. </p>
<h2>Universities need to shoulder the blame</h2>
<p>Universities cannot absolve themselves of this national challenge. At the University of Cape Town data from the <a href="https://www.uct.ac.za/main/teaching-and-learning/courses-impeding-graduation">Courses Impeding Graduation</a> project is being analysed to better understand incoming students’ challenges, specifically in courses like Mathematics 1. </p>
<p>In this course a worrying pattern of performance emerged. A minimum mark of 70% for maths in matric is needed to get into Mathematics 1 at the university. Based on several years of data, an average of 33% of students fail this course. Those students who enter with a 90% mark for maths in matric score a pass in Mathematics 1 with an average mean of 64%. Those students who achieved between 80% and 89% in matric fail the course with an average mean of 47%. Those who achieved between 70% and 79% in matric fail with an average mean of 43%. </p>
<p>Unless a student achieved a distinction for mathematics at school level they are at risk of failing it at university level. Students who fail Mathematics 1 will inevitably take longer to complete their degree and are at higher risk of being excluded from the university.</p>
<h2>Dealing with the problem</h2>
<p>The University of Cape Town is taking responsibility for its share in these dismal results. A number of interventions have been put in place over recent years to provide additional support to students. These include “maths labs”, Saturday workshops, and even providing multilingual resources to support students who are not yet fluent in the medium of instruction.</p>
<p>Expert maths teachers have been appointed to lecture this challenging course. But the overall failure rates of approximately one third of the class have remained stubbornly in place. A decision was taken in 2019 to revise the Mathematics 1 curriculum to ensure a greater alignment between schooling and university curriculum. </p>
<p>This kind of curriculum review raises a number of complex issues: what is the appropriate content to ensure a relatively seamless transition from school maths to university maths? Do different disciplinary areas like actuarial science, chemistry and engineering need different kinds of mathematics courses? How can the pacing of the curriculum accommodate different learning needs? How can educational technology support innovative forms of teaching and learning mathematics? These are global issues, not unique to South Africa.</p>
<p>The national euphoria around the national pass rate means nothing if it hides problems such as declining mathematics performance.</p><img src="https://counter.theconversation.com/content/129563/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Suellen Shay does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.</span></em></p>Performance in mathematics matters for university entrance. Without it, school leavers are not eligible for many programmes.Suellen Shay, Professor, University of Cape TownLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1270132019-12-03T08:47:35Z2019-12-03T08:47:35ZAussie students are a year behind students 10 years ago in science, maths and reading<figure><img src="https://images.theconversation.com/files/304631/original/file-20191202-66982-1gwv3yy.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">The latest OECD PISA results show Australia is doing worse than last time in science and maths.</span> <span class="attribution"><span class="source">from shutterstock.com</span></span></figcaption></figure><p>Australian 15-year-old reading scores are way below those of their peers in ten countries – including Singapore, Estonia, Canada, Finland, Ireland, Korea and Poland.</p>
<p>And around 41% of Australian 15 year olds have failed to meet the minimum national standards in reading – up from 31% in 2000.</p>
<p>These are some of the <a href="http://www.acer.edu.au/ozpisa/reports/">results</a> from the OECD’s 2018 Program for International Student Assessment (PISA) released today, which tested the performance of education systems across 79 countries and economies.</p>
<p>Since PISA first assessed reading literacy in 2000, Australia’s mean score has declined by the equivalent of around three-quarters of a year of schooling. </p>
<p>In maths, Australia trailed 23 countries including Singapore, Japan, Korea, Estonia, the Netherlands, Poland, Canada, the United Kingdom and Ireland. And in science, we were behind 12 countries including Singapore, Estonia, Japan, Finland, Canada, Poland and New Zealand. </p>
<p>The latest results put Australia in 11th place in reading – on par with China, Denmark, Germany, Norway, Sweden, the United Kingdom and the United States. </p>
<p>This placement doesn’t sound bad, but compared to the highest performing OECD countries, Australia is about seven months in reading and 12 months in science behind Estonia, and 15 months behind Japan in maths.</p>
<p>In science, maths and reading, Australia’s students today are almost a full year behind those of more than a decade ago.</p>
<h2>Australia’s performance on a downward trajectory</h2>
<p>PISA is a two-hour test to see how well 15-year-old students in (randomly selected) secondary schools across all 36 OECD countries, and 43 other countries or economies, can apply reading, maths and science to real-life situations.</p>
<p>The three assessment domains are rotated every three years, so one domain is the major focus (the major domain). A larger amount of the assessment time is devoted to this domain compared to the other two (the minor domains). This year, reading was the major domain.</p>
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Read more:
<a href="https://theconversation.com/pisa-results-dont-look-good-but-before-we-panic-lets-look-at-what-we-can-learn-from-the-latest-test-69470">PISA results don’t look good, but before we panic let’s look at what we can learn from the latest test</a>
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<p>Australian students did achieve an average of 503 points in reading. The OECD average – the benchmark against which each country’s performance in PISA 2018 can be compared – was 487 points in reading.</p>
<p>The four provinces of China which participated (Beijing, Shanghai, Jiangsu and Zhejiang) had the highest mean reading score of 555 points. Singapore was the highest performing country with an average of 549 points.</p>
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<p>The results also show 20% of Australian students did not meet the international level of reading proficiency on the PISA performance scale. This is the level the OECD determines a student needs to actively participate in life. In 2000, 12% of Australian students didn’t attain this level in reading.</p>
<p>Australia’s 2018 performance was above the OECD average in science, but it fell to be at the OECD average in maths.</p>
<p>The PISA results show 46% of Australian 15 year olds failed to meet the minimum national standards in mathematics and 42% fell short in science.</p>
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Read more:
<a href="https://theconversation.com/the-pisa-world-education-test-results-are-about-to-drop-is-australia-getting-worse-127011">The PISA world education test results are about to drop. Is Australia getting worse?</a>
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<p>Over the 15 years of measuring maths literacy, Australia’s performance has declined by the equivalent of about one and one-quarter years of schooling. And over the 12 years of measuring science literacy, Australia’s performance has declined by almost one full year of schooling. </p>
<p>Female students across all countries and economies participating in PISA 2018 outperformed male students in reading. In Australia, girls were around the equivalent of one year of schooling ahead of boys.</p>
<h2>How we compare across the nation</h2>
<p>Based on the latest scores, the OECD has labelled Australia as having a “high quality - high equity” education system because scores on both were above the OECD average.</p>
<p>But there was a difference of about three years of schooling in each subject area between students in the highest socioeconomic quarter (advantaged students) and those in the lowest socioeconomic quarter (disadvantaged students).</p>
<p>The OECD labels students who have not reached the <a href="https://www.oecd.org/australia/PISA-2012-low-performers-Australia-ENG.pdf">baseline level of proficiency</a> required to participate fully in modern society as “low performers”.</p>
<p>In reading, one in three disadvantaged students was classed as a “low performer”, compared to just one in ten advantaged students. In maths, the numbers are even more sobering: 37% of disadvantaged students were low performers, compared to 11% of advantaged students. </p>
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<p>Indigenous students were between two and three years behind their non-Indigenous peers across all areas – with 43% (compared to 18%) classed as low performers in reading, 48% (compared to 21%) in maths and 44% (compared to 18%) in science.</p>
<h2>How we compare internationally</h2>
<p>If excelling by international standards means performing to a standard similar to the Asian powerhouses, we have a great deal of work ahead. </p>
<p>The combined four provinces of China that participated – Beijing, Shanghai, Jiangsu and Zhejiang – while by no means representing China as a whole, represent more than 180 million people, and have an average income well below the OECD average. </p>
<p>Their scores are about one and a half years of schooling higher than Australia in reading, three and a half years higher in maths, and three years higher in science. </p>
<p>Participation in international studies such as PISA enable us to stop and look at how Australia’s education system stacks up against those of other countries – including our trading partners. </p>
<p>These findings show, again, that achievement in reading, maths, and science has been in steady decline for many years. We need to push the pause button and take stock of our curriculum, teaching and assessment methods.</p><img src="https://counter.theconversation.com/content/127013/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Sue Thomson does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.</span></em></p>Australian education is still going backwards from where we started in 2000 – new PISA results show.Sue Thomson, Deputy CEO (Research), Australian Council for Educational ResearchLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1252342019-11-04T19:02:35Z2019-11-04T19:02:35Z‘Let’s design a waterproof shoe for a refugee child’: how to teach science and maths so students actually care<p>In a <a href="https://www.chiefscientist.gov.au/2019/05/speech-stem-careers-a-broad-horizon/">May 2019 speech</a>, Australia’s Chief Scientist, Alan Finkel, noted participation in science and maths was slipping in Australian schools. Specifically speaking about STEM (science, technology, engineering and mathematics), he said:</p>
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<p>STEM education addresses real world problems and is useful to us and the wider community in many, many ways.</p>
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<p>Finkel’s predecessor made <a href="http://www.chiefscientist.gov.au/wp-content/uploads/Office-of-the-Chief-Scientist-MES-Report-8-May-2012.pdf">similar assertions</a>, arguing many countries are taking substantial action to address the decline in STEM engagement. </p>
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<a href="https://images.theconversation.com/files/299760/original/file-20191031-187942-1u57yon.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/299760/original/file-20191031-187942-1u57yon.png?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/299760/original/file-20191031-187942-1u57yon.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=2091&fit=crop&dpr=1 600w, https://images.theconversation.com/files/299760/original/file-20191031-187942-1u57yon.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=2091&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/299760/original/file-20191031-187942-1u57yon.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=2091&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/299760/original/file-20191031-187942-1u57yon.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=2627&fit=crop&dpr=1 754w, https://images.theconversation.com/files/299760/original/file-20191031-187942-1u57yon.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=2627&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/299760/original/file-20191031-187942-1u57yon.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=2627&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
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<span class="attribution"><a class="source" href="https://www.chiefscientist.gov.au/wp-content/uploads/Australias-STEM-workforce_full-report.pdf">Australia's STEM workfoce: Science, Technology, Engineering and Mathematics. Report from the office of the Chief Scientist.</a></span>
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<p>STEM education can vary from anything connected to one of the STEM subjects to interdisciplinary integration of the four areas. Students are <a href="https://www.ecu.edu.au/__data/assets/pdf_file/0004/627133/Optimising-STEM-education-in-WA-Full-Research-Report.pdf">often discouraged</a> from engaging in STEM, and many have had negative experiences with the subjects.</p>
<p>In 2016, the Western Australian Education Department commissioned the development of a set of modules that promote schools teaching STEM in a way that integrates several subjects. This resulted in the STEM Learning Project (<a href="http://stemlearning.org.au/stem-learning-project/">SLP</a>), which we spent the last three years evaluating.</p>
<p>More than 1,000 teachers and school leaders from WA metro and regional areas attended professional development workshops on how to guide students – from kindergarten to year 12 – to find solutions to open-ended, real-world problems. </p>
<p>The teachers applied this knowledge in their classrooms. They helped children research a problem and work together to design solutions.</p>
<p>The projects were varied and included: creating a bridge so animals could cross the road safely, designing a shoe for a refugee child, and finding solutions to the excessive heat experienced in Australia. </p>
<h2>Designing a shoe</h2>
<p>One project involved eight- and nine-year-old students designing a pair of shoes, using recyclable materials, for a child in a <a href="https://www.pri.org/stories/2014-02-03/how-shoes-can-tell-plight-refugees-south-sudan">South Sudanese refugee camp</a>.</p>
<p>They researched the conditions in the camp to identify what features the shoes should have. They then used scientific skills to test the suitability of different materials. </p>
<p>The students came up with a variety of designs. Each group used different materials, cutting and sticking them together, while referring to their designs. </p>
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<a href="https://images.theconversation.com/files/299766/original/file-20191031-26419-ilpkhj.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/299766/original/file-20191031-26419-ilpkhj.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/299766/original/file-20191031-26419-ilpkhj.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=338&fit=crop&dpr=1 600w, https://images.theconversation.com/files/299766/original/file-20191031-26419-ilpkhj.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=338&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/299766/original/file-20191031-26419-ilpkhj.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=338&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/299766/original/file-20191031-26419-ilpkhj.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=425&fit=crop&dpr=1 754w, https://images.theconversation.com/files/299766/original/file-20191031-26419-ilpkhj.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=425&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/299766/original/file-20191031-26419-ilpkhj.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=425&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
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<span class="caption">A waterproof shoe designed by a year 3 class for a child in a refugee camp.</span>
<span class="attribution"><span class="license">Author provided</span></span>
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<p>A year 3 class created the shoe pictured above. It was made of clear plastic material as the class identified the importance of the shoe being waterproof. </p>
<p>The teacher who facilitated this activity said:</p>
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<p>Both boys and girls enjoyed the work and they were highly engaged in every part, even the mathematics, and I have children that are not engaged in maths [who] really struggle.</p>
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<p>One of the students said:</p>
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<p>I enjoyed when we were designing our shoes ’cos we could work as a group.</p>
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<p>Another student said they would want to do this every term because it made them creative and they could use their imagination.</p>
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Read more:
<a href="https://theconversation.com/dont-just-solve-for-x-letting-kids-explore-real-world-scenarios-will-keep-them-in-maths-class-124876">Don’t just solve for x: letting kids explore real-world scenarios will keep them in maths class</a>
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<h2>Designing a birdhouse</h2>
<p>In an education support centre, a class of 14 students in years 4 to 6 worked on designing a home for a crow named Russell, who visited the school grounds and had a damaged wing. </p>
<p>Students created designs of the birdhouse and then produced 3D versions of them. </p>
<p>At this stage, members of the local <a href="https://mensshed.org/?gclid=EAIaIQobChMI5tb7os_P5QIVgR0rCh0xcwmfEAAYASAAEgIppvD_BwE">Men’s Shed</a> visited the school to view the designs. The men combined the best elements to produce a wooden version for Russell.</p>
<p>The birdhouse pictured below was a 3D cardboard box version of the students’ design. The groups were asked to consider aesthetics and functionality and this birdhouse managed to address both. </p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/299768/original/file-20191031-187934-1mtaouk.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/299768/original/file-20191031-187934-1mtaouk.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/299768/original/file-20191031-187934-1mtaouk.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=338&fit=crop&dpr=1 600w, https://images.theconversation.com/files/299768/original/file-20191031-187934-1mtaouk.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=338&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/299768/original/file-20191031-187934-1mtaouk.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=338&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/299768/original/file-20191031-187934-1mtaouk.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=425&fit=crop&dpr=1 754w, https://images.theconversation.com/files/299768/original/file-20191031-187934-1mtaouk.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=425&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/299768/original/file-20191031-187934-1mtaouk.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=425&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">A birdhouse designed for Russell the crow, who has a damaged wing.</span>
<span class="attribution"><span class="license">Author provided</span></span>
</figcaption>
</figure>
<p>One of the teachers said the project was wonderful and all the children could contribute their specific abilities. She said: </p>
<blockquote>
<p>Boys and girls both loved it […] they added their own touch with decorating their models and birdhouses.</p>
</blockquote>
<p>The teacher also noted the benefits of involving the community, saying this made the students feel their work was of value.</p>
<h2>Schools should do this more</h2>
<p>Our evaluation found that, due to the hands-on nature and authenticity of the tasks, nearly all students were enthusiastic and engaged.</p>
<p>A teacher whose year 4 students worked to address the decline of bees, said:</p>
<blockquote>
<p>The kids loved it. Whenever they see STEM on the board in the morning they go “yes”. […] I think because there is that element of creativity it does cater to everybody’s abilities […] everyone had a feeling of success.</p>
</blockquote>
<p>Another teacher, who worked with kindergarten students to design a bridge for animals, explained this approach catered </p>
<blockquote>
<p>[…] for a wider selection of learning styles. More children were engaged.</p>
</blockquote>
<p>Schools need to put more emphasis on this type of interdisciplinary STEM learning. Our evaluation shows it helps children remain engaged in STEM subjects while developing important skills for their future.</p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/more-teens-are-dropping-maths-here-are-three-reasons-to-stick-with-it-119745">More teens are dropping maths. Here are three reasons to stick with it</a>
</strong>
</em>
</p>
<hr>
<hr>
<p><em>The Stem Learning Project is a joint undertaking of a consortium in STEM education comprised of the Educational Computing Association of WA (ECAWA), the Mathematical Association of WA (MAWA), the Science Teachers Association of WA (STAWA) and Scitech.</em></p><img src="https://counter.theconversation.com/content/125234/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Paula Mildenhall receives funding from the STEM Learning Project Consortium : Scitech. </span></em></p>In a three-year project, students were taught STEM skills by designing solutions for real-world problems. An evaluation of the project found most students were stimulated and engaged.Paula Mildenhall, Associate Dean (Teaching and Learning), Edith Cowan UniversityLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1197452019-07-31T20:03:57Z2019-07-31T20:03:57ZMore teens are dropping maths. Here are three reasons to stick with it<figure><img src="https://images.theconversation.com/files/284017/original/file-20190715-173366-vircaw.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">If more girls studied maths, we could see a narrowing of the gender wage gap.</span> <span class="attribution"><span class="source">from shutterstock.com</span></span></figcaption></figure><p>The numbers of secondary school students who take higher-level maths and science are low in Australia. In 2012, there were <a href="https://www.chiefscientist.gov.au/wp-content/uploads/2-Science-and-Maths-in-Australian-Secondary-Schools-datasheet-references.pdf">30,000 more Year 12 students</a> than in 1992. But the numbers of students studying physics, chemistry and biology decreased by 8,000, 4,000 and 12,000 respectively. </p>
<p>Enrolments in intermediate and advanced mathematics also <a href="https://search.informit.com.au/documentSummary;dn=685386398396236;res=IELHSS">fell over this period</a>, by 11% and 7% respectively.</p>
<p>The Australian Curriculum <a href="https://educationstandards.nsw.edu.au/wps/portal/nesa/11-12/hsc/subject-selection">mandates maths</a> until Year 10. But we’re seeing more students dropping the subject as soon as they can. </p>
<p>In 2008, 31.2% of the NSW student population were studying maths for the High School Certificate, compared to 28.9% in 2017. This was a <a href="https://amsi.org.au/preview-year-12-mathematics-participation-in-australia-2008-2017/">drop of around</a> 5,300 students.</p>
<p>But studying maths brings many benefits. Here are three reasons to persevere. </p>
<h2>1. You’ll be more likely to get a job</h2>
<p>Many industry and economic <a href="http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.632.1213&rep=rep1&type=pdf">experts predict</a> future economies – specifically those using technology to rapidly create goods and services – will be built on maths and science knowledge and skills. </p>
<p>Research on the changing nature of employment predicts that, by 2030, we will <a href="https://www.fya.org.au/report/the-new-work-smarts/">spend 77% more time</a> on average using science and mathematics skills. With youth (people aged 15-24) <a href="https://tradingeconomics.com/australia/youth-unemployment-rate">unemployment in Australia on the rise</a>, maths skills may offer some protection. </p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/why-it-matters-that-student-participation-in-maths-and-science-is-declining-47559">Why it matters that student participation in maths and science is declining</a>
</strong>
</em>
</p>
<hr>
<p>There are more engineering jobs in Australia than skilled people to fill them. Between 2006 and 2016, the demand for engineers exceeded the number of local graduates. Employers <a href="https://www.engineering.unsw.edu.au/news/australia-is-desperately-short-of-engineers">often look overseas</a> for suitable applicants, with some figures showing more vacancies are filled by overseas engineering graduates than locals.</p>
<h2>2. You’ll probably earn more</h2>
<p>Some studies have shown students taking higher maths at school <a href="https://www.theatlantic.com/business/archive/2013/11/will-studying-math-make-you-richer/281104/">go on to have higher earnings</a> in adulthood. </p>
<p>The relationship between studying higher-level maths and earning more may be one of causation (that maths skills lead to higher earners), correlation (that people with good maths skills are more likely to have other skills that lead to higher earnings), or a bit of both. But, either way, it exists.</p>
<p>According to <a href="https://www.forbes.com/sites/jennagoudreau/2012/05/15/best-top-most-valuable-college-majors-degrees/#743070774dcc">US analysis</a> that compared university majors with median starting pay, median mid-career pay (at least ten years in), growth in salary and wealth of job opportunities, maths and engineering majors reigned supreme.</p>
<p>And a more <a href="https://www.forbes.com/sites/nickmorrison/2019/03/27/the-college-majors-with-the-highest-salaries-and-the-best-prospects/#2706db3a5aa2">recent analysis</a> by the US data researcher PayScale found graduates in maths, science and engineering had the highest mid-career salary.</p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/286195/original/file-20190730-186805-ohsi6a.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/286195/original/file-20190730-186805-ohsi6a.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/286195/original/file-20190730-186805-ohsi6a.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/286195/original/file-20190730-186805-ohsi6a.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/286195/original/file-20190730-186805-ohsi6a.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/286195/original/file-20190730-186805-ohsi6a.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/286195/original/file-20190730-186805-ohsi6a.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/286195/original/file-20190730-186805-ohsi6a.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=503&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Girls aren’t worse than boys at maths, but they drop the subject earlier.</span>
<span class="attribution"><span class="source">from shutterstock.com</span></span>
</figcaption>
</figure>
<p>One of the biggest gender gaps in education is seen in maths. Girls in most countries complete less, or lower level, maths than boys. </p>
<p>The low numbers of girls participating in advanced maths courses is not because girls are worse at maths, as there is <a href="https://www.scientificamerican.com/article/are-boys-better-than-girls-at-math/">no clear gender gap</a> when it comes to maths abilities. But girls do <a href="https://www.scientificamerican.com/article/are-boys-better-than-girls-at-math/">show less confidence</a> in their maths skills and more maths anxiety than boys.</p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/women-in-stem-need-your-support-and-australia-needs-women-in-stem-113054">Women in STEM need your support – and Australia needs women in STEM</a>
</strong>
</em>
</p>
<hr>
<p>Research suggests learning maths is often associated with <a href="https://www.researchgate.net/publication/232599119_Math_Anxiety_in_Elementary_and_Secondary_School_Students/link/02bfe50ef063d8f42f000000/download">student anxiety</a>. This anxiety is related to poor performance, negative attitudes and general avoidance of the <a href="https://psycnet.apa.org/record/1990-15802-001">subject</a>. If girls were encouraged to persist with the challenges presented by advanced levels of maths, we could even see a start to <a href="https://academic.oup.com/ej/article-abstract/126/593/1129/5078109?redirectedFrom=fulltext">a narrowing of</a> the gender wage gap. </p>
<h2>3. You’ll probably be smarter</h2>
<p>A study examined the <a href="https://www.sciencedirect.com/science/article/pii/S0160289606000171">association between intelligence and educational achievement</a> in relation to 25 secondary school subjects in the UK. It showed maths was most strongly associated with the so-called “g” factor, which is a <a href="https://psycnet.apa.org/buy/2008-07564-003">mark of underlying intelligence</a> (English came second). </p>
<p>The g factor, or general ability, is the foundation of cognitive abilities and affects all learning, including in maths and science. Graduates in STEM (science, technology, engineering and mathematics) <a href="https://www.chiefscientist.gov.au/wp-content/uploads/STEM_AustraliasFuture_Sept2014_Web.pdf">disciplines report</a> their degrees led to them developing higher-order skills and qualities (such as logical thinking and creativity).</p>
<p>Another study showed an increase in population IQ <a href="https://www.sciencedirect.com/science/article/pii/S0160289604000789">alongside a rise</a> in access to maths education in the US. Studies show higher levels of maths attainment for a population are strongly linked to <a href="https://www-sciencedirect-com.ezproxy1.library.usyd.edu.au/science/article/pii/S0160289609000063?via%3Dihub">national IQ</a> and national shifts in economic development, such as <a href="https://search.proquest.com/openview/5eb6d99494548f1a11a1ff702d86c930/1?pq-origsite=gscholar&cbl=30967">higher GDP</a> and faster <a href="https://www.semanticscholar.org/paper/National-IQ-and-economic-outcomes-Meisenberg/705cc2e57e187698e4c9dabcd20e7454a2a2c54a#paper-header">economic growth</a>. </p>
<p>A higher g factor is also associated with higher scores on international assessments of educational attainment, such as <a href="https://onlinelibrary.wiley.com/doi/abs/10.1002/per.634">PISA and TIMSS, and IQ tests</a>.</p>
<p>As the Australian system doesn’t require maths after Year 10, it seems it is up to individuals, families and their communities to recognise its importance and support students in persevering in maths for their own good.</p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/what-to-say-if-your-child-asks-whats-the-point-of-maths-69628">What to say if your child asks, 'what's the point of maths?'</a>
</strong>
</em>
</p>
<hr>
<img src="https://counter.theconversation.com/content/119745/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>The authors do not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and have disclosed no relevant affiliations beyond their academic appointment.</span></em></p>Studying maths is likely to make you smarter and more employable.Rachel Wilson, Senior Lecturer - Research Methodology / Educational Assessment & Evaluation, University of SydneyDeborah Chadwick, Lecturer, University of SydneyLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1175032019-06-16T20:04:17Z2019-06-16T20:04:17ZWe asked people to do climate change maths. Their answers depended on their politics<p>In an ideal world, people would look at issues with a clear focus only on the facts. But in the real world, we know that doesn’t happen often. </p>
<p>People often look at issues through the prism of their own particular political identity - and have probably always done so. </p>
<p>However, in an environment of <a href="https://theconversation.com/lies-obfuscation-and-fake-news-make-for-a-dispiriting-and-dangerous-election-campaign-115845">fake news</a>, <a href="https://www.theverge.com/2016/11/16/13653026/filter-bubble-facebook-election-eli-pariser-interview">filter bubbles</a> and <a href="https://www.nytimes.com/roomfordebate/2011/04/21/barack-obama-and-the-psychology-of-the-birther-myth/the-echo-chamber-effect">echo chambers</a>, it seems harder than ever to get people to agree about simple facts.</p>
<p>In research published today in <a href="https://doi.org/10.1080/17524032.2019.1618364">Environmental Communication</a>, my colleague Matthew Nurse and I report that even some of the smartest among us will simply refuse to acknowledge facts about climate change when we don’t like them.</p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/why-old-school-climate-denial-has-had-its-day-117752">Why old-school climate denial has had its day</a>
</strong>
</em>
</p>
<hr>
<h2>Skin cream versus climate change</h2>
<p>The research took place just before Australia’s 2019 federal election. </p>
<p>We asked 252 people who were planning to vote for the Greens and 252 people who were planning to vote for One Nation to consider some data we’d put together. To understand that data, they would need to do some mental maths, just like you would when looking at a typical scientific report.</p>
<p>While there was no significant difference in the mathematical ability between the two groups of voters overall, it seemed that political affiliations can have an impact on how people answered a mathematical question, depending on the subject. </p>
<p>For example, in one experiment we told participants that data in the scientific report was about whether a new skin cream would cure a rash, as shown below. </p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/279355/original/file-20190613-32373-15kdrhr.JPG?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/279355/original/file-20190613-32373-15kdrhr.JPG?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=179&fit=crop&dpr=1 600w, https://images.theconversation.com/files/279355/original/file-20190613-32373-15kdrhr.JPG?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=179&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/279355/original/file-20190613-32373-15kdrhr.JPG?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=179&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/279355/original/file-20190613-32373-15kdrhr.JPG?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=224&fit=crop&dpr=1 754w, https://images.theconversation.com/files/279355/original/file-20190613-32373-15kdrhr.JPG?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=224&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/279355/original/file-20190613-32373-15kdrhr.JPG?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=224&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption"></span>
</figcaption>
</figure>
<p>We asked them to indicate whether the experiment shows that using the new cream is more likely to make the skin condition better or worse. Participants in our study got the correct mathematical answer 48% of the time. </p>
<p>However, when we showed them exactly the same data but said it was about whether closing coal-fired power stations would significantly reduce carbon dioxide emissions in the local area (by 30% or more), we got a very different set of answers. </p>
<p>For example, when the report showed CO₂ emissions would go down significantly, only 27% of One Nation supporters got the right answer.</p>
<p>When the report showed CO₂ emissions would not significantly go down, only 37% of Greens voters got it right. </p>
<p>So it seems our participants were less likely to answer a question correctly when it went against their political ideology.</p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/climate-sceptic-or-climate-denier-its-not-that-simple-and-heres-why-117913">Climate sceptic or climate denier? It's not that simple and here's why</a>
</strong>
</em>
</p>
<hr>
<h2>Spilt people according to maths ability</h2>
<p>But what follows is really the interesting bit. </p>
<p>We decided to find out whether numeracy – maths ability – played a role in people getting the wrong answers. First, we looked at those with below-average numeracy. </p>
<p>We found many of these people just gave their preferred, ideologically aligned answers when it came to the climate change question. This is a well-known effect called <a href="http://psycnet.apa.org/record/1991-06436-001">motivated reasoning</a>.</p>
<p>But surely the more numerate groups of people, those better at maths, would fare better? Well, not really.</p>
<p>The groups of people with above-average numeracy sometimes did worse than the less numerate groups. Some did no better than chance at 50%, and some did far, far worse than that, as the graph below shows.</p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/279346/original/file-20190613-32342-1jlp10w.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/279346/original/file-20190613-32342-1jlp10w.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/279346/original/file-20190613-32342-1jlp10w.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=281&fit=crop&dpr=1 600w, https://images.theconversation.com/files/279346/original/file-20190613-32342-1jlp10w.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=281&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/279346/original/file-20190613-32342-1jlp10w.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=281&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/279346/original/file-20190613-32342-1jlp10w.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=353&fit=crop&dpr=1 754w, https://images.theconversation.com/files/279346/original/file-20190613-32342-1jlp10w.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=353&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/279346/original/file-20190613-32342-1jlp10w.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=353&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">More numerate people are more polarised about climate change data.</span>
<span class="attribution"><a class="source" href="https://doi.org/10.1080/17524032.2019.1618364">Matt Nurse</a>, <span class="license">Author provided</span></span>
</figcaption>
</figure>
<p>When we showed people reports about CO₂ emissions, the more numerate people were much more politically polarised than any other group. For example, the participants considered a report showing that CO₂ would go down significantly, a One Nation supporter with a numeracy score of seven (out of nine) was only 5% as likely to provide the correct answer as a Greens supporter in the same numeracy category.</p>
<h2>Motivations change brain function</h2>
<p>This is counterintuitive, but this isn’t the first study to reveal this effect.</p>
<p>These findings build on research previously done by a Yale professor, <a href="https://law.yale.edu/dan-m-kahan">Dan Kahan</a>. The phenomenon is a type of motivated reasoning called <a href="https://www.cambridge.org/core/journals/behavioural-public-policy/article/motivated-numeracy-and-enlightened-selfgovernment/EC9F2410D5562EF10B7A5E2539063806">motivated numeracy</a>. </p>
<p>While Kahan’s previous research focused on the politically polarising issue of gun control in the United States, some people suggested the same thing might happen with other topics, <a href="https://www.salon.com/2013/09/17/the_most_depressing_discovery_about_the_brain_ever_partner/">particularly climate change</a>.</p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/guns-politics-and-policy-what-can-we-learn-from-al-jazeeras-undercover-nra-sting-114291">Guns, politics and policy: what can we learn from Al Jazeera's undercover NRA sting?</a>
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<hr>
<p>Our research is the first to confirm this.</p>
<p>These findings build on the theory that your desire to give an answer in line with your pre-existing beliefs on climate change can be stronger than your ability or desire to give the right answer. </p>
<p>In fact, more numerate people may be better at doing this because they are have more skills to rationalise their own beliefs in the face of contradictory evidence.</p>
<h2>So what?</h2>
<p>You might ask whether it really matters if people sometimes get the wrong answer on questions like this. </p>
<p>We’d argue yes, it does matter. Successful democracies rely on a majority of voters being able to identify and understand risks, and make the appropriate voting choices.</p>
<p>If people remain entrenched in their ideological corners when threats come along, and are unwilling to face facts, societal problems can fester, potentially becoming much more difficult to resolve later.</p>
<p>Just imagine scientists had discovered human activity was damaging our atmosphere. They said this problem would cause Earth’s climate to get hotter and threaten our livelihoods. Politicians and the people they represented saw this as a legitimate issue worth acting on, regardless of their political views. Imagine the world united to fix this problem, even though it would cost a lot of money.</p>
<p>In fact, we don’t need to imagine too much, as this isn’t just a hypothetical situation. It actually happened when scientists found evidence the use of industrial chemicals was depleting the ozone layer. </p>
<p>In 1987, for the first and only time, all 197 members of the United Nations agreed to sign the <a href="http://web.unep.org/ozonaction/who-we-are/about-montreal-protocol">Montreal Protocol</a> regulating the man-made chemicals that destroy the ozone layer. More than 30 years later we can measure the <a href="http://science.sciencemag.org/content/353/6296/269">benefits of this agreement</a> in our planet’s atmosphere.</p>
<h2>A matter of science, not politics</h2>
<p>Unlike the current <a href="https://theconversation.com/why-old-school-climate-denial-has-had-its-day-117752">climate change debate</a>, people largely saw this risk as a matter of science, not politics. </p>
<p>But it seems people are increasingly encouraged to see risks like this through a <a href="https://theconversation.com/communicating-climate-change-focus-on-the-framing-not-just-the-facts-73028">political frame</a>. When this happens, facts can become irrelevant because no matter how smart people are, many will simply deny the evidence to protect their side of the political debate.</p>
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Read more:
<a href="https://theconversation.com/communicating-climate-change-focus-on-the-framing-not-just-the-facts-73028">Communicating climate change: Focus on the framing, not just the facts</a>
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<p>Societies need to make good choices for their survival and those choices need to be based on facts, regardless of whether everyone likes them or not. </p>
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<p><em>This research was conducted by Matthew Nurse as part of a master’s thesis at the Australian National Centre for the Public Awareness of Science.</em></p><img src="https://counter.theconversation.com/content/117503/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Will J Grant does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.</span></em></p>We asked 252 Australian Greens party supporters and 252 One Nation party supporters to do some simple maths. Their answers changed when we told them it was climate change data.Will J Grant, Senior Lecturer, Australian National Centre for the Public Awareness of Science, Australian National UniversityLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1156462019-05-16T10:31:15Z2019-05-16T10:31:15ZHow to overcome a fear of maths<figure><img src="https://images.theconversation.com/files/274417/original/file-20190514-60529-ktb5t3.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">
</span> <span class="attribution"><span class="source">shutterstock</span></span></figcaption></figure><p>It’s fair to say maths is not everyone’s favourite subject. In fact, for many people, the feelings of tension and anxiety that arise when trying to solve a mathematical problem can be all consuming. This is known as maths anxiety – and this feeling of being a failure at maths can affect people’s <a href="https://www.theguardian.com/commentisfree/2019/mar/14/panic-maths-anxiety-studying-pupils-schools">self-worth for years to come</a>.</p>
<p>For those who suffer with maths anxiety, it can be difficult to shift from a mindset of failure to a more positive outlook when it comes to dealing with numbers. This is why, for many people, maths anxiety can become a lifelong issue.</p>
<p>But <a href="https://www.amazon.co.uk/Elephant-Classroom-Helping-Children-Learn/dp/0285643185/ref=tmm_pap_swatch_0_encoding=UTF8&qid=1557478920&sr=8-1-fkmrnull">research</a> shows that if teachers tackle maths anxiety in the classroom and encourage children to try to approach a problem in a different way – by shifting their mindset – this can be an empowering experience. This is especially the case for pupils from a disadvantaged background. </p>
<h2>Mindset theory</h2>
<p>US psychology professor, Carol Dweck, came up with the idea of “<a href="https://www.ted.com/talks/carol_dweck_the_power_of_believing_that_you_can_improve/discussion">mindset theory</a>”. Dweck realised that people can often be categorised into two groups, those who believe they are bad at something and cannot change, and those who believe their abilities can grow and improve. </p>
<p>This formed the basis of her mindset theory, which states that some people have a “fixed mindset”, meaning they believe their ability to be set in stone and unable to be improved. Other people have a “growth mindset” meaning they believe their ability can change and improve over time with effort and practice. </p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/274418/original/file-20190514-60554-phm6ki.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/274418/original/file-20190514-60554-phm6ki.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/274418/original/file-20190514-60554-phm6ki.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/274418/original/file-20190514-60554-phm6ki.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/274418/original/file-20190514-60554-phm6ki.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/274418/original/file-20190514-60554-phm6ki.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/274418/original/file-20190514-60554-phm6ki.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=503&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
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<span class="caption">Maths can be fun – if only it’s taught properly.</span>
<span class="attribution"><span class="source">Shutterstock</span></span>
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<p>Jo Boaler, the British education author and professor of mathematics education, applied mindset theory to mathematics, subsequently naming her recommendations “mathematical mindsets”. </p>
<p>She has used this theory to encourage learners to develop a growth mindset <a href="https://www.youcubed.org/mathematical-mindset-teaching-guide-teaching-video-and-additional-resources">in the context of mathematics</a>. The idea is that the problems themselves can help to promote a growth mindset in pupils – without them <a href="https://www.amazon.co.uk/tale-Lucy-wanted-learn-spell/dp/1533445001">having to think about their mindset</a> intentionally. </p>
<h2>New ways of thinking</h2>
<p>But while this all sounds well and good, one of the issues with mindset theory is that it is often presented in terms of <a href="https://theconversation.com/what-is-brain-plasticity-and-why-is-it-so-important-55967">brain plasticity</a> or the <a href="https://www.conted.ox.ac.uk/about/brain-resources">brain’s ability to grow</a>. This has lead to <a href="http://www.danielwillingham.com/daniel-willingham-science-and-education-blog/march-13th-2019">complaints</a> about a shortage of neurological evidence supporting mindset theory. <a href="https://authors.elsevier.com/c/1YsHs7sy6LOEAw">Our latest research</a> aimed to address this lack of neurological research. </p>
<p>Generally speaking, for every problem in mathematics there is more than one way to solve it. If someone asks you what three multiplied by four is, you can calculate the answer either as 4+4+4 or as 3+3+3+3, depending on your preference. But if you have not developed sufficient mathematical maturity or have maths anxiety, it can prevent you from <a href="https://www.researchgate.net/publication/326424642_Non-adaptive_strategy_selection_in_adults_with_high_mathematical_anxiety">seeing multiple ways of solving problems</a>. But <a href="https://authors.elsevier.com/c/1YsHs7sy6LOEAw">our new study</a> shows that a “growth mindset” can make maths anxiety a thing of the past.</p>
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Read more:
<a href="https://theconversation.com/maths-six-ways-to-help-your-child-love-it-96441">Maths: six ways to help your child love it</a>
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<p>We measured participants’ motivation to solve mathematical problems by asking about motivation both before and after each problem was presented. We also measured participants’ brain activity, specifically looking at areas associated with motivation, while they solved each problem. This was done using an electroencephalogram (EEG) which records patterns of activation across the brain.</p>
<p>In our research, we phrased questions in different ways to assess how question structure may affect both our participants’ ability to answer the questions and their motivation while tackling maths problems.</p>
<p>Each question appeared in two formats: one of typical mathematical teaching and another adhering to the recommendations of mathematical mindset theory. Both questions asked essentially the same question and had the same answer, like in the following simplified example:</p>
<p>“Find the number which is the sum of 20,000 and 30,000 divided by two” (a typical mathematical problem) and “Find the midpoint number between 20,000 and 30,000” (an example of a mathematical mindset problem). </p>
<h2>Growth mindsets</h2>
<p>Our study provides two important findings.</p>
<p>The first is that participants’ motivation was greater when solving mathematical mindset versions of problems compared to the standard versions – as measured by their brain response when solving the problems. It is assumed this is because the mathematical mindset wording encourages students to treat numbers as points in the space and manipulate spatial constructions.</p>
<p>The second is that participants’ subjective reports of motivation were significantly decreased after attempting the more standard maths questions. </p>
<p>Our research is immediately actionable in that it shows how opening up problems so that there are multiple methods to solving them, or adding a visual component, allows learning to become an empowering experience for all students.</p>
<p>So for people with maths anxiety, you will be relieved to know that you are not innately “bad” at maths and your ability is not fixed. It is actually just a bad habit you have developed due to bad teaching. And the good news is, it can be reverted.</p><img src="https://counter.theconversation.com/content/115646/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>The authors do not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and have disclosed no relevant affiliations beyond their academic appointment.</span></em></p>Maths anxiety can be made a thing of the past, as new research shows.Alexei Vernitski, Senior Lecturer in Mathematics, University of EssexIan Daly, Lecturer in Brain-Computer Interfaces, University of EssexJake Bourgaize, PhD Candidate, University of EssexLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1149232019-04-09T20:03:55Z2019-04-09T20:03:55ZWe’ve found a quicker way to multiply really big numbers<figure><img src="https://images.theconversation.com/files/268273/original/file-20190409-2918-10t3u6l.jpg?ixlib=rb-1.1.0&rect=131%2C176%2C2770%2C1570&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">If you thought multiplication tables at school were hard, imagine multiplying numbers with billions of digits.</span> <span class="attribution"><span class="source">Shutterstock/Nina Buday</span></span></figcaption></figure><p>Multiplication of two numbers is easy, right?</p>
<p>At primary school we learn how to do <a href="https://www.mathsisfun.com/numbers/multiplication-long.html">long multiplication</a> like this:</p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/268281/original/file-20190409-2901-94rv98.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/268281/original/file-20190409-2901-94rv98.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/268281/original/file-20190409-2901-94rv98.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=453&fit=crop&dpr=1 600w, https://images.theconversation.com/files/268281/original/file-20190409-2901-94rv98.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=453&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/268281/original/file-20190409-2901-94rv98.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=453&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/268281/original/file-20190409-2901-94rv98.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=569&fit=crop&dpr=1 754w, https://images.theconversation.com/files/268281/original/file-20190409-2901-94rv98.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=569&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/268281/original/file-20190409-2901-94rv98.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=569&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
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<span class="caption">The long way to multiplication.</span>
<span class="attribution"><span class="source">David Harvey</span></span>
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<p>Methods similar to this go back thousands of years, at least to the ancient Sumerians and Egyptians.</p>
<p>But is this really the best way to multiply two big numbers together?</p>
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Read more:
<a href="https://theconversation.com/six-images-reveal-how-we-see-data-and-capture-invisible-science-102769">Six images reveal how we ‘see' data and capture invisible science</a>
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<p>In long multiplication, we have to multiply every digit of the first number by every digit of the second number. If the two numbers each have <em>N</em> digits, that’s <em>N</em><sup>2</sup> (or <em>N</em> x <em>N</em>) multiplications altogether. In the example above, <em>N</em> is 3, and we had to do 3<sup>2</sup> = 9 multiplications.</p>
<p>Around 1956, the famous Soviet mathematician <a href="https://www.britannica.com/biography/Andrey-Nikolayevich-Kolmogorov">Andrey Kolmogorov</a> conjectured that this is the <em>best possible way</em> to multiply two numbers together.</p>
<p>In other words, no matter how you arrange your calculations, the amount of work you have to do will be proportional to at least <em>N</em><sup>2</sup>. Twice as many digits means <em>four</em> times as much work.</p>
<p>Kolmogorov felt that if a short cut was possible, surely it would have already been discovered. After all, people have been multiplying numbers for thousands of years.</p>
<p>This is a superb example of the logical fallacy known as “the argument from ignorance”.</p>
<h2>A quicker way</h2>
<p>Just a few years later, Kolmogorov’s conjecture was shown to be spectacularly wrong.</p>
<p>In 1960, Anatoly Karatsuba, a 23-year-old mathematics student in Russia, discovered a <a href="http://mathworld.wolfram.com/KaratsubaMultiplication.html">sneaky algebraic trick</a> that reduces the number of multiplications needed.</p>
<p>For example, to multiply four-digit numbers, instead of needing 4<sup>2</sup> = 16 multiplications, Karatsuba’s method gets away with only nine. When using his method, twice as many digits means only <em>three</em> times as much work.</p>
<p>This stacks up to an impressive advantage as the numbers get bigger. For numbers with a thousand digits, Karatsuba’s method needs about 17 times fewer multiplications than long multiplication.</p>
<p>But why on earth would anyone want to multiply such big numbers together?</p>
<p>In fact, there are a tremendous number of applications. One of the most visible and economically significant is in <a href="https://theconversation.com/au/topics/cryptography-2094">cryptography</a>.</p>
<h2>Big numbers in real life</h2>
<p>Every time you engage in encrypted communication on the internet — for example, access your banking website or perform a web search — your device performs a head-spinning number of multiplications, involving numbers with hundreds or even thousands of digits.</p>
<p>Very likely your device uses Karatsuba’s trick for this arithmetic. This is all part of the amazing software ecosystem that keeps our web pages loading as snappily as possible.</p>
<p>For some more esoteric applications, mathematicians have to deal with even larger numbers, with millions, billions or even trillions of digits. For such enormous numbers, even Karatsuba’s algorithm is too slow.</p>
<p>A real breakthrough came in 1971 with the work of the German mathematicians Arnold Schönhage and Volker Strassen. They explained how to use the recently published fast Fourier transform (<a href="https://en.wikipedia.org/wiki/Fast_fourier_transform">FFT</a>) to multiply huge numbers efficiently. Their method is routinely used by mathematicians today to handle numbers in the billions of digits.</p>
<p>The FFT is one of the most important algorithms of the 20th century. One application familiar in daily life is digital audio: whenever you listen to MP3s, music streaming services or digital radio, FFTs handle the audio decoding behind the scenes.</p>
<h2>An even quicker way?</h2>
<p>In their <a href="https://link.springer.com/article/10.1007/BF02242355">1971 paper</a>, Schönhage and Strassen also made a striking conjecture. To explain, I’ll have to get a bit technical for a moment.</p>
<p>The first half of their conjecture is that it should be possible to multiply <em>N</em>-digit numbers using a number of basic operations that is proportional to at most <em>N</em> log (<em>N</em>) (that’s <em>N</em> times the <a href="https://www.britannica.com/science/logarithm#ref795970">natural logarithm</a> of <em>N</em>).</p>
<p>Their own algorithm did not quite reach this target; they were too slow by a factor of log (log <em>N</em>) (the logarithm of the logarithm of <em>N</em>). Nevertheless, their intuition led them to suspect that they were missing something, and that <em>N</em> log (<em>N</em>) should be feasible.</p>
<p>In the decades since 1971, a few researchers have found improvements to Schönhage and Strassen’s algorithm. Notably, an <a href="https://doi.org/10.1137/070711761">algorithm</a> designed by Martin Fürer in 2007 came agonisingly close to the elusive <em>N</em> log (<em>N</em>).</p>
<p>The second (and much more difficult) part of their conjecture is that <em>N</em> log (<em>N</em>) should be the fundamental speed limit — that no possible multiplication algorithm could do better than this.</p>
<p>Sound familiar?</p>
<h2>Have we reached the limit?</h2>
<p>A few weeks ago, <a href="http://www.texmacs.org/joris/main/joris.html">Joris van der Hoeven</a> and I posted a <a href="https://hal.archives-ouvertes.fr/hal-02070778/document">research paper</a> describing a new multiplication algorithm that finally reaches the <em>N</em> log (<em>N</em>) holy grail, thus settling the “easy” part of the Schönhage–Strassen conjecture.</p>
<p>The paper has not yet been peer-reviewed, so some caution is warranted. It is <a href="https://academia.stackexchange.com/questions/16832/why-upload-to-academic-preprint-sites-like-arxiv">standard practice</a> in mathematics to disseminate research results before they have undergone peer review.</p>
<p>Instead of using one-dimensional FFTs — the staple of all work on this problem since 1971 — our algorithm relies on <em>multidimensional</em> FFTs. These gadgets are nothing new: the widely-used JPEG image format depends on 2-dimensional FFTs, and 3-dimensional FFTs have many applications in physics and engineering.</p>
<p>In our paper, we use FFTs with 1,729 dimensions. This is tricky to visualise, but mathematically no more troublesome than the 2-dimensional case.</p>
<h2>Really, really big numbers</h2>
<p>The new algorithm is not really practical in its current form, because the proof given in our paper only works for ludicrously large numbers. Even if each digit was written on a hydrogen atom, there would not be nearly enough room available in the observable universe to write them down.</p>
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Read more:
<a href="https://theconversation.com/why-do-we-need-to-know-about-prime-numbers-with-millions-of-digits-89878">Why do we need to know about prime numbers with millions of digits?</a>
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<p>On the other hand, we are hopeful that with further refinements, the algorithm might become practical for numbers with merely billions or trillions of digits. If so, it may well become an indispensable tool in the computational mathematician’s arsenal.</p>
<p>If the full Schönhage–Strassen conjecture is correct, then from a theoretical point of view, the new algorithm is the end of the road – it is not possible to do any better.</p>
<p>Personally, I would be very surprised if the conjecture turned out to be wrong. But we shouldn’t forget what happened to Kolmogorov. Mathematics can sometimes throw up surprises.</p><img src="https://counter.theconversation.com/content/114923/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>David Harvey receives funding from the Australian Research Council.</span></em></p>To multiply two numbers by hand take a few steps but it’s something we’re taught in school. When dealing with big numbers, really big numbers, we need to a quicker way to do things.David Harvey, Associate professor in mathematics, UNSW SydneyLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/964412018-08-17T12:20:34Z2018-08-17T12:20:34ZMaths: six ways to help your child love it<figure><img src="https://images.theconversation.com/files/230790/original/file-20180806-191028-12mefqt.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">
</span> <span class="attribution"><span class="source">shutterstock</span></span></figcaption></figure><p>There is a widespread perception that mathematics is inaccessible, and ultimately boring. Just mentioning it can cause a negative reaction in people, as many mathematicians witness at any social event when the dreaded question arrives: “what is your job?”</p>
<p>For many people, school maths lessons are the time when any interest in the subject turns into disaffection. And eventually maths becomes a topic many people don’t want to engage with <a href="http://www.bsrlm.org.uk/wp-content/uploads/2016/02/BSRLM-IP-27-1-04.pdf">for the rest of their lives</a>. A percentage of the population, at least 17% – possibly much higher depending on <a href="https://www.frontiersin.org/articles/10.3389/fpsyg.2016.00508/full">the metrics applied</a> – develops maths anxiety. This is a debilitating fear of performing any numerical task, which results in chronic underachievement in subjects involving mathematics.</p>
<p>At the opposite end of the spectrum, professional mathematicians see mathematics as <a href="https://www.lms.ac.uk/library/frames-of-mind">fun, engaging, challenging and creative</a>. And as maths fans, we are trying to address this chasm in perception of mathematics, to allow everybody to access its beauty and power. So here are our six ways you can help children fall back in love with mathematics. </p>
<h2>1. Focus on the whys</h2>
<p>The Australian teacher <a href="https://www.youtube.com/channel/UCq0EGvLTyy-LLT1oUSO_0FQ">Eddie Woo</a> has become an internet sensation for his engaging way of presenting mathematics. He starts from the ideas and, using pictures and graphs, develops the theory. </p>
<p>He does not ask his students to do repetitive exercises, but to work with him in developing intuition. And he asks the most powerful question a learner of mathematics can ask: “Why?”. It is possible to hear throughout his classes the “oohs” and “ahhs” of students in the background, when a novel concept is understood. </p>
<h2>2. Make it relevant</h2>
<p>Traditionally (and in particular in the UK) mathematics is taught in a systematic way, <a href="https://eclass.uoa.gr/modules/document/file.php/MATH103/ELENA%20NARDI/NARDI3.pdf">based on rote learning and individual study</a>. Some students thrive in such a system, others, typically more empathetic students – often female – find such an approach to mathematics isolating and disconnected from their values and their reality.</p>
<p>Connecting mathematical concepts with applications in reality can bring meaning to lessons and lectures, and motivate students to put in the necessary effort to understand. For example, derivatives – ways of calculating rates of change – can be introduced as a way to measure slopes, and slopes are experienced in everyday life – think about the skatepark or the big hill you cycle up. </p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/230791/original/file-20180806-191038-197vk2x.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/230791/original/file-20180806-191038-197vk2x.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/230791/original/file-20180806-191038-197vk2x.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/230791/original/file-20180806-191038-197vk2x.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/230791/original/file-20180806-191038-197vk2x.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/230791/original/file-20180806-191038-197vk2x.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/230791/original/file-20180806-191038-197vk2x.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=503&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
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<span class="caption">Make maths about real life to capture kids imaginations.</span>
<span class="attribution"><span class="source">Pexels</span></span>
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<h2>3. Recognise the challenge</h2>
<p>There is an effort component in learning mathematics. It can be challenging, and understanding it sometimes involves stress, frustration, and struggle over time. This can be an emotionally complex environment for children. But it is one where persistence and perseverance are rewarded when a new concept is understood. </p>
<p>With each success, students gain confidence that they can progress in learning more mathematics. In this way, learning mathematics can be compared to climbing a mountain: plenty of effort, but also some truly blissful moments.</p>
<h2>4. Be a maths role model</h2>
<p>Some people like to climb mountains solo, while others prefer good company to share the effort. Similarly, some people are happy to study mathematics on their own, but others need more help <a href="https://www.nature.com/articles/srep23011">navigating this challenging subject</a>. Research shows that students who are failing in maths tend to be more empathetic than systematising. These are also the students more affected by reactions of people surrounding them: parents, teachers and the media. </p>
<h2>5. Make maths matter</h2>
<p>So given that <a href="https://hpl.uchicago.edu/sites/hpl.uchicago.edu/files/uploads/Maloney%252c%20E.A.%252c%20Schaeffer%252c%20M.W.%252c%20%26%20Beilock%252c%20S.L.%252c%20%25282013%2529.%20Mathematics%20anxiety%20and%20stereotype%20threat.pdf">maths anxiety can spread from one generation</a> to another, parents clearly have a role to play in making sure their children don’t clam up at the very thought of numbers. This is important, because a parent who learns how to avoid passing on mathematical anxiety gives their child a chance to learn a beautiful subject and to access <a href="http://www.bbc.co.uk/news/education-41693230">some of the best paid, most interesting, jobs around</a>. </p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/230792/original/file-20180806-191035-w0uvxk.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/230792/original/file-20180806-191035-w0uvxk.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/230792/original/file-20180806-191035-w0uvxk.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/230792/original/file-20180806-191035-w0uvxk.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/230792/original/file-20180806-191035-w0uvxk.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/230792/original/file-20180806-191035-w0uvxk.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/230792/original/file-20180806-191035-w0uvxk.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=503&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
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<span class="caption">Don’t scared of maths, it could rub off on your child.</span>
<span class="attribution"><span class="source">Shutterstock</span></span>
</figcaption>
</figure>
<h2>6. Join the dots</h2>
<p>When it comes to maths, both inside and outside the classroom, the emphasis should shift from solely the numerical aspect to include connected aspects, such as concepts and links with other subjects and everyday applications. This will allow children to see mathematics as a social practice – where discussing mathematical challenges with classmates, teachers and parents becomes the norm.</p><img src="https://counter.theconversation.com/content/96441/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>The authors do not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and have disclosed no relevant affiliations beyond their academic appointment.</span></em></p>Make maths more fun with these tipsSue Johnston-Wilder, Associate Professor, Mathematics Education, University of WarwickDavide Penazzi, Lecturer in Mathematics, University of Central LancashireLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/973162018-06-07T20:28:49Z2018-06-07T20:28:49ZBees join an elite group of species that understands the concept of zero as a number<figure><img src="https://images.theconversation.com/files/221898/original/file-20180606-137295-1owba2y.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Bees live in complex environments, and make lots of decisions every day that are crucial for survival. </span> <span class="attribution"><a class="source" href="https://www.shutterstock.com/image-photo/honey-bees-kept-bee-box-hive-1099240694?src=73MQBwoOpxtqlXSw7mEAng-1-75">from www.shutterstock.com </a></span></figcaption></figure><p>When it comes to bees, it seems that nothing really does matter. </p>
<p>As shown in a <a href="http://science.sciencemag.org/lookup/doi/10.1126/science.aar4975">paper</a> published today, our research demonstrates that the honeybee can understand the quantitative value of nothing, and place zero in the correct position along a line of sequential numbers. </p>
<p>This is the first evidence showing that an insect brain can understand the concept of zero, and has implications for our understanding of how complex number processing evolved. More broadly, it may help us design better artificial intelligence solutions for operating in complex environments.</p>
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<em>
<strong>
Read more:
<a href="https://theconversation.com/want-a-better-camera-just-copy-bees-and-their-extra-light-sensing-eyes-80385">Want a better camera? Just copy bees and their extra light-sensing eyes</a>
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</em>
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<hr>
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<iframe width="440" height="260" src="https://www.youtube.com/embed/KQkP85I2UJM?wmode=transparent&start=0" frameborder="0" allowfullscreen=""></iframe>
<figcaption><span class="caption">Bee brains are tiny - but they do get that zero is a number.</span></figcaption>
</figure>
<h2>What is ‘zero’, anyway?</h2>
<p>There are <a href="https://www.sciencedirect.com/science/article/pii/S1364661316301255">four stages of understanding the concept of zero</a> in human culture, history, psychology and animal learning.</p>
<p><strong>Stage one:</strong> Understanding zero as the absence of something, such as no food on your plate. This first level is likely enabled at an early stage of visual processing. </p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/221135/original/file-20180531-69490-1ja5sg3.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/221135/original/file-20180531-69490-1ja5sg3.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=370&fit=crop&dpr=1 600w, https://images.theconversation.com/files/221135/original/file-20180531-69490-1ja5sg3.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=370&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/221135/original/file-20180531-69490-1ja5sg3.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=370&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/221135/original/file-20180531-69490-1ja5sg3.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=464&fit=crop&dpr=1 754w, https://images.theconversation.com/files/221135/original/file-20180531-69490-1ja5sg3.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=464&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/221135/original/file-20180531-69490-1ja5sg3.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=464&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Perceiving nothing on your plate requires understanding the absence of information.</span>
<span class="attribution"><span class="source">'Adrian Dyer/RMIT University'</span></span>
</figcaption>
</figure>
<p><strong>Stage two:</strong> Understanding zero as “nothing” vs. “something”, such as the presence or absence of light in a room. “Nothing” is thus treated as a meaningful behavioural category.</p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/221138/original/file-20180531-69497-2kt6a1.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/221138/original/file-20180531-69497-2kt6a1.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=218&fit=crop&dpr=1 600w, https://images.theconversation.com/files/221138/original/file-20180531-69497-2kt6a1.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=218&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/221138/original/file-20180531-69497-2kt6a1.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=218&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/221138/original/file-20180531-69497-2kt6a1.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=274&fit=crop&dpr=1 754w, https://images.theconversation.com/files/221138/original/file-20180531-69497-2kt6a1.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=274&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/221138/original/file-20180531-69497-2kt6a1.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=274&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Perceiving the absence of information relative to a stimulus like a light is the second stage of understanding zero.</span>
<span class="attribution"><span class="source">'Adrian Dyer/RMIT University'</span></span>
</figcaption>
</figure>
<p><strong>Stage three:</strong> Understanding that zero can have a numeric value and belongs at the low end of the positive number line. For example: 0 < 1 < 2 < 3 etc. (where < means “less than”). </p>
<figure class="align-right ">
<img alt="" src="https://images.theconversation.com/files/221133/original/file-20180531-69484-zv83tx.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/221133/original/file-20180531-69484-zv83tx.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=751&fit=crop&dpr=1 600w, https://images.theconversation.com/files/221133/original/file-20180531-69484-zv83tx.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=751&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/221133/original/file-20180531-69484-zv83tx.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=751&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/221133/original/file-20180531-69484-zv83tx.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=944&fit=crop&dpr=1 754w, https://images.theconversation.com/files/221133/original/file-20180531-69484-zv83tx.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=944&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/221133/original/file-20180531-69484-zv83tx.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=944&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">By learning to choose less than options, bees learnt over one day to be able to transfer information and place zero at the lower end of all previously experienced numbers.</span>
<span class="attribution"><span class="source">Scarlett Howard, Adrian Dyer and Jair Garcia/RMIT University</span></span>
</figcaption>
</figure>
<p><strong>Stage four:</strong> Understanding that zero can be assigned a symbolic representation which can be used in modern mathematics and calculations, for example: 1 – 1 = 0.</p>
<p>Our new study shows honeybees have achieved stage three of understanding the concept of zero. </p>
<p>The honeybee now joins the elite few species which have demonstrated an understanding of zero to this advanced level. While <a href="https://www.sciencedirect.com/science/article/pii/S0010027700001128">rhesus monkeys</a>, <a href="https://www.hindawi.com/journals/ijz/2011/806589/">vervet monkeys</a>, a single <a href="https://link.springer.com/article/10.1007/s100710100086">chimpanzee</a>, and one <a href="https://homepages.uni-tuebingen.de/andreas.nieder/Nieder%20(2016)%20TICS.pdf">African grey parrot</a> have demonstrated the ability to learn or spontaneously understand the concept of zero, this is the first time that such a high level of cognitive number processing has been observed in an insect.</p>
<h2>Why care about zero?</h2>
<p>The <a href="https://homepages.uni-tuebingen.de/andreas.nieder/Nieder%20(2016)%20TICS.pdf">importance of zero</a> throughout human history is not to be underestimated. </p>
<p><a href="http://www-groups.dcs.st-and.ac.uk/history/HistTopics/Chinese_numerals.html">Chinese counting rods used a blank space</a> to help represent a place holder in values, however zero went unnoticed as a number with a quantitative value for centuries. For example, Roman numerals do not have a symbol for zero. </p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/221140/original/file-20180531-69501-196wsew.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/221140/original/file-20180531-69501-196wsew.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=218&fit=crop&dpr=1 600w, https://images.theconversation.com/files/221140/original/file-20180531-69501-196wsew.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=218&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/221140/original/file-20180531-69501-196wsew.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=218&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/221140/original/file-20180531-69501-196wsew.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=274&fit=crop&dpr=1 754w, https://images.theconversation.com/files/221140/original/file-20180531-69501-196wsew.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=274&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/221140/original/file-20180531-69501-196wsew.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=274&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Zero in Chinese Rod Calculus around 4th Century B.C.</span>
<span class="attribution"><a class="source" href="https://en.wikipedia.org/wiki/0#/media/File:Zero_in_Rod_Calculus.png">Wikimedia Commons</a></span>
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</figure>
<p>It was not until <a href="https://archive.org/details/Brahmasphutasiddhanta_Vol_1">628AD that zero had a written record</a> which noted it as a number in its own right by Indian mathematician Brahma Gupta in his book Brahmasputha Siddhanta. This is the first written record to provide rules to use when doing calculations with zero. </p>
<p>The earliest record of the symbolic zero (0) we are familiar with today is from an <a href="https://www.livehistoryindia.com/amazing-india/2017/04/29/zero-number-one">Indian inscription on the wall</a> of a temple in Gwalior, India (AD 876). Arabic numerals, along with the modern idea of zero, did not reach the West <a href="https://www.britannica.com/topic/Hindu-Arabic-numerals">until 1200 AD</a>. </p>
<p>Interestingly, while it took centuries for the concept of zero to be fully understood and utilised in human culture, honeybees have learnt to apply previous number knowledge to demonstrate an understanding of zero <em>within a day</em> when presented with training to promote numerical cognition.</p>
<h2>How we asked bees about zero</h2>
<p>Bees often forage in <a href="https://theconversation.com/plants-use-advertising-like-strategies-to-attract-bees-with-colour-and-scent-92673">complex environments</a> and have evolved <a href="https://theconversation.com/which-square-is-bigger-honeybees-see-visual-illusions-like-humans-do-87673">visual processing solutions</a> adapted to this life. </p>
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Read more:
<a href="https://theconversation.com/which-square-is-bigger-honeybees-see-visual-illusions-like-humans-do-87673">Which square is bigger? Honeybees see visual illusions like humans do</a>
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<p>In our research, we tested number processing in bees by individually training them with special apparatus to collect a sugary reward, and learn the rules of “less than” considering the numbers 1 – 6. </p>
<p>An individual bee would need to choose between two numbers each time it returned to the experiment. For example, a bee would be presented with two new numbers (3 vs. 4; 1 vs. 2; 2 vs. 5, etc.) until it had reached, over many learning events, at least 80% accuracy for landing on and thus choosing the lowest number.</p>
<p>Once the bee achieved this, it would be presented with the previously unseen stimulus of “an empty set” representing zero. </p>
<figure class="align-right ">
<img alt="" src="https://images.theconversation.com/files/221707/original/file-20180605-119885-1mp78sb.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/221707/original/file-20180605-119885-1mp78sb.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=837&fit=crop&dpr=1 600w, https://images.theconversation.com/files/221707/original/file-20180605-119885-1mp78sb.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=837&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/221707/original/file-20180605-119885-1mp78sb.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=837&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/221707/original/file-20180605-119885-1mp78sb.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=1052&fit=crop&dpr=1 754w, https://images.theconversation.com/files/221707/original/file-20180605-119885-1mp78sb.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=1052&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/221707/original/file-20180605-119885-1mp78sb.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=1052&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">A honeybee chooses to land on the zero option.</span>
<span class="attribution"><span class="source">Scarlett Howard/RMIT University</span></span>
</figcaption>
</figure>
<p>Surprisingly, bees trained to the “less than” rule preferred to visit the empty set rather than any other higher value number. This means bees understood an empty set was lower in number than a set containing actual elements.</p>
<p>In further experiments, other bees were able to place zero at the low end of the numerical continuum and demonstrated numerical distance effects. Numerical distance effects are demonstrated when accuracy increases as the difference between two numbers increases. The study showed that while bees could differentiate between zero and one, they performed better when the numbers were further apart, such as in the case of zero vs. six.</p>
<p>The next step for research on the processing of zero is to understand how small and seemingly simple brains (like those of bees) represent zero in a neurological sense. </p>
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<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/plants-use-advertising-like-strategies-to-attract-bees-with-colour-and-scent-92673">Plants use advertising-like strategies to attract bees with colour and scent</a>
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<p>Andreas Nieder, an expert in numerical competency in animals from the University of Tübingen in Germany <a href="http://science.sciencemag.org/content/360/6393/1069">writes</a>: </p>
<blockquote>
<p>The advanced numerical skills of bees and other animals raise the question of how their brains transform “nothing” into an abstract concept of zero. </p>
</blockquote>
<p>This new research on bees has created many new questions in the field and also makes it clear that brain size and complexity does not fully determine intelligence and, in particular, numerical ability.</p><img src="https://counter.theconversation.com/content/97316/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Scarlett Howard received funding from The Company of Biologists (JEB Travelling Fellowship) and has an Australian Government Research Training Program Scholarship.</span></em></p><p class="fine-print"><em><span>Adrian Dyer receives funding from The Australian Research Council.</span></em></p><p class="fine-print"><em><span>Aurore Avarguès-Weber a reçu des financements de la fondation Fyssen. </span></em></p>The Romans may not have had a symbol for zero, but bees understand what it means beyond just the simple assumption “there’s nothing there”.Scarlett Howard, PhD candidate, RMIT UniversityAdrian Dyer, Associate Professor, RMIT UniversityAurore Avarguès-Weber, Researcher , Université de Toulouse III – Paul SabatierLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/928582018-03-15T11:20:15Z2018-03-15T11:20:15ZHigh number of adults unable to do basic mathematical tasks<figure><img src="https://images.theconversation.com/files/210274/original/file-20180314-113469-1dxoeka.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">'I don't even know how much this is going to cost.'</span> <span class="attribution"><a class="source" href="https://www.shutterstock.com/download/success?src=_8uSGJoRNieQEMUSqROWJA-1-36">shutterstock</a></span></figcaption></figure><p>Suppose, a litre of cola costs US$3.15. If you buy one third of a litre of cola, how much would you pay?</p>
<p>The above may seem like a rather basic question. Something that you would perhaps expect the vast majority of adults to be able to answer? Particularly if they are allowed to use a calculator. </p>
<p>Unfortunately, the reality is that a large number of adults across the world struggle with even such basic financial tasks (the correct answer is US$1.05, by the way).</p>
<p>Using Organisation for Economic Cooperation and Development (OECD) Programme for International Assessment of Adult Competencies (PIAAC) <a href="http://www.google.co.uk/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0ahUKEwjQqYO009fZAhXLDMAKHRKQBF8QFggnMAA&url=http%3A%2F%2Fwww.oecd.org%2Fskills%2Fpiaac%2F&usg=AOvVaw0doGOG0MDqeIWDq46xfSIa">data</a>, my co-authors and I have looked at how adults from 31 countries answer four <a href="https://johnjerrim.com/piaac/">relatively simple financial questions</a>. </p>
<figure class="align-right zoomable">
<a href="https://images.theconversation.com/files/209099/original/file-20180306-146661-16wex9g.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/209099/original/file-20180306-146661-16wex9g.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/209099/original/file-20180306-146661-16wex9g.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=964&fit=crop&dpr=1 600w, https://images.theconversation.com/files/209099/original/file-20180306-146661-16wex9g.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=964&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/209099/original/file-20180306-146661-16wex9g.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=964&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/209099/original/file-20180306-146661-16wex9g.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=1211&fit=crop&dpr=1 754w, https://images.theconversation.com/files/209099/original/file-20180306-146661-16wex9g.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=1211&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/209099/original/file-20180306-146661-16wex9g.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=1211&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">The estimated proportion of adults who could answer the question correctly.</span>
<span class="attribution"><span class="license">Author provided</span></span>
</figcaption>
</figure>
<p>As well as the question above, participants were asked questions such as: “Suppose, upon your trip to the grocery store you purchase four types of tea packs: Chamomile Tea (US$4.60), Green Tea (US$4.15), Black Tea (US$3.35) and Lemon Tea (US$1.80). If you paid for all these items with a US$20 bill, how much change would you get?”</p>
<p>The results (as seen in the table) allowed us to create an estimated range for the percentage of the adult population who would be able to answer the cola question correctly. These results are based upon a random sample of adults from each country.</p>
<p>We found that Lithuania, Austria and Slovakia were the most successful, but even in these countries, one in four adults failed to give the correct answer. </p>
<p>In many other countries, the situation is even worse. Four in every ten adults in places like England, Canada, Spain and the US can’t make this straightforward calculation – even when they had a calculator to hand. Similarly, less than half of adults in places like Chile, Turkey and South Korea can get the right answer. </p>
<h2>Basic calculations</h2>
<p>Of course, not all groups within each country perform quite so poorly, and there are notable differences in financial literacy skills between different demographic groups. </p>
<p>Across the four financial questions adults were asked, in most countries, men tended to perform slightly better than women. The young (particularly 25- to 34-year-olds) were also found to perform better than the over-55s. </p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/210276/original/file-20180314-113469-bv14d3.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/210276/original/file-20180314-113469-bv14d3.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/210276/original/file-20180314-113469-bv14d3.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/210276/original/file-20180314-113469-bv14d3.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/210276/original/file-20180314-113469-bv14d3.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/210276/original/file-20180314-113469-bv14d3.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/210276/original/file-20180314-113469-bv14d3.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=503&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Many adults struggle with basic financial tasks, like working out what’s better value at a supermarket.</span>
<span class="attribution"><a class="source" href="https://www.shutterstock.com/download/success?src=_8uSGJoRNieQEMUSqROWJA-1-53">Shutterstock</a></span>
</figcaption>
</figure>
<p>The starkest differences were seen by education group. Returning to the first question given above, in many countries adults with a “low” level of education (the equivalent of completing secondary school) had less than a 50% chance of getting the question correct. In places like Canada and United States, this fell to as low as 25%. </p>
<h2>Financial headache</h2>
<p>Our results clearly highlight how many adults are ill equipped to make key financial decisions. And how in fact, many struggle to cope with even very simple financial tasks. </p>
<p>In the long term, this highlights the critical need for financial literacy to be taught in schools, to ensure young people are equipped for the complex financial decisions they will face in the real world. </p>
<p>More immediately, though, given the low level of financial skills among many adults, it is vital that the information provided with financial products is as simple and straightforward to interpret as possible. And in the age of payday loans, and high interest credit cards, adequate advice and guidance must also be available where needed. Because otherwise, there is a real danger that a large proportion of the population is at risk of making serious financial mistakes.</p><img src="https://counter.theconversation.com/content/92858/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>The team who wrote the paper received funding from the OECD. This work was commissioned by the Organisation for Economic Co-operation and Development (OECD) who has granted Cambridge University Technical Services Ltd the right to publish it for non-commercial purposes only. </span></em></p>New research shows that many adults across the world are financially illiterate and unable to complete even basic mathematical calculations.John Jerrim, Lecturer in Economics and Social Statistics, UCLLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/917572018-02-27T15:22:11Z2018-02-27T15:22:11ZMathematics: forget simplicity, the abstract is beautiful - and important<figure><img src="https://images.theconversation.com/files/207820/original/file-20180226-140213-yox11e.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">
</span> <span class="attribution"><span class="source">Shutterstock</span></span></figcaption></figure><p>Why is mathematics so complicated? It’s a question many students will ask while grappling with a particularly complex calculus problem – and their teachers will probably echo while setting or marking tests.</p>
<p>It wasn’t always this way. Many fields of mathematics germinated from the study of real world problems, before the underlying rules and concepts were identified. These rules and concepts were then defined as abstract structures. For instance, algebra, the part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulas and equations was born from solving problems in arithmetic. Geometry emerged as people worked to solve problems dealing with distances and area in the real world. </p>
<p>That process of moving from the concrete to the abstract scenario is known, appropriately enough, as <a href="https://betterexplained.com/articles/learning-to-learn-math-abstraction/">abstraction</a>. Through abstraction, the underlying essence of a mathematical concept can be extracted. People no longer have to depend on real world objects, as was once the case, to solve a mathematical puzzle. They can now generalise to have wider applications or by matching it to other structures can illuminate similar phenomena. An example is the adding of integers, fractions, complex numbers, vectors and matrices. The concept is the same, but the applications are different. </p>
<p>This evolution was necessary for the development of mathematics, and important for other scientific disciplines too. </p>
<p>Why is this important? Because the growth of abstraction in maths gave disciplines like chemistry, physics, astronomy, geology, meteorology the ability to explain a wide variety of complex physical phenomena that occur in nature. If you grasp the process of abstraction in mathematics, it will equip you to better understand abstraction occurring in other tough science subjects like chemistry or physics.</p>
<h2>From the real world to the abstract</h2>
<p>The earliest example of abstraction was when humans counted before symbols existed. A sheep herder, for instance, needed to keep track of his flock of sheep without having any sort of symbolic system akin to numbers. So how did he do this to ensure that none of his sheep wandered away or got stolen?</p>
<p>One solution is to obtain a big supply of stones. He then moved the sheep one-by-one into an enclosed area. Each time a sheep passed, he placed a stone in a pile. Once all the sheep had passed, he got rid of the extra stones and was left with a pile of stones representing his flock. </p>
<p>Every time he needed to count the sheep, he removed the stones from his pile; one for each sheep. If he had stones left over, it means some sheep had wandered away or perhaps been stolen. This one-to-one correspondence helped the shepherd to keep track of his flock. </p>
<p>Today, we use the Arabic numbers (also known as the <a href="https://www.britannica.com/topic/Hindu-Arabic-numerals">Hindu-Arabic numerals</a>): 0,1,2,3,4,5,6,7,8,9 to represent any integer, that is any whole number. </p>
<p>This is another example of abstraction, and it’s powerful. It means we’re able to handle any amount of sheep, regardless of how many stones we have. We’ve moved from real-world objects – stones, sheep – to the abstract. There is real strength in this: we’ve created a space where the rules are minimalistic, yet the games that can be played are endless.</p>
<p>Another advantage of abstraction is that it reveals a deeper connection between different fields of mathematics. Results in one field can suggest concepts and ideas to be explored in a related field. Occasionally, methods and techniques developed in one field can be directly applied to another field to create similar results. </p>
<h2>Tough concepts, better teaching</h2>
<p>Of course, abstraction also has its disadvantages. Some of the mathematical subjects taught at university level – Calculus, Real Analysis, Linear Algebra, Topology, Category Theory, Functional Analysis and Set Theory among them – are very advanced examples of abstraction. </p>
<p>These concepts can be quite difficult to learn. They’re often tough to visualise and their rules rather unintuitive to manipulate or reason with. This means students need a degree of mathematical maturity to process the shift from the concrete to the abstract. </p>
<p>Many high school kids, particularly from developing countries, come to university with an <a href="https://link.springer.com/chapter/10.1007/978-3-319-12688-3_18">undeveloped level</a> of intellectual maturity to handle abstraction. This is because of the way mathematics was taught at high school. I have seen many students struggling, giving up or not even attempting to study mathematics because they weren’t given the right tools at school level and they think that they just “can’t do maths”. </p>
<p>Teachers and lecturers can improve this abstract thinking by being aware of abstractions in their subject and learning to demonstrate abstract concepts through concrete examples. Experiments are also helpful to familiarise and assure students of an abstract concept’s solidity.</p>
<p>This teaching principle is applied in some school systems, such as <a href="http://montessoritraining.blogspot.co.za/2008/07/montessori-philosophy-moving-from.html">Montessori</a>, to help children improve their abstract thinking. Not only does this guide them better through the maze of mathematical abstractions but it can be applied to other sciences as well.</p><img src="https://counter.theconversation.com/content/91757/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Harry Zandberg Wiggins does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.</span></em></p>Through abstraction, the underlying essence of a mathematical concept can be extracted.Harry Zandberg Wiggins, Lecturer, University of PretoriaLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/886782017-12-15T11:14:26Z2017-12-15T11:14:26ZMaths challenge: England has one of the biggest gaps between high and low performing pupils in the developed world<figure><img src="https://images.theconversation.com/files/199038/original/file-20171213-27555-xl6o5f.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">England’s top performing maths pupils achieve a very high standard but the bottom performers lag far behind.</span> <span class="attribution"><span class="source">shutterstock</span></span></figcaption></figure><p>When it comes to maths, many primary school children in the UK are struggling to achieve their potential, <a href="https://epi.org.uk/report/world-class-primary/">according to new research</a>. </p>
<p><a href="https://epi.org.uk/report/world-class-primary/">The recent report</a> from the <a href="https://epi.org.uk/report/world-class-primary/">Education Policy Institute</a> and UCL’s Institute of Education shows that England has one of the biggest gaps between high and low performing students in the developed world. Only New Zealand and Turkey have a bigger disparity.</p>
<p>So while England’s top performing maths pupils achieve a very high standard, the bottom performers lag far behind – with this gap well established before pupils reach secondary school.</p>
<p>It’s not surprising then that “mastery” has become something of a buzzword in the UK in the last five years. <a href="http://www.nama.org.uk/Downloads/Five%20Myths%20about%20Mathematics%20Mastery.pdf">It’s a word with lots of different meanings</a>, but it’s usually linked to how mathematics is taught in East Asia – particularly in Shanghai and Singapore. Both of which are very successful in <a href="https://theconversation.com/pisa-results-four-reasons-why-east-asia-continues-to-top-the-leaderboard-69951">international league tables such as PISA</a>.</p>
<p>In Shanghai and Singapore the mastery method involves whole class <a href="http://beyondlevels.website/wp-content/uploads/2016/05/Mastery-differentiation-and-fixed-ability-thinking-M-Boylan-Learning-first-Sheffield.pdf">interactive teaching as the main approach</a>. The idea is that by using teacher questions, step by step progression, diagrams and carefully designed practice exercises, all pupils progress together. And daily intervention is also used to support those pupils who need extra tuition.</p>
<h2>The maths gap</h2>
<p>Interest in adopting East Asian approaches to maths have recently been made an educational priority by the UK government. In the recent budget, the chancellor Philip Hammond announced <a href="https://schoolsweek.co.uk/budget-2017-hammond-announces-cash-for-computing-and-maths-mastery/">plans to invest £27m in the expansion</a> of the Teaching for Mastery maths programme to a further 3,000 schools. </p>
<p>The government has previously issued funding for a teacher exchange with Shanghai along with a whole raft of other measures to boost the uptake of the mastery approach to British schools. As part of my research, colleagues and I have been <a href="https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/666450/MTE_third_interim_report_121217.pdf">evaluating the teacher exchange programme with Shanghai</a>. </p>
<p>We discovered after the initial exchange, responses were quite varied in the 48 schools that sent and hosted teachers in 2014 and 2015. Some teachers decided the method wasn’t for them, others adopted some practices, while some completely changed their teaching methods. </p>
<figure>
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<p>Schools adopting a mastery approach often follow the official guidance of the <a href="https://www.ncetm.org.uk/resources/47230">National Centre for Teaching Mathematics</a> – but there are lots of other influences. Not only the <a href="https://www.ncetm.org.uk/resources/49739">Shanghai exchange</a> but also independent curriculum and professional development organisations – such as <a href="https://mathsnoproblem.com/">Maths No Problem </a> and <a href="https://www.mathematicsmastery.org/">Mathematics Mastery</a>. On top of all this, “mastery” is also the latest catchphrase for suppliers of resources and educational consultants. </p>
<p>The outcome is often lots of experimentation and variation in schools – and ultimately, lots of different versions of mastery. But overall, the types of changes we saw schools make after the exchange are ones mathematics educators have advocated for a <a href="https://educationendowmentfoundation.org.uk/tools/guidance-reports/maths-ks-two-three/">long time and are backed by research</a>.</p>
<h2>Mastering mastery</h2>
<p>In our evaluation, we found a number of ways schools are implementing the mastery method into their classrooms. For some schools, this has meant using an <a href="https://mathsnoproblem.com/">East Asian inspired textbook</a>. For others, they have continued to select from a wide range of resources, but think more about mastery methods in everyday teaching. </p>
<p>We have seen how schools involved in the exchange have made much greater use of concrete and visual models to support abstract thinking. Equipment that previously might only have been used with young children or those struggling with mathematics, has been dusted off and integrated into teaching more generally – <a href="https://educationendowmentfoundation.org.uk/tools/guidance-reports/maths-ks-two-three/">which has been shown to help children’s understanding</a>.</p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/199042/original/file-20171213-27555-1m0n63s.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/199042/original/file-20171213-27555-1m0n63s.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/199042/original/file-20171213-27555-1m0n63s.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/199042/original/file-20171213-27555-1m0n63s.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/199042/original/file-20171213-27555-1m0n63s.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/199042/original/file-20171213-27555-1m0n63s.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/199042/original/file-20171213-27555-1m0n63s.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=503&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">If England is to be considered world class at primary in maths, the performance of pupils at the bottom must be improved.</span>
<span class="attribution"><span class="source">Shutterstock</span></span>
</figcaption>
</figure>
<p>We have also seen more schools <a href="https://www.tes.com/news/school-news/breaking-views/how-make-mixed-ability-work-let-children-take-control-lesson">teaching in “mixed ability” sessions</a> (the Shanghai way) with teaching at a pace whereby children don’t get left behind – if children don’t “get it” in the lesson, they are given daily catch up support.</p>
<p>But we have found that many of the schools involved in the exchange have been less keen to adopt the mastery way of seating pupils in rows and daily homework. In these schools, pupils are more likely to face the front only some of the time, and instead of daily homework, time is used each day for maths practice within school. </p>
<h2>Making it add up</h2>
<p>But despite many British schools now adopting some form of mastery approach to mathematics, there still tends to be scepticism around the approach with lots of <a href="http://www.nama.org.uk/Downloads/Five%20Myths%20about%20Mathematics%20Mastery.pdf">myths about mastery emerging</a>. </p>
<p>Mastery sceptics point to the <a href="https://www.theguardian.com/world/2014/oct/09/east-asian-school-success-culture-curriculum-teaching">cultural factors</a> and <a href="https://schoolsweek.co.uk/schools-minister-admits-shanghai-maths-teachers-only-do-two-lessons-a-day/">very different working conditions of East Asian teachers</a> as underpinning their success. And there is also concern over <a href="https://schoolsweek.co.uk/what-is-teaching-for-mastery-in-maths/">whether the fastest learners will be held back</a>.</p>
<p>The sceptics might be proved right, but the way maths is taught in many English schools is changing. So if benefits for pupils are shown, then conversations may well shift from “whether” to implement mastery, to “which” aspects of East Asian teaching are most useful when adapted for the Western classroom.</p><img src="https://counter.theconversation.com/content/88678/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Mark Boylan receives funding from the Department for Education, England for evaluating the Mathematics Teacher Exchange: China-England. </span></em></p>But could the influences of Shanghai and Singapore help?Mark Boylan, Professor of Education, Sheffield Hallam UniversityLicensed as Creative Commons – attribution, no derivatives.