tag:theconversation.com,2011:/us/topics/maths-ability-19319/articlesMaths ability – The Conversation2020-12-08T09:02:34Ztag:theconversation.com,2011:article/1502752020-12-08T09:02:34Z2020-12-08T09:02:34ZAustralia lifts to be among top ten countries in maths and science<figure><img src="https://images.theconversation.com/files/373484/original/file-20201208-19-t5es3d.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">
</span> <span class="attribution"><a class="source" href="https://www.shutterstock.com/image-photo/genius-girl-red-glasses-near-blackboard-178739876">Shutterstock</a></span></figcaption></figure><p>Results from the longest running large-scale international assessment of maths and science show <a href="https://research.acer.edu.au/timss_2019/1/">Australia has significantly improved</a> in Year 8 maths and science, and Year 4 science.</p>
<p>More than 580,000 students from 64 countries participated in the latest Trends in International Mathematics and Science Study (<a href="https://timssandpirls.bc.edu/timss2019/index.html">TIMSS</a>). This includes 14,950 Australian students from 571 Australian schools. </p>
<p><strong>In Year 8 maths</strong>, Australia came in equal seventh place in the 2019 assessment cycle (up from equal 13th in 2015), along with a number of countries including Ireland, the United States and England. We came behind Chinese Taipei (Taiwan), Korea, Japan, Hong Kong and Ireland. </p>
<p><strong>In Year 8 science</strong>, Australia also came in equal seventh (up from equal 15th in 2015) along with countries such as Lithuania, Ireland and the US. We were behind Singapore, Chinese Taipei, Japan, Korea, Russia and Finland. </p>
<p><strong>In Year 4 science</strong>, Australia came equal ninth (up from equal 18th in 2015) along with countries including the US, England, Hong Kong and Ireland. Australia was behind Singapore, Korea, Russia, Japan, Chinese Taipei, Finland, Latvia and Norway.</p>
<p><strong>In Year 4 maths</strong>, however, achievement has not changed since 2007. Australia was outperformed by 22 countries in 2019, similar to 2015. It came equal 23rd along with countries such as Germany, Poland and Canada; and behind Singapore, the US, England and Ireland.</p>
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<h2>Not just the rankings</h2>
<p>This is the seventh time the TIMSS test has been administered. Along with completing tests in maths and science, Year 4 and 8 students involved in TIMSS answer questionnaires on their background and experiences in learning maths and science at school.</p>
<p>Participating in TIMSS allows Australia to measure its progress towards national educational goals, which in 2019 included the Melbourne Declaration on Educational Goals for Young Australians (now the Mparntwe Education Declaration). </p>
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Read more:
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<p>In Year 4 maths, Australian students achieved an average score of 516 points. Singapore’s students scored the highest with 625 points, while England achieved 556, Canada 512 and New Zealand 487 points.</p>
<p>Australia’s average score in Year 8 maths was 517 points. This was compared to the highest score of 616 points for Singapore. Australia’s score was not significantly different to that of the US and England, which both achieved 515 points.</p>
<p>Australia not only improved in Year 8 maths and science, and Year 4 science relative to other countries, but also in an absolute sense. Compared to 2015, Australia’s mean score increased by 12 points in Year 8 maths; 16 points in Year 8 science and nine points in Year 4 science. </p>
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<p>The TIMSS intermediate international benchmark is the nationally agreed proficient standard for maths and science achievement, which is 475 score points. In 2019 between 68% and 78% of Australian students achieved the required proficiency benchmark in maths and science at both year levels. In Singapore, more than 90% of students achieved this benchmark in both subject areas at both year levels. </p>
<p>Since 2015, the proportion of Australian students achieving this standard improved by five percentage points in Year 8 science. It did not change significantly in Year 4 maths and science, or Year 8 maths.</p>
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Read more:
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<p>TIMSS results also provide a measure of Australia’s progress towards the United Nations 2030 Sustainable Development Goal for universal quality education. The TIMSS low international benchmark is an agreed global indicator of minimum proficiency in maths at the end of lower secondary schooling. </p>
<p>In the 2019 study, 90% of Australian Year 8 students achieved this benchmark, which was similar to 2015 and slightly higher than the 2019 international median of 87%. Meanwhile, 98% of students in Singapore and Chinese Taipei, and 99% of students in Japan achieved minimum proficiency in Year 8 maths.</p>
<h2>Differences between groups</h2>
<p>While of course these findings are positive, there are cautions evident when making comparisons among demographic groups.</p>
<p>There was no significant difference between the average performance of Australian girls and boys in Year 8 maths, Year 4 science or Year 8 science. </p>
<p>But boys outperformed girls in Year 4 maths in 27 of the 58 participating countries, including Australia. </p>
<p>The proportion of students who attained the national proficient standard was about the same for boys and girls (69% for girls, 70% for boys). But the proportion of boys who achieved the advanced benchmark (12%) was significantly higher than the proportion of girls (8%) who achieved at this level.</p>
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<p>While the achievement of First Nations Australian students and other Australian students has converged slightly in Year 4 and Year 8 science since 1995, the gaps are glaringly wide in both subject areas, but particularly in maths. </p>
<p>At Year 4 level in maths, 42% of First Nations students achieved the national proficient standard, compared to 72% of other Australian students. And 25% of First Nations students did not achieve the low benchmark, compared to 8% of other Australian students. </p>
<p>In Year 8 maths, 39% of First Nations students compared to 70% of other Australian students achieved the National Proficient standard, while 29% of First Nations students compared to 8% of other Australian students did not achieve the Low benchmark.</p>
<h2>Student socioeconomic background</h2>
<p>The largest gaps in achievement at school are often those defined by a students’ socioeconomic background. In TIMSS, several measures are used to define socioeconomic background, but the common method for Year 4 and Year 8 is simple but effective. Students are asked to estimate the number of books in their home within five categories. These are then collapsed into three:</p>
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<li><p>0-10: few books</p></li>
<li><p>11-200: average number of books</p></li>
<li><p>more than 200: many books. </p></li>
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<p><a href="https://kathyhirshpasek.com/wp-content/uploads/sites/9/2018/04/Pace-et-al.-2017.pdf">Analysis</a> has shown living in a home with many books influences academic achievement (or by implication, having a home environment that values literacy, the acquisition of knowledge and general academic support) in a positive manner.</p>
<p>In Year 4, 17% of students identified as living in a home with many books, and 28% with few books. In Year 8, 20% of students said their home had many books and 31% few books.</p>
<p>The differences between students with many books and those with few books is large at both year levels and for both subject areas. For example:</p>
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<li><p>in Year 8 maths, 83% of students living in a home with many books achieved the national proficient standard, compared to 48% of those from homes with few books </p></li>
<li><p>in Year 8 science, 90% of students from homes with many books achieved the standard, compared to 52% of those from homes with few books</p></li>
<li><p>in Year 8 maths and science, around 3% of students from homes with many books compared to around 20% of students from homes with few books did not achieve the low benchmark.</p></li>
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<p>Acknowledging the primary underlying factor behind poor achievement is socioeconomic background, and finding ways of redressing the imbalance in opportunities and resources available to these students, will help lift achievement for all Australian students.</p>
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Read more:
<a href="https://theconversation.com/one-quarter-of-australian-11-12-year-olds-dont-have-the-literacy-and-numeracy-skills-they-need-148912">One quarter of Australian 11-12 year olds don't have the literacy and numeracy skills they need</a>
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<p class="fine-print"><em><span>Sue Thomson does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.</span></em></p>Results from the world’s longest running large-scale international assessment of maths and science show Australia has significantly improved in Year 8 maths and science, and Year 4 science.Sue Thomson, Deputy CEO (Research), Australian Council for Educational ResearchLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/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/1178162019-06-04T23:07:19Z2019-06-04T23:07:19ZWe taught bees a simple number language – and they got it<figure><img src="https://images.theconversation.com/files/277567/original/file-20190603-69075-14sttar.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Maybe the differences between human and non-human animals are not as great as we might previously have thought.</span> <span class="attribution"><a class="source" href="https://www.shutterstock.com/image-photo/honey-bees-kept-bee-box-hive-1099240676?src=22bjom8C9tiWb2AEKphJYA-1-6">from www.shutterstock.com</a></span></figcaption></figure><p>Most children learn that written numbers represent quantities in pre-school or junior primary school. </p>
<p>Now our <a href="https://royalsocietypublishing.org/doi/10.1098/rspb.2019.0238">new study</a> shows that honeybees too can learn to match symbols and numerosities, much like we humans do with Arabic and Roman numerals.</p>
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<span class="caption">Honeybees have learnt to associate signs with numerosities.</span>
<span class="attribution"><span class="source">Scarlett Howard</span>, <span class="license">Author provided</span></span>
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Read more:
<a href="https://theconversation.com/can-bees-do-maths-yes-new-research-shows-they-can-add-and-subtract-108074">Can bees do maths? Yes – new research shows they can add and subtract</a>
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<h2>Human language and mathematics</h2>
<p>Language is the ability to learn and use a system of symbolic representations for communication. This includes a capacity to relate signs to abstract information. </p>
<p>For example, letters grouped together make a word which we can read, and sounded words put together in the correct order allow us to have a conversation. Human language can incorporate spoken, written, visually <a href="https://theconversation.com/explainer-what-is-sign-language-21453">signed</a>, or tactile forms like <a href="https://theconversation.com/good-vibrations-bring-braille-into-the-21st-century-27002">braile</a>.</p>
<p>Around the world humans have developed many different spoken and written languages. However, mathematics in particular is often regarded as a “<a href="https://www.learner.org/interactives/dailymath/language.html">universal language</a>” since the mathematical concepts that describe values and equations do not depend on cultural or other frameworks. </p>
<p>We are interested in the question of whether numerical symbols are truly universal – that is, whether they also work for species that are not human. </p>
<h2>The language of honeybees</h2>
<p>The <a href="https://australianmuseum.net.au/learn/animals/insects/honey-bee/">honeybee</a> is a super organism for the study of comparative information processing in a brain. In 1973 <a href="https://www.nobelprize.org/prizes/medicine/1973/frisch/facts/">Karl von Frisch</a> was awarded a Nobel Prize in the field of Physiology and Medicine for his demonstrations that the honeybee can communicate with hive mates via a symbolic dance language.</p>
<p>von Frisch showed that a foraging bee which locates rewarding flowers can fly back to a hive and signal both the direction and distance of the nutritious flowers via a “<a href="https://animalwise.org/2011/08/25/the-honeybee-waggle-dance-%E2%80%93-is-it-a-language/">waggle dance</a>”. Other bees can interpret the dance language to know where to fly to collect nectar.</p>
<p>We wondered if such an impressive communication system meant that honeybees could learn another type of symbolic language, a basic symbolic number system. </p>
<p>Interestingly, <a href="https://link.springer.com/content/pdf/10.1007/s100710100086.pdf">chimpanzees</a>, <a href="https://pdfs.semanticscholar.org/299d/f17abb1f87c4675f9105e3652abd35a0be17.pdf">Rhesus monkeys</a>, <a href="https://link.springer.com/content/pdf/10.1007/s100710050048.pdf">pigeons</a>, and a single African grey parrot named <a href="https://www.sciencedirect.com/science/article/pii/S0010027712001394">Alex</a> have demonstrated the skill to learn either Arabic numerals or English names for numbers. This shows us that while no non-human species appear to have developed a symbolic representation of number, it is not because they lack the brain capacity to understand such representations.</p>
<p>Our work has already shown honeybees can learn and apply challenging numerical concepts such as greater vs. lesser items, a quantitative valuation of “<a href="https://theconversation.com/bees-join-an-elite-group-of-species-that-understands-the-concept-of-zero-as-a-number-97316">zero</a>”, and <a href="https://theconversation.com/can-bees-do-maths-yes-new-research-shows-they-can-add-and-subtract-108074">simple arithmetic</a>. </p>
<p>We took this knowledge a step further with our latest research. </p>
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Read more:
<a href="https://theconversation.com/bees-join-an-elite-group-of-species-that-understands-the-concept-of-zero-as-a-number-97316">Bees join an elite group of species that understands the concept of zero as a number</a>
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<h2>How do bees learn?</h2>
<p>To train honeybees to match symbols (called “signs”) and number amounts (called “numerosities”), we used a subset of the symbols previously used to train pigeons on a similar task. </p>
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<span class="caption">The signs and numerosities used in the study.</span>
<span class="attribution"><span class="source">Scarlett Howard</span>, <span class="license">Author provided</span></span>
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<p>Bees were trained to fly into a Y-shaped maze. Inside the maze the bee would view a stimulus. The bee would then fly into the decision chamber were it would view two options, one correct and one incorrect. </p>
<p>One group of bees was trained to match a sign to a numerosity, while a second group was trained to match a numerosity to a sign. </p>
<p>If bees were learning to match a sign to a numerosity, they would first see the sign and then have the option to choose two or three shapes. If bees were learning to match a numerosity to a sign, they would first see a number of items, such as three squares, and then have the option to choose from two signs.</p>
<p>For example, if a bee viewed an N-shaped sign, she would need to choose a display presenting two items. She would need to be able to do this regardless of the shape, pattern, or colour of the items presented. </p>
<p>If the bee chose correctly she would receive a sugar solution, but if she chose incorrectly, she would taste bitter quinine (which does not hurt the bee but is not pleasant for her). Importantly, neither the quinine nor the sugar can be smelled by the bee, so the only cue for decision making is the visual one.</p>
<h2>Matching symbol to number</h2>
<p>Bees were trained for 50 trials to match an N-shape sign with the number “two”, and an inverted T-shape sign with the number “three”, and achieved an accuracy of about 75%. This is the first time symbol matching to number has been shown in an invertebrate.</p>
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<a href="https://images.theconversation.com/files/276612/original/file-20190527-193522-dg4u0j.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/276612/original/file-20190527-193522-dg4u0j.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/276612/original/file-20190527-193522-dg4u0j.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=566&fit=crop&dpr=1 600w, https://images.theconversation.com/files/276612/original/file-20190527-193522-dg4u0j.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=566&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/276612/original/file-20190527-193522-dg4u0j.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=566&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/276612/original/file-20190527-193522-dg4u0j.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=712&fit=crop&dpr=1 754w, https://images.theconversation.com/files/276612/original/file-20190527-193522-dg4u0j.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=712&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/276612/original/file-20190527-193522-dg4u0j.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=712&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 Y-maze apparatus and examples of stimuli used. Bees were trained to either match a sign with a numerosity or a numerosity with a sign.</span>
<span class="attribution"><span class="source">Scarlett Howard</span>, <span class="license">Author provided</span></span>
</figcaption>
</figure>
<p>After training was completed bees were tested in several conditions with completely novel patterns, colours and shapes and continued to prefer to match the sign with the numerosity, or the numerosity with the sign. </p>
<p>Interestingly, however, we found bees were unable to reverse their learnt tasks. If a bee had learnt to match a sign to a numerosity, she could not then match a numerosity to a sign, or vice versa. It appears the association between the number and the symbolic representation was only learnt in one direction and was unable to be reversed. </p>
<p>Interestingly, these kinds of learning outcomes – referred to as “<a href="https://www.simplypsychology.org/piaget.html#schema">operational schemas</a>” – are sometimes applicable to how humans learn too. </p>
<h2>What does this mean?</h2>
<p>While no other species besides humans has spontaneously developed a language for numbers, our research suggests an insect can understand and learn basic representation of numbers through symbols.</p>
<p>The system we taught to bees was limited in several ways. For example, we trained bees to link just two quantities and two symbols. Also we do not yet know if bees gave quantitative value to the symbols; we simply know that they can link the symbol and quantity together.</p>
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Read more:
<a href="https://theconversation.com/our-bee-eye-camera-helps-us-support-bees-grow-food-and-protect-the-environment-110022">Our 'bee-eye camera' helps us support bees, grow food and protect the environment</a>
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<p>And yet it is remarkable bees displayed some capacity to understand numbers through symbols. </p>
<p>We’re left wondering whether we as humans are so very special after all – that perhaps the ability to learn mathematics could be universal. </p>
<p>Despite the limitations of the current research, we have demonstrated, to a small extent, symbolic communication with an insect species, which we have been separated from by over 600 million years of evolution. </p>
<p>Our research is laying the foundations for developing a communication system with very different animal species, and shows the differences between human and non-human animals are not as great in some regards as we might previously have thought.</p><img src="https://counter.theconversation.com/content/117816/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Scarlett Howard received funding from the Australian Government Research Training Program (RTP) Scholarship and is currently funded by the Fyssen Foundation.</span></em></p><p class="fine-print"><em><span>Adrian Dyer receives funding from the Australian Research Council, and is an Academic Editor for the journal PLoS One.</span></em></p><p class="fine-print"><em><span>Andrew Greentree receives funding from the Australian Research Council, and is an Academic Editor for the journal Scientific Reports. </span></em></p>We’re left wondering whether we as humans are so very special after all – that perhaps the ability to learn mathematics could be universal.Scarlett Howard, Postdoctoral research fellow, Université de Toulouse III – Paul SabatierAdrian Dyer, Associate Professor, RMIT UniversityAndrew Greentree, Professor of Quantum Physics and Australian Research Council Future Fellow, RMIT UniversityLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1156462019-05-16T10:31:15Z2019-05-16T10:31:15ZHow to overcome a fear of maths<figure><img src="https://images.theconversation.com/files/274417/original/file-20190514-60529-ktb5t3.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">
</span> <span class="attribution"><span class="source">shutterstock</span></span></figcaption></figure><p>It’s fair to say maths is not everyone’s favourite subject. In fact, for many people, the feelings of tension and anxiety that arise when trying to solve a mathematical problem can be all consuming. This is known as maths anxiety – and this feeling of being a failure at maths can affect people’s <a href="https://www.theguardian.com/commentisfree/2019/mar/14/panic-maths-anxiety-studying-pupils-schools">self-worth for years to come</a>.</p>
<p>For those who suffer with maths anxiety, it can be difficult to shift from a mindset of failure to a more positive outlook when it comes to dealing with numbers. This is why, for many people, maths anxiety can become a lifelong issue.</p>
<p>But <a href="https://www.amazon.co.uk/Elephant-Classroom-Helping-Children-Learn/dp/0285643185/ref=tmm_pap_swatch_0_encoding=UTF8&qid=1557478920&sr=8-1-fkmrnull">research</a> shows that if teachers tackle maths anxiety in the classroom and encourage children to try to approach a problem in a different way – by shifting their mindset – this can be an empowering experience. This is especially the case for pupils from a disadvantaged background. </p>
<h2>Mindset theory</h2>
<p>US psychology professor, Carol Dweck, came up with the idea of “<a href="https://www.ted.com/talks/carol_dweck_the_power_of_believing_that_you_can_improve/discussion">mindset theory</a>”. Dweck realised that people can often be categorised into two groups, those who believe they are bad at something and cannot change, and those who believe their abilities can grow and improve. </p>
<p>This formed the basis of her mindset theory, which states that some people have a “fixed mindset”, meaning they believe their ability to be set in stone and unable to be improved. Other people have a “growth mindset” meaning they believe their ability can change and improve over time with effort and practice. </p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/274418/original/file-20190514-60554-phm6ki.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/274418/original/file-20190514-60554-phm6ki.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/274418/original/file-20190514-60554-phm6ki.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/274418/original/file-20190514-60554-phm6ki.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/274418/original/file-20190514-60554-phm6ki.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/274418/original/file-20190514-60554-phm6ki.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/274418/original/file-20190514-60554-phm6ki.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=503&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
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<span class="caption">Maths can be fun – if only it’s taught properly.</span>
<span class="attribution"><span class="source">Shutterstock</span></span>
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</figure>
<p>Jo Boaler, the British education author and professor of mathematics education, applied mindset theory to mathematics, subsequently naming her recommendations “mathematical mindsets”. </p>
<p>She has used this theory to encourage learners to develop a growth mindset <a href="https://www.youcubed.org/mathematical-mindset-teaching-guide-teaching-video-and-additional-resources">in the context of mathematics</a>. The idea is that the problems themselves can help to promote a growth mindset in pupils – without them <a href="https://www.amazon.co.uk/tale-Lucy-wanted-learn-spell/dp/1533445001">having to think about their mindset</a> intentionally. </p>
<h2>New ways of thinking</h2>
<p>But while this all sounds well and good, one of the issues with mindset theory is that it is often presented in terms of <a href="https://theconversation.com/what-is-brain-plasticity-and-why-is-it-so-important-55967">brain plasticity</a> or the <a href="https://www.conted.ox.ac.uk/about/brain-resources">brain’s ability to grow</a>. This has lead to <a href="http://www.danielwillingham.com/daniel-willingham-science-and-education-blog/march-13th-2019">complaints</a> about a shortage of neurological evidence supporting mindset theory. <a href="https://authors.elsevier.com/c/1YsHs7sy6LOEAw">Our latest research</a> aimed to address this lack of neurological research. </p>
<p>Generally speaking, for every problem in mathematics there is more than one way to solve it. If someone asks you what three multiplied by four is, you can calculate the answer either as 4+4+4 or as 3+3+3+3, depending on your preference. But if you have not developed sufficient mathematical maturity or have maths anxiety, it can prevent you from <a href="https://www.researchgate.net/publication/326424642_Non-adaptive_strategy_selection_in_adults_with_high_mathematical_anxiety">seeing multiple ways of solving problems</a>. But <a href="https://authors.elsevier.com/c/1YsHs7sy6LOEAw">our new study</a> shows that a “growth mindset” can make maths anxiety a thing of the past.</p>
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Read more:
<a href="https://theconversation.com/maths-six-ways-to-help-your-child-love-it-96441">Maths: six ways to help your child love it</a>
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<p>We measured participants’ motivation to solve mathematical problems by asking about motivation both before and after each problem was presented. We also measured participants’ brain activity, specifically looking at areas associated with motivation, while they solved each problem. This was done using an electroencephalogram (EEG) which records patterns of activation across the brain.</p>
<p>In our research, we phrased questions in different ways to assess how question structure may affect both our participants’ ability to answer the questions and their motivation while tackling maths problems.</p>
<p>Each question appeared in two formats: one of typical mathematical teaching and another adhering to the recommendations of mathematical mindset theory. Both questions asked essentially the same question and had the same answer, like in the following simplified example:</p>
<p>“Find the number which is the sum of 20,000 and 30,000 divided by two” (a typical mathematical problem) and “Find the midpoint number between 20,000 and 30,000” (an example of a mathematical mindset problem). </p>
<h2>Growth mindsets</h2>
<p>Our study provides two important findings.</p>
<p>The first is that participants’ motivation was greater when solving mathematical mindset versions of problems compared to the standard versions – as measured by their brain response when solving the problems. It is assumed this is because the mathematical mindset wording encourages students to treat numbers as points in the space and manipulate spatial constructions.</p>
<p>The second is that participants’ subjective reports of motivation were significantly decreased after attempting the more standard maths questions. </p>
<p>Our research is immediately actionable in that it shows how opening up problems so that there are multiple methods to solving them, or adding a visual component, allows learning to become an empowering experience for all students.</p>
<p>So for people with maths anxiety, you will be relieved to know that you are not innately “bad” at maths and your ability is not fixed. It is actually just a bad habit you have developed due to bad teaching. And the good news is, it can be reverted.</p><img src="https://counter.theconversation.com/content/115646/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>The authors do not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and have disclosed no relevant affiliations beyond their academic appointment.</span></em></p>Maths anxiety can be made a thing of the past, as new research shows.Alexei Vernitski, Senior Lecturer in Mathematics, University of EssexIan Daly, Lecturer in Brain-Computer Interfaces, University of EssexJake Bourgaize, PhD Candidate, University of EssexLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1101072019-01-28T14:50:26Z2019-01-28T14:50:26ZMaths: should English schools look to Switzerland rather than Shanghai for inspiration?<figure><img src="https://images.theconversation.com/files/254992/original/file-20190122-100295-1yfl9lx.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">Pexels</span></span></figcaption></figure><p>When it comes to education, how countries rank against each other in league tables has become a big influence on education policy. And one of the biggest rankings is <a href="https://theconversation.com/pisa-results-four-reasons-why-east-asia-continues-to-top-the-leaderboard-69951">the Programme for International Student Assessment</a> – also known as PISA. This is a regular comparison of the performance of 15-year-olds in different countries, including in maths. </p>
<p>Increasingly politicians want to see their countries rise up the league tables, which has led to attempts to import ways of teaching from overseas. In England, many schools have adopted East Asian methods in maths teaching to try <a href="https://theconversation.com/maths-challenge-england-has-one-of-the-biggest-gaps-between-high-and-low-performing-pupils-in-the-developed-world-88678">to climb the league tables</a>. This has come be to be called the “<a href="https://theconversation.com/explainer-what-is-the-mastery-model-of-teaching-maths-25636">mastery maths</a>” model.</p>
<p><a href="https://schoolsweek.co.uk/what-is-south-asian-mastery-maths/">Singapore and Shanghai</a> both do very well in international PISA tests compared to England, but the way both places approach mastery is slightly different. The mastery method adopted in English schools has mostly been modelled on the Shanghai system – and has involved teachers from England going to Shanghai and having Shanghai teachers go to England.</p>
<p>We have spent the past four years researching whether the Shanghai exchange would lead to changes in teaching in England and whether this <a href="https://www.gov.uk/government/publications/evaluation-of-the-maths-teacher-exchange-china-and-england">would lead to better test scores</a>. We found that in many of the schools that were involved in the first exchange in 2014-2015 there have been a lot of changes – and many adopted Shanghai-style maths teaching. These changes have involved slowing down the curriculum, using more learning by heart, more interaction between teacher and pupils, and using different ways of representing maths ideas. Schools have also adopted ways to give all children access to challenging maths.</p>
<p>But when we compared the test scores to similar schools who have not adopted the mastery method, we found there had been no change in the test results of 11-year-olds. For seven-year-olds we found a small change but nothing that would suggest a massive improvement in scores from the new mastery method.</p>
<h2>Importing education</h2>
<p>Perhaps this isn’t surprising though, because teaching methods are not the <a href="https://theconversation.com/pisa-results-four-reasons-why-east-asia-continues-to-top-the-leaderboard-69951">only reason for East Asian success</a>. And in some ways, Shanghai maths hasn’t yet had a fair test in England. UK teachers have been expected to adopt Shanghai approaches, but have not had the same amount of time for professional development or to plan lessons.</p>
<p>There’s also the fact that in Shanghai primary schools, children are generally taught by the same teacher for two to three years – so the teacher gets to know the pupils very well. Policies in China that have led to many parents only having one child also mean that young children get a lot of adult attention from parents and grandparents – which could also help their development.</p>
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Read more:
<a href="https://theconversation.com/maths-challenge-england-has-one-of-the-biggest-gaps-between-high-and-low-performing-pupils-in-the-developed-world-88678">Maths challenge: England has one of the biggest gaps between high and low performing pupils in the developed world</a>
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<p>Although Shanghai maths imported to England has not had the effect on results that was hoped for, it does not meant that with more time it cannot lead to improvements. And there are particular ideas in the Shanghai maths approach – such as high quality mathematical talk and <a href="https://www.cambridgemaths.org/espresso/view/mastery-in-mathematics/">careful choice of how to represent maths ideas</a> – that do have <a href="https://www.mdpi.com/2227-7102/8/4/202">evidence for success in England as well as other countries</a>.</p>
<h2>Further afield</h2>
<p>If East Asian methods do not import easily because of other factors, then perhaps politicians should broaden where they look for ideas in maths. Switzerland, for example, was the top <a href="https://www.oecd.org/pisa/pisa-2015-results-in-focus.pdf">European performer in maths in PISA in 2015</a> – not far behind East Asian countries. </p>
<p>Canada also did significantly better than England. Though recently, Canadians have also started <a href="https://theconversation.com/why-canada-fails-to-be-an-education-superpower-82558">worrying about how their performance</a>.</p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/254994/original/file-20190122-100270-1lo642k.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/254994/original/file-20190122-100270-1lo642k.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/254994/original/file-20190122-100270-1lo642k.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/254994/original/file-20190122-100270-1lo642k.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/254994/original/file-20190122-100270-1lo642k.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/254994/original/file-20190122-100270-1lo642k.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/254994/original/file-20190122-100270-1lo642k.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">Children as young as two are grouped by ability in English nurseries.</span>
<span class="attribution"><span class="source">Shutterstock</span></span>
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<p>There’s also more that can be learnt from PISA and other international tests. It seems, for example, that all high-performing education systems have some common features. These include: supporting teachers with good pay, conditions and status. Teachers that are given the freedom to decide what and how to teach with support from researchers but without political interference, also seems to be another contributing factor. As does having an emphasis on good outcomes for everyone – not just the highest performing children – most high performing countries do not group children by ability from a young age, as often happens in England.</p>
<p>In any case, different tests tell different stories. Another international test – <a href="https://nces.ed.gov/timss/">Trends in Maths and Science study</a> – shows England’s results in maths have been <a href="https://dera.ioe.ac.uk/28040/1/TIMSS_2015_England_Report_FINAL_for_govuk_-_reformatted.pdf">steadily improving for the past 20 years</a>. Perhaps then, the most important lesson from England’s mastery experiment is to stop worrying so much about <a href="https://theconversation.com/international-pisa-tests-show-how-evidence-based-policy-can-go-wrong-77847">international league table positions</a> – and for schools to focus on encouraging all pupils to be the best they can be.</p>
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<p>
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Read more:
<a href="https://theconversation.com/why-global-education-rankings-dont-reveal-the-whole-picture-72134">Why global education rankings don't reveal the whole picture</a>
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<img src="https://counter.theconversation.com/content/110107/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Mark Boylan receives funding from Department for Education, England and the Education Endowment Foundation for research in areas related to this article.</span></em></p>The Shanghai maths method is considered to be one the best in the world for teaching students mathematics, but it doesn’t necessarily translate well into English schools.Mark Boylan, Professor of Education, Sheffield Hallam UniversityLicensed 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/928582018-03-15T11:20:15Z2018-03-15T11:20:15ZHigh number of adults unable to do basic mathematical tasks<figure><img src="https://images.theconversation.com/files/210274/original/file-20180314-113469-1dxoeka.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">'I don't even know how much this is going to cost.'</span> <span class="attribution"><a class="source" href="https://www.shutterstock.com/download/success?src=_8uSGJoRNieQEMUSqROWJA-1-36">shutterstock</a></span></figcaption></figure><p>Suppose, a litre of cola costs US$3.15. If you buy one third of a litre of cola, how much would you pay?</p>
<p>The above may seem like a rather basic question. Something that you would perhaps expect the vast majority of adults to be able to answer? Particularly if they are allowed to use a calculator. </p>
<p>Unfortunately, the reality is that a large number of adults across the world struggle with even such basic financial tasks (the correct answer is US$1.05, by the way).</p>
<p>Using Organisation for Economic Cooperation and Development (OECD) Programme for International Assessment of Adult Competencies (PIAAC) <a href="http://www.google.co.uk/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0ahUKEwjQqYO009fZAhXLDMAKHRKQBF8QFggnMAA&url=http%3A%2F%2Fwww.oecd.org%2Fskills%2Fpiaac%2F&usg=AOvVaw0doGOG0MDqeIWDq46xfSIa">data</a>, my co-authors and I have looked at how adults from 31 countries answer four <a href="https://johnjerrim.com/piaac/">relatively simple financial questions</a>. </p>
<figure class="align-right zoomable">
<a href="https://images.theconversation.com/files/209099/original/file-20180306-146661-16wex9g.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/209099/original/file-20180306-146661-16wex9g.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/209099/original/file-20180306-146661-16wex9g.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=964&fit=crop&dpr=1 600w, https://images.theconversation.com/files/209099/original/file-20180306-146661-16wex9g.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=964&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/209099/original/file-20180306-146661-16wex9g.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=964&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/209099/original/file-20180306-146661-16wex9g.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=1211&fit=crop&dpr=1 754w, https://images.theconversation.com/files/209099/original/file-20180306-146661-16wex9g.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=1211&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/209099/original/file-20180306-146661-16wex9g.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=1211&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">The estimated proportion of adults who could answer the question correctly.</span>
<span class="attribution"><span class="license">Author provided</span></span>
</figcaption>
</figure>
<p>As well as the question above, participants were asked questions such as: “Suppose, upon your trip to the grocery store you purchase four types of tea packs: Chamomile Tea (US$4.60), Green Tea (US$4.15), Black Tea (US$3.35) and Lemon Tea (US$1.80). If you paid for all these items with a US$20 bill, how much change would you get?”</p>
<p>The results (as seen in the table) allowed us to create an estimated range for the percentage of the adult population who would be able to answer the cola question correctly. These results are based upon a random sample of adults from each country.</p>
<p>We found that Lithuania, Austria and Slovakia were the most successful, but even in these countries, one in four adults failed to give the correct answer. </p>
<p>In many other countries, the situation is even worse. Four in every ten adults in places like England, Canada, Spain and the US can’t make this straightforward calculation – even when they had a calculator to hand. Similarly, less than half of adults in places like Chile, Turkey and South Korea can get the right answer. </p>
<h2>Basic calculations</h2>
<p>Of course, not all groups within each country perform quite so poorly, and there are notable differences in financial literacy skills between different demographic groups. </p>
<p>Across the four financial questions adults were asked, in most countries, men tended to perform slightly better than women. The young (particularly 25- to 34-year-olds) were also found to perform better than the over-55s. </p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/210276/original/file-20180314-113469-bv14d3.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/210276/original/file-20180314-113469-bv14d3.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/210276/original/file-20180314-113469-bv14d3.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/210276/original/file-20180314-113469-bv14d3.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/210276/original/file-20180314-113469-bv14d3.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/210276/original/file-20180314-113469-bv14d3.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/210276/original/file-20180314-113469-bv14d3.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=503&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Many adults struggle with basic financial tasks, like working out what’s better value at a supermarket.</span>
<span class="attribution"><a class="source" href="https://www.shutterstock.com/download/success?src=_8uSGJoRNieQEMUSqROWJA-1-53">Shutterstock</a></span>
</figcaption>
</figure>
<p>The starkest differences were seen by education group. Returning to the first question given above, in many countries adults with a “low” level of education (the equivalent of completing secondary school) had less than a 50% chance of getting the question correct. In places like Canada and United States, this fell to as low as 25%. </p>
<h2>Financial headache</h2>
<p>Our results clearly highlight how many adults are ill equipped to make key financial decisions. And how in fact, many struggle to cope with even very simple financial tasks. </p>
<p>In the long term, this highlights the critical need for financial literacy to be taught in schools, to ensure young people are equipped for the complex financial decisions they will face in the real world. </p>
<p>More immediately, though, given the low level of financial skills among many adults, it is vital that the information provided with financial products is as simple and straightforward to interpret as possible. And in the age of payday loans, and high interest credit cards, adequate advice and guidance must also be available where needed. Because otherwise, there is a real danger that a large proportion of the population is at risk of making serious financial mistakes.</p><img src="https://counter.theconversation.com/content/92858/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>The team who wrote the paper received funding from the OECD. This work was commissioned by the Organisation for Economic Co-operation and Development (OECD) who has granted Cambridge University Technical Services Ltd the right to publish it for non-commercial purposes only. </span></em></p>New research shows that many adults across the world are financially illiterate and unable to complete even basic mathematical calculations.John Jerrim, Lecturer in Economics and Social Statistics, UCLLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/917572018-02-27T15:22:11Z2018-02-27T15:22:11ZMathematics: forget simplicity, the abstract is beautiful - and important<figure><img src="https://images.theconversation.com/files/207820/original/file-20180226-140213-yox11e.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">
</span> <span class="attribution"><span class="source">Shutterstock</span></span></figcaption></figure><p>Why is mathematics so complicated? It’s a question many students will ask while grappling with a particularly complex calculus problem – and their teachers will probably echo while setting or marking tests.</p>
<p>It wasn’t always this way. Many fields of mathematics germinated from the study of real world problems, before the underlying rules and concepts were identified. These rules and concepts were then defined as abstract structures. For instance, algebra, the part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulas and equations was born from solving problems in arithmetic. Geometry emerged as people worked to solve problems dealing with distances and area in the real world. </p>
<p>That process of moving from the concrete to the abstract scenario is known, appropriately enough, as <a href="https://betterexplained.com/articles/learning-to-learn-math-abstraction/">abstraction</a>. Through abstraction, the underlying essence of a mathematical concept can be extracted. People no longer have to depend on real world objects, as was once the case, to solve a mathematical puzzle. They can now generalise to have wider applications or by matching it to other structures can illuminate similar phenomena. An example is the adding of integers, fractions, complex numbers, vectors and matrices. The concept is the same, but the applications are different. </p>
<p>This evolution was necessary for the development of mathematics, and important for other scientific disciplines too. </p>
<p>Why is this important? Because the growth of abstraction in maths gave disciplines like chemistry, physics, astronomy, geology, meteorology the ability to explain a wide variety of complex physical phenomena that occur in nature. If you grasp the process of abstraction in mathematics, it will equip you to better understand abstraction occurring in other tough science subjects like chemistry or physics.</p>
<h2>From the real world to the abstract</h2>
<p>The earliest example of abstraction was when humans counted before symbols existed. A sheep herder, for instance, needed to keep track of his flock of sheep without having any sort of symbolic system akin to numbers. So how did he do this to ensure that none of his sheep wandered away or got stolen?</p>
<p>One solution is to obtain a big supply of stones. He then moved the sheep one-by-one into an enclosed area. Each time a sheep passed, he placed a stone in a pile. Once all the sheep had passed, he got rid of the extra stones and was left with a pile of stones representing his flock. </p>
<p>Every time he needed to count the sheep, he removed the stones from his pile; one for each sheep. If he had stones left over, it means some sheep had wandered away or perhaps been stolen. This one-to-one correspondence helped the shepherd to keep track of his flock. </p>
<p>Today, we use the Arabic numbers (also known as the <a href="https://www.britannica.com/topic/Hindu-Arabic-numerals">Hindu-Arabic numerals</a>): 0,1,2,3,4,5,6,7,8,9 to represent any integer, that is any whole number. </p>
<p>This is another example of abstraction, and it’s powerful. It means we’re able to handle any amount of sheep, regardless of how many stones we have. We’ve moved from real-world objects – stones, sheep – to the abstract. There is real strength in this: we’ve created a space where the rules are minimalistic, yet the games that can be played are endless.</p>
<p>Another advantage of abstraction is that it reveals a deeper connection between different fields of mathematics. Results in one field can suggest concepts and ideas to be explored in a related field. Occasionally, methods and techniques developed in one field can be directly applied to another field to create similar results. </p>
<h2>Tough concepts, better teaching</h2>
<p>Of course, abstraction also has its disadvantages. Some of the mathematical subjects taught at university level – Calculus, Real Analysis, Linear Algebra, Topology, Category Theory, Functional Analysis and Set Theory among them – are very advanced examples of abstraction. </p>
<p>These concepts can be quite difficult to learn. They’re often tough to visualise and their rules rather unintuitive to manipulate or reason with. This means students need a degree of mathematical maturity to process the shift from the concrete to the abstract. </p>
<p>Many high school kids, particularly from developing countries, come to university with an <a href="https://link.springer.com/chapter/10.1007/978-3-319-12688-3_18">undeveloped level</a> of intellectual maturity to handle abstraction. This is because of the way mathematics was taught at high school. I have seen many students struggling, giving up or not even attempting to study mathematics because they weren’t given the right tools at school level and they think that they just “can’t do maths”. </p>
<p>Teachers and lecturers can improve this abstract thinking by being aware of abstractions in their subject and learning to demonstrate abstract concepts through concrete examples. Experiments are also helpful to familiarise and assure students of an abstract concept’s solidity.</p>
<p>This teaching principle is applied in some school systems, such as <a href="http://montessoritraining.blogspot.co.za/2008/07/montessori-philosophy-moving-from.html">Montessori</a>, to help children improve their abstract thinking. Not only does this guide them better through the maze of mathematical abstractions but it can be applied to other sciences as well.</p><img src="https://counter.theconversation.com/content/91757/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Harry Zandberg Wiggins does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.</span></em></p>Through abstraction, the underlying essence of a mathematical concept can be extracted.Harry Zandberg Wiggins, Lecturer, University of PretoriaLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/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/449002015-08-09T20:34:50Z2015-08-09T20:34:50ZWeapons of maths destruction: are calculators killing our ability to work it out in our head?<figure><img src="https://images.theconversation.com/files/91101/original/image-20150807-9952-vo72z3.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">from www.shutterstock.com.au</span></span></figcaption></figure><p>Since the 1980s we have had access to calculators of various types. Today, we can include computers and smartphones – which are attached to our hip 24/7. So does this ubiquitous access to calculators affect our ability to do maths in our heads like we used to?</p>
<p>Thirty years ago calculators promised immense opportunity – opportunity, alas, that brought considerable controversy. The sceptics predicted students would not be able to compute even simple calculations mentally or on paper. Multiplication, basic facts, knowledge would disappear. Calculators would become a crutch. </p>
<p>The controversy has not dissipated over time. As recently as 2012, the UK government announced it <a href="http://connection.ebscohost.com/c/opinions/83406522/does-maths-add-up">intended</a> to ban calculators from primary classrooms on the grounds that students use them too much and too soon.</p>
<p>Research conducted in response to this <a href="http://thenferblog.org/2014/11/12/subtracting-calculators-from-maths-tests-doesnt-add-up/">found little difference</a> in performance tests whether students used calculators or not. An earlier US study had <a href="http://www.jstor.org/stable/42802150?seq=1#page_scan_tab_contents">found the same</a>: the calculator had no positive or negative effects on the attainment of basic maths skills.</p>
<p>Researchers recommended moving the conversation on. What types of tasks and activities suit calculators? How can calculators complement and reinforce mental and written methods of arithmetic in maths?</p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/91093/original/image-20150807-18724-1aiqnoz.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/91093/original/image-20150807-18724-1aiqnoz.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/91093/original/image-20150807-18724-1aiqnoz.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/91093/original/image-20150807-18724-1aiqnoz.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/91093/original/image-20150807-18724-1aiqnoz.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/91093/original/image-20150807-18724-1aiqnoz.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/91093/original/image-20150807-18724-1aiqnoz.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/91093/original/image-20150807-18724-1aiqnoz.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">Studies have found the use of calculators doesn’t reduce the ability to compute in our heads.</span>
<span class="attribution"><span class="source">from www.shutterstock.com</span></span>
</figcaption>
</figure>
<h2>Using calculators to extend maths</h2>
<p>Teachers had high hopes that calculators would be used in enhancing and extending the learning of mathematics. While standard procedures for the four operations (+, -, x, ÷) would still be taught and the basic facts of arithmetic would still need to be mastered, calculators could facilitate the study of number patterns and the absence of tedious calculations would free students up to pose, model and solve interesting and relevant problems.</p>
<p>Rather than replacing mental computation, calculators actually make calculating more efficient. Even the simple four-function calculator is a powerful instrument for investigating a range of concepts that previously were not so easily accessed by young children independently. </p>
<p>Counting, skip counting, negative numbers, relationships between common and decimal fractions and other number patterns all open up. The calculator lets students investigate and generalise patterns in numbers that they have previously not had access to. </p>
<p>The “constant” function means young children can explore numbers to infinity, if they fancy, without being restricted to charts or number lines. Skip-counting is also possible using the constant function. </p>
<p>Multiplication tables are no longer limited to 12 x 12. In the diagram below the child is exploring the pattern made by entering 11+11 and continuing to press the Equals sign to see what happens to the pattern once you count beyond 99 by elevens.</p>
<figure class="align-left zoomable">
<a href="https://images.theconversation.com/files/90538/original/image-20150803-17164-ucxli9.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/90538/original/image-20150803-17164-ucxli9.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/90538/original/image-20150803-17164-ucxli9.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=923&fit=crop&dpr=1 600w, https://images.theconversation.com/files/90538/original/image-20150803-17164-ucxli9.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=923&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/90538/original/image-20150803-17164-ucxli9.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=923&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/90538/original/image-20150803-17164-ucxli9.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=1160&fit=crop&dpr=1 754w, https://images.theconversation.com/files/90538/original/image-20150803-17164-ucxli9.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=1160&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/90538/original/image-20150803-17164-ucxli9.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=1160&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Lots of number patterns are possible.</span>
<span class="attribution"><span class="license">Author provided</span></span>
</figcaption>
</figure>
<p>Calculators have great potential in concept development. For example, what happens when you multiply or divide a number by 10 or 100? These generalisations are spectacularly demonstrated and discovered with a calculator, which frees students to ask more questions about number patterns.</p>
<p><a href="http://search.informit.com.au/documentSummary;dn=462445434680297;res=IELHSS">In a 1997 review</a> of the extent to which calculators were being used in schools, numerous studies were examined that indicated the use of calculators at primary levels had no detrimental effects on students’ arithmetic abilities.</p>
<p>Unfortunately, the research indicated that calculators were still being used for trivial things like checking answers and were making little difference in mathematics education. </p>
<p>Although teachers indicated their support for the use of calculators across all levels of primary school, there was little evidence that these ideas were being taken up and implemented. Parental disapproval of the use of calculators was cited as a possible cause of the limited take-up.</p>
<h2>Calculators’ potential is not being achieved</h2>
<p><a href="http://espace.library.uq.edu.au/view/UQ:176139">In a 2008 study</a> this finding was reiterated. Researchers reported that despite educators’ high hopes for digital technologies to transform maths education, the uptake, both internationally and in Australia, had been disappointing. </p>
<p>Influential in this has been the lack of professional development to assist teachers in planning and implementing teaching approaches that take advantage of the technology. British technologist Conrad Wolfram said in his <a href="http://www.ted.com/talks/conrad_wolfram_teaching_kids_real_math_with_computers?language=en">TED talk</a>:</p>
<blockquote>
<p>From rockets to stock markets, many of humanity’s most thrilling creations are powered by math. So why do kids lose interest in it?</p>
</blockquote>
<figure class="align-right zoomable">
<a href="https://images.theconversation.com/files/90390/original/image-20150731-18735-o27k24.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/90390/original/image-20150731-18735-o27k24.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/90390/original/image-20150731-18735-o27k24.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=423&fit=crop&dpr=1 600w, https://images.theconversation.com/files/90390/original/image-20150731-18735-o27k24.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=423&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/90390/original/image-20150731-18735-o27k24.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=423&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/90390/original/image-20150731-18735-o27k24.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=532&fit=crop&dpr=1 754w, https://images.theconversation.com/files/90390/original/image-20150731-18735-o27k24.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=532&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/90390/original/image-20150731-18735-o27k24.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=532&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">We’re not harnessing calculators’ full potential.</span>
<span class="attribution"><a class="source" href="https://www.flickr.com/photos/dominicspics/3915942881/">Dominic Alves/Flickr</a>, <a class="license" href="http://creativecommons.org/licenses/by-sa/4.0/">CC BY-SA</a></span>
</figcaption>
</figure>
<p>Wolfram pointed out that students in mathematics classes across the globe spend up to 80% of their time learning and practising mathematical procedures. This time could be spent more productively if the digital technology already in the classrooms was used more effectively and efficiently. </p>
<p>While mathematics is popular, challenging and useful in the real world, kids are rapidly losing interest in the subject in schools. Wolfram blames teaching that focuses on calculation by hand: it’s tedious and mostly irrelevant to real mathematics and the real world.</p>
<p>Sadly, the potential for calculators to transform school mathematics and enhance our facility with mental arithmetic is not being achieved. We are not being provided with opportunities to solve real and interesting mathematical problems in the most effective ways. </p>
<p>So to answer whether calculators are affecting our mental arithmetic: not as much as we would like them to.</p><img src="https://counter.theconversation.com/content/44900/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Jeanne Carroll 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>Smartphones double as calculators and are attached to our hip 24/7. Does the ubiquitous access to calculators affect our ability to do maths in our heads like we used to?Jeanne Carroll, Senior Lecturer, College of Education, Victoria UniversityLicensed as Creative Commons – attribution, no derivatives.