tag:theconversation.com,2011:/uk/topics/maths-education-9103/articlesMaths education – The Conversation2024-02-28T13:11:56Ztag:theconversation.com,2011:article/2239412024-02-28T13:11:56Z2024-02-28T13:11:56ZUnderstanding how the brain works can transform how school students learn maths<figure><img src="https://images.theconversation.com/files/578023/original/file-20240226-29-lwslum.jpg?ixlib=rb-1.1.0&rect=11%2C176%2C7337%2C4726&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/school-kid-doing-math-exercise-homework-2090861887">SrideeStudio/Shutterstock</a></span></figcaption></figure><p>School mathematics teaching is stuck in the past. An adult revisiting the school that they attended as a child would see only superficial changes from what they experienced themselves. </p>
<p>Yes, in some schools they might see a room full of electronic tablets, or the teacher using a touch-sensitive, interactive whiteboard. But if we zoom in on the details – the tasks that students are actually being given to help them make sense of the subject – things have <a href="https://bera-journals.onlinelibrary.wiley.com/doi/10.1002/curj.159">hardly changed at all</a>.</p>
<p>We’ve learnt a huge amount in recent years about cognitive science – how our brains work and how people learn most effectively. This understanding has the potential to revolutionise what teachers <a href="https://www.deansforimpact.org/tools-and-resources/the-science-of-learning">do in classrooms</a>. But the design of mathematics teaching materials, such as textbooks, has <a href="https://www.tandfonline.com/doi/full/10.1080/14794802.2022.2158122">benefited very little from this knowledge</a>.</p>
<p>Some of this knowledge is counter-intuitive, and therefore unlikely to be applied unless done so deliberately. What learners prefer to experience, and what teachers think is likely to be most effective, often isn’t what will help the most.</p>
<p>For example, cognitive science <a href="https://link.springer.com/article/10.3758/s13423-014-0588-3">tells us</a> that practising similar kinds of tasks all together generally leads to less effective learning than mixing up tasks that require different approaches. </p>
<p>In mathematics, practising similar tasks together could be a page of questions each of which requires addition of fractions. Mixing things up might involve bringing together fractions, probability and equations in immediate succession.</p>
<p>Learners make more mistakes when doing mixed exercises, and are likely to feel frustrated by this. Grouping similar tasks together is therefore likely to be much easier for the teacher to manage. But the mixed exercises give the learner important practice at deciding what method they need to use for each question. This means that more knowledge is retained afterwards, making this what is known as a <a href="https://bjorklab.psych.ucla.edu/wp-content/uploads/sites/13/2016/04/EBjork_RBjork_2011.pdf">“desirable difficulty”</a>.</p>
<h2>Cognitive science applied</h2>
<p>We are just now beginning to apply findings like this from cognitive science to design better teaching materials and to support teachers in using them. Focusing on school mathematics makes sense because mathematics is a compulsory subject which many people find difficult to learn.</p>
<p>Typically, school teaching materials are chosen by gut reactions. A head of department looks at a new textbook scheme and, based on their experience, chooses whatever seems best to them. What else can they be expected to do? But even the best materials on offer are generally not designed with cognitive science principles such as “desirable difficulties” in mind.</p>
<p>My colleagues and I have been researching <a href="https://bera-journals.onlinelibrary.wiley.com/doi/10.1002/curj.249">educational design</a> that applies principles from <a href="https://psycnet.apa.org/record/2015-00153-003">cognitive science</a> to mathematics teaching, and are developing <a href="https://www.lboro.ac.uk/services/lumen/curriculum/">materials for schools</a>. These materials are not designed to look easy, but to include “desirable difficulties”. </p>
<p>They are not divided up into <a href="https://www.foster77.co.uk/Foster,%20Teach%20Secondary,%20Stop%20planning%20lessons.pdf">individual lessons</a>, because this pushes the teacher towards moving on when the clock says so, regardless of student needs. Being responsive to students’ developing understanding and difficulties requires materials designed according to the size of the ideas, rather than what will fit conveniently onto a double-page spread of a textbook or into a 40-minute class period.</p>
<h2>Switching things up</h2>
<p>Taking an approach led by cognitive science also means changing how mathematical concepts are explained. For instance, diagrams have always been a prominent feature of mathematics teaching, but often they are used haphazardly, based on the teacher’s personal preference. In textbooks they are highly restricted, due to space constraints. </p>
<p>Often, similar-looking diagrams are used in different topics and for very different purposes, leading to confusion. For example, three circles connected as shown below can indicate partitioning into a sum (<a href="https://www.ncetm.org.uk/classroom-resources/primm-102-introducing-whole-and-parts-part-part-whole/">the “part-whole model”</a>) or a product of prime factors. </p>
<p>These involve two very different operations, but are frequently represented by the same diagram. Using the same kind of diagram to represent conflicting operations (addition and multiplication) leads to learners muddling them up and becoming confused.</p>
<figure class="align-center ">
<img alt="Diagram of connected circles with numbers inside, as described above." src="https://images.theconversation.com/files/577980/original/file-20240226-16-w2ab9l.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/577980/original/file-20240226-16-w2ab9l.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=228&fit=crop&dpr=1 600w, https://images.theconversation.com/files/577980/original/file-20240226-16-w2ab9l.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=228&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/577980/original/file-20240226-16-w2ab9l.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=228&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/577980/original/file-20240226-16-w2ab9l.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=286&fit=crop&dpr=1 754w, https://images.theconversation.com/files/577980/original/file-20240226-16-w2ab9l.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=286&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/577980/original/file-20240226-16-w2ab9l.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=286&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Number diagrams showing numbers that add together to make six and numbers that multiply to make six.</span>
<span class="attribution"><span class="source">Colin Foster</span></span>
</figcaption>
</figure>
<p>The <a href="https://www.cambridge.org/core/books/abs/multimedia-learning/coherence-principle/4E80B70CB76E2166B76E5653EBDE7D3E">“coherence principle”</a> from cognitive science means avoiding diagrams where their drawbacks outweigh their benefits, and using diagrams and animations in a purposeful, consistent way across topics.</p>
<p>For example, <a href="https://www.foster77.co.uk/Foster,%20Using%20coherent%20representations%20of%20number%20in%20the%20school%20mathematics%20curriculum.pdf">number lines</a> can be introduced at a young age and incorporated across many topic areas to bring coherence to students’ developing understanding of number. Number lines can be used to solve equations and also to represent probabilities, for instance. </p>
<p>Unlike with the circle diagrams above, the uses of number lines shown below don’t conflict but reinforce each other. In each case, positions on the number line represent numbers, from zero on the left, increasing to the right.</p>
<figure class="align-center ">
<img alt="Number line in red and black demonstrating how to solve an equation, as described above" src="https://images.theconversation.com/files/578260/original/file-20240227-16-wz37l0.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/578260/original/file-20240227-16-wz37l0.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=133&fit=crop&dpr=1 600w, https://images.theconversation.com/files/578260/original/file-20240227-16-wz37l0.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=133&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/578260/original/file-20240227-16-wz37l0.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=133&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/578260/original/file-20240227-16-wz37l0.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=167&fit=crop&dpr=1 754w, https://images.theconversation.com/files/578260/original/file-20240227-16-wz37l0.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=167&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/578260/original/file-20240227-16-wz37l0.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=167&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">A number line used to solve an equation.</span>
<span class="attribution"><span class="source">Colin Foster</span></span>
</figcaption>
</figure>
<figure class="align-center ">
<img alt="Number line with values from left to right: 0, unlikely, even chance, likely, 1." src="https://images.theconversation.com/files/577987/original/file-20240226-17-ys3jg7.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/577987/original/file-20240226-17-ys3jg7.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=80&fit=crop&dpr=1 600w, https://images.theconversation.com/files/577987/original/file-20240226-17-ys3jg7.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=80&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/577987/original/file-20240226-17-ys3jg7.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=80&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/577987/original/file-20240226-17-ys3jg7.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=101&fit=crop&dpr=1 754w, https://images.theconversation.com/files/577987/original/file-20240226-17-ys3jg7.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=101&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/577987/original/file-20240226-17-ys3jg7.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=101&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">A number line used to show probability.</span>
<span class="attribution"><span class="source">Colin Foster</span></span>
</figcaption>
</figure>
<p>There are disturbing <a href="https://theconversation.com/gcse-and-higher-results-show-worsening-gap-between-richer-and-poorer-pupils-pandemic-assessment-shows-we-should-reconsider-exams-216409">inequalities</a> in the learning of mathematics, with students from poorer backgrounds underachieving relative to their wealthier peers. There is also a huge <a href="https://www.wisecampaign.org.uk/a-level-results-2023/">gender participation gap</a> in maths, at A-level and beyond, which is taken by far more boys than girls. </p>
<p>Socio-economically advantaged families have always been able to buy their children out of difficulties by using private tutors, but less privileged families cannot. Better-quality teaching materials, based on insights from cognitive science, mitigate the impact for students who have traditionally been disadvantaged by gender, race or financial background in the learning of mathematics.</p><img src="https://counter.theconversation.com/content/223941/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Colin Foster receives funding from Research England and UKRI Economic and Social Research Council. He works for Loughborough University and is Director of the Loughborough University Mathematics Education Network.</span></em></p>Principles from cognitive science can help help in the design of more effective teaching materials for maths.Colin Foster, Reader in Mathematics Education, Loughborough UniversityLicensed 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/1905292022-12-28T21:09:29Z2022-12-28T21:09:29ZThe history and mystery of Tangram, the children’s puzzle game that harbours a mathematical paradox or two<figure><img src="https://images.theconversation.com/files/498377/original/file-20221201-20-cw8scj.jpg?ixlib=rb-1.1.0&rect=0%2C39%2C6630%2C4337&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>Have you played the puzzle game Tangram? </p>
<p>I remember, as a child, being fascinated by how just seven simple wooden triangles and other shapes could offer endless entertainment. Unlike LEGO, the Tangram pieces do not snap together, and unlike the pieces of a jigsaw puzzle, they do not form a painted picture.</p>
<p>Instead, Tangram invites you to fit all the pieces together to form countless varieties of shapes. You can make your own shapes or you can try to form shapes that others have created. For instance, here’s one way to form a swan shape using Tangram pieces:</p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/498376/original/file-20221201-26-syova6.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="A swan shape in Tangram." src="https://images.theconversation.com/files/498376/original/file-20221201-26-syova6.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/498376/original/file-20221201-26-syova6.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/498376/original/file-20221201-26-syova6.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/498376/original/file-20221201-26-syova6.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/498376/original/file-20221201-26-syova6.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/498376/original/file-20221201-26-syova6.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/498376/original/file-20221201-26-syova6.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">This is one of several ways to make a swan shape using Tangram. Can you find another?</span>
<span class="attribution"><span class="source">Shutterstock</span></span>
</figcaption>
</figure>
<p>But it’s not the only way to make a swan. Can you find others? If you do not have the physical puzzle at hand, you can <a href="https://toytheater.com/tangram/">use</a> a virtual version of Tangram.</p>
<p>Tangram is accessible and yet challenging, and an excellent <a href="https://link.springer.com/article/10.1007/BF02354839">educational tool</a>. It’s still <a href="https://education.nsw.gov.au/teaching-and-learning/curriculum/mathematics/mathematics-curriculum-resources-k-12/mathematics-k-6-resources/how-to-make-a-tangram">used</a> in <a href="https://education.nsw.gov.au/teaching-and-learning/curriculum/mathematics/mathematics-curriculum-resources-k-12/mathematics-k-6-resources/how-to-make-a-tangram">schools</a> today to help illustrate mathematical concepts and develop mathematical thinking skills. It even features a paradox or two.</p>
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Read more:
<a href="https://theconversation.com/5-math-skills-your-child-needs-to-get-ready-for-kindergarten-103194">5 math skills your child needs to get ready for kindergarten</a>
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<h2>A long history of rearrangement puzzles</h2>
<p>Tangram is one of many rearrangement puzzles that have appeared throughout the ages. The earliest known rearrangement puzzle, the <a href="https://mathworld.wolfram.com/Stomachion.html">Stomachion</a>, was invented by Greek mathematician Archimedes 2,200 years ago and was popular for centuries among Greeks and Romans. </p>
<p>It consists of 14 puzzle pieces that can fit together in the form of many different shapes. There are <a href="https://mathweb.ucsd.edu/%7Efan/stomach/tour/stomach.html">536 different ways</a> to fit the pieces together as a square. </p>
<p>Then there’s the <a href="https://www.mathpuzzle.com/eternity.html">Eternity Puzzle</a>, released in 1999, which consists of 209 blue puzzle pieces that together form a big circle-like shape. It was very popular and sold <a href="https://en.wikipedia.org/wiki/Eternity_puzzle">500,000 copies</a> worldwide, perhaps due to the 1 million British pounds promised to whoever first solved it. </p>
<p>Less than a year later, the mathematicians Alex Selby and Oliver Riordan <a href="https://plus.maths.org/content/prize-specimens">solved the puzzle</a> and claimed the prize. The creator of the puzzle, the <a href="https://en.wikipedia.org/wiki/Christopher_Monckton,_3rd_Viscount_Monckton_of_Brenchley">controversial</a> Christopher Monckton, said at the time he had to <a href="http://news.bbc.co.uk/1/hi/entertainment/992393.stm">sell his house</a> to raise the prize money. </p>
<p>The origins of Tangram stretch back to the third century Chinese mathematician <a href="https://en.wikipedia.org/wiki/Liu_Hui">Liu Hui</a>. Among many other <a href="https://www.jstor.org/stable/2691200">accomplishments</a>, Liu Hui used rearrangements of geometrical shapes to elegantly explain mathematical facts such as the <a href="https://en.wikipedia.org/wiki/Pythagorean_theorem">Gougu Rule</a>, also known as Pythagoras’ Theorem. </p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/498587/original/file-20221201-16-l7rcjr.gif?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="Rearrangement proof of Pythagorean theorem" src="https://images.theconversation.com/files/498587/original/file-20221201-16-l7rcjr.gif?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/498587/original/file-20221201-16-l7rcjr.gif?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=345&fit=crop&dpr=1 600w, https://images.theconversation.com/files/498587/original/file-20221201-16-l7rcjr.gif?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=345&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/498587/original/file-20221201-16-l7rcjr.gif?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=345&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/498587/original/file-20221201-16-l7rcjr.gif?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=433&fit=crop&dpr=1 754w, https://images.theconversation.com/files/498587/original/file-20221201-16-l7rcjr.gif?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=433&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/498587/original/file-20221201-16-l7rcjr.gif?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=433&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Shapes can be rearranged to explain the Gougu Rule, also known as Pythagoras’ Theorem.</span>
<span class="attribution"><a class="source" href="https://commons.wikimedia.org/wiki/File:Animated_gif_version_of_SVG_of_rearrangement_proof_of_Pythagorean_theorem.gif">Animation by William B. Faulk, CC BY-SA 4.0, via Wikimedia Commons</a>, <a class="license" href="http://creativecommons.org/licenses/by/4.0/">CC BY</a></span>
</figcaption>
</figure>
<p>This rearrangement approach to geometry was later evident in the creation of 12th century <a href="https://www.wired.com/2011/01/games-for-the-hands-and-mind-chinese-puzzles-at-the-moca/">Chinese banquet tables</a> (rectangular tables designed to be arranged into patterns that might please or entertain dinner guests).</p>
<p>A different version, known as a <a href="https://www.logicagiochi.com/en/the-history/">butterfly table</a>, was popularised in the early 17th century and featured a broader variety of shapes. A surviving table set can be seen in the <a href="https://www.chinadiscovery.com/jiangsu/suzhou/lingering-garden.html">Lingering Garden (Liu Yuan)</a> which is part of a <a href="https://whc.unesco.org/en/list/813/">UNESCO World Cultural Heritage</a> site in Suzhou.</p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/484166/original/file-20220913-1734-sepc5v.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="A Tangram puzzle lies on a table." src="https://images.theconversation.com/files/484166/original/file-20220913-1734-sepc5v.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/484166/original/file-20220913-1734-sepc5v.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/484166/original/file-20220913-1734-sepc5v.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/484166/original/file-20220913-1734-sepc5v.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/484166/original/file-20220913-1734-sepc5v.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/484166/original/file-20220913-1734-sepc5v.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/484166/original/file-20220913-1734-sepc5v.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 Tangram was popularised as a puzzle game around the year 1800.</span>
<span class="attribution"><span class="source">Shutterstock</span></span>
</figcaption>
</figure>
<h2>The Tangram craze</h2>
<p>According to <a href="https://www.amazon.com/Tangram-Book-Jerry-Slocum/dp/1402704135">The Tangram Book</a> by Jerry Slocum and other authors, the Tangram was popularised as a puzzle game around the year 1800. </p>
<p>They report the inventor, an unknown Chinese person using the pen name Yang-Cho-Chu-Shih (“Dimwitted recluse”), published Ch'i chi'iao t'u (“Pictures Using Seven Clever Pieces”), a book containing hundreds of Tangram puzzle shapes. </p>
<figure class="align-right ">
<img alt="Patterns from a Tangram puzzle and solution books, China c. 1815 (British Library 15257.d.5, 15257.d.14)" src="https://images.theconversation.com/files/497605/original/file-20221128-18-d9qelw.png?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/497605/original/file-20221128-18-d9qelw.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=968&fit=crop&dpr=1 600w, https://images.theconversation.com/files/497605/original/file-20221128-18-d9qelw.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=968&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/497605/original/file-20221128-18-d9qelw.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=968&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/497605/original/file-20221128-18-d9qelw.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=1216&fit=crop&dpr=1 754w, https://images.theconversation.com/files/497605/original/file-20221128-18-d9qelw.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=1216&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/497605/original/file-20221128-18-d9qelw.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=1216&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Patterns from a Tangram puzzle and solution books, China c. 1815 (British Library 15257.d.5, 15257.d.14)</span>
<span class="attribution"><span class="source">British Library</span></span>
</figcaption>
</figure>
<p>This sparked a craze for the game in China. Other Tangram puzzle books were soon published, with some eventually making their way to Japan, the United States and England, where they were translated and extended. </p>
<p>During 1817-18, the Tangram <a href="https://collections.libraries.indiana.edu/lilly/exhibitions_legacy/collections/overview/puzzle_docs/Tangram-Worlds_First_Puzz_Craze.pdf">craze</a> spread like <a href="https://www.puzzlemuseum.com/month/picm09/2009-03-early-tangram.htm">wildfire</a> to France, Denmark and other European countries. Worldwide interest in Tangram has endured ever since. </p>
<h2>An educational tool harbouring a paradox or two</h2>
<p>The lasting popularity of Tangram might partly be due to it allowing so many shapes with so few pieces. </p>
<p>Researchers have found that Tangram can help students’ <a href="https://journaljesbs.com/index.php/JESBS/article/view/765">visual and geometric thinking</a> and even their <a href="https://www.tandfonline.com/doi/abs/10.1080/15248372.2012.725186">arithmetic skills</a>.</p>
<p>Tangram may help in the assessment of children’s learning of <a href="https://journals.sagepub.com/doi/10.1177/2332858419829723">written languages</a> and of their <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6798005/">emotional regulation skills</a>.</p>
<p>For most people, though, Tangram is just a fun and creative challenge.</p>
<p>There are also some Tangram “paradox” puzzles discussed in <a href="https://www.amazon.com/Tangram-Book-Jerry-Slocum/dp/1402704135">The Tangram Book</a> and elsewhere online, where Tangram pieces are arranged to make two seeming identical shapes (but where one appears to have a leftover piece). </p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/498373/original/file-20221201-14-oyfja5.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="The Monk puzzle" src="https://images.theconversation.com/files/498373/original/file-20221201-14-oyfja5.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/498373/original/file-20221201-14-oyfja5.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=505&fit=crop&dpr=1 600w, https://images.theconversation.com/files/498373/original/file-20221201-14-oyfja5.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=505&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/498373/original/file-20221201-14-oyfja5.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=505&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/498373/original/file-20221201-14-oyfja5.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=634&fit=crop&dpr=1 754w, https://images.theconversation.com/files/498373/original/file-20221201-14-oyfja5.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=634&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/498373/original/file-20221201-14-oyfja5.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=634&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 two monks Tangram paradox.</span>
<span class="attribution"><a class="source" href="https://commons.wikimedia.org/wiki/File:Two_monks_tangram_paradox.svg">AlphaZeta, CC0, via Wikimedia Commons</a>, <a class="license" href="http://creativecommons.org/licenses/by/4.0/">CC BY</a></span>
</figcaption>
</figure>
<p>Can you explain the “paradox” – why one has a triangular “foot” and the other does not, even though both images use all seven pieces? </p>
<p>As a bonus challenge, perhaps you can you solve the similar infinite chocolate bar “paradox” popularised on Instagram and TikTok.</p>
<p><iframe id="tc-infographic-795" class="tc-infographic" height="400px" src="https://cdn.theconversation.com/infographics/795/af484f026421a1a75b5436ba26c883774684659d/site/index.html" width="100%" style="border: none" frameborder="0"></iframe></p>
<p>Good luck and happy puzzling!</p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/learn-how-to-make-a-sonobe-unit-in-origami-and-unlock-a-world-of-mathematical-wonder-171390">Learn how to make a sonobe unit in origami – and unlock a world of mathematical wonder</a>
</strong>
</em>
</p>
<hr>
<img src="https://counter.theconversation.com/content/190529/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>The Conversation bought the author a Tangram set to play with so he could write this article.</span></em></p>Tangram is accessible yet challenging, and an excellent educational tool. It’s still used in schools today to help illustrate mathematical concepts and develop mathematical thinking skills.Thomas Britz, Senior Lecturer, UNSW SydneyLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1817652022-05-17T09:13:08Z2022-05-17T09:13:08ZMore maths testing could be good for primary schoolchildren – if done in the right way<figure><img src="https://images.theconversation.com/files/463288/original/file-20220516-26-mskf5f.jpg?ixlib=rb-1.1.0&rect=5%2C0%2C3589%2C2398&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-adorable-asia-kid-girl-doing-501754417">BlurryMe/Shutterstock</a></span></figcaption></figure><p>Recently published <a href="https://www.bbc.co.uk/news/education-60846684">UK government plans</a> proposed that by 2030, 90% of children leaving primary school in England should reach the expected standards in reading, writing and maths, compared with 65% in 2019. </p>
<p>As part of efforts to achieve this, the government is introducing more testing. In June 2022, year four pupils (aged eight to nine) must take a <a href="https://www.gov.uk/government/collections/multiplication-tables-check">multiplication tables check</a>. This means that, for mathematics, children will be tested four times during primary school. </p>
<p>The multiplication tables check joins a <a href="https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/868099/2020_Assessment_Framework_Reception_Baseline_Assessment.pdf">baseline assessment</a> in numeracy as well as literacy, communication and language, introduced in 2021 for children aged four joining reception class. Children also take standardised Sats tests in year two (aged six to seven) and year six (aged 10 to 11). </p>
<p>Although test results can be informative, more testing will not necessarily help children who struggle. In fact, test situations induce anxiety, and preparing for high-stakes tests can turn classrooms into <a href="https://www.scientificamerican.com/article/researchers-find-that-frequent-tests-can-boost-learning/">test-preparation factories</a>. By the end of primary school, many children have sat through countless maths classes feeling anxious and having no clue what is going on. This is the problem that really needs to be addressed.</p>
<h2>Struggles with maths</h2>
<p>Research suggests that, in general, there are two main culprits when it comes to failure in maths. One is <a href="https://theconversation.com/dyscalculia-maths-dyslexia-or-why-so-many-children-struggle-with-numbers-104655">developmental dyscalculia</a> – a specific learning disorder, which affects about <a href="https://bpspsychub.onlinelibrary.wiley.com/doi/abs/10.1111/bjop.12322">one in 20 children</a>. The other is <a href="https://www.cam.ac.uk/research/news/report-examines-origins-and-nature-of-maths-anxiety">maths anxiety</a>, which is an even more common problem. According to a <a href="https://www.oecd.org/pisa/keyfindings/pisa-2012-results-gender-eng.pdf">large-scale international study</a>, about one in three adolescents get very nervous when they have to do maths. </p>
<p><a href="https://www.bdadyslexia.org.uk/dyslexia/neurodiversity-and-co-occurring-differences/dyscalculia-and-maths-difficulties">Dyscalculia</a> is a developmental disability that involves persistent, severe difficulties with learning and doing mathematics, which are present from a young age. These difficulties <a href="https://inews.co.uk/news/long-reads/what-dyscalculia-blind-spot-maths-problematic-dyslexia-disability-explained-1570606">significantly interfere</a> with academic or occupational performance, and even with daily activities. For example, a person with dyscalculia may struggle to read a clock, have problems estimating the time needed for different activities, or find measuring ingredients for cooking difficult.</p>
<p><div data-react-class="Tweet" data-react-props="{"tweetId":"1499436977632030728"}"></div></p>
<p>On the other hand, <a href="https://www.youtube.com/watch?v=7snnRaC4t5c&list=RDCMUCsooa4yRKGN_zEE8iknghZA&start_radio=1">maths anxiety</a> is a feeling of tension and fear that many people experience when they are faced with maths problems or when they have to deal with numbers in their everyday life. </p>
<p>It can lead to behavioural problems in class in the case of pupils, as well as to a variety of unpleasant physiological symptoms, such as a <a href="https://www.theguardian.com/education/2019/mar/14/maths-anxiety-causing-fear-and-despair-in-children-as-young-as-six">racing heart or butterflies in the stomach</a>. <a href="https://link.springer.com/article/10.1007/s00221-017-5128-8">A study</a> even found that doing arithmetic while being evaluated by an observer led to changes in people’s posture. They adopted positions which resembled reactions to the fear of falling when standing on an elevated surface.</p>
<p>Although the same person may be affected by both maths anxiety and dyscalculia, this is not necessarily the case. <a href="https://psycnet.apa.org/doiLanding?doi=10.1037%2Fedu0000222">Research</a> suggests that about 80% of children with high maths anxiety show average or above average maths performance.</p>
<p>The effects of dyscalculia and maths anxiety are present from the <a href="https://theconversation.com/what-a-fear-of-maths-does-to-children-new-research-150108">first school grades</a>, which means that they could be identified and helped from very early on. However, while the reception year baseline check offers an early measurement point where children with difficulties could be identified, this is not how the results of this test are used. </p>
<p>First of all, these results are not shared with schools. Instead, they are recorded in the national pupil database and used to create a cohort-level progress measure for schools at the end of <a href="https://www.gov.uk/national-curriculum/key-stage-1-and-2">key stage two</a>. There are also no standards to which children’s scores are compared. In fact, individual children are not presented with the same questions, so their scores are not directly comparable.</p>
<h2>Early intervention</h2>
<p>Any effective educational policy that aims to improve maths achievement needs to tackle both dyscalculia and maths anxiety, and these interventions should start very early. Early testing, if it was used to identify children who need help, could be very beneficial. </p>
<p>Early identification of maths anxiety could be easily done with self-report questionnaires, which ask children to report on how they feel in different situations related to maths learning. These questionnaires can detect maths anxiety in children as young as <a href="https://www.frontiersin.org/articles/10.3389/fpsyg.2020.01014/full">six years of age</a>. </p>
<figure class="align-center ">
<img alt="Boy looking apprehensively at homework" src="https://images.theconversation.com/files/463294/original/file-20220516-25-qyppey.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/463294/original/file-20220516-25-qyppey.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/463294/original/file-20220516-25-qyppey.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/463294/original/file-20220516-25-qyppey.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/463294/original/file-20220516-25-qyppey.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/463294/original/file-20220516-25-qyppey.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/463294/original/file-20220516-25-qyppey.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">Maths anxiety can affect pupils of all skill levels.</span>
<span class="attribution"><a class="source" href="https://www.shutterstock.com/image-photo/tired-boring-boy-dont-want-do-331750409">Oksana Mizina/Shutterstock</a></span>
</figcaption>
</figure>
<p>Our <a href="https://www.lboro.ac.uk/media-centre/press-releases/2021/november/centre-for-early-mathematics-learning/">research group</a> is also currently developing a dyscalculia screening tool for primary school-age children. If pupils with these problems are identified early, there is a much higher chance of positive outcomes.</p>
<p>MP Matt Hancock has recently proposed the introduction of <a href="https://www.redbrick.me/universal-dyslexia-screening-with-matt-hancock/">universal dyslexia screening</a> for primary school pupils. If the aim of the government is to improve both literacy and numeracy standards, a similar approach should be taken in relation to dyscalculia as well.</p>
<p>For now, a child with dyslexia is <a href="https://digest.bps.org.uk/2018/09/18/uk-study-finds-children-with-maths-difficulties-sldm-dyscalculia-are-100-times-less-likely-to-receive-an-official-diagnosis-than-peers-with-dyslexia/">about a hundred times more likely</a> to be diagnosed and to receive educational support than a child with dyscalculia. Currently, support for dyscalculic pupils mostly comes from charities and organisations without significant government funding, such as the <a href="https://www.dyscalculianetwork.com/">Dyscalculia Network</a>.</p>
<p>While dyscalculia can lead to permanently very low performance in affected pupils, mathematics anxiety may be most debilitating for students with <a href="https://www.lboro.ac.uk/media-centre/press-releases/2022/march/maths-anxiety-cuppa-with-a-scientist/">average or high mathematics potential</a>. These students underperform in <a href="https://www.oecd-ilibrary.org/docserver/5js6b2579tnx-en.pdf?expires=1651135411&id=id&accname=guest&checksum=8AFA4AFE2FF6FA301196C8DFA0462174">important test situations</a> and lack the confidence to make the most of their skills. Of course, maths anxiety may affect children of all abilities. </p>
<p>Although the tools to tackle the sources of failure in maths do exist, there is a long way to go before these will become available for every child in every classroom. Testing done right could be a first step to prevent the development of maths difficulties, without increasing levels of stress among younger children. In time, it could also raise national standards in maths to somewhere near the government’s new target.</p><img src="https://counter.theconversation.com/content/181765/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Kinga Morsanyi 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>More testing will not necessarily help children who struggle.Kinga Morsanyi, Senior Lecturer in Mathematical Cognition, Loughborough UniversityLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1779182022-03-02T19:06:33Z2022-03-02T19:06:33ZMany students don’t know how to manage their money. Here are 6 ways to improve financial literacy education<figure><img src="https://images.theconversation.com/files/449074/original/file-20220301-21-xrvkgd.jpg?ixlib=rb-1.1.0&rect=7%2C7%2C5168%2C3437&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>How we can improve the teaching of financial literacy in high school? And why is it important?</p>
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<a href="https://images.theconversation.com/files/449061/original/file-20220301-19-18d6aj7.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="Cover of report on Financial Literacy of Young Australians" src="https://images.theconversation.com/files/449061/original/file-20220301-19-18d6aj7.png?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/449061/original/file-20220301-19-18d6aj7.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=850&fit=crop&dpr=1 600w, https://images.theconversation.com/files/449061/original/file-20220301-19-18d6aj7.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=850&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/449061/original/file-20220301-19-18d6aj7.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=850&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/449061/original/file-20220301-19-18d6aj7.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=1068&fit=crop&dpr=1 754w, https://images.theconversation.com/files/449061/original/file-20220301-19-18d6aj7.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=1068&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/449061/original/file-20220301-19-18d6aj7.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=1068&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.financialbasics.org.au/research-reports.aspx">Financial Basics Foundation</a></span>
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<p>People need a basic understanding of financial concepts to make good financial decisions. <a href="https://www.financialbasics.org.au/uploads/media/documents/FBF%20Financial%20Literacy%20of%20Young%20Australians%20March%202022.pdf">Our newly released research</a> found most students generally do not know a lot about personal finance. This includes being able to apply basic numeracy to real-life financial situations, such as making purchasing decisions that are value-for-money and understanding interest on loans and investments.</p>
<p>Our report also makes six recommendations to improve financial literacy education in schools.</p>
<p>Our findings were consistent with <a href="https://www.oecd.org/pisa/publications/PISA2018_VolIV_AUScountrynote.pdf">previous evidence</a> that 16% of Australian 15-year-olds lack even the basic level of financial literacy they need to participate in society. There is <a href="https://research.acer.edu.au/cgi/viewcontent.cgi?article=1049&context=ozpisa">evidence</a> that financial literacy in this age group is declining. </p>
<hr>
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<em>
<strong>
Read more:
<a href="https://theconversation.com/aussie-kids-financial-knowledge-is-on-the-decline-the-proposed-national-curriculum-has-downgraded-it-even-further-163110">Aussie kids' financial knowledge is on the decline. The proposed national curriculum has downgraded it even further</a>
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<p>This trend is concerning. The senior years of high school are a time when students take on more personal responsibility and financial independence. The <a href="https://link.springer.com/article/10.1007/s10964-009-9432-x">financial habits they form</a> then may last through adulthood. Low financial literacy is persistently <a href="https://sjes.springeropen.com/articles/10.1186/s41937-019-0027-5">linked to poorer financial outcomes</a>.</p>
<p>The <a href="https://www.australiancurriculum.edu.au/resources/curriculum-connections/portfolios/consumer-and-financial-literacy/">Australian Curriculum</a> acknowledges students need financial literacy to operate in our financial world. However, this curriculum only covers up to year 10. In years 11 and 12, the years that are particularly important in shaping students’ financial capability, financial literacy is taught only in lower-level maths subjects. </p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/449076/original/file-20220301-17-1uhl89f.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="Infographic comparing Australia and other countries on variation in financial literacy and use of mobile apps and phones for financial transactions." src="https://images.theconversation.com/files/449076/original/file-20220301-17-1uhl89f.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/449076/original/file-20220301-17-1uhl89f.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=149&fit=crop&dpr=1 600w, https://images.theconversation.com/files/449076/original/file-20220301-17-1uhl89f.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=149&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/449076/original/file-20220301-17-1uhl89f.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=149&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/449076/original/file-20220301-17-1uhl89f.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=187&fit=crop&dpr=1 754w, https://images.theconversation.com/files/449076/original/file-20220301-17-1uhl89f.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=187&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/449076/original/file-20220301-17-1uhl89f.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"></a>
<figcaption>
<span class="caption">How Australia compares to other countries in the PISA 2018 assessment of students’ financial literacy.</span>
<span class="attribution"><a class="source" href="https://www.acer.org/files/PISA-2018-Financial-Literacy-infographic.pdf">ACER/PISA 2018</a>, <a class="license" href="http://creativecommons.org/licenses/by-nc-nd/4.0/">CC BY-NC-ND</a></span>
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<h2>What did the study find?</h2>
<p><a href="https://www.financialbasics.org.au/uploads/media/documents/FBF%20Financial%20Literacy%20of%20Young%20Australians%20March%202022.pdf">Our research</a> explored the financial literacy of students in years 10, 11 and 12 at two urban and two rural schools. We found what students do know about financial literacy has been learned from home, maths or business studies. Students who were undertaking business studies were far more informed than other students.</p>
<p>Home life <a href="https://static1.squarespace.com/static/597b61a959cc68be42d2ee8c/t/599cc1cfe4fcb561252d6449/1503445457034/Wave-2-Report.pdf">has been found</a> to have a huge impact on a child’s financial literacy. There are often <a href="https://www.smh.com.au/money/planning-and-budgeting/financial-literacy-should-be-a-bigger-part-of-the-school-curriculum-20190705-p524gm.html">calls for parents to teach their children about personal finance</a>. However, that assumes parents are able and willing to do that. </p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/how-to-teach-your-kids-to-think-more-critically-about-money-84699">How to teach your kids to think more critically about money</a>
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<p>The students we spoke to were incredibly diverse. Household structures varied greatly, with many students not living with their parent/s. There was also evidence of parents not being able to provide financial guidance.</p>
<p>Nearly half the surveyed students preferred not to think about their financial situation. </p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/449059/original/file-20220228-25-pj8z6v.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="Chart showing proportions agreeing or disagreeing with proposition 'I don't like to think about my financial situation'." src="https://images.theconversation.com/files/449059/original/file-20220228-25-pj8z6v.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/449059/original/file-20220228-25-pj8z6v.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=330&fit=crop&dpr=1 600w, https://images.theconversation.com/files/449059/original/file-20220228-25-pj8z6v.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=330&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/449059/original/file-20220228-25-pj8z6v.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=330&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/449059/original/file-20220228-25-pj8z6v.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=415&fit=crop&dpr=1 754w, https://images.theconversation.com/files/449059/original/file-20220228-25-pj8z6v.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=415&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/449059/original/file-20220228-25-pj8z6v.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=415&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.financialbasics.org.au/uploads/media/documents/FBF%20Financial%20Literacy%20of%20Young%20Australians%20March%202022.pdf">De Zwaan & West 2022, Financial Literacy of Young Australians</a></span>
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</figure>
<p>We talked to a lot of the students about maths and found this was not the most effective curriculum area for learning about personal finance. When taught as part of the maths curriculum it tends to result in students fixating on formulas and calculations, without understanding the underlying concepts. As one student said:</p>
<blockquote>
<p>“I only really remember the formula because that’s all we got taught.”</p>
</blockquote>
<p>Many students also dislike maths. This means they are disengaged from learning at the outset. One student told us:</p>
<blockquote>
<p>“If I was in class doing that [a simple question about interest], I would just read it, keep reading it, but not actually process it or try it because I’d just give up.” </p>
</blockquote>
<p>There was also often a disconnect between the financial scenarios students were learning about and their experiences in their own lives. </p>
<p>Students who could remember financial concepts would often recall an experience or something from history when talking about it. This suggests stories may be more effective in communicating financial concepts. For example, one student said of inflation: </p>
<blockquote>
<p>“Over time, because obviously more money is being printed […] people think printing money creates more money and you’re richer, when in reality you’re just making the currency you have worthless, because there’s so much of it, that it’s not difficult to acquire it at all. I learned most of that from history.”</p>
</blockquote>
<p>Interestingly, we found evidence of young women in particular needing more context to make financial decisions. When asked financial questions, they wondered about different aspects of the question rather than quickly answering. Test questions commonly used to assess financial knowledge often offer little context. </p>
<p>About one in three students agreed they found managing their personal finances difficult and confusing. </p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/449060/original/file-20220228-19-1cw96h8.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="Chart showing proportions agreeing or disagreeing with proposition 'I find managing my finances difficult and confusing'." src="https://images.theconversation.com/files/449060/original/file-20220228-19-1cw96h8.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/449060/original/file-20220228-19-1cw96h8.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=334&fit=crop&dpr=1 600w, https://images.theconversation.com/files/449060/original/file-20220228-19-1cw96h8.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=334&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/449060/original/file-20220228-19-1cw96h8.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=334&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/449060/original/file-20220228-19-1cw96h8.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=419&fit=crop&dpr=1 754w, https://images.theconversation.com/files/449060/original/file-20220228-19-1cw96h8.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=419&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/449060/original/file-20220228-19-1cw96h8.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=419&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"></span>
<span class="attribution"><a class="source" href="https://www.financialbasics.org.au/uploads/media/documents/FBF%20Financial%20Literacy%20of%20Young%20Australians%20March%202022.pdf">De Zwaan & West 2022, Financial Literacy of Young Australians</a></span>
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<p>Finally, we noted many students were not learning financial strategies, such as moderating spending, that have lifelong benefits.</p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/would-you-pass-this-financial-literacy-quiz-many-wont-and-its-affecting-expensive-aged-care-decisions-175063">Would you pass this financial literacy quiz? Many won't – and it's affecting expensive aged care decisions</a>
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<h2>How can we improve?</h2>
<p>Given the importance of financial literacy for student well-being, our report makes these recommendations:</p>
<ol>
<li><p>financial literacy education should be elevated in high schools, ideally as a standalone program, but also by injecting principles of financial literacy into as many curriculum areas as possible – particularly in the well-being and pastoral care area</p></li>
<li><p>financial literacy education in maths needs to be improved, using a range of approaches – not limited to calculation activities</p></li>
<li><p>financial literacy education should be expanded to subjects other than maths and business, in line with shifting the focus from financial calculations to financial concepts</p></li>
<li><p>learning activities should be aligned with the students’ general level of financial experience</p></li>
<li><p>students need more exposure to effective financial strategies, in particular how to moderate (or control) spending for saving</p></li>
<li><p>a range of assessment methods should be offered to enable students to show what they have learnt. Assessment tasks should go beyond calculations and could include written pieces, visual or dramatic presentations, or oral explanations. These could be presented by groups or individuals.</p></li>
</ol><img src="https://counter.theconversation.com/content/177918/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Laura de Zwaan has received funding from Ecstra Foundation and the Financial Basics Foundation. She is an affiliate member of the Financial Planning Association and is a member of the Financial Planning Academic Forum. She has also been a member of the Wealth Academy Advisory Board. </span></em></p><p class="fine-print"><em><span>Tracey West has undertaken consultancy work for ECSTRA Foundation and Treasury on financial literacy. She has also received grant funding from ECSTRA Foundation and the Financial Basics Foundation.</span></em></p>A study of how schools deliver financial literacy education has identified better ways to help students master the basics they all need to know for real-life financial situations.Laura de Zwaan, Lecturer, Department of Accounting, Finance and Economics, Griffith UniversityTracey West, Lecturer in Behavioural Finance, Griffith UniversityLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1661062021-09-22T19:56:03Z2021-09-22T19:56:03ZChildren learn science in nature play long before they get to school classrooms and labs<p>The number of preschools pursuing learning through nature play is growing fast worldwide. However, the effectiveness and impacts of this approach is largely untested, and we recently completed the first large-scale study in the world to explicitly research nature play in early childhood education. </p>
<p>By mapping the learning of scientific concepts in nature play in a range of early childhood settings, we demonstrated how young children engage with science long before they get to school classrooms and labs.</p>
<p>Our <a href="http://www.childhoodnatureplay.com/the-mudbook-nature-play-framework/">research shows nature play</a> is a highly effective way of embedding STEM — science, technology, engineering and mathematics — in early childhood education. These areas share connections and practices, and <a href="https://www.proquest.com/docview/873954028?pq-origsite=gscholar&fromopenview=true">research</a> increasingly shows that “regardless of ability, young children are ready, willing, and able to engage in STEM activities”. </p>
<h2>What exactly is nature play?</h2>
<p>Nature play is a popular way to respond to parent and teacher concerns about children’s limited time in nature and potentially too much screen time. It’s generally seen as unstructured play in natural settings, involving child-led interactions with nature. </p>
<p>Inspiration for nature play is often attributed to Scandinavian “<a href="https://www.growingwildforestschool.org/post/the-brief-history-heritage-of-forest-schools-around-the-world">forest school</a>” models. However, its origins run far deeper. Indigenous practices, for instance, notably understandings of Country and self as entangled, rather than separate, <a href="https://sk.sagepub.com/reference/the-sage-handbook-of-outdoor-play-and-learning/i2516.xml">support many of the key features of nature play</a>. </p>
<p>Early childhood education in some countries such as Germany, Finland and Denmark has a <a href="https://www.cambridge.org/core/journals/history-of-education-quarterly/article/abs/friedrich-froebel-a-selection-from-his-writings-by-irene-m-lilley-cambridge-cambridge-university-press-1967-180-viii-pp-475/381D5F9FDE73834FA6AE6F4F05227092">long tradition of nature play</a>. For instance, “kindergarten” means “children and garden” in German, showing kindergarten’s roots in nature-based learning.</p>
<h2>What was the research project?</h2>
<p>Our <a href="http://www.childhoodnatureplay.com/">research project</a> in urban and regional early childhood settings in Queensland uncovered a vast number of key concepts explored through nature play. Many were connected with Indigenous ways of knowing about the planet. Others were more aligned with environmental science or STEM concepts. </p>
<p>With funding from the Queensland government’s <a href="https://education.qld.gov.au/about-us/reporting-data-research/research/research-funding/education-horizon">Education Horizon</a> scheme, our team worked with 20 early childhood education centres. There were ten sites in South-East Queensland, nine in Central Queensland and one in far north-western Queensland. </p>
<p>The project design involved both children and early childhood educators as researchers — 31 educators and 152 children (aged four to five) in all. The children and the educators collected data to research their own nature play experiences and practices. </p>
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<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/dont-worry-your-childs-early-learning-doesnt-stop-just-because-theyre-not-in-childcare-134668">Don’t worry, your child’s early learning doesn’t stop just because they’re not in childcare</a>
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<p>We explored children’s activities, ideas and beliefs about nature, and their relationships with/as nature. Understandings were diverse and ranged from seeing humans as separate from nature, to humans being part of nature — humans as nature. </p>
<p>The recently published <a href="https://www.researchgate.net/publication/339925347_Research_Handbook_on_Childhoodnature_Assemblages_of_Childhood_and_Nature_Research_Assemblages_of_Childhood_and_Nature_Research">Research Handbook of Childhoodnature</a> found centring childhood in nature, as childhoodnature — with humans being understood as part of nature — is a vital foundation for nature play. As one four year old said: </p>
<blockquote>
<p>“When I’m outside I learn about nature. Nature is what we’re in now. The trees are nature. The sky is nature. The creek is nature. The ants are nature. We are nature too, because we look after nature – and not break it.”</p>
</blockquote>
<p>We found educators’ lack of confidence or understanding of science concepts need not limit exploration of STEM in early childhood education. Instead, participating educators reframed any limits to their knowledge as “<a href="https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.680.1528&rep=rep1&type=pdf">an opportunity rather than an embarrassment</a>”. </p>
<p>The educators became active co-learners alongside children, rejecting the traditional perception of teachers as the source of all knowledge. To make the most of STEM opportunities in nature play, educators must understand their role as curious “<a href="https://www.naeyc.org/resources/pubs/yc/jul2016/beyond-bouncing-ball-toddlers-and-teachers-investigate-physics">scientists in action</a>”. They problem-solve, investigate and discover alongside children. </p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/let-them-play-kids-need-freedom-from-play-restrictions-to-develop-117586">Let them play! Kids need freedom from play restrictions to develop</a>
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<p>Our research identified environmental science concepts as the area of scientific learning participants most often engaged with through nature play. This means environmental science, as a discipline of teaching and learning within STEM, has an important contribution to make to children’s scientific learning. </p>
<p>Like all STEM disciplines, environmental science emerges in the early years and will build in complexity throughout a child’s life. The educators in this study embraced nine distinct nature play practices and lessons:</p>
<ol>
<li>place/Country-responsive play — such as bushwalks and other excursions on Country and learning from and with local Aboriginal and Torres Strait Islander Elders</li>
<li>non-human play — deep observation of plants, clouds, natural objects and other species</li>
<li>slow play — giving children the time and freedom for sustained, unhurried, uninterrupted play, including child-directed free play and artmaking</li>
<li>sensorial play — stimulating children’s senses and an awareness of the body through noticing, paying attention, foraging, smelling, feeling, touching and deepening connection </li>
<li>risky play — climbing trees, hanging upside down, balancing, rope swings, navigating creeks, building campfires, using tools, wrestling and exploring without adult supervision<br></li>
<li>imaginative play — also known as make-believe play, fantasy play, symbolic play, pretend play and dramatic play. Children often role-play as a way of exploring and making sense of the world </li>
<li>construction/creative play — whittling, sawing wood, building tunnels and bridges, painting, drawing, dancing, singing, drumming, nature journaling, nature collage, weaving, felting, sculpting, and clay work</li>
<li> discovery play — using a digital microscope, experimenting with natural resources, exploring shadows and light, floating and sinking, and watching insect and animal behaviour, as a way to think deeply about the world and learn how it works</li>
<li>death play — observing dead animals decomposing over time, role-playing death/dying and learning about life cycles to explore death, dying or grief.<br></li>
</ol>
<p>The project uncovered a vast number of key scientific concepts and terms explored through nature play. These were organised under the key areas of earth, ecologies, relations, materials, bodies, time and weathering. </p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/419626/original/file-20210906-17-1ulwifo.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/419626/original/file-20210906-17-1ulwifo.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/419626/original/file-20210906-17-1ulwifo.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=922&fit=crop&dpr=1 600w, https://images.theconversation.com/files/419626/original/file-20210906-17-1ulwifo.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=922&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/419626/original/file-20210906-17-1ulwifo.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=922&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/419626/original/file-20210906-17-1ulwifo.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=1158&fit=crop&dpr=1 754w, https://images.theconversation.com/files/419626/original/file-20210906-17-1ulwifo.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=1158&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/419626/original/file-20210906-17-1ulwifo.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=1158&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Common science concepts and terms identified within nature play.</span>
</figcaption>
</figure>
<p>This is not a prescriptive list, nor are these the only scientific concepts nature play enables. Rather, they are starting points to activate discussion and help children learn. When STEM concepts are inspired by the children’s interests, curiosities and questions, learning is more powerful, engaging and enduring. </p>
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Read more:
<a href="https://theconversation.com/should-i-let-my-kid-climb-trees-we-asked-five-experts-125871">Should I let my kid climb trees? We asked five experts</a>
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<img src="https://counter.theconversation.com/content/166106/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Amy Cutter-Mackenzie-Knowles receives funding from the Queensland Government Department of Education Horizon funding scheme.</span></em></p><p class="fine-print"><em><span>Alexandra Lasczik receives funding from the Queensland Government Department of Education Horizon funding scheme.</span></em></p><p class="fine-print"><em><span>Karen Malone receives funding from Queensland Government under their HORIZON funding scheme. </span></em></p><p class="fine-print"><em><span>Linda Knight receives funding from Queensland Government Department of Education Horizon Scheme</span></em></p><p class="fine-print"><em><span>Maia Osborn receives funding from receives funding from the Queensland Government Department of Education Horizon funding scheme.</span></em></p><p class="fine-print"><em><span>Mahi Paquette 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>New research demonstrates the many aspects of nature play that make it a great way for young children to gain STEM knowledge.Amy Cutter-Mackenzie-Knowles, Executive Dean, Faculty of Education, Southern Cross UniversityAlexandra Lasczik, Associate Professor, Arts & Education, Southern Cross UniversityKaren Malone, Professor, Environmental Sustainability and Childhood Studies, Swinburne University of TechnologyLinda Knight, Associate Professor, Early Childhood: Creative Practice and Digital Media, RMIT UniversityMahi Paquette, Research Associate, Faculty of Education, Southern Cross UniversityMaia Osborn, Research Fellow, Faculty of Education, Southern Cross UniversityLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1574072021-06-07T20:06:37Z2021-06-07T20:06:37ZWhy too many recorded lecture videos may be bad for maths students’ learning<figure><img src="https://images.theconversation.com/files/397499/original/file-20210428-23-1e1lnuo.jpg?ixlib=rb-1.1.0&rect=0%2C0%2C6000%2C3988&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/asian-woman-teacher-teaching-online-lesson-1783859852">Shutterstock</a></span></figcaption></figure><p>Screen-based devices have <a href="https://www.nielsen.com/au/en/insights/article/2018/screen-time-skyrocketing/">increasingly</a> become part of our human experience – <a href="https://www.washingtonpost.com/technology/2020/03/24/screen-time-iphone-coronavirus-quarantine-covid/">even more so</a> since the pandemic began. This trend includes watching more and more videos. For example, before COVID-19, the average American watched <a href="http://www.nielsen.com/us/en/insights/reports/2018/q1-2018-total-audience-report.html">about six hours of videos a day</a> on devices ranging from televisions to desktop computers and mobile phones. By <a href="https://www.wsj.com/articles/how-covid-19-has-transformed-the-amount-of-time-we-spend-online-01596818846">one estimate</a>, this figure has “surged” more than 40% during the pandemic.</p>
<p>In higher education, the online use of recorded lecture videos has also increased greatly. How is this affecting learning? For undergraduate mathematics, a <a href="https://link.springer.com/article/10.1007/s13394-021-00369-8">recently published review</a> confirmed the findings of a <a href="https://www.tandfonline.com/doi/full/10.1080/0020739X.2011.646325?src=recsys">2012 study</a> that, overall, the more often students watched such videos the poorer their performance in their course. </p>
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Read more:
<a href="https://theconversation.com/covid-killed-the-on-campus-lecture-but-will-unis-raise-it-from-the-dead-152971">COVID killed the on-campus lecture, but will unis raise it from the dead?</a>
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<p>Recent research has identified a possible reason for this. It might help explain why the findings of these two reviews differ from those of studies of learning from videos in other disciplines. </p>
<h2>How might videos depress learning?</h2>
<p>Of course, correlation is not causation. It’s possible, for example, that weaker mathematics students tend to rely on videos more than stronger students. </p>
<p>However, an equally plausible explanation is that regular use of these videos is somehow depressing students’ learning. A two-part study was designed to investigate this possibility. </p>
<p>The <a href="https://www.tandfonline.com/doi/abs/10.1080/0020739X.2018.1458339">first study</a> involved two groups of students studying engineering mathematics courses in Australia and the UK. At the beginning and end of each course, students completed a questionnaire to assess how they approached their studying. </p>
<p>In both settings, regular video users were found to become more surface learners over the course of the semester. Those accessing few or no videos were unchanged in their study approaches. This was despite regular video users, as compared to low users, being older in Australia and initially better at mathematics in the UK.</p>
<p>This gave rise to a <a href="https://doi.org/10.1080/0020739X.2021.1930221">second study</a> that used interviews with Australian participants to explore how they were using the videos to advance their understanding of mathematics. First, to provide some insight into underlying processes and thus the design of the second study, a review of the cognitive research on the use of television was conducted. <a href="https://books.google.com.au/books?hl=en&lr=&id=Sicxx9FBZWMC&oi=fnd&pg=PR11&dq=Kubey,+Csikszentmihalyi&ots=EXvADrPNHw&sig=pimBbUjZ9JTdx7GMnjVmXWSsOMs#v=onepage&q=Kubey%2C%20Csikszentmihalyi&f=false">Kubey and Csikszentmihalyi</a> sum up this research:</p>
<blockquote>
<p>“[…] in every sample we have studied, with different demographic groups and with subjects ranging in age from 10 to 82, and with groups from more than one country, it has been found that people consistently report their experiences with television as being passive, relaxing, and involving relatively little concentration.” </p>
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<figure class="align-center ">
<img alt="couple's feet in socks in front of a TC screen" src="https://images.theconversation.com/files/397500/original/file-20210428-13-yiqrvv.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/397500/original/file-20210428-13-yiqrvv.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/397500/original/file-20210428-13-yiqrvv.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/397500/original/file-20210428-13-yiqrvv.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/397500/original/file-20210428-13-yiqrvv.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/397500/original/file-20210428-13-yiqrvv.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/397500/original/file-20210428-13-yiqrvv.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">For many people, the TV screen is the cue for a passive and relaxing experience, involving relatively little concentration.</span>
<span class="attribution"><a class="source" href="https://www.shutterstock.com/image-photo/couple-socks-woolen-stockings-watching-movies-1275793150">Shutterstock</a></span>
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Read more:
<a href="https://theconversation.com/who-learns-in-maths-classes-depends-on-how-maths-is-taught-21013">Who learns in maths classes depends on how maths is taught</a>
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<p>With this understanding, cognitive processes associated with the use of lecture videos were considered as a dual-process system, meaning people tend to think using two channels:</p>
<ol>
<li><p>“type 1” thinking: fast and intuitive with little to no working memory used.</p></li>
<li><p>“type 2” thinking: slow and analytical with working memory used. </p></li>
</ol>
<p>Working memory has been <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4207727/">defined as</a> “the small amount of information that can be held in mind and used in the execution of cognitive tasks”. </p>
<p>The mathematics videos were viewed outside of typical lecture or classroom settings. Students actively controlled their use. Therefore, the second study interview questions focused on the critical point at which students judge their own learning to determine, for example, whether they move on to new learning or not. </p>
<p>All Australian participants were interviewed at the end of the course. The analysis of their responses showed regular users were more prone to type 1 thinking when judging their learning. They relied mostly on “feelings of rightness” rather than, for example, checking that correct procedures were followed. In mathematics, the former may lead to wrong (“<a href="https://link.springer.com/article/10.1023/A:1002998529016">pseudo-analytical</a>”) thinking, while the latter typically results in the correct solution. </p>
<h2>Findings differ in other disciplines. Why?</h2>
<p>At first glance, this discovery contrasts sharply with findings from a <a href="https://journals.sagepub.com/doi/10.3102/0034654321990713">recent systematic review</a> that <a href="https://theconversation.com/videos-wont-kill-the-uni-lecture-but-they-will-improve-student-learning-and-their-marks-142282">concluded</a> the use of videos was “consistently good for learning”. However, a closer look at the review reveals almost all the included studies (96%) related to instruction in applied undergraduate disciplines, such as health sciences, which represented over 80% of the included studies. Studies on the use of video in mathematics or other abstract disciplines that demand high-level conceptual thinking were not part of the review. </p>
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<em>
<strong>
Read more:
<a href="https://theconversation.com/videos-wont-kill-the-uni-lecture-but-they-will-improve-student-learning-and-their-marks-142282">Videos won't kill the uni lecture, but they will improve student learning and their marks</a>
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<p>This might suggest the use of video will help learning if the level of thinking required is relatively low, such as learning medical procedures, but not necessarily where it is high, such as gaining conceptual understanding in mathematics.</p>
<p>More research is certainly needed. We still know very little about thought processes when viewing lecture videos. </p>
<p>One question arising from research in undergraduate mathematics is: have we somehow become conditioned by almost a century of television use so that when presented with a simple video recording of a lecture, the medium subconsciously signals its viewers to tone down any mental effort? This is enough to achieve better learning outcomes where low-level cognitive processing is sufficient, but could be detrimental where high-level processing is required.</p>
<p>Put another way, and more broadly, under what circumstances and with which people can screens act as cognitive cues signalling us to relax mentally, in much the same way <a href="https://pubmed.ncbi.nlm.nih.gov/27820842/">viewing food can make us salivate</a>?</p><img src="https://counter.theconversation.com/content/157407/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Sven Trenholm 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>Why might maths students’ performance suffer from relying on videos? A new study suggests we might be conditioned to watch video in a way that hinders the sort of thinking needed in maths.Sven Trenholm, Adjunct Lecturer in Mathematics Education, University of South AustraliaLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1298162020-06-25T16:08:16Z2020-06-25T16:08:16ZMaths teachers in South Africa: case study shows what’s missing<figure><img src="https://images.theconversation.com/files/309937/original/file-20200114-151862-e2xfe2.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">A vicious cycle: the academic gaps in schools start at the teacher training institutions. </span> <span class="attribution"><span class="source">Shutterstock</span></span></figcaption></figure><p>South African students are bad at maths compared to other countries. This is clear from results of South African learners in the <a href="https://timssandpirls.bc.edu/timss-landing.html">International Mathematics and Science Study</a>. The <a href="http://www.timss-sa.org.za/download/TIMSS-2015-Grade-9-National-Report.pdf">results</a> show that South Africa’s performance is far from competitive in relation to other countries. </p>
<p>To try and understand the reasons for this poor performance, I did a <a href="https://journalhosting.ucalgary.ca/index.php/ajer/article/view/67915">qualitative case study</a> focusing on a year-long post graduate course taken by aspiring teachers. I focused particularly on a Post Graduate Certificate in Education with a maths focus offered by one of the country’s university of technologies. </p>
<p>I looked at three key themes – the curriculum and its delivery, partnerships during delivery and policy influencing delivery. My research findings show that the success of the Post Graduate Certificate in Education in preparing maths teachers is not without concern and its delivery, in the case study context, needs rethinking.</p>
<p>My findings underscore earlier <a href="https://www.section27.org.za/wp-content/uploads/2013/10/Spaull-2013-CDE-report-South-Africas-Education-Crisis.pdf">research</a> that has suggested that a shortage of competent and confident qualified mathematics teachers is a key contributing factor to the low maths performance of South African school children.</p>
<h2>Constraints</h2>
<p>The one-year Post Graduate Certificate in Education offered at South African universities is a key qualification for aspiring teachers. This is taken after completing a diploma or degree in other fields such as engineering, business and hospitality. It offers an opportunity to university graduates to become a professionally qualified teacher in one-year instead of pursuing a career in industry.</p>
<p>My research highlights the constraints identified by students and lecturers of the post graduate certificate programme, in particular as it relates to the teaching of maths. </p>
<p>The first constraint I identified involved inadequate support structures as well as information, communication and technology infrastructure to meaningfully support the ever-increasing numbers of students taking up the course. The numbers have <a href="https://journalhosting.ucalgary.ca/index.php/ajer/article/view/67915">grown exponentially</a> – from 10 in 1994 to 100 in 2014 and then 207 in 2015. In short, the university has been expected to do more with less. </p>
<p>The second constraint I identified was a potential over reliance on using Bachelors in Education content designed to be delivered over four years. This was evident from the statements from lecturers clarifying how they identify and select content to present during lectures.</p>
<p>This is a constraint as the four year Bachelors in Education content is not always suitable for the Post Graduate Certificate in Education context. This indicates a need to develop context specific content to make the best of the one-year post graduate certificate. </p>
<p>The third constraint was a limited partnership to develop professional learning communities. These should ideally involve lecturers and students, university representatives evaluating students during compulsory classroom teaching periods and the teachers in schools hosting students.</p>
<p>The main reason for this constraint appeared to be that most lecturers were part-time as the course was offered in the afternoon or evening. This meant that lecturers and students had limited time to engage. This affected the outcomes and the quality of the course. </p>
<p>Another outcome from the lack of engagement between the part-time lecturers was that lecturers duplicated content offered in other programme modules. Students and graduates noted this as one of their main concerns. Unnecessary duplication is a major problem because the post graduate certificate programme has a limited time-frame of just one year. </p>
<p>The fourth and final constraint was a lack of oversight over university policy stipulations linked to the delivery and assessment of the post graduate qualification. </p>
<p>For example, university policy <a href="https://journalhosting.ucalgary.ca/index.php/ajer/article/view/67915">stipulates</a> that an assessment plan, programme and calendar must be provided to students. Such a document wasn’t provided to students as noted during interviews. Policy also stipulates that students must re-do practical teaching if they miss more than five days during the study period. One student noted that he was absent for a whole week during this period and no one noticed. He was awarded a pass for practical teaching.</p>
<p>My research found that lecturers didn’t follow all the university’s policies. This suggested that they weren’t being monitored by the relevant authorities. This lack of oversight by the university is clearly a major problem. </p>
<h2>Next steps</h2>
<p>I conclude from my findings that, to become confident and competent maths teachers, graduates who have passed the Post Graduate Certificate in Education need further development and support. If this isn’t provided, South Africa is unlikely to see an improvement in the performance of its school children.</p><img src="https://counter.theconversation.com/content/129816/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Jacques Verster is affiliated with the Parliament of the Republic of South Africa in the capacity as a Parliamentray Official</span></em></p>A shortage of competent and qualified maths teachers is a key contributing factor to the low maths performance of South African school children.Jacques Verster, CPUT Doctorate graduate, Cape Peninsula University of TechnologyLicensed 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/1208612019-07-31T12:52:56Z2019-07-31T12:52:56ZCoding in South African schools: what needs to happen to make it work<figure><img src="https://images.theconversation.com/files/285538/original/file-20190724-110187-17b8a56.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">In the near future, the ability to code will be as essential as knowing how to read, write and count.</span> <span class="attribution"><span class="source">Shutterstock</span></span></figcaption></figure><p><em>South Africa is training a group of teachers to learn how to code and how to teach coding. The subject will be piloted at 1000 schools across five provinces, starting in the 2020 academic year. The announcement has resulted in debates around the country’s ability to deliver on such a commitment, particularly when considering the low literacy and numeracy skills of learners. The Conversation’s Nontobeko Mtshali spoke to Professor Ulrike Rivett to find out more about this.</em></p>
<p><strong>What is coding? Are there African countries teaching it nationally at school level?</strong> </p>
<p>The Department of Basic Education <a href="https://www.education.gov.za/CodingCurriculum010419.aspx">describes</a> coding as the writing of instructions for computation using a programming language to achieve a specific goal or to solve a problem. In simple terms, coding refers to using a language that a computer understands to develop computer programmes, mobile applications, websites etc. </p>
<p>Coding is therefore similar to introducing a new language in the school curriculum. The misconception has often been created that coding requires a talent in maths or physics, but that’s not necessarily the case. Coding, similar to any language we use, has certain structures and rules – like grammar – and these rules have to be learnt and practised. While the discussion around coding has been very closely linked to that of the maths curriculum, there is no reason to believe that students with subjects such as maths literacy cannot learn how to code. The challenges of introducing coding as a subject are manifold, but maths education is not one of them. </p>
<p>There are a number of schools that have already introduced coding. Most are well-equipped schools or private institutions. This is also true for most African countries. </p>
<p>Countries like the UK have well-established national policies. In the UK this was done in 2013. Others that followed included Austria, Bulgaria, the Czech Republic, Denmark, Estonia, France, Hungary, Ireland, Lithuania, Malta, Spain, Poland, Portugal and Slovakia. Some of these countries have included coding in their national curricula. </p>
<p><strong>What are the challenges in the way of making this a regular subject in schools?</strong> </p>
<p>It’s great that South Africa has decided to roll out coding nationally. But the complexity is that the foundations are not in place for effective implementation. Dr Mmaki Jantjies, a senior lecturer at the University of the Western Cape’s Department of Information Systems, <a href="https://theconversation.com/five-things-south-africa-must-get-right-for-tech-in-schools-to-work-118612">cites</a> five core elements that need to be in place for effective rollout. These include:</p>
<ul>
<li><p>infrastructure, </p></li>
<li><p>teacher training and support, </p></li>
<li><p>localised learning content, </p></li>
<li><p>technical support, and </p></li>
<li><p>safety and security. </p></li>
</ul>
<p>To provide a good foundation in digital skills, computers have to be available on the school premises together with the relevant IT infrastructure and internet connectivity. This translates effectively into having an IT department at the school that can manage the equipment, keep it up and running and be able to support teachers and learners when problems arise. This requirement translates directly into a cost factor that is not a once-off investment, but rather a regular addition to the annual budget in the form of a recurrent cost item.</p>
<p>The second challenge involves teachers and a curriculum. Teacher training is expensive and currently teachers don’t learn how to code. To develop an integrated and sustainable curriculum, it will be essential to reflect on the current requirements for teachers, and to understand how they are trained.</p>
<p>Another challenge of making coding and robotics a regular subject at school is time. In an already crowded timetable, which subject do we remove or allocate less time to? Do learners have to spend more time at school? In the UK, a solution was found by integrating digital skills into other subjects.</p>
<p>In South Africa coding and robotics will be introduced through the existing technology subject taught until Grade 9, or through a new subject called “digital skills”.</p>
<p>The curriculum is expected to provide learners with the necessary knowledge and skills to become “inventors of new technologies to make a valuable contribution towards the global community”. </p>
<p><strong>What are the risks if school children don’t attain this skill at the basic education level?</strong> </p>
<p>The need for coding is becoming ubiquitous. In the same way that employees are currently expected to have the ability to read, write and count, in the near future there will be an expectation to have the literacy of coding. This will allow learners to harness the power of computers.</p>
<p>Right now, the most sought after careers are in the IT space. From the retail sector to financial institutions, our world is becoming digital. Online shopping, online banking, online TV watching – the risk of not being able to attain the skill of coding will be a risk of not attaining a job.</p>
<p><strong>What needs to be done going forward?</strong> </p>
<p>Throwing equipment such as tablets or laptops at schools without addressing the training of teachers hasn’t resulted in any sustainable solutions on the continent.</p>
<p>An opportunity that should be more widely investigated is the engagement of universities in the initiative. Many of the computer labs of higher education institutions are empty for 26 weeks of the year. We took the opportunity to link up with CodeSpace during the June vacation to host a <a href="https://www.codespace.co.za/blog/high-school-robotics-robocampct">coding camp for high school learners on UCT campus</a> - the labs were filled with excitement in an otherwise deadly quiet time and it gave us insight on the potential of using our resources to fill a real need. </p>
<p>With the experience of hindsight, South Africans know that curriculum changes have not always been as successful as had been hoped and that a radical change - such as making coding and robotics a school subject - might be too much for some schools. Will the country end up with another subject that creates “have and have-nots”? </p>
<p>This is an opportunity to engage, to grapple with a difficult challenge and for higher education institutions to draw alongside the Department of Education, our schools, teachers and learners. This might be the one time where the lofty heights of academia can provide some insight and practical space to introduce a subject that will provide our children with a skill for future success.</p><img src="https://counter.theconversation.com/content/120861/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Ulrike Rivett receives funding from the National Research Foundation which is not connected to this article</span></em></p>South Africa’s introducing coding as a school subject but until teacher education, IT infrastructure and internet connectivity issues, among others are addressed, the country has a long way to go.Ulrike Rivett, Professor, Information Communication Technologies, University of Cape TownLicensed 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">
<figcaption>
<span class="caption">Make maths about real life to capture kids imaginations.</span>
<span class="attribution"><span class="source">Pexels</span></span>
</figcaption>
</figure>
<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">
<figcaption>
<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/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/702892016-12-13T09:47:31Z2016-12-13T09:47:31ZPressured South African schools had no choice but to relax maths pass mark<figure><img src="https://images.theconversation.com/files/149835/original/image-20161213-1615-vu7id5.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">By the time pupils who struggle with Maths reach Grade 9, there are huge bottlenecks in the system.</span> <span class="attribution"><span class="source">REUTERS/Ryan Gray</span></span></figcaption></figure><p>Starting now, South Africa’s pupils will be able to obtain as <a href="http://www.education.gov.za/Portals/0/Documents/Publications/Circular%20A3%20of%202016.pdf?ver=2016-12-07-154005-723">little as 20%</a> in mathematics in Grades 7, 8 and 9 and still progress to the next year of learning. This has been touted by many as evidence of an alleged inexorable decline in educational standards.</p>
<p>The country is already known for its <a href="http://www.telegraph.co.uk/education/2016/11/29/revealed-world-pupil-rankings-science-maths-timss-results/">poor performance</a> in international standardised assessments in mathematics. This latest move may be misconstrued as condoning such poor achievement.</p>
<p>But the truth is a little more complex.</p>
<p>For Grades 7 and 8 – when pupils should be between 14 and 15 years of age – this strategy of “pushing through” to avoid repeated student retention is not new. It has been part of standard policy. This means that by the time pupils reach Grade 9, there’s a bottleneck in the system. It was inevitable that this pressure would need to be relieved.</p>
<p>To understand why, one must consider the confluence of a number of factors, including: the over-inflated importance of mathematics; a curriculum packed too full to allow for any slip-ups or slower learning rates, and the country’s struggling maths teachers. <a href="http://mg.co.za/article/2016-12-09-00-home-is-where-the-learning-is">Maths performance correlates directly with poverty factors</a>, meaning these challenges affect more than 75% of South Africa’s schools. </p>
<h2>Inflated value of maths</h2>
<p>In the past 20 years there’s been a major shift internationally towards thinking of education in purely economic terms (as opposed to critical citizenry, creativity or self-actualization). This reduction of education to purely economic ends, coupled with the conflation between mathematical prowess and problem-solving skills for the “knowledge economy”, has resulted in mathematics being isolated as “essential knowledge”. Its proponents insist that maths is required for an education of value.</p>
<p>To fully appreciate this shift in thinking, South Africans need to suspend their collective amnesia: passing mathematics was not a requirement to move into Grade 10 a generation ago. And yet adults from this era are often economically productive, creative and academically accomplished. Many would publicly acknowledge their own struggles with numbers.</p>
<p>The vast majority of jobs of many flavours and incomes do not require the type of maths taught even in Grade 9. This is forgotten when mathematics is positioned as supremely important for the job market, or for students’ personal development.</p>
<h2>Moving targets</h2>
<p>Against the backdrop of this increased emphasis on mathematics, it’s useful to consider key features of the <a href="http://www.education.gov.za/Portals/0/Documents/Policies/PolicyProgPromReqNCS.pdf?ver=2015-02-03-154857-397">National Policy Pertaining to the Promotion Requirements of the National Curriculum Statement</a>.</p>
<p>An excessive emphasis on mathematics permeates this policy. Passing mathematics with “moderate” performance (that is, 40% or more) is now a criterion for passing in every grade. It’s a criterion many students <a href="http://www.education.gov.za/Portals/0/Documents/Reports/REPORT%20ON%20THE%20ANA%20OF%202014.pdf?ver=2014-12-04-104938-000">do not meet</a>.</p>
<p>The second issue is the “maximum four years in phase” policy. According to this, a pupil may not repeat more than one year in each three year phase of compulsory schooling. If a pupil has already repeated a year in a phase, they are “progressed” through into the next grade – whether they meet the promotion/pass criteria or not.</p>
<p>This “maximum four years in phase” policy bites at the end of Grade 9. Pushing pupils through without passing maths was a viable option in lower grades, as there was a “next grade” to progress to. But leaving Grade 9 without passing means leaving school without the <a href="http://www.saqa.org.za/docs/pol/2003/getc.pdf">General Education and Training</a> certificate required for admission to a technical college.</p>
<p>In the past, officials and schools have often suspended the “max four years” criterion to give pupils another opportunity to try and attain a recognisable school leaving qualification, requiring a maths score of higher than 40%. For pupils who have been failing maths for years, this is almost <a href="http://www.iol.co.za/dailynews/news/dismal-10-average-for-grade-9-maths-1791182">impossible</a>.</p>
<p>The pressure to move learners through the system is immense. Each year, principals and senior teachers suffer validation meetings, an event where schools justify their decisions to the provincial education department about whether students who failed should repeat or progress.</p>
<p>As a former mathematics Head of Department who has attended such meetings, I came to appreciate the lottery involved about who was “progressed” and who was not, as officials clandestinely tweak results until the number of students moved through was politically acceptable. Often those with 20% or more would have their marks “adjusted” to 30% for what is referred to as a “condoned pass”. As teachers, we are told to “find marks” in assessments to justify passing or condoning borderline students.</p>
<p>But sometimes there are just not enough marks to find.</p>
<h2>Huge learning backlogs</h2>
<p>The second policy that adds to the conundrum is the Curriculum and Assessment Policy Statement (CAPS). This demands strict adherence to pacing and content. Mathematics in CAPS moves at breakneck speed: ten jam-packed weeks of content per term, even though there are often only eight weeks of actual lessons.</p>
<p>Curriculum advisers regularly correct teachers who deviate from the stated content and pacing of curriculum documents. That means a teacher who has the confidence and ability to address learning backlogs by professionally interpreting the curriculum to meet a pupil’s needs is often criticised for doing so. Teachers without this confidence or skill will not even attempt the task.</p>
<p>Such rigidity is in stark contradiction to the National Policy Pertaining to the Promotion Requirements, which is peppered with phrases regarding tailoring learning to address backlogs and learning barriers.</p>
<p>Primary schools pragmatically push over-age (16 years old) Grade 7 pupils through to Grade 8 in senior schools. Senior schools then receive under-prepared pupils who are too old to refer to schools of skills or special needs schools – the maximum referral age is 14. There is nothing to be done but to try and teach struggling learners, knowing they will be pushed up into Grade 9 where they will get stuck or <a href="https://africacheck.org/spot_check/south-africas-matric-pass-rate-obscures-dropout-rate/">drop out</a>. After Grade 9, the pupil enrolment dwindles rapidly as students lose the protection of being pushed through by the conveyor belt.</p>
<p>Together, these policies effectively put pupils on a one way track into Grade 9 irrespective of their performance in mathematics at lower grades. Then it has kept them in Grade 9 by insisting they meet the pass criteria… until now.</p>
<h2>Struggling mathematics teachers</h2>
<p>Two urgent issues, most concentrated in schools that serve the country’s poorest learners, further exacerbate what is already an obviously disastrous situation.</p>
<p>Firstly, the mathematics abilities of primary school teachers is a problem experienced in many countries, including the <a href="http://washingtonmonthly.com/2016/06/15/elementary-school-teachers-struggle-with-common-core-math-standards/">US</a> and the <a href="https://www.theguardian.com/education/2010/feb/14/primary-teachers-fail-maths-tests">UK</a>, but particularly in <a href="http://www.cde.org.za/wp-content/uploads/2013/10/MATHEMATICS%20OUTCOMES%20IN%20SOUTH%20AFRICAN%20SCHOOLS.pdf">South Africa</a>. Mathematics specialists are appointed in high schools. Primary school teachers are trained as generalists. Yet it is in primary school where the learning backlog begins.</p>
<p>Secondly, teachers’ working conditions in poorer schools are abysmal. Those teachers who can leave often do, and mathematics teachers in particular often possess transferable skills. They <a href="http://www.education.gov.za/Portals/0/Documents/Reports/Teachers%20for%20the%20future%2016%20NOV%202005.pdf?ver=2008-03-05-111025-000">relocate</a> to other schools or other industries for better working conditions.</p>
<p>Primary schools thus struggle to provide the crucial foundations for maths, and secondary schools struggle to retain the specialists who might be able to address the problem later.</p>
<h2>Relieving the self-applied pressure</h2>
<p>It’s no wonder then that <a href="http://www.education.gov.za/Portals/0/Documents/Publications/Education%20Statistic%202013.pdf?ver=2015-03-30-144732-767">Grade 9 is the largest cohort in South Africa’s senior schools</a>. Nor should it come as a surprise that large percentages of these classes are extremely weak at mathematics. Many pupils have barriers to learning that have been unaddressed for so long that there is little to be done at this late stage.</p>
<p>The Department of Basic Education has snookered itself by applying tight Grade 9 promotion criteria based on mathematics, without providing the means to meet them. This latest move is simply a welcome, realistic – and long overdue – acknowledgement that the ability to factorise quadratic functions is not a prerequisite for an educated child.</p><img src="https://counter.theconversation.com/content/70289/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Sara Muller works at the University of Cape Town as a researcher and PhD candidate.
She receives funding from the Canon Collins Educational and Legal Assistance Trust in support of her PhD research, and is an active member of the Education Fishtank group, an open forum for engaging in education discussions in Cape Town.
All opinions expressed in her articles are her own.</span></em></p>The truth behind South Africa’s decision to allow 20% as a maths pass mark in some grades is a little more complex than many have suggested.Sara Black, Researcher: Teacher Development and Sociology of Education, University of Cape TownLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/588892016-06-01T10:10:44Z2016-06-01T10:10:44ZMaths anxiety is creating a shortage of young scientists … here’s a solution<figure><img src="https://images.theconversation.com/files/123758/original/image-20160524-11017-1c2ucf.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">If we don’t change the way we teach science and maths, we might come to regret it. </span> <span class="attribution"><span class="source">wavebreakmedia/www.shutterstock.com</span></span></figcaption></figure><p>Does the thought of doing long division, or solving a bit of algebra give you the shivers? You’re likely to have maths anxiety. In <a href="http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0153857">our recent research</a>, my colleagues and I found that in 80% of countries, girls have more negative feelings towards maths than boys. </p>
<p>But this higher level of maths anxiety in girls is not justified by their actual level of performance and may put them off continuing a career in maths-related subjects, such as physics and computer science.</p>
<p>Our research showed that there are considerable international differences in the degree to which boys and girls suffer from maths anxiety. The figure below shows maths anxiety scores in ten countries from the 2012 Programme for International Student Assessment (PISA), which tests performance in maths, reading and science in 15-year-olds around the world. Higher scores on the graph indicate higher levels of mathematics anxiety. Girls in the countries on the left side of the figure have a higher level of mathematics anxiety than boys. </p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/124587/original/image-20160531-1933-la3vlk.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/124587/original/image-20160531-1933-la3vlk.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/124587/original/image-20160531-1933-la3vlk.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=539&fit=crop&dpr=1 600w, https://images.theconversation.com/files/124587/original/image-20160531-1933-la3vlk.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=539&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/124587/original/image-20160531-1933-la3vlk.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=539&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/124587/original/image-20160531-1933-la3vlk.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=677&fit=crop&dpr=1 754w, https://images.theconversation.com/files/124587/original/image-20160531-1933-la3vlk.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=677&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/124587/original/image-20160531-1933-la3vlk.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=677&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Examples of countries with a large gender gap (left) and a countries with no statistically significant gender gap (right) in mathematics anxiety. Red bars indicate data of girls and blue of boys in the OECD’s 2012 PISA.</span>
<span class="attribution"><span class="source">Gijsbert Stoet</span></span>
</figcaption>
</figure>
<p>In the UK and other gender-equal developed countries, the gender difference is relative high. Paradoxically, we cannot really learn much from countries such as Albania, Bulgaria, Indonesia, Romania or Turkey, where this gender difference is nonexistent or small. This is because these countries have lower overall maths scores, they have higher overall maths anxiety, and they typically score lower on <a href="http://reports.weforum.org/global-gender-gap-report-2015/rankings/">gender equality</a> and <a href="http://hdr.undp.org/en">human development</a>. </p>
<p>Fortunately, we know at the very least that general improvements in maths performance will be associated with lower levels of maths anxiety. Gender differences in maths anxiety are hard to eradicate, yet a good start can be made by creating a well-planned and well-supported educational system, including highly qualified, well-paid and respected teachers, and well-maintained school facilities. With this investment, maths anxiety can possibly be reduced to levels where it might no longer form a psychological barrier for further study of science, mathematics, engineering or technology (STEM) subjects.</p>
<h2>Skills shortage</h2>
<p>But there is still an overall general shortage of students in these subjects. Not only is there a labour shortage among computer programmers and engineers, there is also a severe shortage among teachers in those subjects. This problem is so severe that in 2015 the <a href="http://www.theguardian.com/education/2015/mar/11/15000-teaching-bursaries-maths-and-physics-graduates-students-david-cameron">UK government created financial incentives</a> for students to become teachers in maths and physics. The situation in other Western countries is similar: <a href="https://phystec.physics.cornell.edu/content/crisis-physics-education">52% of New York schools</a> cannot offer physics due to the teacher shortage, while <a href="http://www.nw.de/lokal/kreis_herford/herford/herford/20717073_Wachstumsformel-fuer-Physiklehrer-Nachwuchs-gesucht.html">Germany</a> reports general difficulties with recruiting physics teachers.</p>
<p>I believe that one of the main reasons for the low enrolment in non-organic STEM subjects – the study of non-living matter, such as physics or computing – is that children are allowed to drop these subjects too early, well before they have experienced the subjects sufficiently to make informed and rational decisions about their future career track. </p>
<p>Other researchers have also raised this issue, arguing that 14-year olds are <a href="http://www.telegraph.co.uk/education/educationnews/10658289/Schoolchildren-not-ready-to-choose-their-GCSEs-at-14.html">simply not mature</a> enough to make life-determining choices about which GCSE subjects to take. A <a href="http://www.heraldscotland.com/news/13768124.Half_of_girls_aged_12_think_science_and_maths_are_too_tough/">recent Scottish survey</a> among 12-year old Scottish girls confirmed that they are often misguided about what STEM subjects can mean.</p>
<h2>Change the curriculum</h2>
<p>Instead of giving children the option to drop difficult but important subjects such as maths and physics, in England and Wales we should make the GCSE subjects physics, engineering, and computing compulsory until age 16 and make mathematics compulsory at A-Level – the exams most students take when the leave school or college at 18-years-old. Currently, maths is compulsory in the UK until age 16 while physics is optional.</p>
<p>The good thing is that the government has already taken some steps in the right direction. For example, <a href="http://www.bbc.co.uk/news/education-23925033">since 2013</a>, students in England who did not perform well in maths in the GSCEs need to study it until age 18 so that they will end up with at least a reasonable GCSE-level maths skill. Nonetheless, internationally, the UK has relatively few 16-18 year olds choosing maths at A-Level, and <a href="http://www.furthermaths.org.uk/docs/Towards_universal_participation_in_post_16_maths_v_FINAL.pdf">there is a lot we can learn from other countries</a>.</p>
<p>In China, physics is compulsory until age 16 and maths all the way through secondary education. The Chinese do an impressive job in training their children and they lead the <a href="http://www.telegraph.co.uk/education/10490225/OECD-education-report-Shanghais-formula-is-world-beating.html">international education league tables</a> (even though not all of China is included).</p>
<p>The Chinese educational system surely has its own challenges, such as a gap in educational opportunities between <a href="http://www.nytimes.com/2014/09/05/opinion/sunday/chinas-education-gap.html">those in rural and urban areas </a>. Nevertheless, Chinese girls are excellent in maths and science – and the Chinese generally are <a href="http://www.nature.com/nature/supplements/nature-index-2015-china/">rapidly expanding</a> their role in the science and technology sector.</p>
<p>If the UK and other Western nations don’t copy the Chinese approach to education, we might well come to regret it soon. A lack of investment in teaching the subjects that will be essential in a technology-driven world, means we risk losing the capacity to play a leading role in the development and production of cutting edge technology.</p>
<p>Unfortunately, even in the current system, the UK does not have enough qualified physics teachers, so it will be impossible to make the subject compulsory immediately – that is how far behind we and other Western nations are. We better get working on this now, before it is too late.</p><img src="https://counter.theconversation.com/content/58889/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Gijsbert Stoet 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>It’s a mistake to allow teenagers to drop maths – it should be made compulsory at A-Level.Gijsbert Stoet, Reader in Psychology, University of GlasgowLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/545022016-03-22T10:52:07Z2016-03-22T10:52:07ZChildren put in the bottom maths group at primary believe they’ll never be any good<figure><img src="https://images.theconversation.com/files/115116/original/image-20160315-9242-1k6jl97.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">A policy that doesn't add up. </span> <span class="attribution"><span class="source">Lorena Fernandez/www.shutterstock.com</span></span></figcaption></figure><p>Jayden wasn’t getting on with his maths work. “Can I help you Jayden?” I asked. “I can’t do this work, Miss, I’m only a moped.” </p>
<p>Jayden was six years old. Like many primary schools across the country, Jayden’s separates children into different groups according to their ability – in his case, named after different vehicles.</p>
<p>Jayden knew he was a moped and not a Ferrari, and had made a link between being a moped and not being good at maths. Whether groups are labelled by vehicles or animals, colours or shapes, children and their parents understand the implied meanings. </p>
<p>As ability-grouping becomes <a href="http://onlinelibrary.wiley.com/doi/10.1080/01411926.2012.659721/abstract;jsessionid=5FE47E7AD2E42B734AA7EE1AEFD85523.f04t04">increasingly common</a> in primary schools, my <a href="http://criticalpublishing.com/ability-grouping-in-primary-schools-case-studies-and-critical-debates.html">recently-published research</a> looked at the experiences and feelings of the young children affected. </p>
<p>While teachers, children and parents often concern themselves with the level of the tasks assigned to each group, I found that group labels do more than this – they say something to and about the children in the groups, too.</p>
<h2>Ferraris and mopeds</h2>
<p>Grouping children by ability seems like a reasonable response to government directives to schools to address the needs of every child. It also fits nicely with the idea in English society that being “good” at something, or having a “talent” – be it sport, music or maths – is more about having the right genes than putting in effort, and that we can assess and group by “ability”. </p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/115118/original/image-20160315-9276-1md349t.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/115118/original/image-20160315-9276-1md349t.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=401&fit=crop&dpr=1 600w, https://images.theconversation.com/files/115118/original/image-20160315-9276-1md349t.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=401&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/115118/original/image-20160315-9276-1md349t.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=401&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/115118/original/image-20160315-9276-1md349t.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=504&fit=crop&dpr=1 754w, https://images.theconversation.com/files/115118/original/image-20160315-9276-1md349t.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=504&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/115118/original/image-20160315-9276-1md349t.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=504&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">The top stream?</span>
<span class="attribution"><span class="source">Ferrari via Bankoo/Shutterstock.com</span></span>
</figcaption>
</figure>
<p>But we now know that <a href="http://geniusblog.davidshenk.com/">genes do not dictate destinies</a>. We also know that while <a href="https://theconversation.com/streaming-six-year-olds-by-ability-only-benefits-the-brightest-32065">being in a top stream may benefit some children</a>, ability-grouping is not a panacea to raising attainment. It may also have detrimental effects on children’s attitudes to a subject. </p>
<p>There are other problems, too. <a href="http://discovery.ucl.ac.uk/1474027/1/Campbell%202015%20-%20Stereotyped%20at%20Seven%20-%20accepted%20manuscript.pdf">Teacher stereotypes</a>, the <a href="http://www.ifs.org.uk/comms/r80.pdf">month of birth</a>, <a href="http://eprints.soton.ac.uk/173595/">social background and special educational needs</a> all impact on which group a child might be placed in, and therefore on the educational opportunities afforded to them.</p>
<p>Despite a wealth of <a href="https://theconversation.com/forcing-schools-to-set-by-ability-is-not-backed-up-by-evidence-31315">research arguing against the use of ability-grouping</a>, this has <a href="http://www.tandfonline.com/doi/abs/10.1080/0305764X.2015.1093095?journalCode=ccje20&">little impact in schools</a>. Primary school children, sometimes <a href="http://www.cambridge-news.co.uk/Cambridge-school-groups-reception-children/story-26637365-detail/story.html">from the age of four</a>, are increasingly experiencing structured forms of ability grouping.</p>
<h2>Children understand</h2>
<p>Children know what their placement means. Eight year-old Louise, sat on the bottom table, told me: “It makes you know you’re worst at maths.” </p>
<p>These views were not uncommon among the 24 primary-aged children <a href="https://kclpure.kcl.ac.uk/portal/files/13068102/Studentthesis-Rachel_Marks_2012.pdf">I interviewed</a> from both top and bottom groups, who all study maths as part of the National Curriculum. Over 70% had fixed <a href="http://www.youcubed.org/wp-content/uploads/14_Boaler_FORUM_55_1_web.pdf">mindsets</a>, believing that maths ability was determined at birth. </p>
<p>Nine-year-old Yolanda, who was in a bottom group, explained why some children were good at maths: “Their brain’s bigger … it just happens. They were born like that. They were born clever.” </p>
<p>Children bought into the ability labels they were given, but also felt constrained by them. Despite being in a top group, Peter, who was about to embark on secondary school, adamantly stated that his improvement could only be minimal because: “There’s only so much you can do, isn’t there?” </p>
<p>Labelling or grouping children by ability appears to place real limits on the willingness of many to “have a go”. Many children in my study also saw their ability as fixed not just now, but in the future, too. As Samuel, also at the end of primary school, reported angrily: “I’ve always been last in every maths group … I’ll just be low now in my next school, too.” </p>
<p>Sadly, Samuel’s assertion may well be true. Ability-driven group placements appear to <a href="http://www.wwwords.co.uk/rss/abstract.asp?j=forum&aid=2561">persist into adulthood</a>. The mopeds may always be the mopeds.</p>
<h2>Splitting up friends</h2>
<p>In some schools, young children are expected to move to different sets (and so to different classrooms with different teachers) for different lessons – essentially a secondary school practice brought into the primary environment. But this can simply be too much for a young child whose main concern may only be who they’re going to play with at lunchtime. Being in different classes, children have to manage a greater range of friendship groups. </p>
<p>As Louise told me: “You know in the groups? It takes you away from your friends.” This is important. By breaking up friendship groups, teachers may actually limit the possibility of collaborative work. Ability-grouping also takes young children away from the pastoral support of their class teacher.</p>
<p>Many children rely on school to provide nurture and consistency. Traditionally, the primary school teacher develops a holistic understanding of their class, knowing how well each is doing, what motivates them, their fears, interests, aspirations and home background. Teaching children in sets and streams may make this harder.</p>
<p>The increase in ability-grouping in primary schools brings with it many different experiences for young children. Grouping children by ability affects how children feel about themselves, both now and in the future. I believe these are not the experiences and feelings we want such young children to have.</p><img src="https://counter.theconversation.com/content/54502/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Rachel Marks previously received funding from the Economic and Social Research Council (award number: PTA-031-2006-00387) to conduct the PhD research on which this piece is based.</span></em></p>Tell a child they’re a ‘moped’ rather than a ‘Ferrari’ and they’ll understand exactly what it means.Rachel Marks, Senior Lecturer in Mathematics Education (Primary), University of BrightonLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/564232016-03-18T02:09:16Z2016-03-18T02:09:16ZUniversities should require science, engineering and commerce students to know their maths<figure><img src="https://images.theconversation.com/files/115536/original/image-20160317-3199-1abn0jp.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Many university degrees require a high level of maths skill.</span> <span class="attribution"><span class="source">Shutterstock</span></span></figcaption></figure><p>In 2013, a meeting of academics specialising in teaching first year undergraduate mathematics (known as the <a href="http://fyimaths.org.au/">FYiMaths</a> network) identified that the broad removal of mathematics prerequisites for many undergraduate degrees had created the biggest challenge they faced in teaching. </p>
<p>Many individuals had made attempts to pass this message up the management line at their universities. But at that time, staff believed that reintroducing prerequisites would never happen. </p>
<p>However, earlier this year The University of Sydney announced it <a href="http://sydney.edu.au/news-opinion/news/2016/02/01/mathematics-to-become-a-prerequisite-for-university-of-sydney-ad.html">would do exactly that</a>, by requiring students studying science, engineering, commerce and IT to have completed at least intermediate level mathematics in high school.</p>
<p>The Australian Academy of Science’s <a href="https://www.science.org.au/support/analysis/decadal-plans-science/decadal-plan-mathematical-sciences-australia-2016-2025">Decadal Plan for the Mathematical Sciences</a>, launched in Canberra yesterday, continues this push. One of its <a href="https://www.science.org.au/files/userfiles/support/reports-and-plans/2016/mathematics-decade-plan-2016-vision-for-2025.pdf">key recommendations</a> is the reinstatement of mathematics prerequisites for science, engineering and commerce degrees. </p>
<p>But will it improve the level of maths education? Will it bolster mathematics skills in those studying science, engineering and commerce?</p>
<h2>Opting out</h2>
<p>A prerequisite study for entry to a degree is considered to be essential background knowledge that students need in order to be successful in that degree. A student cannot be selected into the degree if they do not have the stated prerequisite or an equivalent to it. </p>
<p>Over the past two decades, most universities have moved away from mathematics prerequisites, replacing them with assumed knowledge statements. This means that students can be selected without verifying that they have in fact completed this background study.</p>
<p>So what’s wrong with that?</p>
<p>In most cases, the assumed knowledge statements are unclear and often difficult to find, so students may not be aware of the assumed requirements. The removal of mathematics prerequisites also grossly underplays the level of mathematical facility required for these courses and trivialises the learning and skill development required to acquire it. </p>
<p>It places the burden on students to decide what should or should not be known in order to succeed in a course, and to assume the risk of those decisions, even though they are in no position to know what the risks are.</p>
<p>As a consequence, large numbers of students have been enrolling in mathematics-dependent courses without the assumed knowledge. </p>
<p>Over the last decade or more, numbers of students studying intermediate and advanced level mathematics in school has been in steady decline. Students have been free to make subject choices based on maximising their ATAR score rather than choosing the subjects that will best prepare them for their chosen career. </p>
<p>Since intermediate and advanced mathematics subjects are seen as hard and deemed not necessary for entry, students have been allowed – in some cases even encouraged – to opt out.</p>
<p>On the other side of the enrolment gate, consequences for students include being required to undertake bridging courses (some at extra cost) and having limited pathways through their degrees. Students do not generally know this at the end of Year 10 when they decide on which subjects they will choose for their Year 12.</p>
<p>Neither do they know that these choices may impact on their ability to succeed in their tertiary studies. Failure and attrition rates are generally high in first-year STEM subjects. And lack of the requisite background in mathematics plays a significant part in this. </p>
<p>Students who enter university without the assumed knowledge in mathematics also generally have lower success rates than students who have the assumed knowledge from school, even after they have completed bridging courses. In consumer terms, this buyer beware approach is not working.</p>
<p>So, where does that leave us?</p>
<h2>One piece of the puzzle</h2>
<p>Universities have a responsibility to determine what minimum background knowledge students require to be successful in a course. Once that determination is made, they should be required to ensure that the students they accept have that required knowledge. </p>
<p>Reintroducing appropriate mathematics prerequisites should increase participation in intermediate and advanced level mathematics at school. It has to. </p>
<p>We want students to take full advantage of the excellent education that is available to them through our secondary school system rather than trying to play catchup for years later.</p>
<p>Engaging students in the study of mathematics at school needs to be addressed on many levels. Certainly, making strong statements about prerequisites is one piece of the puzzle, but not the only one.</p>
<p>The Decadal Plan also calls for an urgent increase in the provision of professional development for teachers, especially those teaching mathematics out-of-field. It is essential that we support our teachers at all levels of education, so that we can give students the best possible education in mathematics that we must.</p><img src="https://counter.theconversation.com/content/56423/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>John Rice is the Executive Director of the Australian Council of Deans of Science (ACDS). The opinions expressed in this article, however, are his own, and do not necessarily reflect those of the ACDS.</span></em></p><p class="fine-print"><em><span>Deborah King 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>Lowering maths prerequisites to study science, engineering and commerce at university has led to students playing catch up for years. This should be fixed.Deborah King, Associate Professor in Mathematics, The University of MelbourneJohn Rice, Honorary Professor, University of SydneyLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/552662016-02-25T09:09:29Z2016-02-25T09:09:29ZAsian cities tussle for top spot in new education ranking as London left behind<p>Singapore, Hong Kong and Shanghai have come top of <a href="https://johnjerrim.files.wordpress.com/2016/02/gla_paper_final.pdf">a new ranking</a> of how teenagers in cities and states around the world perform on global maths, reading and science tests. London, despite showing a <a href="https://theconversation.com/hard-evidence-why-do-students-in-london-do-better-at-school-34090">marked improvement</a> in domestic exam results in recent years, has not come out highly on the ranking. </p>
<p>The <a href="http://www.oecd.org/pisa/">Programme for International Student Assessment</a> (PISA) is perhaps the world’s most influential educational assessment. Conducted every three years by the Organisation for Economic Co-Operation and Development (OECD), it is widely used to compare educational standards across the world.</p>
<p>Results <a href="https://theconversation.com/uk/topics/pisa">from PISA</a> are typically reported at the country level – setting out how the reading, science and mathematics skills of 15-year-olds in one country compare to their peers in another. Now the OECD has expanded its interest into benchmarking regional economies, such as Canadian provinces, Chinese cities and American states. Perhaps the most prominent example is Shanghai, China, which topped the PISA mathematics, reading and science rankings in both 2009 and 2012.</p>
<p>In my <a href="https://johnjerrim.files.wordpress.com/2016/02/gla_paper_final.pdf">new research</a>, using combined data from the PISA tests in 2009 and 2012, I have estimated PISA scores for a number of major world cities for the first time. These results are presented in the graph below, focusing on how educational standards in London compare to some of the world’s other major regional economies.</p>
<iframe src="https://datawrapper.dwcdn.net/KnShX/1/" frameborder="0" allowtransparency="true" allowfullscreen="allowfullscreen" webkitallowfullscreen="webkitallowfullscreen" mozallowfullscreen="mozallowfullscreen" oallowfullscreen="oallowfullscreen" msallowfullscreen="msallowfullscreen" width="100%" height="594"></iframe>
<p>There are some striking results. With an average PISA mathematics score of around 480, 15-year-olds in London are around three school years behind their peers in Shanghai. The average score across OECD countries is 500, and for the rest of around 495. In London, where the data covered 42 schools and 1,057 pupils, only the top 10% of children can match the mathematics skills of the average 15-year-old in Shanghai. On the other hand, children in Riga, Latvia, achieve at or above the OECD average across the PISA reading, science and mathematics domains.</p>
<p>There are several possible explanations for this result. Countries differ in many ways, including education systems, teaching methods, use of out-of-school tuition and the role parents play in shaping their children’s education. It would therefore be wrong to interpret these results as suggesting there is a problem with London schools. Yet, what it clearly does show is that the reading, mathematics and science skills of the average 15-year-old in London is way below that in several other major world economies – a situation that needs to be resolved.</p>
<p>As PISA grows in terms of its political influence, it is likely that interest in such regional estimates is only likely to grow. <a href="http://www.bbc.co.uk/news/education-35305586">Some commentators</a> have argued that such comparisons are likely to be much more meaningful than the standard PISA country-level reports. I agree and think it’s good news that the OECD has now announced the launch of <a href="http://www.oecd.org/callsfortenders/CfT%20100001311%20Longitudinal%20Study%20of%20Social%20and%20Emotional%20Skills%20in%20Cities.pdf">a new study</a> on social and emotional skills in cities, and the further benchmarking of regional economies in upcoming waves of the PISA tests.</p><img src="https://counter.theconversation.com/content/55266/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>John Jerrim 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>Teenagers in Shanghai, Singapore and Hong Kong outperformed those in London, Madrid and Dubai.John Jerrim, Lecturer in Economics and Social Statistics, UCLLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/532982016-01-18T03:15:36Z2016-01-18T03:15:36ZSaying ‘I’m not good at maths’ is not cool – negative attitudes are affecting business<figure><img src="https://images.theconversation.com/files/108388/original/image-20160118-13800-ejeozo.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Changing attitudes: why is it 'cool' to be bad at maths?</span> <span class="attribution"><a class="source" href="http://www.shutterstock.com">from www.shutterstock.com</a></span></figcaption></figure><p>How many times have you heard people say “I’m not good at maths”? </p>
<p>Perhaps you’ve said it yourself. Often people make the statement with pride, almost implying it’s “cool” to be bad at maths. </p>
<p>Imagine if the same number of people claimed “I’m not good at reading”. I don’t think it would be deemed socially acceptable – in fact, most people would be embarrassed to make that claim. </p>
<p>So why is it okay to by openly negative about mathematics? Why do so many openly claim to dislike mathematics, and why is mathematics seen as a domain only accessible to an elite group of “smart” people? </p>
<p><a href="http://www.pnas.org/content/103/33/12649.short">Research</a> has proven humans are born numerate, so what happens in those few years when children are in school to make them hate maths?</p>
<p>A <a href="http://www.aigroup.com.au/portal/binary/com.epicentric.contentmanagement.servlet.ContentDeliveryServlet/LIVE_CONTENT/Publications/Reports/2016/AIG9675_EMAIL.pdf">new report</a> by the Australian Industry group claims that low literacy and numeracy skills in the Australian workforce are affecting business. </p>
<p>It calls for a renewed focus on literacy and numeracy skills to ensure we are able to address economic needs. </p>
<p>Does this mean teachers aren’t spending enough time on literacy and numeracy, or are there other issues? </p>
<p>The mere mention of mathematics within a social situation often strikes fear into the hearts of young and old. A lack of confidence with basic numeracy and mathematics has significant implications in any workplace that ultimately result in decreased profit and productivity, yet issues surrounding confidence and ability with mathematics can be addressed early.</p>
<h2>Negative attitudes can impact on subjects children choose</h2>
<p>With the new school year looming, we need to promote more positive attitudes to mathematics and numeracy and turn things around for Australia’s economic future. </p>
<p>Parents need to think carefully about how they talk to their children about mathematics. Regardless of how they experienced school mathematics and how they perceive mathematics, claims like “I was never good at maths when I was at school” are not helpful. Children notice. </p>
<p>Molly, a year 6 participant in <a href="http://link.springer.com/article/10.1007/s13394-013-0081-8#page-1">my research</a> on student engagement, made this comment when asked about what her family think about mathematics: </p>
<blockquote>
<p>“My mum doesn’t really like me asking her because she thinks she doesn’t have a maths brain. She thinks that she’s got more of an English brain than anything else.” </p>
</blockquote>
<p>Not surprisingly, Molly was not the only child who made that kind of comment.</p>
<p>Parents’ negative attitudes or beliefs do have the potential to negatively influence children – “not having a maths brain” can be used as an excuse for opting out of mathematics in the senior years of schooling. </p>
<p>Evidence of this influence on children’s thinking can be seen in this quote, where Kristie, another participant, was describing her friends’ attitudes towards mathematics: </p>
<blockquote>
<p>“Maybe some just don’t enjoy it the way I do, they just think maybe it’s not their subject. They might enjoy English.”</p>
</blockquote>
<h2>Promoting positive attitudes to maths</h2>
<p>So what can parents do to promote positive attitudes towards mathematics? </p>
<p>Above all, they should never make negative comments about the subject. </p>
<p>If you are a parent and you are having difficulty with helping your child, seek help. In the primary years, many schools are happy to provide parent workshops to help parents understand new teaching methods. Workshops could also be held to help parents “brush up” on their own mathematics skills. </p>
<p>If your child is in secondary school and the mathematics they are learning requires more than a quick revision, don’t panic. It’s okay to say “I don’t know” or “I don’t remember how to do that”. </p>
<p>Try and find a way to assist your child in finding an explanation. This could be by seeking help online, encouraging them to seek help from their teacher, or, if required, finding an appropriate tutor who may be able to provide some remediation. It’s better to seek help early.</p>
<p>One of the challenges with mathematics is that the concepts are hierarchical. That is, if children don’t develop a deep understanding of foundational topics such as place value, gaps in learning begin to occur. </p>
<p>When mathematics becomes more complex, children who struggle with the foundations of mathematics cannot keep up with their peers and fall behind, often leading to negative attitudes, poor self-efficacy, and disengagement.</p>
<p>We need to stop allowing those around us, in our lives and in the media, to make such negative statements about mathematics – if we don’t take a stand things will never change.</p><img src="https://counter.theconversation.com/content/53298/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Catherine Attard is the Vice-President of the Mathematical Association of New South Wales.</span></em></p>You wouldn’t feel so confident about claiming you weren’t good at reading, so why is it okay to be openly negative about mathematics?Catherine Attard, Associate Professor, Mathematics Education, Western Sydney UniversityLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/494952015-11-04T19:03:35Z2015-11-04T19:03:35ZBringing maths into bedtime stories can help children learn – and make the subject less scary for parents too<figure><img src="https://images.theconversation.com/files/100686/original/image-20151104-25334-mapcqn.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">When parents are stressed about maths, their children can develop the same negative feelings towards the subject.</span> <span class="attribution"><span class="source">www.shutterstock.com</span></span></figcaption></figure><p>As parents, we know how important it is to read to our children. Many families include this as a regular part of the bedtime routine. </p>
<p>While we feel confident this is contributing to our child’s literacy development,
<a href="http://www.sciencemag.org/content/350/6257/196">new research</a> shows that this nightly routine could also be used to help improve maths skills.</p>
<h2>How reading can help your child learn maths</h2>
<p>The study by <a href="http://www.sciencemag.org/content/350/6257/196">researchers in the US</a> gave 587 students in year 1 (between 6 and 7 years old) tablets featuring an app with short passages to read with their parents. </p>
<p>Parents would read these passages with their child and then answer questions based on the text. Families used the app on average 4 times a week between the Autumn and Spring of 2013-14.</p>
<p>One group read stories which contained a mathematical focus, which allowed children and their parents to discuss maths in a natural way and complete simple problems together. </p>
<p>Each passage came with five questions ranging in difficulty from preschool to fifth-grade level and covered topics including counting and arithmetic, fractions, geometry and probability. </p>
<p>There was also an additional bank of questions for families who wished to explore the passage further. Families could complete as many questions as they were comfortable with after reading the story. </p>
<p>A second, comparison group read the same passage with the specific maths content removed and answered questions which focused on recalling facts, inferring information and spelling.</p>
<p>The results were overwhelming. </p>
<p>The students were tested before and at the end of the study and those who read the maths stories, adapted from the Bedtime Math <a href="http://bedtimemath.org/">app</a>, showed significant improvement in their overall mathematics learning during the year. </p>
<p>When comparing the children in each group who used the app most frequently, the study saw a three month advancement in maths achievement for those who read the maths-focused stories.</p>
<h2>Helping parents boost their confidence in maths</h2>
<p><a href="http://www.tandfonline.com/doi/abs/10.1080/10409280801963913">Research</a> shows that parents tend to place more importance on language learning than on mathematical development when their children are young. A reason for this could be that parents don’t feel as comfortable with teaching maths, compared to literacy.</p>
<p>But <a href="http://pss.sagepub.com/content/early/2015/08/06/0956797615592630.abstract">research shows</a> that when parents are stressed about maths, their children learn less mathematics over the school year and can also develop the same negative feelings towards the subject.</p>
<p>Children who feel anxious about maths are also less likely to engage in the classroom and will avoid mathematical tasks. </p>
<p>This avoidance leads to missed learning opportunities and a greater sense of potential failure. </p>
<p>Once the cycle has begun, it can be hard to redirect this momentum. </p>
<p>While the research focused on stories designed for an electronic device, the findings highlight some key points for parents. </p>
<p>Sharing stories with a mathematical focus, and the discussions which are then created, can contribute to an increase in achievement at school. </p>
<p>For parents who are struggling with their own mathematical anxieties, this comes as welcome news. The study goes on to suggest that this sharing of stories and discussing maths with our children, can help parents become less anxious in this space. </p>
<p>The federal Government recently committed $6.4m to support the development of maths resources for students. This forms a part of the <a href="https://ministers.education.gov.au/birmingham/bringing-maths-real-world-students">government’s agenda</a> to improve the teaching of science, technology, engineering and maths subjects in our schools. </p>
<p>So how can parents use books to help improve their child’s maths skills? Here are some suggestions:</p>
<h2>Reading tips for parents</h2>
<p>Read books with mathematical concepts to your children. </p>
<p>In some books the content is obvious - we are all familiar with Eric Carle’s <em>The Very Hungry Caterpillar</em>. </p>
<p>Try reading these as well:</p>
<ul>
<li><em>365 Penguins</em> by Jean-Luc Fromental</li>
<li><em>Leaping lizards</em> by Stuart Murphy</li>
<li><em>Math for all seasons: Mind-stretching Maths Riddles</em> by Greg Tang</li>
<li><em>My Grandmother’s Clock</em> by Geraldine McCaughrean</li>
</ul>
<p>Consider asking your local librarian for some other ideas. Look for books with amusing pictures and colourful illustrations - we know how this attracts children to read.</p>
<p>Talk about the book with your child, as you would with any other story. </p>
<p>The mathematical elements will naturally come into the conversation and should be encouraged – this will help children to see maths as part of everyday life. </p>
<p>By simply including books which include mathematical concepts in nighttime routines, parents can feel more confident that they are contributing to the mathematical development of their child outside the classroom at the same time as creating a less stressful environment for discussing mathematics.</p>
<hr>
<p><em>Kylie will be taking part in an Ask An Expert Q&A on Twitter from noon to 1pm on Thursday, November. Head over to Twitter and post your questions about learning and teaching maths using #AskAnExpert.</em></p><img src="https://counter.theconversation.com/content/49495/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Kylie Robson 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>Research shows that reading stories with a maths focus can boost grades and also help parents become less anxious about discussing maths.Kylie Robson, Clinical Teaching Specialist - Mathematics and Literacy Education, Faculty of ESTeM, University of Canberra, University of CanberraLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/492222015-10-22T19:09:49Z2015-10-22T19:09:49ZWhat is the secret to being good at maths?<figure><img src="https://images.theconversation.com/files/98774/original/image-20151019-25125-147fqvr.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Why do Asian children perform so well at maths?</span> <span class="attribution"><span class="source">www.shutterstock.com</span></span></figcaption></figure><p>There is a common belief that Asians are naturally gifted at maths. </p>
<p>Asian countries like Singapore and Japan lead the ranks in first and second position on maths performance in the <a href="http://www.oecd.org/pisa/">Program for International Student Assessment (PISA)</a> tables – an international survey that ranks education systems worldwide – while Australia sits around 12th.</p>
<p>What is the secret to being good at maths? Are you simply born clever, or is it the result of a lot of hard work? </p>
<p>To understand the reasons behind exceptional maths performance, I travelled to Japan to see how <a href="https://www.youtube.com/watch?v=0ftjsOHv-Z4">Japanese children are able to instantly multiply three- or four-digit numbers together in their head</a>. </p>
<h2>How children are taught maths in Japan</h2>
<p>From the age of 7 or 8, all Japanese children are taught the times table jingle kuku.</p>
<p>“Ku” is the Japanese word for “nine”, and the title reflects the final line of the jingle, which is simply “nine nine (is) eight-one”. </p>
<p>Children rote learn the jingle and are made to recite it with speed in class and at home.</p>
<p>Local competitions pitch second-graders against each other to see how fast they can rap all 81 lines of the kuku. </p>
<p>This takes lots of practice with a stopwatch. The <a href="https://theconversation.com/heres-how-to-get-kids-to-remember-times-tables-40471">constant association between the problem and the correct answer</a> eventually allows the child to know the answer to the problem as soon as they see it. </p>
<p>As the popular science writer <a href="https://books.google.com.au/books?id=FA_HwoEzSQUC&pg=PA66&lpg=PA66&dq=alex+bellos+kuku&source=bl&ots=bggDgHLJIH&sig=jsuHhWkuj1Jmm-RXgZoUD50g4ds&hl=en&sa=X&ved=0CDAQ6AEwA2oVChMIj_3U9s_QyAIVQyqmCh3lgAkD#v=onepage&q=alex%20bellos%20kuku&f=false">Alex Bellos</a> noted, Japanese adults know that 7x7=49, not because they can remember the maths, but because the music of “seven seven forty-nine” sounds right.</p>
<figure class="align-left ">
<img alt="" src="https://images.theconversation.com/files/99283/original/image-20151022-7999-1s1ut8f.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/99283/original/image-20151022-7999-1s1ut8f.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=440&fit=crop&dpr=1 600w, https://images.theconversation.com/files/99283/original/image-20151022-7999-1s1ut8f.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=440&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/99283/original/image-20151022-7999-1s1ut8f.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=440&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/99283/original/image-20151022-7999-1s1ut8f.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=553&fit=crop&dpr=1 754w, https://images.theconversation.com/files/99283/original/image-20151022-7999-1s1ut8f.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=553&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/99283/original/image-20151022-7999-1s1ut8f.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=553&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 with the abacus.</span>
<span class="attribution"><a class="source" href="http://pictures.reuters.com/C.aspx?VP3=SearchResult&VBID=2C0FCIRSXUGF&SMLS=1&RW=1769&RH=1221&RW=1769&RH=1221#/SearchResult&VBID=2C0FCIRSXUGF&SMLS=1&RW=1769&RH=1221&POPUPPN=10&POPUPIID=2C04082TULOVX">Issei Kato/Reuters</a></span>
</figcaption>
</figure>
<p>Some Japanese children also attend after-school maths programs. In May, I visited a school in Tokyo specialising in abacus instruction for primary and high school students. This was one of <a href="http://www.theguardian.com/science/alexs-adventures-in-numberland/2012/oct/25/abacus-number-joy-japan">about 20,000</a> schools operating independently throughout Japan.</p>
<p>Here, the students start by learning how to use a physical abacus to perform arithmetic calculations. They then progress to using the <a href="https://www.youtube.com/watch?v=uKCb-ek9Vs8">mental abacus</a> by simply imagining the movement of the beads. </p>
<p>Children at the abacus school dedicate a phenomenal one to two hours on two to four evenings a week to practising arithmetic drills on pre-set worksheets at speed. </p>
<p>This is on top of the four 45-minute maths lessons per week allotted by the <a href="http://www.mext.go.jp/a_menu/shotou/new-cs/youryou/syo/index.htm">Japanese government</a>. </p>
<p>After a couple of years at the school, the very best students can multiply seven- and eight-digit numbers in their head faster than Australian children can say the solution to 7x8.</p>
<h2>Why Australian schools are against rote learning</h2>
<p>Despite the impressive performance of these Japanese children, the intensive “drill and kill” approach used by abacus schools is derided in countries like Australia where educators explicitly discourage such practice.</p>
<p><a href="http://www.theage.com.au/victoria/modern-maths-no-textbooks-year-levels-or-rote-learning-20150826-gj7z91.html">In Victoria</a>, schools have recently been encouraged to throw away textbooks and old worksheets, teachers discouraged from teaching mathematical formula, and children warned against learning their times tables by rote. </p>
<p>These recommendations follow from the ideas of American psychologist <a href="http://psycnet.apa.org/psycinfo/1962-00777-001">Jerome Bruner</a> who argued that learning is most effective when children actively discover concepts for themselves. </p>
<p>Since then, rote learning methods in which children spend most of their time memorising facts, following prescribed formula and completing drills are <a href="http://eatmorecake.co.uk/is_rote_learning_effective/">widely perceived</a> to contribute poorly to deep understanding of mathematics. </p>
<p>However, research suggests that <a href="https://theconversation.com/chalk-and-talk-teaching-might-be-the-best-way-after-all-34478">memorisation and rote learning remain important classroom techniques</a>. </p>
<p>According to cognitive psychologist <a href="http://www.aft.org/sites/default/files/periodicals/willingham.pdf">Daniel Willingham</a>, children cannot appreciate the relationship between mathematical concepts if all of their mental resources are used to execute simple arithmetic operations. </p>
<p>As problems become more difficult, practice and rote learning are essential in speeding up some of these operations so they become automatic. This allows the child to devote more of their cognitive resources towards higher-level understanding. </p>
<p>Unfortunately, <a href="https://books.google.com.au/books?hl=en&lr=&id=8SDs8LZl41EC&oi=fnd&pg=PR5&dq=willingham+why+don%27t+students+like+school+memory+routine&ots=INA9BfW1hO&sig=KW4SaYRw9PcB4EegcT2OXBScrIk#v=onepage&q&f=false">repetitive practice is not always fun</a>. </p>
<p>One reason educators shy away from rote learning techniques is because they <a href="http://www.youcubed.org/fluency-without-fear/">undermine children’s engagement and motivation</a>. </p>
<h2>The drive to succeed</h2>
<p>But Japanese children at the abacus school <a href="http://www.theguardian.com/science/alexs-adventures-in-numberland/2012/oct/25/abacus-number-joy-japan">enjoy performing calculations at speed</a>. </p>
<figure class="align-left ">
<img alt="" src="https://images.theconversation.com/files/99280/original/image-20151022-7993-199z89g.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/99280/original/image-20151022-7993-199z89g.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=395&fit=crop&dpr=1 600w, https://images.theconversation.com/files/99280/original/image-20151022-7993-199z89g.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=395&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/99280/original/image-20151022-7993-199z89g.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=395&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/99280/original/image-20151022-7993-199z89g.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=496&fit=crop&dpr=1 754w, https://images.theconversation.com/files/99280/original/image-20151022-7993-199z89g.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=496&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/99280/original/image-20151022-7993-199z89g.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=496&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Japanese children compete to move beads on the abacus.</span>
<span class="attribution"><a class="source" href="http://pictures.reuters.com/C.aspx?VP3=SearchResult&VBID=2C0FCIRSXUGF&SMLS=1&RW=1769&RH=1221&RW=1769&RH=1221#/SearchResult&VBID=2C0FCIRSXUGF&SMLS=1&RW=1769&RH=1221&POPUPPN=12&POPUPIID=2C04082TULAQP">Issei Kato/Reuters</a></span>
</figcaption>
</figure>
<p>Many treat mental calculation like a sport and participate in various local, regional and national competitions. These are not restricted to boys. I attended a regional competition for young girls while I was in Japan.</p>
<p>This contrasts with <a href="http://www.abc.net.au/news/2014-04-01/earl-aussie-kids-play-to-win-lets-keep-it-that-way/5358070">an increasing avoidance of competition in Australia</a>, where children are cocooned from the realities of failure as well as the rewards of success. </p>
<p>In junior Australian Football League sporting policy, for example, children under 10 now play football with <a href="http://www.heraldsun.com.au/news/victoria/no-scoreboard-ladder-or-match-results-for-junior-footballers-under-changes-to-be-unveiled-by-afl/story-fni0fit3-1226869120535">no points, no scoreboards, no awards and no recognition of individual performance</a>.</p>
<p>Removing these objective benchmarks of performance leaves children with nothing to strive for.</p>
<h2>When passion breeds talent</h2>
<p><a href="https://theconversation.com/our-obsession-with-natural-talent-is-harming-students-11549">Stars are made, not born</a>. Research shows it takes <a href="http://www.actionkarateonline.com/wp-content/uploads/2013/10/HarvardBusinessReview_DeliberatePractice.pdf">at least 10,000 hours of intense training</a> to become expert in a particular area. High achievers in maths sustain these hours because they are motivated to excel. </p>
<p>But <a href="http://doi.apa.org/psycinfo/1993-40718-001">deliberate practice</a> is hard work. From ever faster times in kuku recitation to increasingly longer mental arithmetic problems, my observations in Japan show that Japanese children use competition to fuel their passion for maths.</p>
<p>Such competition is lacking in Australia. </p>
<p>Discovery-based methods for maths instruction might be more enjoyable, but they are also <a href="http://spp.sagepub.com/content/2/2/174.short">less effective at producing fast and accurate performance at an elite level</a>.</p>
<p>How can we encourage Australians to share the Asian love of competitive maths? </p>
<p>In China, the television game show <a href="https://en.wikipedia.org/wiki/The_Brain_%28game_show%29">Super Brain</a> attracted <a href="http://www.japantimes.co.jp/news/2015/03/19/national/china-in-shock-after-japanese-girl-wins-brain-battle/#.ViepWW7Udua">22 million viewers in March</a> as contestants battled to solve increasingly difficult arithmetic problems. </p>
<p>So given the recent success of <a href="http://www.smh.com.au/entertainment/tv-and-radio/the-great-australian-spelling-bee-gets-the-nation-buzzing-over-spelling-20150803-giqqjp.html">The Great Australian Spelling Bee in generating renewed interest in spelling</a>, perhaps what we need now is The Great Australian Times Tables to motivate children to achieve the same levels of maths performance as our Asian neighbours. </p>
<hr>
<p><em>Steson will be on hand for an Author Q&A between 3 and 4pm AEDT on Friday, October 23, 2015. Post your questions in the comments section below.</em></p><img src="https://counter.theconversation.com/content/49222/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Steson Lo received funding from the Australian Government and the University of Sydney to conduct research in Japan. </span></em></p><p class="fine-print"><em><span>Sally Andrews receives funding from Australian Research Council. </span></em></p>Memorising facts and completing drills is likely to improve your maths skills – just so long as you find a way to stay motivated.Steson Lo, PhD candidate, University of SydneySally Andrews, Professor of Cognitive Psychology, University of SydneyLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/429622015-06-24T04:44:15Z2015-06-24T04:44:15ZWhen there’s meaning in mathematical mistakes<figure><img src="https://images.theconversation.com/files/86093/original/image-20150623-19415-ch5ouv.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Teachers can learn a great deal from their pupils' mistakes in maths.</span> <span class="attribution"><span class="source">From www.shutterstock.com</span></span></figcaption></figure><p>A grade one learner is enjoying school tremendously, but one day she comes home unhappy. Her mother asks why she is so upset and the child replies: “First my teacher told me that 3+3 = 6, then she told me that 4+2 = 6 and then she told me that 5+1 = 6. Until she makes up her mind, I am not going back to school.”</p>
<p>This story usually makes people smile or laugh out loud. The reason it does so provides a lesson for mathematics teachers. The learner is clearly mathematically incorrect and yet there is something about the way she is thinking that seems reasonable to an adult. Her reasoning might be something like this: “When I add 4+2, there is only one answer. So when I get an answer – 6 – there should be only one set of numbers that adds to give that answer.”</p>
<p>Research <a href="http://www.cirtl.net/node/2628">has shown</a> that learners often have underlying conceptions that produce errors. These are misconceptions – ideas that make sense to learners and are reasonable in relation to what they know, but are incorrect mathematically. </p>
<p>Many teachers and parents believe that if learners make mistakes in mathematics it means they do not understand, they have not listened, or they have not done enough work. The opposite may actually be true: the learner may be thinking more deeply than we expect. Learner errors and misconceptions are important tools for teachers. They show teachers that the learner is thinking mathematically, even though she does not yet have enough knowledge to produce the correct answer.</p>
<h2>Reasons for errors</h2>
<p>Misconceptions are often remarkably consistent across different countries, which suggests that misconceptions are not the result of particular approaches to teaching and learning.</p>
<p>Misconceptions usually arise when learners take knowledge that is correct in one area of mathematics and apply it in another area where it’s <a href="http://www.jstor.org/stable/749095">no longer correct</a>. For example, learners often think that 0.568 is bigger than 0.67 because they know that in whole numbers 568 is bigger than 67. Their prior knowledge conflicts with new knowledge about decimals. Having two reasonable but conflicting sets of knowledge makes it difficult for learners to judge which is correct.</p>
<p>Interestingly, learners who apply this misconception may get some examples correct. They would say, for instance, that 0.568 is bigger than 0.45, which is correct. That misconceptions can produce correct answers as well as errors can make them difficult to detect. Learners can get their mathematics correct for the wrong reasons, which may hinder their learning later on.</p>
<p>One key challenge with misconceptions is that they may not be <a href="http://people.ucsc.edu/%7Egwells/Files/Courses_Folder/ED%20261%20Papers/Misconceptions%20reconceived.pdf">easy to correct</a> because they come from long-term knowledge which holds true in many situations. Teachers therefore need to engage learners about their thinking and find ways to explain where their reasoning is valid as well as where – and why – it is not.</p>
<p>In South Africa, many learners struggle with mathematics and mathematics results are <a href="http://www.iol.co.za/news/south-africa/probe-after-dismal-grade-9-maths-mark-1.1791175#.VYK3Qfmqqko">generally poor</a> at all levels of the system. Many learner challenges stem from errors and misconceptions that have not been dealt with. If these misconceptions are dealt with, they can help teachers to support stronger learning of mathematics among learners.</p>
<h2>Finding meaning in mistakes</h2>
<p>The Data Informed Practice Improvement Project at the University of the Witwatersrand in Johannesburg is <a href="http://www.wits.ac.za/academic/humanities/education/staff/karinbrodie/7981/research.html">working with teachers</a> to analyse the reasoning behind learner errors and to think about how best to deal with them.</p>
<p>Teachers analyse errors in tests, classwork and in lesson videotapes. They also interview learners about their thinking. They read research about common learner errors and misconceptions and plan lessons together to help reveal and engage with learner errors.</p>
<p>Over the past five years we have worked with ten government high schools, with communities of teachers working within and across schools. Each small community has between four and eight teachers who meet regularly to discuss learner errors.</p>
<p>Research in the project has shown that through working on the activities, many teachers do identify and engage with learner errors in class. We have found that the full range of activities is necessary. The error analysis and learner interviews enable teachers to start understanding learner thinking in more depth. </p>
<p>However, teachers are not often able to act on these new insights in the first round of classroom teaching. Reflecting on their videotaped lessons helps the teachers to see how they might have responded differently and how they might do so in future. Error analysis without subsequent follow up, lesson planning and reflection is unlikely to be useful.</p>
<p>Our approach is very different to the kind of analysis that teachers are required to do with South Africa’s Annual National Assessments, which test learners’ numeracy at different grade levels. These tick-the-box analyses do not support new classroom practices and may promote, rather than prevent, blaming of learners and teachers for mathematical mistakes.</p><img src="https://counter.theconversation.com/content/42962/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>For the project described in this article, I received funding from the Gauteng Education Development Trust and from the National Research Foundation.
I am affiliated with a number of professional and research organisations, including SAARMSTE and AMESA.
</span></em></p>What if instead of dismissing wrong answers as a sign of failure, maths teachers tried to understand how their pupils came to that answer and then guided them in the right direction?Karin Brodie, Professor of Education and Mathematics Education, University of the WitwatersrandLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/434182015-06-17T23:04:26Z2015-06-17T23:04:26ZEast Asian maths teaching method boosts English children’s progress by a month<figure><img src="https://images.theconversation.com/files/85368/original/image-20150617-23259-jhfs43.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Mastered it!</span> <span class="attribution"><span class="source">Girl maths via NataSnow/www.shutterstock.com</span></span></figcaption></figure><p>There has been <a href="https://theconversation.com/how-east-asian-children-get-so-far-ahead-of-their-classmates-32703">much discussion</a> in recent years about why East Asian children perform so well on international education tests. I’ve <a href="https://johnjerrim.files.wordpress.com/2013/07/australia_asia_paper.pdf">argued before that</a> there is no one reason for these countries’ stellar results, but that home background and culture plays an important role. In the UK, moves to introduce teaching methods popular in countries such as Singapore into the classroom have <a href="https://www.gov.uk/government/speeches/elizabeth-truss-speaks-about-improving-teaching">been heralded by politicians</a> eager to replicate some of the successes of East Asian education systems. </p>
<p>We are beginning to see whether these borrowed methods are working in the classroom. My <a href="http://www.johnjerrim.com/papers">new study</a>, which looked at a <a href="https://theconversation.com/explainer-what-is-the-mastery-model-of-teaching-maths-25636">method</a> called “Mathematics Mastery” that was introduced in primary and secondary schools in England, has shown a small impact on children’s progress in maths after one year. In the programme, fewer topics are covered than in a standard maths lesson and in greater depth. All the children are expected to master the material before the rest of the class moves on. </p>
<p>Over the last two and a half years I have been evaluating the “Mathematics Mastery” programme along with Anna Vignoles from the University of Cambridge. The study involved more than 10,000 pupils in Year 1 (5-6 years old) at 90 primary schools and Year 7 (11-12 years old) at 50 secondary schools. Half of the schools were taught using the new method, after training and resources from the education charity and academy chain sponsor ARK, and half were taught with standard maths lessons.</p>
<p>We evaluated the <a href="http://educationendowmentfoundation.org.uk/projects/mathematics-mastery/">impact of the approach</a> via two randomised controlled trials – one for the primary schools and one for the secondary schools – funded by the Education Endowment Foundation. We have since written an <a href="http://www.johnjerrim.com/papers">academic paper</a> on the findings. </p>
<h2>Early signs of success</h2>
<p>The two trials both pointed towards a small positive effect of the maths mastery programme, though neither reached statistical significance independently. When combining the evidence across the two trials, we found children exposed to the programme made around a month more progress in mathematics than those who did not. To put this another way, in a school with a 100 children, the child would move from being ranked 50th in maths to being ranked 47th. </p>
<p>There is of course quite a bit of uncertainty surrounding this result. For instance, it is not clear how far one can extrapolate results from this trial to the wider population. Also, the fact that the trial has been based on only a sample of schools means that the “true” effect size could be a lot bigger (double) or smaller (essentially zero) than we report. </p>
<p>There is no escaping that the effect size we found was small. This suggests that introducing such methods across the education system would be unlikely to springboard England to the top of the Programme for International Student Assessment rankings. As I <a href="https://johnjerrim.files.wordpress.com/2013/07/australia_asia_paper.pdf">have noted previously</a>, there are likely to be a lot of other factors at play in high-performing Asian countries.</p>
<p>Yet, at the same time, effects of this magnitude are also not trivial, particularly given the low cost per pupil. It costs around £130 per pupil in the first year, dropping to below £50 per pupil in subsequent years once teachers are trained in the programme. For instance, <a href="http://cee.lse.ac.uk/ceedps/ceedp43.pdf">effects of a similar magnitude</a> were reported for The Literacy Hour – a daily hour set aside for literacy in primary schools – which many consider to be a good example of a low-cost intervention that was a success. </p>
<h2>Not enough to build national policy on</h2>
<p>Our trials only considered the impact after just one year, the first year such methods were used in these schools. But programmes like Maths Mastery are meant to develop children’s skills over several years, and so may result in bigger gains in the long-run. However, there is currently no empirical evidence available for us to judge whether this is indeed the case or not.</p>
<p>Given the above, our advice is that we need to proceed with investigations into the impact of East Asian teaching methods, while also exercising caution. The empirical evidence currently available does not have sufficient scope or depth to base national policy upon, despite showing some positive signs. What is now needed is further research establishing the long-run impact of such methods after they have been implemented within schools for several years, and after teachers have more experience with this different approach.</p><img src="https://counter.theconversation.com/content/43418/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>John Jerrim receives funding from the Economic and Social Research Council</span></em></p>Analysis of a maths teaching method popular in East Asia shows promise, but not enough to roll out nationally yet.John Jerrim, Lecturer in Economics and Social Statistics, UCLLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/425422015-05-29T02:21:24Z2015-05-29T02:21:24ZCompulsory science and maths is great but there’s more to be done<figure><img src="https://images.theconversation.com/files/83311/original/image-20150529-24247-d4bo18.jpg?ixlib=rb-1.1.0&rect=0%2C12%2C2733%2C2102&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">We need to start teaching maths and science as early as possible to get the most benefit.</span> <span class="attribution"><a class="source" href="https://www.flickr.com/photos/matsurika27/6654080347/in/photolist-b8ZUge-6bTUqJ-daAjSU-9kiXKA-4UUkLE-eyFFik-6ohCwy-9gVWDo-gnpZxX-Gu5qY-6bU4ZA-9gSTkK-9gVYEQ-9gVWR3-97aGY8-9gSTwn-9gVYRm-7rfZZy-8wZQvt-682ozp-88bgji-97dMdh-4KgiQw-8ML3xv-8MPazf-drdN2F-aF2sq9-e1ovo8-8ML5hB-6tSFn3-97aGaD-7MMSrV-pnUqgS-5dikgj-8MKZnr-e1uaHf-6h7niN-9LWkFY-gntarD-gnsugL-gnsuvJ-gnsMfr-9gVYzu-4a8NLi-5sidGk-pxABq-6Db85p-9gVYr1-9gSRFe-9gVYV1">JJ Losier/Flickr</a>, <a class="license" href="http://creativecommons.org/licenses/by/4.0/">CC BY</a></span></figcaption></figure><p>Federal Education and Training Minister Christopher Pyne today <a href="http://www.9news.com.au/national/2015/05/29/06/58/education-ministers-headed-for-showdown">met with his state counterparts</a> to confirm his proposal to make <a href="http://www.smh.com.au/federal-politics/political-news/christopher-pyne-pushes-for-maths-or-science-to-be-compulsory-for-year-11-and-12-students-20150525-gh9kjv.html">science and maths compulsory for year 11 and 12</a> students. This is to be applauded by the scientific community as a step in the right direction, as it will produce a more scientifically literate society at a time of rapid technological change. </p>
<p>It will enable Australia to remain highly competitive in the areas of science and technology in an environment where rapid technological change and development is taking place in the East Asian nations, who are our competitors in the international high technology markets.</p>
<h2>Steady decline</h2>
<p>Australian policy makers and governments have to be worried since the picture that has emerged in the international comparisons of science, technology, engineering and mathematics (STEM) studies are not very flattering. The <a href="http://www.chiefscientist.gov.au/2014/12/benchmarking-australian-science-technology-engineering-mathematics/">Benchmarking Australian Science, Technology, Engineering and Mathematics</a> report, released by Chief Scientist Ian Chubb in November 2014, revealed a decline in the participation rates of Australian year 12 students in the major scientific disciplines: physics, chemistry and biology. </p>
<p>What is even more worrying is the <a href="http://amsi.org.au/publications/participation-year-12-mathematics-2004-2013/">decline in Advanced and Intermediate Mathematics</a>, which underpins university studies in the physical sciences, engineering and medicine. </p>
<p>Instead, students have embraced Entry Mathematics (a much lower level mathematics program) in droves. The percentage of year 12 students doing Entry Mathematics has <a href="http://eprints.qut.edu.au/73153/1/Continuing_decline_of_science_proof.pdf">jumped from 40% to 48%</a> in the period 1992 to 2012. </p>
<p>On the teaching side of the equation, only about 57% of the teachers in physics (years 11-12) and 67% in chemistry (years 11-12) have methodology training in these two subjects. The statistics for mathematics teachers (years 11-12) are much better. However, <a href="http://www.chiefscientist.gov.au/2014/12/benchmarking-australian-science-technology-engineering-mathematics/">only 76% of mathematics teachers</a> have methodology training in mathematics. These statistics do not augur well for the scientific estate.</p>
<h2>Teaching the teachers</h2>
<p>The issue facing Pyne at the moment is not the question of making mathematics compulsory for years 11 and 12 but ensuring that 100% of the teachers have the necessary qualifications and expertise in mathematics, physics and chemistry. </p>
<p>Unless the issue is solved we will be on a perpetual merry-go-round for the next ten years. Depending on the university, there is between 20 to 30% of HSC students enrolling in science and engineering programs without proper mathematics, physics and chemistry backgrounds. </p>
<p>This places a tremendous strain on university resources to get these students up to speed so that they can continue their studies and thus allow the universities to keep their retention rates high.</p>
<p>However, it is a job that can be done more cheaply in schools and thus save taxpayers’ money.</p>
<h2>Lasting legacy</h2>
<p>Another quite alarming statistic that emerges from the <a href="http://www.chiefscientist.gov.au/wp-content/uploads/BenchmarkingAustralianSTEM_Web_Nov2014.pdf">Chief Scientist’s report</a> is the low level of formal time that is spent on teaching science in primary schools across the country. In 2011 the average time spent on science was a paltry 5.7%. This is well below the OECD average of 7.4%. In fact, Finland spends over 10.5% of the time on science, while Japan spends over 8.4%.</p>
<p>If Pyne is serious about STEM, he should be having a closer look at what goes on in science teaching in primary schools and get the formal time spent on science up to at least 10%. Primary schools must lay the foundation for STEM studies. </p>
<p>He should place a greater emphasis on the training of primary school teachers in basic science so that they can inspire young boys and girls to engage in the exciting wonderland of science. There are already sufficient science teaching materials produced by the <a href="https://www.science.org.au/curriculum-resources">Australian Academy of Science</a>. </p>
<p><a href="https://www.primaryconnections.org.au/">Primary Connections</a> follows the scientific method that has been used very successfully in hands-on science centres in our competitor countries, such as the US, Korea and Singapore.</p>
<p>Pyne’s priorities should be that science and maths in schools work at a higher efficiency, thereby enhancing the teaching and learning of these subjects in both primary and HSC classes. </p>
<p>If he is successful, it will be his lasting legacy to the scientific estate in Australia and it will place Australia among the top nations in the teaching and learning of science and benefit long term economic growth.</p><img src="https://counter.theconversation.com/content/42542/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Ragbir Bhathal 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>Compulsory maths and science in years 11 and 12 will have a lasting benefit, but we need to boost the skills of teachers and start teaching science even earlier.Ragbir Bhathal, Lecturer in physics, Western Sydney UniversityLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/417082015-05-20T04:27:22Z2015-05-20T04:27:22ZAfter school learning makes kids masters of their own maths destiny<figure><img src="https://images.theconversation.com/files/81407/original/image-20150512-22586-1avx5jx.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Children struggle to develop the basic "building blocks" of maths if they're just copying down everything the teacher tells them without understanding it.</span> <span class="attribution"><span class="source">From www.shutterstock.com</span></span></figcaption></figure><p>When you walk into a maths class at a South African school, don’t be surprised if the pupils are chanting. Learners are often encouraged to learn by rote and memorise formulas, then recite these back to the teacher parrot-style.</p>
<p>Maths requires learners to actively construct and build new knowledge on existing foundations. This is known as a progressive subject. But in South Africa these building blocks and basic number sense are sorely lacking among younger children. By their fifth year at school, many children are almost two grades <a href="http://www.sciencedirect.com/science/article/pii/S0738059312001381">behind curriculum expectations</a>.</p>
<p>There have been a number of curriculum revisions and systemic interventions over the past two decades that have tried to tackle these problems. None have done the trick. Part of the problem is that the current school system doesn’t give children the agency they need to take charge of their own learning.</p>
<h2>The case for after-school learning</h2>
<p>The South African Numeracy Chair Project at Rhodes University has conducted research that suggests after-school maths clubs could be valuable spaces for changing children’s learning habits and attitudes.</p>
<p>Research has been conducted in the US about the role of <a href="http://www.rand.org/pubs/research_briefs/RB9819.html">“out of school time”</a> - particularly summer schools and after-school calculus clubs for high school students. There is a solid base of evidence to suggest that these non-classroom spaces can be <a href="http://eric.ed.gov/?id=ED505962">hugely beneficial</a>.</p>
<p>But even internationally there has been very little research into how after-school clubs or classes could benefit learners in the foundation phase of grades 1 to 3.</p>
<p>The local research goes some way to close this gap. It was conducted in Grahamstown, a small city in one of South Africa’s <a href="http://www.timeslive.co.za/local/2011/07/27/eastern-cape-poorest-province-study">poorest provinces</a>, the Eastern Cape.</p>
<p>After-school maths clubs were set up at schools whose pupils tend to perform poorly in the Annual National Assessments, which <a href="http://www.education.gov.za/LinkClick.aspx?fileticket=ajR9otls4HM%3d&tabid=569&mid=2131">test numeracy</a> at different grade levels. The schools are poorly resourced and don’t always have enough teachers. The pupils come from a poor community with high adult unemployment levels.</p>
<p>The clubs have created the space and time for learners to work at their own pace. This is very useful for children who learn faster or more slowly than the majority of their classmates.</p>
<p>The research team discovered that many children relish the opportunity to do their homework at these clubs because they are managing their own time instead of trying to keep up with teachers and classmates. In the the first Grade 3 (year four) club we established, each learner was given a 48-page homework book and encouraged to complete a page each day, from Monday to Friday.</p>
<p>This meant that they ought to come to the next session with five pages done, though it was also made clear that they needn’t stop at just five. Half of the learners returned the following week with all 48 pages completed. They wanted the next book in the series.</p>
<p>This experience was repeated in subsequent clubs and prompted the introduction of a very successful homework drive in the teacher development programme that forms part of the South African Numeracy Chair Project.</p>
<p>The teachers also found that those learners who took part in the after-school clubs were keen to explain how they had solved a particular problem. These pupils have become “helpers”, guiding their classmates through different methods of finding a solution.</p>
<p>Teachers use club learners experiences to start conversations in the classroom. They ask, “Explain how you got that answer?” or “Which method is more efficient and why do you say so?” - questions that lead to rich mathematical discussions. This engagement teaches other learners about active participation.</p>
<h2>Implications of the research</h2>
<p>It is important to consider the long-term and larger impact of producing learners who are passive, dependent on teachers to feed them answers and information, and are uncritical. These children will eventually go into the workforce and risk taking these qualities with them. More urgently, though, South Africa needs to tackle its <a href="http://www.iol.co.za/news/south-africa/probe-after-dismal-grade-9-maths-mark-1.1791175#.VVCIi_mqqko">dismal Mathematics results</a>.</p>
<p>The club model is easy to replicate. All of the material produced for the Grahamstown maths clubs can be downloaded for free from the South African Numeracy Chair Project <a href="http://www.ru.ac.za/sanc/">website</a>. The clubs can be held in a classroom, at somebody’s house or in a community centre.</p>
<p>The after-school maths clubs and homework drive have emerged as a way to strengthen agency by developing more active, independent and persevering learners. They have also <a href="http://www.ru.ac.za/media/rhodesuniversity/content/sanc/documents/Post%20examination%20edit%20DAS%20Thesis%2010OCT.pdf">bolstered</a> learners’ maths marks.</p><img src="https://counter.theconversation.com/content/41708/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Mellony Graven receives funding from the National Research Foundation, the First Rand Foundation, Anglo De Beers Chairman's Fund and the South African Department of Science and Technology</span></em></p>When rote learning and parroted answers replace real engagement with the material, children are bound to battle with maths. After-school homework clubs offer a different way of thinking.Mellony Graven, Full Professor (South African Numeracy Chair - Mathematics Education), Rhodes UniversityLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/404712015-04-30T20:48:09Z2015-04-30T20:48:09ZHere’s how to get kids to remember times tables<figure><img src="https://images.theconversation.com/files/79051/original/image-20150423-3136-uu2cl6.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">It's hard for kids to remember a string of arbitrary numbers</span> <span class="attribution"><span class="source">from www.shutterstock.com.au</span></span></figcaption></figure><p>Lots of kids have trouble remembering their times tables. Learning them by rote can mean a child can accurately recite the times tables, but has no idea what the numbers actually mean or how to apply this knowledge in a maths problem. </p>
<p>Practice is essential to effective learning, but it is important to keep a balance between practice and application.</p>
<h2>Children need to know why they need to learn times tables</h2>
<p>The number system underlying the times tables can often seem fairly arbitrary. A child can be forgiven for thinking it’s just a complex system of numbers that they have to learn because the teacher says so. </p>
<p>If you have no idea why you are required to learn something, it is very difficult to develop sufficient motivation to persist with the practice that is often necessary to master the material.</p>
<p>One way to demonstrate the usefulness of the times tables is to engage a child in a counting task. The task could be timed, such that determining the number of elements quickly will mean something for the ultimate result (for example, beating a time limit results in a positive outcome, failing to beat the limit means the task starts again). </p>
<p>The multiplication facts in the times tables can then be demonstrated as short cuts in the counting process (if you can arrange the elements into four groups of eight, then knowing the answer to “4 x 8 = ?” will result in faster performance than having to rely on counting all of the 32 elements). </p>
<p>Many computer games and apps (like <a href="http://www.ixl.com/">IXL Maths</a>) possess this feature. They also involve many other features designed to maintain the interest of a child, which can help keep them motivated enough to persist with the task. Ultimately, the more practice, the better the knowledge.</p>
<h2>Get to know the sums individually, not as a song lyric</h2>
<p>Memory can often be a good reflection of what we do. If we regularly sing along to a favourite song, each line tends to remind us of the next line. However, if we then try to sing the song by ourselves, without the aid of an accompanying recording, we often find that forgetting one line means subsequent lines also can’t be recalled. </p>
<p>A similar thing can happen if we engage in rote recitation of the times tables. This method is only useful if we want to have a method to fall back upon when all other methods fail. Basically this method can only produce the equivalent of a song lyric where, remembering what “4 8s” are is only possible if you can remember “4 6s are 24” and “4 7s are 28”.</p>
<p>A better form of knowledge is one where a child knows the answer to each multiplication problem as soon as they see it, much like being able to read a word as soon as you see it. </p>
<p>Knowing the answer to each problem is then independent of knowing the answer to other times table problems. This type of knowledge can be gained only by practice at producing the answer. </p>
<p>One method for undertaking this type of practice is something like the old flash-card method. Write a problem on one side of a card (4 x 8 = ?), and the answer on the other side. With a shuffled deck of cards representing all of the problems in the times tables, a child can practise producing the answer to each problem, and then check their response by turning over the card. </p>
<p>Occasionally an adult can ask the child to do this out loud to ensure they are doing the task correctly. Initially the child may have to guess the correct answer, or work it out with their fingers or some other method. But they always have the benefit of immediate feedback by turning over the card. </p>
<p>Eventually, with enough practice, the constant association of the problem with the correct answer will begin to stick in their memory. A similar method can be easily programmed on to a computer or tablet. Plenty of <a href="http://www.bigbrainz.com">commercial apps</a> are available that will mimic this procedure.</p>
<h2>Apply the times tables knowledge</h2>
<p>Knowledge of the times tables is not useful by itself. A child must learn to apply the knowledge in a mathematical context. </p>
<p>It is important, though, that a child’s knowledge of the times tables is not allowed to remain as a list of independent facts. A child needs to engage in activities that demonstrate the connections between the multiplication facts in the times tables. It is important to see how 4 x 8 and 8 x 4 are connected. </p>
<p>Ultimately they will also need to see how 4 x 8 = ? and 32 ÷ 8 = ? are connected. To achieve this the child should be provided with activities that require the application of their arithmetic knowledge in a way that can demonstrate and lead the child to uncover these connections. </p>
<p>Practice with this sort of material can help kids develop a knowledge base that results in reliable retrieval of facts and the sort of flexible application of this knowledge that is required in higher-order problems, such as solving for x in 2x + 3 = 11. If you struggle to come up with an answer to this problem, I would not suggest relying on a times tables song to help you out.</p><img src="https://counter.theconversation.com/content/40471/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Craig Speelman receives funding from the Australian Research Council, Edith Cowan University, the WA Department of Education, the Association of Independent Schools WA, and the Collier Charitable Fund.</span></em></p>Lots of kids have trouble remembering their times tables. Learning them by rote can mean a child knows the numbers but not what they mean.Craig Speelman, Professor of Psychology, Edith Cowan UniversityLicensed as Creative Commons – attribution, no derivatives.