tag:theconversation.com,2011:/fr/topics/maths-study-12785/articlesMaths study – The Conversation2023-06-20T13:12:31Ztag:theconversation.com,2011:article/2070632023-06-20T13:12:31Z2023-06-20T13:12:31ZEngland’s plan to introduce east Asia-style maths textbooks widely rejected by primary schools<figure><img src="https://images.theconversation.com/files/531598/original/file-20230613-26-m9x1lj.jpg?ixlib=rb-1.1.0&rect=0%2C23%2C5184%2C3422&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/group-school-children-can-be-seen-298453535">DGLimages/Shutterstock</a></span></figcaption></figure><p>Prime Minister Rishi Sunak recently <a href="https://www.gov.uk/government/news/prime-minister-outlines-his-vision-for-maths-to-18#:%7E:text=Prime%20Minister%20Rishi%20Sunak%20outlines,skills%20they%20need%20to%20succeed.&text=We%20must%20change%20our%20anti,today%20%5BMonday%2017%20April%5D">outlined a plan</a> to improve maths skills in England, which will see young people study the subject at school until they are 18. This sounds straightforward but it’s worth considering how tricky new educational policy is to get right. </p>
<p>Take, for example, a previous attempt by the UK government to improve children’s maths skills. In 2016, a multi-million pound initiative was launched offering more than 8,000 primary schools in England funding to buy maths textbooks featuring teaching methods based on those used in some east Asian countries.</p>
<p>We don’t yet know if the schools who used the textbooks saw any effect on their pupils’ attainment. The results of SATs – tests taken at the end of primary school – haven’t been published since 2019 due to the COVID pandemic.</p>
<p>However, <a href="https://research.brighton.ac.uk/en/publications/the-prevalence-and-use-of-textbooks-and-curriculum-resources-in-p">my research with colleagues</a> shows this initiative, which ran until the 2021-22 academic year, was not widely popular with teachers and school leaders – and that the majority of English primary schools did not take up the funding. Of those that did, more than a third have subsequently stopped using the textbooks completely.</p>
<p>Data suggests that on average, children in England do pretty well at maths compared with other countries. The <a href="https://timss2019.org/reports/achievement/#math-4">latest international study</a> shows the performance of England’s nine- to ten-year-olds has increased steadily, now ranking eighth out of 58 jurisdictions. </p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/530566/original/file-20230607-19-idyoc2.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="Chart showing England's international standing in mathematics attainment for nine- to ten-year-olds, with England in eighth position and well above the centerpoint for all jurisdictions." src="https://images.theconversation.com/files/530566/original/file-20230607-19-idyoc2.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/530566/original/file-20230607-19-idyoc2.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=330&fit=crop&dpr=1 600w, https://images.theconversation.com/files/530566/original/file-20230607-19-idyoc2.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=330&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/530566/original/file-20230607-19-idyoc2.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=330&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/530566/original/file-20230607-19-idyoc2.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=414&fit=crop&dpr=1 754w, https://images.theconversation.com/files/530566/original/file-20230607-19-idyoc2.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=414&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/530566/original/file-20230607-19-idyoc2.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=414&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">England’s international standing in mathematics attainment for nine- to ten-year-olds (data extracted from TIMSS 2019 report).</span>
<span class="attribution"><span class="source">Author created from publicly available data.</span>, <a class="license" href="http://creativecommons.org/licenses/by-nc-nd/4.0/">CC BY-NC-ND</a></span>
</figcaption>
</figure>
<p>But challenge lies behind the averages. England has one of the <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">largest gaps in the world</a> between the highest and lowest performers, and a <a href="https://www.nottingham.ac.uk/research/groups/crme/documents/maths-pipeline-report.pdf">persistent gap in maths attainment</a> between pupils from disadvantaged and non-disadvantaged backgrounds.</p>
<p>Wanting to change these patterns for our youngest learners, the government looked to the teaching practices of the highest performers internationally – predominantly east Asian regions – to see what England could “borrow”. </p>
<p>Several <a href="https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/773320/MTE_main_report.pdf">exchange projects</a> later saw the “<a href="https://theconversation.com/explainer-what-is-the-mastery-model-of-teaching-maths-25636">mastery</a>” teaching approach <a href="https://www.mdpi.com/2227-7102/8/4/202">pushed in English primary schools</a>. The mastery method breaks learning down into small blocks and requires that a pupil is competent in a topic before they can move on to another. </p>
<p>Schools minister Nick Gibb <a href="https://www.gov.uk/government/news/south-asian-method-of-teaching-maths-to-be-rolled-out-in-schools">announced extended funding</a> in 2016 supporting this push, with a central strand being provision for around 8,000 eligible schools to purchase maths textbooks through matched-funding grants of £2,000.</p>
<p>Schools could choose from two government-approved <a href="https://www.ncetm.org.uk/teaching-for-mastery/mastery-explained/textbooks/">textbook schemes</a>: <a href="https://mathsnoproblem.com/">Maths – No Problem!</a> and <a href="https://www.pearson.com/international-schools/british-curriculum/primary-curriculum/power-maths.html">Power Maths</a>. Each scheme included physical textbooks, workbooks for pupils to write in (which must be renewed each year), and subscription-accessed online material including lessons and teacher guides.</p>
<p>To assess the popularity and effectiveness of this approach, we distributed a <a href="https://research.brighton.ac.uk/en/publications/the-prevalence-and-use-of-textbooks-and-curriculum-resources-in-p">nationwide survey</a> to all 17,038 state primary schools in England in 2021-22. We received 664 responses, a representative sample. We wanted to find out more about the resources teachers were using to teach maths and how far this included the government-approved mastery textbooks. </p>
<p>We were taken aback to discover that more than 100 different maths resources are in use in primary schools across England. These vary from complete schemes to topic-focused resources, from online to physical and from free to pay-per-view. </p>
<p>We also found that teachers spend considerable time sourcing and adapting material, with more than a third of primary teachers spending their own money purchasing resources. This clearly clashes with the government aspiration that schools should move to teaching predominantly through textbooks.</p>
<h2>A mismatched approach</h2>
<p>Our survey found that two-thirds of the schools eligible for textbook funding under the scheme launched in 2016 did not take it up. While some were unaware they were eligible, others made a resolved choice not to participate. </p>
<p>Participants from these schools told us of an ideological dislike of textbook-based teaching. A quarter of schools felt they couldn’t meet the matched-funding element, or the ongoing costs. This shouldn’t come as a surprise, given that <a href="https://ifs.org.uk/publications/school-spending-and-costs-coming-crunch">costs to schools are growing more quickly</a> than previously experienced.</p>
<p>Of greater concern – especially looked at from a value-for-money perspective – was that 37% of primary schools that took up the funding have since completely stopped using the textbooks. A further 24% are only using the purchased textbook schemes in a partial way – for example, still using the physical textbooks but not purchasing pupil workbooks or renewing their online subscriptions to support materials.</p>
<p>In all, only just over 10% of primary schools that were eligible for the textbook scheme took it up and are still using it in full.</p>
<p><strong>Summary of our survey results:</strong></p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/531704/original/file-20230613-2513-ghz533.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="Infographic illustrating percentages outlined in previous paragraph." src="https://images.theconversation.com/files/531704/original/file-20230613-2513-ghz533.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/531704/original/file-20230613-2513-ghz533.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=278&fit=crop&dpr=1 600w, https://images.theconversation.com/files/531704/original/file-20230613-2513-ghz533.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=278&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/531704/original/file-20230613-2513-ghz533.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=278&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/531704/original/file-20230613-2513-ghz533.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=349&fit=crop&dpr=1 754w, https://images.theconversation.com/files/531704/original/file-20230613-2513-ghz533.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=349&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/531704/original/file-20230613-2513-ghz533.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=349&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption"></span>
<span class="attribution"><span class="source">Author created from survey data</span></span>
</figcaption>
</figure>
<p>The government’s shift to <a href="https://www.nytimes.com/2017/08/05/world/asia/china-textbooks-britain.html">learning from the east Asian education system</a> was a complete about-turn. It meant importing practices that sat at odds with primary school approaches in England, where teachers look after all needs of their class, rather than being subject specialists.</p>
<p>Textbooks, particularly in primary maths, have <a href="https://www.cambridgeassessment.org.uk/Images/181744-why-textbooks-count-tim-oates.pdf">not been popular</a> in primary schools for some time. As well as being costly, they can be seen as <a href="https://www.sciencedirect.com/science/article/pii/S0738059307000685#aep-section-id18">a threat to professional identity</a> by taking away teacher control.</p>
<p>Our research underlines that we need a solid understanding of how maths teaching is done in England before adding in any new initiatives or policy – not only what’s happening in classrooms, but the complex reasons behind why it is happening. We hope governments learn from the inefficient administration reported here before implementing further new or borrowed policies.</p><img src="https://counter.theconversation.com/content/207063/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Rachel Marks received funding for this project from The Nuffield Foundation. She is affiliated with the University of Brighton and was supported in this research by Dr Nancy Barclay and Dr Alison Barnes.</span></em></p>Our research found a multi-million pound scheme to boost maths learning was under-used and had minimal impact on practice.Rachel Marks, Principal Lecturer in Mathematics Education (Primary), University of BrightonLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1713902022-01-04T19:12:29Z2022-01-04T19:12:29ZLearn how to make a sonobe unit in origami – and unlock a world of mathematical wonder<figure><img src="https://images.theconversation.com/files/433304/original/file-20211122-13-1uohlvq.jpg?ixlib=rb-1.1.0&rect=0%2C6%2C4031%2C2257&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">
</span> <span class="attribution"><span class="source">Julia Collins</span>, <span class="license">Author provided</span></span></figcaption></figure><p><em>This article is part of a <a href="https://theconversation.com/au/topics/how-to-guides-113946">series</a> explaining how readers can learn the skills to take part in activities that academics love doing as part of their work.</em></p>
<hr>
<p>Many of us could happily fold a <a href="https://origami.me/crane/">paper crane</a>, yet few feel confident solving an equation like <em>x</em>³ – 3 <em>x</em>² – <em>x</em> + 3 = 0, to find a value for <em>x</em>.</p>
<p>Both activities, however, share similar skills: precision, the ability to follow an algorithm, an intuition for shape, and a search for pattern and symmetry. </p>
<p>I’m a mathematician whose hobby is origami, and I love introducing people to mathematical ideas through crafts like paper folding. Any piece of origami will contain mathematical ideas and skills, and can take you on a fascinating, creative journey.</p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/why-bother-calculating-pi-to-62-8-trillion-digits-its-both-useless-and-fascinating-166271">Why bother calculating pi to 62.8 trillion digits? It's both useless and fascinating</a>
</strong>
</em>
</p>
<hr>
<h2>The ‘building blocks’ of origami models</h2>
<p>As a geometer (mathematician who studies geometry), my favourite technique is modular origami. That’s where you use several pieces of folded paper as “building blocks” to create a larger, often symmetrical structure.</p>
<p>The building blocks, called units, are typically straightforward to fold; the mathematical skill comes in assembling the larger structure and discovering the patterns within them. </p>
<p>Many modular origami patterns, although they may use different units, have a similar method of combining units into a bigger creation. </p>
<p>So, for a little effort you are rewarded with a vast number of models to explore.</p>
<p>My website <a href="https://www.mathscraftaus.org/resources">Maths Craft Australia</a> contains a range of modular origami patterns, as well as patterns for other crafts such as crochet, knitting and stitching. </p>
<p>They require no mathematical background but will take you in some fascinating mathematical directions.</p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/432338/original/file-20211117-23-ujn9or.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/432338/original/file-20211117-23-ujn9or.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/432338/original/file-20211117-23-ujn9or.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=555&fit=crop&dpr=1 600w, https://images.theconversation.com/files/432338/original/file-20211117-23-ujn9or.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=555&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/432338/original/file-20211117-23-ujn9or.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=555&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/432338/original/file-20211117-23-ujn9or.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=697&fit=crop&dpr=1 754w, https://images.theconversation.com/files/432338/original/file-20211117-23-ujn9or.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=697&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/432338/original/file-20211117-23-ujn9or.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=697&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 model, folded by the author, uses a design from the book Perfectly Mindful Origami - The Art and Craft of Geometric Origami by Mark Bolitho.</span>
</figcaption>
</figure>
<h2>Building 3D shapes from smaller 2D units</h2>
<p>In mathematics, the shapes with the most symmetry are called the <a href="https://en.wikipedia.org/wiki/Platonic_solid">Platonic solids</a>. They’re named after the ancient Greek philosopher Plato (although they almost certainly predate him and have been discovered in ancient civilisations around the world). </p>
<p>The Platonic solids are 3D shapes made from regular 2D shapes (also known as regular polygons) where every side and angle is identical: equilateral triangles, squares, pentagons.</p>
<p>While there are infinitely many regular polygons, there are, surprisingly, only five Platonic solids: </p>
<ul>
<li><p>the tetrahedron (four triangles)</p></li>
<li><p>the cube (six squares)</p></li>
<li><p>the octahedron (eight triangles)</p></li>
<li><p>the dodecahedron (12 pentagons) and</p></li>
<li><p>the icosahedron (20 triangles). </p></li>
</ul>
<p>To build Platonic solids in origami, the best place to start is to master what’s known as the “<a href="https://momath.org/home/math-monday-introducing-the-sonobe-unit/">sonobe unit</a>”.</p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/433363/original/file-20211123-25-1r7jrtk.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="Sonobe units, like these ones piled in a stack, can be put together to create 3D shapes." src="https://images.theconversation.com/files/433363/original/file-20211123-25-1r7jrtk.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/433363/original/file-20211123-25-1r7jrtk.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=450&fit=crop&dpr=1 600w, https://images.theconversation.com/files/433363/original/file-20211123-25-1r7jrtk.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=450&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/433363/original/file-20211123-25-1r7jrtk.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=450&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/433363/original/file-20211123-25-1r7jrtk.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=566&fit=crop&dpr=1 754w, https://images.theconversation.com/files/433363/original/file-20211123-25-1r7jrtk.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=566&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/433363/original/file-20211123-25-1r7jrtk.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=566&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Sonobe units, like these ones piled in a stack, can be put together to create 3D shapes.</span>
<span class="attribution"><span class="source">Julia Collins</span>, <span class="license">Author provided</span></span>
</figcaption>
</figure>
<h2>Enter the sonobe unit</h2>
<p>A sonobe unit (sometimes called the sonobe module) looks a bit like a parallelogram with two flaps folded behind.</p>
<p>I’ve got instructions for how to make a sonobe unit <a href="https://static1.squarespace.com/static/59699ab4b8a79b10f84ba4cd/t/59b92716e5dd5b882846ee5b/1505306394805/Sonobe-unit-instructions.pdf">on my website</a> and there are plenty of videos online, like this one:</p>
<figure>
<iframe width="440" height="260" src="https://www.youtube.com/embed/TKGW2W168H0?wmode=transparent&start=0" frameborder="0" allowfullscreen=""></iframe>
<figcaption><span class="caption">How to make a sonobe unit.</span></figcaption>
</figure>
<p>Sonobe units are fast and simple to fold, and can be fitted together to create beautiful, intriguing 3D shapes like these:</p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/432142/original/file-20211116-13-1vvh9l2.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/432142/original/file-20211116-13-1vvh9l2.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=338&fit=crop&dpr=1 600w, https://images.theconversation.com/files/432142/original/file-20211116-13-1vvh9l2.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=338&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/432142/original/file-20211116-13-1vvh9l2.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=338&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/432142/original/file-20211116-13-1vvh9l2.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=424&fit=crop&dpr=1 754w, https://images.theconversation.com/files/432142/original/file-20211116-13-1vvh9l2.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=424&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/432142/original/file-20211116-13-1vvh9l2.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=424&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Three sonobe origami models by Julia Collins.</span>
</figcaption>
</figure>
<p>You will need six sonobe units to make a cube like the yellow-blue-green one pictured above, 12 to make an octahedron (the red-pink-purple one), and 30 to make an icosahedron (the golden one). (Interestingly, it’s not possible to build a tetrahedron and dodecahedron from sonobe units).</p>
<p>I’ve got written instructions for building the cube <a href="https://static1.squarespace.com/static/59699ab4b8a79b10f84ba4cd/t/59b9273ab7411cfd32068b83/1505306433027/Sonobe-unit-instructions-cube.pdf">on my website</a>, and some quick searching online will find you instructions for the larger models.</p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/433364/original/file-20211123-13-1g66xxm.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="Sonobe units can be put together to build wondrous shapes." src="https://images.theconversation.com/files/433364/original/file-20211123-13-1g66xxm.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/433364/original/file-20211123-13-1g66xxm.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=450&fit=crop&dpr=1 600w, https://images.theconversation.com/files/433364/original/file-20211123-13-1g66xxm.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=450&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/433364/original/file-20211123-13-1g66xxm.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=450&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/433364/original/file-20211123-13-1g66xxm.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=566&fit=crop&dpr=1 754w, https://images.theconversation.com/files/433364/original/file-20211123-13-1g66xxm.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=566&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/433364/original/file-20211123-13-1g66xxm.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=566&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Sonobe units can be put together to build wondrous shapes.</span>
<span class="attribution"><span class="source">Julia Collins</span>, <span class="license">Author provided</span></span>
</figcaption>
</figure>
<h2>Into the mathematical rabbit hole</h2>
<p>Once you’ve mastered the basic structure of each 3D shape, you may find yourself (as <a href="https://www.polypompholyx.com/2017/01/modularorigami/">others have done</a>) pondering deeper mathematical questions.</p>
<p>Can you arrange the sonobe units so two units of the same colour never touch, if you only have three colours? </p>
<p>Are larger symmetric shapes possible? (Answer: yes!) </p>
<p>Are there relationships between the different 3D shapes? (For example, the icosahedron is basically built of triangles, but can you spot the pentagons lurking within? Or the triangles in the dodecahedron?)</p>
<p>One seemingly innocent question can easily lead to a mathematical rabbit hole.</p>
<p>Questions about colouring will lead you to the mathematics of graphs and networks (and big questions that remained <a href="https://en.wikipedia.org/wiki/Four_color_theorem">unsolved for many centuries</a>). </p>
<p>Questions about larger models will lead you to the <a href="https://en.wikipedia.org/wiki/Archimedean_solid">Archimedean solids</a> and the <a href="https://en.wikipedia.org/wiki/Johnson_solid">Johnson solids</a>. These 3D shapes have a lot of symmetry, though not as much as the Platonic solids. </p>
<p>Then, for a truly mind-bending journey, you might land on the concept of <a href="https://en.wikipedia.org/wiki/List_of_regular_polytopes_and_compounds">higher-dimensional symmetric shapes</a>. </p>
<p>Or perhaps your questions will lead you in the opposite direction. </p>
<p>Instead of using origami to explore new ideas in mathematics, some researchers have used mathematical frameworks to explore new ideas in origami.</p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/433365/original/file-20211123-27-1h94v50.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="Origami can take you into the mathematical rabbit hole." src="https://images.theconversation.com/files/433365/original/file-20211123-27-1h94v50.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/433365/original/file-20211123-27-1h94v50.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=600&fit=crop&dpr=1 600w, https://images.theconversation.com/files/433365/original/file-20211123-27-1h94v50.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=600&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/433365/original/file-20211123-27-1h94v50.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=600&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/433365/original/file-20211123-27-1h94v50.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=754&fit=crop&dpr=1 754w, https://images.theconversation.com/files/433365/original/file-20211123-27-1h94v50.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=754&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/433365/original/file-20211123-27-1h94v50.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=754&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Origami can take you into the mathematical rabbit hole.</span>
<span class="attribution"><span class="source">Julia Collins</span>, <span class="license">Author provided</span></span>
</figcaption>
</figure>
<h2>Solving old problems in new ways</h2>
<p>Perhaps the most famous mathematical origami artist is the US-based former NASA physicist <a href="https://langorigami.com/">Robert Lang</a>, who designs computer programs that generate crease patterns for fantastically complicated models. </p>
<p>His models include segmented tarantulas and ants, stags with twisted antlers and soaring, feathered birds.</p>
<figure>
<iframe width="440" height="260" src="https://www.youtube.com/embed/DJ4hDppP_SQ?wmode=transparent&start=0" frameborder="0" allowfullscreen=""></iframe>
<figcaption><span class="caption">Credit: Great Big Story/YouTube.</span></figcaption>
</figure>
<p>Robert Lang and others have also created crease patterns for use in new engineering contexts such as <a href="https://langorigami.com/article/eyeglass-telescope/">folding telescope lenses</a>, <a href="https://royalsocietypublishing.org/doi/10.1098/rsos.160429">air bags</a> and <a href="https://www.nasa.gov/jpl/news/origami-style-solar-power-20140814">solar panels</a>.</p>
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<em>
<strong>
Read more:
<a href="https://theconversation.com/curved-origami-offers-a-creative-route-to-making-robots-and-other-mechanical-devices-150253">Curved origami offers a creative route to making robots and other mechanical devices</a>
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</p>
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<p>My final example of the power of origami goes back to the cubic equation I mentioned at the outset:</p>
<p><em>x</em>³ – 3 <em>x</em>² – <em>x</em> + 3 = 0</p>
<p>Cubic equations relate to some “impossible” mathematical problems, such as <a href="https://mathworld.wolfram.com/AngleTrisection.html">trisecting an angle</a> (splitting an arbitrary angle into three equal angles). Or <a href="https://en.wikipedia.org/wiki/Doubling_the_cube">doubling a cube</a> (which is finding a cube with double the volume of a given cube). </p>
<figure class="align-right zoomable">
<a href="https://images.theconversation.com/files/433368/original/file-20211123-17-19aazig.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="A blue and purple origami shape sits on a grey background." src="https://images.theconversation.com/files/433368/original/file-20211123-17-19aazig.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/433368/original/file-20211123-17-19aazig.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=554&fit=crop&dpr=1 600w, https://images.theconversation.com/files/433368/original/file-20211123-17-19aazig.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=554&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/433368/original/file-20211123-17-19aazig.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=554&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/433368/original/file-20211123-17-19aazig.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=696&fit=crop&dpr=1 754w, https://images.theconversation.com/files/433368/original/file-20211123-17-19aazig.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=696&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/433368/original/file-20211123-17-19aazig.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=696&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Any piece of origami will contain mathematical ideas and skills.</span>
<span class="attribution"><span class="source">Julia Collins</span>, <span class="license">Author provided</span></span>
</figcaption>
</figure>
<p>Famously, these problems cannot be solved using the classical methods of a straightedge (ruler without the markings) and compass. </p>
<p>In 1980, however, Japanese mathematician Hisashi Abe showed how to <a href="https://plus.maths.org/content/trisecting-angle-origami">solve all these problems using origami</a>.</p>
<p>I am excited to see where mathematics and origami will intersect in future. Grab some paper today, make a few models and start your own journey of mathematical exploration. </p>
<hr>
<p><em>You can read other articles in this series <a href="https://theconversation.com/au/topics/how-to-guides-113946">here</a>.</em></p><img src="https://counter.theconversation.com/content/171390/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Julia Collins 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>I’m a mathematician whose hobby is origami. It has inspired mathematicians to solve problems once thought impossible, and create folding telescope lenses, airbags and solar panels.Julia Collins, Lecturer of Mathematics, Edith Cowan UniversityLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1634962021-08-11T03:34:42Z2021-08-11T03:34:42ZWhich maths subject should I take in years 11 and 12? Here’s what you need to know<figure><img src="https://images.theconversation.com/files/415598/original/file-20210811-17-bxhu65.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/back-view-high-school-student-solving-1821464747">Shutterstock</a></span></figcaption></figure><p><em>This article is part of a <a href="https://theconversation.com/au/topics/senior-subjects-series-107516">series</a> providing school students with evidence-based advice for choosing subjects in their senior years.</em></p>
<p>Maths prepares students for the ultimate test — life beyond school. As maths is everywhere, regardless of where life leads you, the more maths you learn, the better prepared you may be to understand the world.</p>
<p>The <a href="https://www.australiancurriculum.edu.au/">Australian Curriculum</a> intends to provide some consistency in what is taught at school, regardless of where you live. Maths is one of 15 senior secondary subjects.</p>
<p>However, states and territories maintain responsibility for local education. So there is variation in the range, focus and difficulty of maths subjects offered.</p>
<h2>How many senior students do maths?</h2>
<p>It’s not compulsory to study senior maths across Australia, but most year 11 and 12 students still do so. <a href="https://www.acara.edu.au/reporting/national-report-on-schooling-in-australia/national-report-on-schooling-in-australia-data-portal/year-12-subject-enrolments#view2">Available data</a> suggests just over 70% of year 12 students study maths, with slightly fewer girls doing so than boys. </p>
<p>However, enrolments are on the decline. For instance, between 2001 and 2013 the <a href="https://www.theaustralian.com.au/nation/maths-to-be-compulsory-for-all-students/news-story/fa8b2bdb4319d2f48bd5f4e9c82af288">proportion of students studying</a> the high school certificate in New South Wales, who did not take a maths subject, tripled from 3.2% to almost 10%. NSW has announced it <a href="https://www.nsw.gov.au/media-releases/maths-to-be-compulsory-for-students">intends to make maths mandatory</a> in years 11 and 12 to arrest the decline in enrolments, but there has not yet been a timeline set for this move. Victoria is also <a href="https://www.theage.com.au/national/victoria/victoria-to-introduce-new-vce-maths-subject-20191217-p53kst.html">widening its maths offering</a> to senior secondary students.</p>
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Read more:
<a href="https://theconversation.com/fewer-australians-are-taking-advanced-maths-in-year-12-we-can-learn-from-countries-doing-it-better-149148">Fewer Australians are taking advanced maths in Year 12. We can learn from countries doing it better</a>
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<h2>What subjects are available for me to choose from?</h2>
<p>The <a href="https://www.australiancurriculum.edu.au/senior-secondary-curriculum/mathematics/senior-secondary-mathematics-subjects/">Australian Curriculum</a> describes four senior secondary maths subjects, with each organised into four units, usually studied over the four semesters of year 11 and 12. </p>
<p>They are essential mathematics, general mathematics, mathematical methods and specialist mathematics. In Queensland, these are the subject names used. However, there are different names for different types of maths in each state and territory with some being more closely aligned with the Australian Curriculum than others. For example, in NSW <a href="https://educationstandards.nsw.edu.au/wps/portal/nesa/k-10/understanding-the-curriculum/curriculum-syllabuses-NSW/nsw-and-the-australian-curriculum">the equivalent subjects</a> have completely different names and also arrange content and concepts differently. </p>
<p>But all maths subjects have similarities when it comes to the knowledge and skills students will develop. They also teach students how to think, reason and communicate mathematically, describe and analyse data and evidence, and use digital technologies.</p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/415572/original/file-20210811-19-1hqvrzz.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="Coins stacked on graphs and charts." src="https://images.theconversation.com/files/415572/original/file-20210811-19-1hqvrzz.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/415572/original/file-20210811-19-1hqvrzz.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=401&fit=crop&dpr=1 600w, https://images.theconversation.com/files/415572/original/file-20210811-19-1hqvrzz.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=401&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/415572/original/file-20210811-19-1hqvrzz.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=401&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/415572/original/file-20210811-19-1hqvrzz.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/415572/original/file-20210811-19-1hqvrzz.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/415572/original/file-20210811-19-1hqvrzz.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">Maths subjects will teach you about important concepts, such as financial modelling.</span>
<span class="attribution"><a class="source" href="https://www.shutterstock.com/image-photo/various-type-financial-investment-products-bond-1165589407">Shutterstock</a></span>
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</figure>
<p><a href="https://senior-secondary.scsa.wa.edu.au/syllabus-and-support-materials/mathematics/mathematics-essential">Essential mathematics</a> (most closely aligned with <a href="https://www.vcaa.vic.edu.au/curriculum/vce/vce-study-designs/foundationmathematics/Pages/Index.aspx">foundation mathematics</a> in year 11 in Victoria) focuses on students developing and using maths knowledge and skills to investigate realistic problems. The subject or subjects include the study of data and statistics and financial modelling. Students selecting these courses typically have work or a vocational education and training course in mind once they leave school.</p>
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<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/more-teens-are-dropping-maths-here-are-three-reasons-to-stick-with-it-119745">More teens are dropping maths. Here are three reasons to stick with it</a>
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<p><a href="https://www.vcaa.vic.edu.au/curriculum/vce/vce-study-designs/generalmathematics/Pages/Index.aspx">General mathematics</a> (most closely aligned with <a href="https://www.vcaa.vic.edu.au/curriculum/vce/vce-study-designs/generalmathematics/Pages/Index.aspx">general mathematics</a> in year 11 and <a href="https://www.vcaa.vic.edu.au/curriculum/vce/vce-study-designs/furthermathematics/Pages/Index.aspx">further mathematics</a> in year 12 in Victoria) includes the study of financial modelling, geometric problems, and statistics. These are areas many of us encounter in our work and life. Students selecting this subject typically plan to go to university and study a course where maths may have practical and/or theoretical relevance. General mathematics is a pre-requisite for courses like aviation, ICT, and health science at <a href="https://www.swinburne.edu.au/study/course/MathsLink-Further-NN-MLFTH/local">Swinburne University</a>.</p>
<p><a href="https://senior-secondary.scsa.wa.edu.au/syllabus-and-support-materials/mathematics/mathematics-methods">Mathematical methods</a> is where students are introduced to calculus. This is the study of relationships and change. For instance, is the spread of a particular virus increasing? Can we describe trends and patterns observed and make predictions about the future? Can we describe the total number of cases over a given time period and assess the impact of government intervention?</p>
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<p>Students are also introduced to statistical analysis, which is describing and analysing phenomena involving uncertainty and variation. Students who choose mathematical methods are likely intending to study maths-related subjects at university such as science, <a href="https://www.deakin.edu.au/course/bachelor-software-engineering-honours">engineering</a>, medicine and IT related degrees. </p>
<p><a href="https://www.sace.sa.edu.au/web/specialist-mathematics">Specialist mathematics</a> should be taken together with mathematical methods, as it deepens and extends key ideas studied there. Students who do specialist mathematics and mathematical methods (or <a href="https://education.nsw.gov.au/teaching-and-learning/curriculum/key-learning-areas/mathematics/stage-6/mathematics-extension-1">extension</a> and <a href="https://education.nsw.gov.au/teaching-and-learning/curriculum/key-learning-areas/mathematics/stage-6/mathematics-advanced">advanced</a> mathematics in NSW) intend to do maths related courses at university.</p>
<p>When we were teaching in school, many students studied two maths subjects in year 12 (mathematical methods and specialist mathematics, or mathematical methods and general mathematics). Everyone had different ideas on which maths they found the hardest.</p>
<h2>Which one should I choose?</h2>
<p>Parents and teachers frame subject selection around the question, “What are your plans for the future?” </p>
<p>Having an idea what you want to do once you finish year 12 will determine your interest in maths and motivation to learn it. </p>
<p>The future is uncertain with study and career pathways that are dynamically evolving. <a href="https://www.fya.org.au/wp-content/uploads/2017/07/FYA_TheNewWorkSmarts_July2017.pdf">Research</a> shows a 15-year-old today could have 17 different jobs over five careers in their lifetime. Maths is essential to a range of study and career choices — including vocational trades, nursing, teaching and mathematical sciences. </p>
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<strong>
Read more:
<a href="https://theconversation.com/thinking-of-choosing-a-science-subject-in-years-11-and-12-heres-what-you-need-to-know-164778">Thinking of choosing a science subject in years 11 and 12? Here's what you need to know</a>
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<p>If you do choose maths, you should choose the maths subject that interests you and offers the best preparation for your destination beyond school, be it work, TAFE or university.</p>
<p>Unsurprisingly, studying senior maths at school <a href="https://research.acer.edu.au/higher_education/62/">increases your success</a> when studying university maths units and courses. Some <a href="https://www.sydney.edu.au/study/how-to-apply/undergraduate/mathematics-prerequisite.html">universities</a> have pages where you can easily search by maths subjects rather than course.</p>
<p>School careers counsellors are an excellent resource for advising students on possible study and career paths and what maths subjects you may need. </p>
<p>It can also help to speak with maths teachers you know and trust, and family members and friends who have taken different subjects. Some people say some maths subjects are harder than others, but others argue it really depends on your interests and effort to take advantage of available opportunities to learn.</p>
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<p>Be wary about the university and vocational education and training prerequisites and recommended subjects. Often students see a subject is recommended but not required, and opt not to take that subject.</p>
<p>However, when they enrol in the TAFE or university course in question, they might find a maths equivalent to a year 12 course is more or less squashed into a first semester unit. It is often easier to learn this content in year 12 with the support of a dedicated maths teacher than to try doing so in one semester in a new environment with unfamiliar teachers and peers.</p>
<h2>What should I know about scaling?</h2>
<p>In calculating the ATAR, all subjects are <a href="https://this.deakin.edu.au/study/vce-study-scores-understanding-raw-and-scaled-scores">scaled</a> to account for the competition in the subject — not the level of difficulty. Maths and languages have additional scaling. </p>
<p>Scaling is to even the playing field, and students who take more challenging subjects usually get scaled up. Specialist mathematics is taken to be more difficult than mathematical methods which is taken to be more difficult than general mathematics. For mathematics, the subjects are compared against each other as well as against all other studies.</p>
<p>For example, <a href="https://www.vtac.edu.au/files/pdf/reports/scaling-report-20-21.pdf">in 2020 in Victoria</a>, an initial study score of 30 was scaled to 27 in further mathematics, 34 in mathematical methods and to 41 in specialist mathematics.</p>
<p>Maths has never been more important or visible to making sense of the world. We believe there is a maths for every student and a choice that keep your options open for the future. </p>
<p><em>Read the other articles in our series on choosing senior subjects, <a href="https://theconversation.com/au/topics/senior-subjects-series-107516">here</a>.</em></p><img src="https://counter.theconversation.com/content/163496/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 prepares students for the ultimate test — life beyond school. Maths is everywhere, regardless of where life leads you. The more maths you learn, the better you can understand the world.Jill P Brown, Senior Lecturer in Mathematics Education, Deakin UniversityCarly Sawatzki, Lecturer in Primary Mathematics Education, Deakin 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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<strong>
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>
</blockquote>
<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">
<figcaption>
<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>
</figcaption>
</figure>
<hr>
<p>
<em>
<strong>
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>
</strong>
</em>
</p>
<hr>
<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>
<hr>
<p>
<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>
</strong>
</em>
</p>
<hr>
<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/1607242021-05-30T20:07:48Z2021-05-30T20:07:48ZMultiple-choice exams favour boys over girls, worsening the maths gender gap<figure><img src="https://images.theconversation.com/files/403264/original/file-20210528-18-196n7i0.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/student-hand-testing-doing-test-exam-1472765504">Shutterstock</a></span></figcaption></figure><p>Boys perform better than girls in tests made up of multiple-choice questions. </p>
<p>Multiple-choice questions are considered objective and easy to mark. But my <a href="https://melbourneinstitute.unimelb.edu.au/__data/assets/pdf_file/0003/3769050/ri2021n05.pdf">research shows</a> they give an advantage to males.</p>
<p>I compared around 500,000 test results of boys and girls who sat the same international test, but whose exam papers differed by detail (although not difficulty). The difference included a varied proportion of multiple-choice questions as opposed to open-ended questions.</p>
<p>I found the gender gap in math scores widened with the share of multiple-choice questions in the exam — advantaging males.</p>
<p>This shows the generally better performance of males in maths exams has to do more with the format of the test than their maths knowledge.</p>
<h2>How I conducted my research</h2>
<p>Standardised exams are widely used to test students and screen job candidates. Australians take several standardised tests throughout their education — such as the NAPLAN, High School Certificate (HSC) and the OECD’s Programme for International Student Assessment (PISA).</p>
<p>Such exams, especially when maths is involved, regularly include multiple-choice questions. </p>
<p>For example, more than 70% of <a href="https://www.acara.edu.au/assessment/naplan/naplan-2012-2016-test-papers">NAPLAN’s 2016 numeracy section</a> was made up of multiple-choice questions. Every year, the maths <a href="https://ace.nesa.nsw.edu.au/higher-school-certificate">HSC tests</a> include a section with multiple-choice questions.</p>
<p>These prompt students to identify the correct response from a set of possible answers.</p>
<p>I analysed data from PISA 2012 and 2015. <a href="https://www.oecd.org/pisa/">PISA</a> is the largest international standardised test in maths, reading and science. Every three years, more than 500,000 students aged 15, from more than 60 countries, including Australia, take the test.</p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/the-pisa-world-education-test-results-are-about-to-drop-is-australia-getting-worse-127011">The PISA world education test results are about to drop. Is Australia getting worse?</a>
</strong>
</em>
</p>
<hr>
<p>Each student taking the PISA receives a different set of questions which are of similar context and difficulty. But there is a random variation in the proportion of multiple-choice questions each student gets in their test booklet.</p>
<p>For instance, in 2015, some students received an exam mostly made up of multiple-choice questions (70%), while other students’ exam papers contained only 30% multiple-choice questions.</p>
<p>I exploited this random variation in the proportion of multiple-choice questions to investigate how gender differences in maths performance vary. </p>
<h2>What I found</h2>
<p>Females performed worse than males on multiple-choice questions — this was especially the case when they received an exam booklet with 60% or more multiple-choice questions.</p>
<p>An increase in the share of multiple-choice questions by ten percetage points (such as from 50% to 60%) increased the gender gap in maths scores by 50% in favour of boys. </p>
<hr>
<iframe src="https://flo.uri.sh/visualisation/6272666/embed" title="Interactive or visual content" frameborder="0" scrolling="no" style="width:100%;height:600px;" sandbox="allow-same-origin allow-forms allow-scripts allow-downloads allow-popups allow-popups-to-escape-sandbox allow-top-navigation-by-user-activation" width="100%" height="400"></iframe>
<div style="width:100%!;margin-top:4px!important;text-align:right!important;"><a class="flourish-credit" href="https://public.flourish.studio/visualisation/6272666/?utm_source=embed&utm_campaign=visualisation/6272666" target="_top"><img alt="Made with Flourish" src="https://public.flourish.studio/resources/made_with_flourish.svg"> </a></div>
<hr>
<h2>Why is this happening?</h2>
<p>I also analysed how students approached the answers by tracking the time it took them to respond to a question, as well as the number of questions each student skipped. </p>
<p>PISA data allows me to identify students who answer questions too fast (say in under three seconds, which does not allow for careful reading of the question). </p>
<p>Answering questions too fast or skipping them entirely can be seen as a sign of low effort or inattentiveness.</p>
<p>I found a gender difference in the approach students took to answering questions.</p>
<iframe src="https://flo.uri.sh/visualisation/6272762/embed" title="Interactive or visual content" frameborder="0" scrolling="no" style="width:100%;height:600px;" sandbox="allow-same-origin allow-forms allow-scripts allow-downloads allow-popups allow-popups-to-escape-sandbox allow-top-navigation-by-user-activation" width="100%" height="400"></iframe>
<div style="width:100%!;margin-top:4px!important;text-align:right!important;"><a class="flourish-credit" href="https://public.flourish.studio/visualisation/6272762/?utm_source=embed&utm_campaign=visualisation/6272762" target="_top"><img alt="Made with Flourish" src="https://public.flourish.studio/resources/made_with_flourish.svg"> </a></div>
<p>Overall, boys were less engaged in the test than girls. They answered questions faster and skipped more of them. However, this difference started to reverse the more multiple-choice questions there were in the test. </p>
<p>Girls who received an exam with more multiple-choice questions were more likely to show a lack of effort than when there were more open-ended questions. </p>
<p><a href="https://www.tandfonline.com/doi/abs/10.1080/08957340902754635?casa_token=TQyOdyCueZUAAAAA:j-NU-mqczMCe2hOmiY5u4qa-XkSBA0sFqISwPjUiQvW1VbJpbWhxyQLsn8Wx4QFg9CjpS4Vpy6iyXKs">Previous research</a> supports the idea girls can be less engaged with multiple-choice questions. Girls tend to prefer questions that require more analysis and varied solutions while boys are more likely to just state their answers.</p>
<h2>Confidence matters too</h2>
<p>A student’s confidence in their maths knowledge can also play a part in their performance. For example, a higher level of confidence affects how fast students can rule out an incorrect responses.</p>
<p>PISA 2015 didn’t provide a measure of students’ levels of confidence.</p>
<p>However, <a href="https://bera-journals.onlinelibrary.wiley.com/doi/full/10.1002/berj.3329">previous research</a> has shown girls with mothers working in science, technology, engineering or maths (STEM) occupations are more confident in maths and less likely to believe the stereotypes boys are better than girls. </p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/girls-score-the-same-in-maths-and-science-as-boys-but-higher-in-arts-this-may-be-why-they-are-less-likely-to-pick-stem-careers-131563">Girls score the same in maths and science as boys, but higher in arts – this may be why they are less likely to pick STEM careers</a>
</strong>
</em>
</p>
<hr>
<p>So, I used maternal occupation as a measure of girls’ level of confidence and beliefs in their maths abilities. I found the negative effect of multiple-choice questions on girls’ performance actually disappeared in girls whose mothers worked in STEM-related occupations.</p>
<p>These findings suggest multiple-choice exams may not be the most appropriate tools to measure students’ levels of knowledge.</p><img src="https://counter.theconversation.com/content/160724/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Silvia Griselda receives funding from AXA Research Lab on Gender Equality at Bocconi University. Silvia Griselda also acknowledges the financial support from the University of Melbourne’s FBE Doctoral Program Scholarship for this research. </span></em></p>An analysis of data from the Programme for International Student Assessment (PISA) has found the gender gap in maths tests increased where papers contained more multiple choice questions.Silvia Griselda, Postdoctoral research fellow, The University of MelbourneLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1506312021-04-28T06:06:24Z2021-04-28T06:06:24ZNot every student needs senior maths, but we can make maths more engaging in the earlier school years<figure><img src="https://images.theconversation.com/files/397460/original/file-20210428-19-mmrtuc.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/business-person-standing-against-blackboard-data-129864713">Shutterstock</a></span></figcaption></figure><p>In late 2019, <a href="https://www.nsw.gov.au/media-releases/maths-to-be-compulsory-for-students">New South Wales announced</a> it would make maths compulsory all through school. Victoria will have an additional, easier, <a href="https://www.theage.com.au/politics/victoria/new-year-12-maths-subject-delayed-20210202-p56yqw.html">year 12 maths subject</a> in 2023 to boost the numbers of maths students in senior levels.</p>
<p>Moves to push more students into senior maths partly stem from the idea students need to be equipped with skills for jobs of the future, largely driven by automation. The <a href="https://www.education.gov.au/national-stem-education-resources-toolkit/why-stem-important-0">federal government considers STEM</a> (science, technology, engineering and maths) skills as “crucial for Australia’s changing future”. A resource kit for STEM educators, developed by the federal government, <a href="https://www.education.gov.au/national-stem-education-resources-toolkit/why-stem-important-0">states</a>:</p>
<blockquote>
<p>It’s predicted that future workers will spend more than twice as much time on job tasks requiring science, maths and critical thinking than today.</p>
</blockquote>
<p>But the number of students taking higher level maths has <a href="https://www.smh.com.au/national/nsw/we-ve-bottomed-out-hsc-maths-enrolments-flatline-over-the-decade-20201013-p564k5.html">bottomed-out</a>.
Nationally, <a href="https://theconversation.com/fewer-australians-are-taking-advanced-maths-in-year-12-we-can-learn-from-countries-doing-it-better-149148">less than 30% of students choose</a> upper level, calculus based, maths — down dramatically in the past 20 years. </p>
<p>There are many arguments for how to get more students to take senior maths. They include making the subject more engaging, ensuring enough specialist teachers and, of course, making maths compulsory.</p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/fewer-australians-are-taking-advanced-maths-in-year-12-we-can-learn-from-countries-doing-it-better-149148">Fewer Australians are taking advanced maths in Year 12. We can learn from countries doing it better</a>
</strong>
</em>
</p>
<hr>
<p>At the moment, only <a href="https://www.abc.net.au/news/2018-02-06/stem-subjects-australian-education-system-jobs-atlassian/9373456">Tasmania requires</a> students to take basic maths through to year 12. Students <a href="https://www.smh.com.au/national/nsw/nsw-to-make-maths-mandatory-for-students-in-years-11-and-12-20191023-p533ma.html#:%7E:text=The%20NSW%20government%20will%20make,it%20mandatory%20for%20the%20HSC.&text=Mathematics%20will%20be%20made%20compulsory%20for%20students%20in%20years%2011%20and%2012.">in the ACT and NSW</a> can finish studying maths in year 10 if they choose to. <a href="https://www.sace.sa.edu.au/web/mathematics">South Australia</a>, the <a href="https://www.sace.sa.edu.au/coordinating/ntcet">Northern Territory</a> and <a href="https://www.elc.net.au/new-qce-maths-subjects-explained/">Queensland</a> require students to take just <a href="https://www.abc.net.au/news/2018-02-06/stem-subjects-australian-education-system-jobs-atlassian/9373456">one unit of maths</a> in the two final years of high school. </p>
<p>But how important is it for every student to have graduated school with high level maths?</p>
<h2>Maths and the future of work</h2>
<p>The argument every student needs advanced maths for his or her career doesn’t always hold. A <a href="https://www.livescience.com/29017-which-jobs-actually-use-math.html#:%7E:text=But%20something%20doesn't%20add,on%20the%20job%2C%20research%20suggests.&text=And%20highly%20skilled%20blue%2Dcollar,than%20their%20white%2Dcollar%20peers.">2013 study</a> of 2,300 workers in the United States found less than 25% of them use maths beyond fractions in their current jobs. </p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/397481/original/file-20210428-13-11mj0gd.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="A group of professionals having a discussion at a boardroom table." src="https://images.theconversation.com/files/397481/original/file-20210428-13-11mj0gd.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/397481/original/file-20210428-13-11mj0gd.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=399&fit=crop&dpr=1 600w, https://images.theconversation.com/files/397481/original/file-20210428-13-11mj0gd.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=399&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/397481/original/file-20210428-13-11mj0gd.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=399&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/397481/original/file-20210428-13-11mj0gd.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=502&fit=crop&dpr=1 754w, https://images.theconversation.com/files/397481/original/file-20210428-13-11mj0gd.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=502&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/397481/original/file-20210428-13-11mj0gd.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=502&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Human skills, like relationship building, are important to employers.</span>
<span class="attribution"><a class="source" href="https://www.shutterstock.com/image-photo/making-great-decisions-young-beautiful-woman-370390046">Shutterstock</a></span>
</figcaption>
</figure>
<p>But we’re told the nature of work is rapidly changing and that employment in jobs requiring STEM skills is <a href="https://www.dese.gov.au/newsroom/articles/stem-jobs-growing-almost-twice-fast-other-jobs">growing faster</a> than in others. This may be true. Although the federal <a href="https://joboutlook.gov.au/careers/future-outlook/">government also highlights</a> growing industries aren’t all focused on STEM skills. They include:</p>
<ul>
<li><p>health care and social assistance</p></li>
<li><p>education and training</p></li>
<li><p>construction</p></li>
<li><p>customer service.</p></li>
</ul>
<p>Most of these jobs will require strong numeracy and computational thinking skills, including problem-solving that can come from subjects outside maths.</p>
<p>A <a href="https://www2.deloitte.com/au/en/pages/building-lucky-country/articles/path-prosperity-future-work.htm">Deloitte report</a> into the future of work also noted the importance of human skills in automated industries:</p>
<blockquote>
<p>[…] jobs increasingly need us to use our hearts — the interpersonal and creative roles, with uniquely human skills like creativity, customer service, care for others and collaboration.</p>
</blockquote>
<p>A <a href="https://www.nationalskillscommission.gov.au/skills-future">federal government report</a> echoes this by advising those looking for work to:</p>
<blockquote>
<p>remember to emphasise your employability skills, rather than just the technical skills […] Communication, reliability, team work, patience, resilience and initiative are required for all jobs, and this will continue to be the case in the future […] Some 75% of employers considered employability skills to be as important, if not more important, than technical skills.</p>
</blockquote>
<p>Maths is embedded in most of these skills. But it’s certainly not the only subject that teaches them.</p>
<h2>What subjects can give students the skills they need?</h2>
<p>Broadly speaking, <a href="https://www.topuniversities.com/student-info/careers-advice/future-skills-youll-need-your-career-2030">some of the skills</a> students will need in their future — in both their work and daily life — include:</p>
<ul>
<li><p>cognitive flexibility: the ability to adapt to the changing world and information around you; to be a lifelong learner</p></li>
<li><p>traditional and digital literacies: basic literacy, numeracy and media literacy (including the use of technology)</p></li>
<li><p>creativity and imagination: the human traits that separate us from machines and bring a human perspective to our work</p></li>
<li><p>computational thinking: problem solving processes we need in our work and life</p></li>
<li><p>ethical and sustainable practice: a commitment to do no harm to each other or the planet</p></li>
<li><p>Indigenous perspectives and cultural competence: promoting reconciliation and working successfully and respectfully across cultures and customs </p></li>
<li><p>well-being: taking care of our minds, bodies and our mob.</p></li>
</ul>
<p>These skills are not taught just in maths but across the disciplines, <a href="https://www.monash.edu/education/research/projects/numeracy-across-the-curriculum-research-project">including</a> science, geography, visual arts, health and physical education, languages, history and design.</p>
<h2>What kind of maths skills do students need?</h2>
<p>In his 2016 book, <a href="https://www.goodreads.com/en/book/show/23258874-the-math-myth">The Maths Math: And Other STEM Delusions</a>, bestselling US author Andrew Hacker proposes we allow students to explore their passions in the latter school years instead of pushing advanced maths onto them.</p>
<p>He also recommends we teach basic maths so well students gain computational and critical thinking skills they can use throughout their lives.</p>
<p>Computational skills are the <a href="https://www.bbc.co.uk/bitesize/guides/zp92mp3/revision/1">ability to understand</a> a complex problem, develop possible solutions and then present these solutions in a way a computer, human, or both, can understand. </p>
<p>These skills are what primary maths should aim toward, emphasising interdisciplinary connections across key learning areas. And strong basic numeracy skills build a foundation for a lifetime.</p>
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Read more:
<a href="https://theconversation.com/dont-just-solve-for-x-letting-kids-explore-real-world-scenarios-will-keep-them-in-maths-class-124876">Don’t just solve for x: letting kids explore real-world scenarios will keep them in maths class</a>
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<p>But <a href="https://reports.acara.edu.au/Home/Results#results">NAPLAN numeracy results</a> in the past decade, as well as scores in the OECD’s <a href="https://www.oecd.org/pisa/publications/PISA2018_CN_AUS.pdf">Programme for International Student Assessment</a>, indicate many teachers are not prepared to teach primary maths effectively to an increasingly diverse student population. </p>
<p>Current <a href="https://theconversation.com/fewer-australians-are-taking-advanced-maths-in-year-12-we-can-learn-from-countries-doing-it-better-149148">maths assessments</a> tend to limit the possibilities and the interdisciplinary connections by teaching math discretely. </p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/397484/original/file-20210428-15-n7u8kf.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="Boy and girl working on making a small robot." src="https://images.theconversation.com/files/397484/original/file-20210428-15-n7u8kf.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/397484/original/file-20210428-15-n7u8kf.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/397484/original/file-20210428-15-n7u8kf.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/397484/original/file-20210428-15-n7u8kf.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/397484/original/file-20210428-15-n7u8kf.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/397484/original/file-20210428-15-n7u8kf.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/397484/original/file-20210428-15-n7u8kf.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>
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<span class="caption">We need to teach maths as part of other subjects to make it more engaging.</span>
<span class="attribution"><a class="source" href="https://www.shutterstock.com/image-photo/boy-girl-doing-group-project-making-1070348063">Shutterstock</a></span>
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<p>Many schools are using projects and portfolios to develop these relevant skills, with learning outcomes based on ‘doing’ rather than regurgitating facts. This is not a move away from the goal of traditional numeracy skills. Rather, it’s the way we teach them and honour their relevance in multiple contexts outside of maths that makes the subject more engaging.</p>
<p>It’s important then for maths-related lessons to allow students to create, design, make, build, exhibit and present.</p>
<p>These ideas are at the heart of the current reviews into the <a href="https://nswcurriculumreform.nesa.nsw.edu.au/home/homePageContent/view">NSW Curriculum</a> and the <a href="https://www.acara.edu.au/curriculum/curriculum-review">Australian curriculum</a>. </p>
<p>Armed with these foundational “basics”, all students could connect their passions as teenagers with the STEM skills they need for the future they envision - and many may then choose advanced maths courses with confidence.</p><img src="https://counter.theconversation.com/content/150631/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>John Fischetti does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.</span></em></p>We’re told jobs requiring science and maths skills are growing faster than others. But industry reports also highlight human skills will be more important in the age of automation.John Fischetti, Professor, Pro Vice-Chancellor of the College of Human and Social Futures, University of NewcastleLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1491482020-11-10T19:01:06Z2020-11-10T19:01:06ZFewer Australians are taking advanced maths in Year 12. We can learn from countries doing it better<figure><img src="https://images.theconversation.com/files/368185/original/file-20201109-23-1gcxbtn.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/maths-formulas-written-by-white-chalk-317431127">Shutterstock</a></span></figcaption></figure><p>A <a href="https://www.smh.com.au/national/nsw/we-ve-bottomed-out-hsc-maths-enrolments-flatline-over-the-decade-20201013-p564k5.html">recent New South Wales report</a> showed about one quarter of Year 12 students did not take any Higher School Certificate (HSC) maths courses over the last decade. This was compared to around 6% students who opted out of HSC maths in 2000.</p>
<p>In Queensland, <a href="https://www.couriermail.com.au/subscribe/news/1/?sourceCode=CMWEB_WRE170_a_GGL&dest=https%3A%2F%2Fwww.couriermail.com.au%2Feducation%2Fmaths-dropout-rate-that-could-kill-cheap-university-dream%2Fnews-story%2F4de547c60855fd2fa28b192c0d86f6fe&memtype=anonymous&mode=premium&v21suffix=155-a">reports</a> show nearly one-third of senior students drop out of the intermediate mathematical methods subject, which includes algebra and calculus. The number of Year 11 students choosing the easiest maths subject (not automatically counted towards the ATAR), essential mathematics, has soared by 45% this year — from 12,687 in 2019 to 18,431 in 2020.</p>
<p>Because of the move towards automation, some recent <a href="https://publications.csiro.au/publications/#publication/PIcsiro:EP161054">industry reports</a> note 75% of the fastest growing occupations will require high-level skills in STEM (science, maths, engineering and technology). But studies consistently show in Australia, participation in secondary school advanced maths continues to decline. </p>
<p>Although national <a href="https://amsi.org.au/wp-content/uploads/2020/05/amsi-discipline-profile-2020.pdf">participation rates</a> in Year 12 maths subjects are still high — at around 80% — the proportion of students choosing advanced (calculus-based) maths subjects has declined sharply in the last 20 years. In every year of the last decade, fewer than 30% of students chose intermediate or higher mathematics.</p>
<h2>Changes at university level aren’t enough</h2>
<p>Strategies designed to improve participation in maths include reintroducing maths <a href="https://www.chiefscientist.gov.au/sites/default/files/2020-09/mapping_university_prerequisites_in_australia.pdf">prerequisites</a> for certain areas of university study (such as engineering) and offering <a href="https://www.matrix.edu.au/university-bonus-points/">bonus points for university entry</a> for students who have done advanced maths. The government’s recent job-ready graduates legislation will also make <a href="https://theconversation.com/the-government-is-making-job-ready-degrees-cheaper-for-students-but-cutting-funding-to-the-same-courses-141280">STEM degrees cheaper to study</a>.</p>
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Read more:
<a href="https://theconversation.com/the-government-is-making-job-ready-degrees-cheaper-for-students-but-cutting-funding-to-the-same-courses-141280">The government is making ‘job-ready’ degrees cheaper for students – but cutting funding to the same courses</a>
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<p>These strategies all focus on improving the flow to tertiary education. </p>
<p>But students’ engagement with maths, including their level of achievement and attitude to its importance, are <a href="https://www.iea.nl/studies/iea/timss">formed much earlier</a> than senior secondary school. This means the impact of the above initiatives may not be as effective as intended.</p>
<p>Recent <a href="https://www.smh.com.au/national/nsw/we-ve-bottomed-out-hsc-maths-enrolments-flatline-over-the-decade-20201013-p564k5.html">NSW data</a> shows the University of Sydney’s reintroduction of prerequisites for a wide range of their degrees has failed to shift the dial significantly for falling enrolments in HSC mathematics.</p>
<p>A <a href="http://www.acds-tlcc.edu.au/wp-content/uploads/sites/14/2019/12/ACDS-2019-Final-Report_2-December-2019.pdf">2019 report</a> by the Australian Council for Educational Research, suggested that, for the Group of Eight universities in the study, most students entering science degrees had in fact completed an appropriate level of maths even though they weren’t required to.</p>
<h2>What about other countries?</h2>
<p>It is hard to get standardised data useful for comparing Australian and international participation in upper level, high school maths. There are differences in curriculum structures and content across and within countries. </p>
<p>For example, comparing participation in countries where maths is compulsory until the end of school, for example, <a href="https://www.abc.net.au/news/2018-02-06/stem-subjects-australian-education-system-jobs-atlassian/9373456#:%7E:text=Maths%20matters%20more%20elsewhere%20in%20the%20world&text=Countries%20which%20have%20made%20maths,%2C%20Finland%2C%20Taiwan%20and%20Estonia.">Sweden, Japan, Korea, Russia, Finland, Taiwan, and Estonia</a>,to those where it is not, makes little sense. </p>
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<a href="https://images.theconversation.com/files/368206/original/file-20201109-23-1gbctw0.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="A young Asian boy writing calculations on a chalk board." src="https://images.theconversation.com/files/368206/original/file-20201109-23-1gbctw0.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/368206/original/file-20201109-23-1gbctw0.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=450&fit=crop&dpr=1 600w, https://images.theconversation.com/files/368206/original/file-20201109-23-1gbctw0.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=450&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/368206/original/file-20201109-23-1gbctw0.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=450&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/368206/original/file-20201109-23-1gbctw0.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=566&fit=crop&dpr=1 754w, https://images.theconversation.com/files/368206/original/file-20201109-23-1gbctw0.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=566&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/368206/original/file-20201109-23-1gbctw0.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=566&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
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<span class="caption">Maths is compulsory until the end of school in many countries.</span>
<span class="attribution"><a class="source" href="https://www.shutterstock.com/image-photo/asian-grade-school-student-solving-geometry-609137588">Shutterstock</a></span>
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<p>Some interesting comparisons, however, can still be made. <a href="https://nsf.gov/statistics/2018/nsb20181/report/sections/elementary-and-secondary-mathematics-and-science-education/high-school-coursetaking-in-mathematics-and-science#highest-mathematics-courses-taken-by-high-school-completers">In the US</a>, where maths is not compulsory, only 19% of students who completed high school in 2013 took calculus-based courses. </p>
<p>The United Kingdom, after <a href="https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/630488/AS_review_report.pdf">recognising participation in advanced maths</a> was in serious decline, launched a national campaign to reverse the trend. This included a £67 million initiative to improve teacher supply in maths and physics. While there was some improvement after the campaign, almost three-quarters of students who achieved good marks in maths still chose not to study it after the age of 16. </p>
<p>Participation rates in higher level maths can predict the number of tertiary STEM graduates and the future of the STEM workforce. But strong levels of achievement in maths earlier in the school years are essential to feed the pipeline. </p>
<p>Maths achievement scores for Australian 15-16 year olds, based on international comparative reports — such as the Programme for International Student Assessment <a href="https://www.oecd.org/pisa/">PISA</a> and the Trends in International Mathematics and Science Study <a href="https://www.iea.nl/studies/iea/timss">TIMSS</a> — have shown steady decline since 2003. Perhaps even more concerning is that the ranking-gap between Australia and top performing countries is widening. </p>
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Read more:
<a href="https://theconversation.com/estonia-didnt-deliver-its-pisa-results-on-the-cheap-and-neither-will-australia-128455">Estonia didn't deliver its PISA results on the cheap, and neither will Australia</a>
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<p>In recent TIMSS <a href="https://research.acer.edu.au/cgi/viewcontent.cgi?article=1002&context=timss_2015">reports</a>, which also provide information about students’ attitudes to maths, Australian Year 8 students place almost the same value on maths as their international peers. But a striking difference in attitude emerges from the data — Australian students are significantly less satisfied and engaged with maths than their international peers. </p>
<p><a href="https://amsi.org.au/wp-content/uploads/2020/05/amsi-discipline-profile-2020.pdf">Half</a> of our students don’t like maths, compared to 38% of students in other countries. About one-quarter of our students find maths teaching unengaging, compared to 17% for international students. </p>
<h2>What can we do?</h2>
<p>Australia can look to successful strategies overseas.</p>
<p><a href="https://www.usatoday.com/story/news/education/2020/02/28/math-scores-high-school-lessons-freakonomics-pisa-algebra-geometry/4835742002/">Estonia</a>, the highest ranked European country for maths in PISA in 2018, has small classes and almost no high-stakes tests for school children, leaving more time for instruction. </p>
<p>In Australia, the introduction of NAPLAN has resulted in no perceivable improvement in student <a href="https://theconversation.com/naplan-has-done-little-to-improve-student-outcomes-86049">outcomes</a>. NAPLAN has come under <a href="https://www.ieuvictas.org.au/files/2515/5598/7033/NAPLAN_Reporting_Review_March_2019.pdf">increased criticism</a>, particularly around the amount of valuable class time that may be devoted to NAPLAN style tasks.</p>
<p>Australia needs to concentrate on high-quality student instruction not testing, and improving attitudes to, and engagement in, mathematics.</p>
<p>Australia has one of the highest rates of out-of-field teaching (teaching outside field of expertise) in <a href="https://acola.org/wp-content/uploads/2018/12/saf02-stem-country-comparisons.pdf">mathematics and science</a> in the world. Only in the United States, Brazil and Australia does this occur on a large scale. And it appears to be worse in Australia than the United States.</p>
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Read more:
<a href="https://theconversation.com/more-teens-are-dropping-maths-here-are-three-reasons-to-stick-with-it-119745">More teens are dropping maths. Here are three reasons to stick with it</a>
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<p>Over half of school principals in 2017 <a href="https://amsi.org.au/wp-content/uploads/2017/10/discipline-profile-2017-web.pdf">reported</a> they had maths and science classes being taught by teachers who weren’t fully qualified in the discipline. <a href="https://amsi.org.au/wp-content/uploads/2019/05/amsi-occasional-paper-2.pdf">Research</a> has also found 22% of Australian Year 8 students were taught by out-of-field teachers, compared to an international average of 13%.</p>
<p>The Australian government has tried to close this gap by providing A$9.5 million for professional learning and <a href="https://www.education.gov.au/online-teaching-and-learning-resources-support-mathematics-and-numeracy">resources for teachers</a> from primary to secondary school. But more funding needs to be directed towards out-of-field maths teachers in higher year levels to reach international standards.</p>
<p>In Ireland, for example, about <a href="https://researchoutreach.org/articles/blended-learning-programme-out-of-field-mathematics-teaching/">€7 million</a> has been committed towards professional development for out-of-field maths teachers in the post-primary years. </p>
<p>Australian maths curricula are ambitious, including a strong emphasis on calculus. And they have recently expanded the amount of statistics included at upper year levels. </p>
<p><a href="https://www.ft.com/content/2e4c61f2-4ec8-11e6-8172-e39ecd3b86fc">The UK</a> has looked to successful STEM-education countries like Singapore. Half of its primary schools will adopt their model of deep learning of maths. This moves away from simple rote learning to focus on teaching children how to problem solve. It also covers fewer topics in far greater depth. </p>
<p>Whatever strategies Australia adopts over the next decade to improve maths participation for school children, all levels of education must be involved and include teacher professional development.</p><img src="https://counter.theconversation.com/content/149148/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>The authors do not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and have disclosed no relevant affiliations beyond their academic appointment.</span></em></p>The proportion of students choosing advanced maths subjects has declined sharply in the last 20 years. Australia also has some of the highest rates of maths teachers outside their field of expertise.Linda Galligan, Associate professor, University of Southern QueenslandDeborah King, Director, Bachelor of Science, The University of MelbourneMegan Axelsen, Researcher, University of Southern QueenslandLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1312462020-02-16T14:33:50Z2020-02-16T14:33:50ZWhat connects Shaka Zulu, decolonisation and mathematical models<figure><img src="https://images.theconversation.com/files/315264/original/file-20200213-11023-1kzv7y8.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">There's a body of historical African examples that universities can use to teach a more inclusive mathematical sciences curriculum. </span> <span class="attribution"><span class="source">GettyImages</span></span></figcaption></figure><p>Is it possible to <a href="https://journals.co.za/content/journal/10520/EJC-1aaa3ba0f5">decolonise mathematical sciences</a>? </p>
<p>Some researchers argue that it’s not. They cite numerous reasons why. Two include the fact that decolonisation is extremely difficult for the “pure sciences” such as mathematics. And that the concept of decolonising is “<a href="https://www.sajs.co.za/article/view/5175">poorly defined and contentious, in this domain</a>”.</p>
<p>But <a href="https://journals.co.za/docserver/fulltext/linga_v18_n2_a1.pdf?expires=1579860992&id=id&accname=57837&checksum=EC2A8B2AE4AE0FD99CD19F08CDDB3B38">our research</a> shows that it is possible to achieve the goal of decolonising teaching material for mathematics. This process refers to getting <a href="http://dx.doi.org/10.4102/the.v1i1.9">rid</a> of teaching and learning methods and research that reflects a colonial mindset. It’s the transformation of the curriculum to one that’s inclusive and non-discriminatory. </p>
<p>We argue that by rediscovering and recovering African examples in the teaching of maths, it’s possible to “deconstruct” an exclusive Western body of knowledge. </p>
<p>We focused on the operational research curriculum as an example of a mathematical science. Classical operational research is mainly concerned with the use of mathematical techniques and models used to <a href="https://www.mdpi.com/2079-8954/7/1/5">make decisions</a>. Both quantitative modelling – for example, mathematical and computational techniques – and qualitative modelling (problem structuring methods) are used to analyse complex problems.</p>
<p>The discipline was developed in European universities in the late 1930s and early 1940s. It was further developed during World War II, when mathematical techniques were used in warfare. </p>
<p>But this is a very narrow version of the history of operational research. It excludes similar practices elsewhere in the world. For example, there are a number of examples from African history that are similar to Western problem situations. These also typically solved complex problems by using operational research models and techniques.</p>
<p>Operational research is an important subject and taught at most South African universities at undergraduate and postgraduate levels. It’s often taught under different names. These include: quantitative management, management science, decision science, business analytics and industrial engineering. </p>
<p>But no attempt has been made to investigate the decolonisation of operational research in South Africa. This would require, among other things, an <a href="http://dx.doi.org/10.17159/2520-9868/i74a01">inclusive curriculum</a> by replacing existing material with examples from Africa. </p>
<h2>Examples from Africa</h2>
<p>We identified a range of examples in agriculture and warfare from the continent that could be used in teaching operational research.</p>
<p><strong>Agriculture:</strong> We identified three historical agricultural examples. These were <a href="https://www.aehnetwork.org/wp-content/uploads/2016/01/Green.Production-Systems-in-Pre-Colonial-Africa.pdf">market days</a>, maize production and integration between <a href="http://www.fao.org/fileadmin/templates/lead/pdf/05_article01_en.pdf">grazing livestock</a>, crops and <a href="https://www.ajol.info/index.php/orion/article/view/34279">wildlife</a>. </p>
<p>In pre-colonial Africa market days were organised and rotated between different villages. Finding the right village for a market day was comparable to an operational research problem involving a host of criteria and a great deal of decision-making. The criteria would include factors such as availability, cost considerations, population (clients), facilities and fair rotating of locations. </p>
<p>The maize production example reflects the fact that farming the crop had to be integrated into the forest zones of West Africa. Farmers had to <a href="https://www.aehnetwork.org/wp-content/uploads/2016/01/Green.Production-Systems-in-Pre-Colonial-Africa.pdf">create complex fallow systems</a> by resting sections of land between crops to restore the land’s fertility or to manage surplus production. This too required a typical operational research approach. </p>
<p>These are typical examples of problem situations in an African context, where operational research models functioned in their own unique way.</p>
<p><strong>War strategies:</strong> There are remarkable similarities between operational research applications developed in World War II and African warfare. To illustrate these similarities, we analysed the <a href="https://www.worldcat.org/title/myth-of-iron-shaka-in-history/oclc/65188289">war strategies</a> of <a href="https://www.cambridge.org/core/books/creation-of-the-zulu-kingdom-18151828/B8D56BDA08FFB09833820A6F256538B6">King Shaka Zulu</a>. </p>
<p>King Shaka Zulu is one of the best-known leaders in African war history. His life and work are widely recognised in <a href="https://dl4.globalstf.org/products-page/proceedings/bizstrategy/applicability-of-shaka-zulus-leadership-and-strategies-to-business/">various disciplines</a> as having had a profound influence on South African history. </p>
<p>Here, we also found possible links with operational research techniques and models. For example, an operational research assignment model is aimed at determining the most efficient assignment of people to projects. This is so that the total cost or time to perform a task is minimised. </p>
<p>Shaka Zulu <a href="https://apps.dtic.mil/dtic/tr/fulltext/u2/a612214.pdf">divided his soldiers into regiments</a> – a typical assignment problem where soldiers are assigned based on criteria such as age, skill and physical capabilities. </p>
<p>The problem may also be viewed as a labour planning problem, where staffing needs (number of soldiers) over specific time periods or for specific purposes (battles) are required. </p>
<p>We also identified an operational research application in selection models. Here, people (soldiers) are selected on the basis of strengths and weaknesses of warriors in the context of the expected battle. </p>
<h2>Going forward</h2>
<p>Including examples like this in the curriculum would benefit students who have been marginalised by the exclusive use of Western examples in academia. It would also legitimise knowledge that’s embedded in their own <a href="https://www.amazon.com/Decolonizing-Methodologies-Research-Indigenous-Peoples/dp/1848139500">histories</a>. And it would show how operational research is fundamentally linked to Africa, its people and its history. </p>
<p>Including African examples would also show how knowledge systems are <a href="https://www.amazon.com/As-Fire-South-African-University-ebook/dp/B072353MFV">intertwined</a> and create a new frame of reference. </p>
<p>A few practical pointers could include:</p>
<ul>
<li><p>Identifying examples from African history that are similar to Western problem situations that are typically solved using mathematical models.</p></li>
<li><p>Ensuring the focus is on <a href="https://www.journals.ac.za/index.php/sajhe/article/view/709">decentering Western knowledge</a>, not simply replacing the Western ownership of mathematical sciences with an African discipline. </p></li>
<li><p>An acknowledgement that using African examples is just the starting point. The curriculum then needs to be <a href="http://mg.co.za/article/2015-04-17-what-is-an-african-curriculum/">expanded</a>.</p></li>
</ul>
<p>The decolonisation of mathematical sciences should be treated as a continuous process. It involves <a href="https://www.amazon.com/Indigenous-Research-Methodologies-Bagele-Chilisa/dp/1412958822">dreaming</a> but also laborious research and development.</p><img src="https://counter.theconversation.com/content/131246/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>Decolonising mathematical sciences is possible. The answer lies in rediscovering existing African examples of teaching maths and including them in the Western body of knowledge.Anné H. Verhoef, Professor in Philosophy, North-West UniversityHennie A Kruger, Professor of Computer Science and Information Systems, North-West UniversityLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1199482019-08-22T07:34:29Z2019-08-22T07:34:29ZSTEM: efforts to inspire more children could be entrenching educational inequalities<figure><img src="https://images.theconversation.com/files/288049/original/file-20190814-136230-1d3n6ay.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/download/success?u=http%3A%2F%2Fdownload.shutterstock.com%2Fgatekeeper%2FW3siZSI6MTU2NTgyMjEzMywiYyI6Il9waG90b19zZXNzaW9uX2lkIiwiZGMiOiJpZGxfMTA2MzIxMTczMiIsImsiOiJwaG90by8xMDYzMjExNzMyL21lZGl1bS5qcGciLCJtIjoxLCJkIjoic2h1dHRlcnN0b2NrLW1lZGlhIn0sIjBpQXFCK1Q4Mitzek5EcnJaeVBISTNRVk41WSJd%2Fshutterstock_1063211732.jpg&pi=33421636&m=1063211732&src=E-Be9u9aVk1Q5kvLGi7GeQ-1-1">Shutterstock</a></span></figcaption></figure><p>Science, technology, engineering and mathematics (STEM) education is a priority for governments around the world. For example, the UK’s current commitment to increasing investment in research and development to 2.4% of GDP by 2027 means that we need to train 260,000 more researchers to <a href="http://www.ukpol.co.uk/chris-skidmore-2019-speech-on-research-talent/">carry out this work</a>.</p>
<p>There has long been a perceived shortage in such skills and knowledge. And this drives policy measures in education, skills and immigration to address the situation.</p>
<p>In their STEM strategies, governments are increasingly focused on addressing the large disparities in participation between different social groups. For example, in the UK only 15% of scientists come from <a href="https://www.nature.com/news/is-science-only-for-the-rich-1.20650">working-class households</a>, just 7% of patents are <a href="https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/514320/Gender-profiles-in-UK-patenting-An-analysis-of-female-inventorship.pdf">filed by women</a>, and among start-up founders men outnumber <a href="https://www.nesta.org.uk/blog/some-ideas-are-more-equal-others/">women four to one</a>. The problem is often discussed in terms of a “leaky pipeline”, the idea that potential STEM professionals are lost at particular points along defined pathways.</p>
<h2>Plugging the leak</h2>
<p>This spurs governments around the world to target activities at young people, aiming to foster STEM engagement from an early stage. “STEM inspiration” is one way to do this, by offering STEM-related activities to school-age children beyond usual subject teaching. This could take place within schools, or informally through visits to museums or in the home or community.</p>
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Read more:
<a href="https://theconversation.com/ai-is-in-danger-of-becoming-too-male-new-research-121229">AI is in danger of becoming too male – new research</a>
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<p>The Department for Business, Energy and Industrial Strategy (BEIS) funds STEM inspiration in the UK, spending £103m annually on programmes delivered through bodies such as STEM Learning Ltd, the Wellcome Trust, and the British Science Association. </p>
<p>But is all this activity having the desired effect or could it even be doing more harm than good?</p>
<p>First, we know that there is just not enough provision. For example, <a href="https://www.nesta.org.uk/report/opportunity-lost-how-inventive-potential-squandered-and-what-do-about-it/">our mapping of invention programmes</a> found that they reach just 1.5% of the UK school population annually. Overall, participation in STEM careers activities is low, with less than 30% of 11- to 14-year-olds reporting having <a href="https://www.engineeringuk.com/media/156187/state-of-engineering-report-2018.pdf">taken part in 2017</a>. In light of evidence that it takes around four role model encounters for effects to be seen <a href="https://www.nfer.ac.uk/publications/seoz01/seoz01.pdf">on students’ aspirations</a>, it is likely a very small and select group that receives effective provision. </p>
<p>Also, provision continues to exclude students and communities who need it most – those who are traditionally less likely to take part in STEM. <a href="http://discovery.ucl.ac.uk/1570519/1/ISL%20richer%20paper%20rev2_July%202017.pdf">UCL’s ASPIRES team has found</a> that while significant proportions of the school population report never having had access to STEM inspiration, this is particularly the case among <a href="https://www.ucl.ac.uk/ioe/departments-and-centres/departments/education-practice-and-society/science-capital-research">disadvantaged groups</a>.</p>
<h2>Competition equals inspiration?</h2>
<p>Our own research looked in more detail at one particular type of STEM inspiration activity: competitions. STEM competitions are an increasingly popular model in the UK and internationally, challenging students individually or in teams to apply STEM skills and knowledge to hands-on projects. </p>
<p>There are around 50 STEM and innovation competitions in the UK. Government departments run their own – for example, the <a href="https://awards.yisc.org.uk/">Youth Industrial Strategy Competition</a> by BEIS, and <a href="https://www.ncsc.gov.uk/section/education-skills/11-19-year-olds">CyberFirst</a> by the National Cyber Security Centre. The model is also very popular in the US and China, and reflects a strategic focus on STEM for economic growth. However, in some countries, such as Finland, competitions are treated more as opportunities to collaborate and share knowledge than promote individual success; and in Singapore, there is a noticeable emphasis on creativity in STEM.</p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/287874/original/file-20190813-9400-15bl9er.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/287874/original/file-20190813-9400-15bl9er.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/287874/original/file-20190813-9400-15bl9er.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/287874/original/file-20190813-9400-15bl9er.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/287874/original/file-20190813-9400-15bl9er.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/287874/original/file-20190813-9400-15bl9er.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/287874/original/file-20190813-9400-15bl9er.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">Schools play a key role in developing STEM engagement.</span>
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<p>We looked at participation in STEM competitions in England and compiled a dataset of 179 schools that had teams shortlisted, from 13 competitions in total. While two competitions, the <a href="https://leadersaward.com/">Leaders Award</a> and <a href="https://faraday-secondary.theiet.org/faraday-challenge-days/">IET Faraday</a>, provided complete lists of all participating schools, only shortlisted schools were available for other programmes. </p>
<p>Classifying schools by type, we found that 21% were independent schools, a large over-representation (independent schools make up just 10% of all schools in England). This is probably because, while over 80% of independent schools offer STEM competitions as an extracurricular activity, <a href="https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/818679/An_Unequal_Playing_Field_report.pdf">only half of all state schools do</a>.</p>
<p>After excluding independent schools, we added data on state schools’ deprivation levels using eligibility for the pupil premium (extra funding allocated to schools to support students from disadvantaged backgrounds) as an indicator. We found that almost half (45%) were in the least deprived fifth of all state schools. In other words, there is a strong skew towards schools serving richer populations. </p>
<p>Other studies show that this pattern holds in different fields, too. For example, independent schools are also over-represented in enterprise competitions, and theoretical work suggests that such competitions reproduce inequalities between participants, schools and communities. Academics question the educational value of competitions, observing that such exercises emphasise the extrinsic reward of achievement, so that participants engage in tasks to <a href="http://researchprofiles.herts.ac.uk/portal/en/publications/we-need-to-talk-about-competitions(690e93a4-370f-4c6f-bfae-c5c3751ff0f7).html">win rather than to learn</a>.</p>
<p>However, competitions can be designed with a commitment to equity, meaningful learning, and long-term outcomes for communities, by organisations that draw on research evidence and lessons learned through their own practice. For example, the <a href="https://www.nesta.org.uk/case-study/primary-engineer/">Leaders Award run by Primary Engineer</a> asks children, “If you were an engineer, what would you do?”, challenging them to apply engineering principles to a problem of their choice. The programme runs 16 distinct regional competitions, reaches 60,000 students annually, and emphasises local community and industry links.</p>
<p>As ever, Finland provides an inspiring example. <a href="https://start.luma.fi/en/">StarT</a> is an international programme run by the LUMA Centre, a network of Finnish universities dedicated to ensuring high-quality science, technology and mathematics teaching.</p>
<p>Students develop projects based on their own interests, with the requirement that projects are related to science, maths and/or technology (interdisciplinary projects, and those which incorporate other subjects such as arts, are encouraged), and that they address one of <a href="https://start.luma.fi/en/about-start/themes/">the StarT themes</a>. These projects can then be shared at events, where children peer-assess each others’ work.</p>
<p>A key feature of the programme is the learning community: schools, kindergartens, extracurricular clubs and even families register as learning communities to support projects and are invited to share best practices within this network. </p>
<h2>What’s good practice?</h2>
<p>From our review of STEM competitions and the research behind them, we’ve identified four principles of good practice.</p>
<p>First, equity. Competitions should be designed with those who are most excluded in mind, so that provision is practically and conceptually inclusive.</p>
<p>Second, congruence. The offer should relate to <a href="https://www.ucl.ac.uk/ioe/departments-and-centres/departments/education-practice-and-society/science-capital-research/science-capital-teaching-approach">students’ own experiences</a>, and facilitate the move to further study.</p>
<p>Third, intensity. One-off experiences are rarely effective. Sustained and joined-up support is needed for long-term outcomes.</p>
<p>Finally, reflection. For both participants and providers, it’s important to build in opportunities for reflecting on and integrating learning into further study or further iterations of programmes.</p>
<p>If these four foundations are put in place, STEM inspiration can better serve students, and through them, society in general.</p><img src="https://counter.theconversation.com/content/119948/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Juliet Ollard 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>Overall, participation in STEM careers activities is low, with less than 30% of UK 11- to 14-year-olds reporting having taken part in 2017.Juliet Ollard, Researcher, NestaLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1197452019-07-31T20:03:57Z2019-07-31T20:03:57ZMore teens are dropping maths. Here are three reasons to stick with it<figure><img src="https://images.theconversation.com/files/284017/original/file-20190715-173366-vircaw.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">If more girls studied maths, we could see a narrowing of the gender wage gap.</span> <span class="attribution"><span class="source">from shutterstock.com</span></span></figcaption></figure><p>The numbers of secondary school students who take higher-level maths and science are low in Australia. In 2012, there were <a href="https://www.chiefscientist.gov.au/wp-content/uploads/2-Science-and-Maths-in-Australian-Secondary-Schools-datasheet-references.pdf">30,000 more Year 12 students</a> than in 1992. But the numbers of students studying physics, chemistry and biology decreased by 8,000, 4,000 and 12,000 respectively. </p>
<p>Enrolments in intermediate and advanced mathematics also <a href="https://search.informit.com.au/documentSummary;dn=685386398396236;res=IELHSS">fell over this period</a>, by 11% and 7% respectively.</p>
<p>The Australian Curriculum <a href="https://educationstandards.nsw.edu.au/wps/portal/nesa/11-12/hsc/subject-selection">mandates maths</a> until Year 10. But we’re seeing more students dropping the subject as soon as they can. </p>
<p>In 2008, 31.2% of the NSW student population were studying maths for the High School Certificate, compared to 28.9% in 2017. This was a <a href="https://amsi.org.au/preview-year-12-mathematics-participation-in-australia-2008-2017/">drop of around</a> 5,300 students.</p>
<p>But studying maths brings many benefits. Here are three reasons to persevere. </p>
<h2>1. You’ll be more likely to get a job</h2>
<p>Many industry and economic <a href="http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.632.1213&rep=rep1&type=pdf">experts predict</a> future economies – specifically those using technology to rapidly create goods and services – will be built on maths and science knowledge and skills. </p>
<p>Research on the changing nature of employment predicts that, by 2030, we will <a href="https://www.fya.org.au/report/the-new-work-smarts/">spend 77% more time</a> on average using science and mathematics skills. With youth (people aged 15-24) <a href="https://tradingeconomics.com/australia/youth-unemployment-rate">unemployment in Australia on the rise</a>, maths skills may offer some protection. </p>
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Read more:
<a href="https://theconversation.com/why-it-matters-that-student-participation-in-maths-and-science-is-declining-47559">Why it matters that student participation in maths and science is declining</a>
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<p>There are more engineering jobs in Australia than skilled people to fill them. Between 2006 and 2016, the demand for engineers exceeded the number of local graduates. Employers <a href="https://www.engineering.unsw.edu.au/news/australia-is-desperately-short-of-engineers">often look overseas</a> for suitable applicants, with some figures showing more vacancies are filled by overseas engineering graduates than locals.</p>
<h2>2. You’ll probably earn more</h2>
<p>Some studies have shown students taking higher maths at school <a href="https://www.theatlantic.com/business/archive/2013/11/will-studying-math-make-you-richer/281104/">go on to have higher earnings</a> in adulthood. </p>
<p>The relationship between studying higher-level maths and earning more may be one of causation (that maths skills lead to higher earners), correlation (that people with good maths skills are more likely to have other skills that lead to higher earnings), or a bit of both. But, either way, it exists.</p>
<p>According to <a href="https://www.forbes.com/sites/jennagoudreau/2012/05/15/best-top-most-valuable-college-majors-degrees/#743070774dcc">US analysis</a> that compared university majors with median starting pay, median mid-career pay (at least ten years in), growth in salary and wealth of job opportunities, maths and engineering majors reigned supreme.</p>
<p>And a more <a href="https://www.forbes.com/sites/nickmorrison/2019/03/27/the-college-majors-with-the-highest-salaries-and-the-best-prospects/#2706db3a5aa2">recent analysis</a> by the US data researcher PayScale found graduates in maths, science and engineering had the highest mid-career salary.</p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/286195/original/file-20190730-186805-ohsi6a.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/286195/original/file-20190730-186805-ohsi6a.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/286195/original/file-20190730-186805-ohsi6a.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/286195/original/file-20190730-186805-ohsi6a.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/286195/original/file-20190730-186805-ohsi6a.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/286195/original/file-20190730-186805-ohsi6a.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/286195/original/file-20190730-186805-ohsi6a.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/286195/original/file-20190730-186805-ohsi6a.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=503&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
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<span class="caption">Girls aren’t worse than boys at maths, but they drop the subject earlier.</span>
<span class="attribution"><span class="source">from shutterstock.com</span></span>
</figcaption>
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<p>One of the biggest gender gaps in education is seen in maths. Girls in most countries complete less, or lower level, maths than boys. </p>
<p>The low numbers of girls participating in advanced maths courses is not because girls are worse at maths, as there is <a href="https://www.scientificamerican.com/article/are-boys-better-than-girls-at-math/">no clear gender gap</a> when it comes to maths abilities. But girls do <a href="https://www.scientificamerican.com/article/are-boys-better-than-girls-at-math/">show less confidence</a> in their maths skills and more maths anxiety than boys.</p>
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Read more:
<a href="https://theconversation.com/women-in-stem-need-your-support-and-australia-needs-women-in-stem-113054">Women in STEM need your support – and Australia needs women in STEM</a>
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<p>Research suggests learning maths is often associated with <a href="https://www.researchgate.net/publication/232599119_Math_Anxiety_in_Elementary_and_Secondary_School_Students/link/02bfe50ef063d8f42f000000/download">student anxiety</a>. This anxiety is related to poor performance, negative attitudes and general avoidance of the <a href="https://psycnet.apa.org/record/1990-15802-001">subject</a>. If girls were encouraged to persist with the challenges presented by advanced levels of maths, we could even see a start to <a href="https://academic.oup.com/ej/article-abstract/126/593/1129/5078109?redirectedFrom=fulltext">a narrowing of</a> the gender wage gap. </p>
<h2>3. You’ll probably be smarter</h2>
<p>A study examined the <a href="https://www.sciencedirect.com/science/article/pii/S0160289606000171">association between intelligence and educational achievement</a> in relation to 25 secondary school subjects in the UK. It showed maths was most strongly associated with the so-called “g” factor, which is a <a href="https://psycnet.apa.org/buy/2008-07564-003">mark of underlying intelligence</a> (English came second). </p>
<p>The g factor, or general ability, is the foundation of cognitive abilities and affects all learning, including in maths and science. Graduates in STEM (science, technology, engineering and mathematics) <a href="https://www.chiefscientist.gov.au/wp-content/uploads/STEM_AustraliasFuture_Sept2014_Web.pdf">disciplines report</a> their degrees led to them developing higher-order skills and qualities (such as logical thinking and creativity).</p>
<p>Another study showed an increase in population IQ <a href="https://www.sciencedirect.com/science/article/pii/S0160289604000789">alongside a rise</a> in access to maths education in the US. Studies show higher levels of maths attainment for a population are strongly linked to <a href="https://www-sciencedirect-com.ezproxy1.library.usyd.edu.au/science/article/pii/S0160289609000063?via%3Dihub">national IQ</a> and national shifts in economic development, such as <a href="https://search.proquest.com/openview/5eb6d99494548f1a11a1ff702d86c930/1?pq-origsite=gscholar&cbl=30967">higher GDP</a> and faster <a href="https://www.semanticscholar.org/paper/National-IQ-and-economic-outcomes-Meisenberg/705cc2e57e187698e4c9dabcd20e7454a2a2c54a#paper-header">economic growth</a>. </p>
<p>A higher g factor is also associated with higher scores on international assessments of educational attainment, such as <a href="https://onlinelibrary.wiley.com/doi/abs/10.1002/per.634">PISA and TIMSS, and IQ tests</a>.</p>
<p>As the Australian system doesn’t require maths after Year 10, it seems it is up to individuals, families and their communities to recognise its importance and support students in persevering in maths for their own good.</p>
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Read more:
<a href="https://theconversation.com/what-to-say-if-your-child-asks-whats-the-point-of-maths-69628">What to say if your child asks, 'what's the point of maths?'</a>
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<img src="https://counter.theconversation.com/content/119745/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>The authors do not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and have disclosed no relevant affiliations beyond their academic appointment.</span></em></p>Studying maths is likely to make you smarter and more employable.Rachel Wilson, Senior Lecturer - Research Methodology / Educational Assessment & Evaluation, University of SydneyDeborah Chadwick, Lecturer, University of SydneyLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/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">
<figcaption>
<span class="caption">Maths can be fun – if only it’s taught properly.</span>
<span class="attribution"><span class="source">Shutterstock</span></span>
</figcaption>
</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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<p>
<em>
<strong>
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>
</strong>
</em>
</p>
<hr>
<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/1141282019-04-03T14:11:27Z2019-04-03T14:11:27ZNot all autistic people are good at maths and science – despite the stereotypes<figure><img src="https://images.theconversation.com/files/266774/original/file-20190401-177187-3prt5s.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>Despite increased awareness of autism and the impact it can have on people’s lives, many autistic people continue to struggle against misleading stereotypes.</p>
<p>Being autistic, for example, doesn’t automatically make you a “<a href="https://www.dailymail.co.uk/femail/article-1240909/The-extraordinary-love-affair-British-scientist-Paul-Dirac-chatterbox-divorcee.html">human calculator</a>” or a “<a href="https://patrickscasestudies.wordpress.com/2017/10/02/the-living-google/">living Google</a>” – despite what some people may think. And it also doesn’t mean you can’t grasp fiction or have a love of novels.</p>
<p>I’m an autistic lecturer in English and creative writing. Literature is my way into the world. It helps me to better understand people –- including myself. Plus, in novels and poems, words are freed from the weight of body language.</p>
<p>But according to stereotypes (and worse, expectations) around autism, I should not be able to grasp fiction –- let alone lecture or publish papers on it. Autistic people are supposedly good at STEM subjects (science, technology, engineering, maths), <a href="https://www.wired.com/2001/12/aspergers/">not the arts</a>. </p>
<h2>‘Minds wired for science’</h2>
<p>For more than 20 years, the University of Cambridge’s Autism Research Centre has proclaimed that autism is linked with “<a href="https://www.wired.co.uk/article/simon-baron-cohen">minds wired for science</a>” – which can be taken to mean minds not “wired” for creative or critical thinking. The association of STEM subjects with autism has been widely popularised by the centre’s director, <a href="https://www.autismresearchcentre.com/people_Baron-Cohen">Simon Baron-Cohen</a>. </p>
<p>But my new book <a href="https://www.amazon.co.uk/Naming-Adult-Autism-Culture-Identity-ebook/dp/B074X3JNM3/ref=sr_1_fkmrnull_1?keywords=naming+adult+autism&qid=1553717423&s=gateway&sr=8-1-fkmrnull">Naming Adult Autism</a> uncovers various scientific oversights which may have misguided Baron-Cohen’s research findings from the outset. And it seems flaws in a <a href="http://docs.autismresearchcentre.com/papers/2001_BCetal_AQ.pdf">major questionnaire</a> used to determine autistic traits could mean that many autistic adults remain undiagnosed – simply because they enjoy reading novels.</p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/266593/original/file-20190329-71012-1dvf3bp.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/266593/original/file-20190329-71012-1dvf3bp.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/266593/original/file-20190329-71012-1dvf3bp.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/266593/original/file-20190329-71012-1dvf3bp.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/266593/original/file-20190329-71012-1dvf3bp.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/266593/original/file-20190329-71012-1dvf3bp.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/266593/original/file-20190329-71012-1dvf3bp.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">Yes, people with autism can understand literature.</span>
<span class="attribution"><span class="source">Shutterstock</span></span>
</figcaption>
</figure>
<p>The <a href="http://docs.autismresearchcentre.com/papers/2001_BCetal_AQ.pdf">Adult Autism Quotient</a> test counts autistic “traits” relating to routine, communication and socialising and is used to help diagnose people with autism. It was designed by Baron-Cohen and academic Sally Wheelwright, plus three undergraduates. It launched in 2001 and continues to be reproduced across websites, books and magazines worldwide. It is also the basis of <a href="https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0141229">ongoing national surveys</a> of autistic traits.</p>
<p>The introduction of the questionnaire aimed to create a new means to help GPs decide whether to refer patients for further <a href="https://s3.amazonaws.com/academia.edu.documents/40528113/Screening_Adults_for_Asperger_Syndrome_U20151130-16058-1r644iq.pdf?AWSAccessKeyId=AKIAIWOWYYGZ2Y53UL3A&Expires=1553721131&Signature=XEO50blJAUP1O6qanWpTpBmwtLY%3D&response-content-disposition=inline%3B%20filename%3DScreening_Adults_for_Asperger_Syndrome_U.pdf">autism assessment</a>. But a second purpose seems <a href="https://www.amazon.co.uk/Naming-Adult-Autism-Culture-Identity-ebook/dp/B074X3JNM3/ref=sr_1_fkmrnull_1?keywords=naming+adult+autism&qid=1553717423&s=gateway&sr=8-1-fkmrnull">scientifically questionable</a> in its support of Baron-Cohen’s then new, headline-friendly theory that mathematicians and scientists typically show higher numbers of autistic traits than the general population.</p>
<p>The questionnaire also includes carefully-scored questions regarding maths and the arts. If your answers indicate an interest in maths, that will automatically raise your autism score. All answers suggesting an interest in fiction or art score towards “neurotypicality” – or non-autism. </p>
<p>This means that if you are autistic but you like reading novels, your autism quotient will be lower. So you could be less likely to be referred on to autism specialists for assessment. It also means that mathematicians may score higher on the questionnaire because they are interested in numbers –- but not necessarily because they are autistic. </p>
<h2>Autism and literature</h2>
<p>This “minds wired for science” idea about autistic people also creeps into literature itself – and assumptions that autistic people don’t “get” fiction are widespread in novels. </p>
<p>From romantic comedy – Graeme Simsion’s <a href="https://www.penguin.co.uk/books/193470/the-rosie-project/9781405912792.html">Rosie Project</a> – to literary fiction – Margaret Atwood’s <a href="http://margaretatwood.ca/maddaddam-trilogy/">Maddaddam trilogy</a> – adult autism is often reduced to caricatures. This is nearly always of a white, able-bodied male who excels at science or maths. Commendably, Simsion’s recent book <a href="http://theconversation.com/graeme-simsions-the-rosie-result-puts-autism-front-and-centre-110032">The Rosie Result</a> adopts a far more critical approach to autism. Even so, the cultural stereotype of the autistic scientist is still hard to shake off.</p>
<p>This fixation on autistic minds just being wired for science needs rethinking, because expectations that autistic people will succeed at either science or nothing are disabling. And this association risks streamlining future generations of autistics.</p>
<h2>The future of autism</h2>
<p>These <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2677582/">stereotypes matter</a> because they are misrepresenting what people with autism are actually like. They often present autistics to be “a certain way”, a loner or socially awkward – when in fact this varies person to person (autistic or not). </p>
<p>This is particularly important given that “prevention” of autism via prenatal screening may soon become available. <a href="https://www.thelancet.com/journals/lancet/article/PIIS0140673609608916/fulltext">Baron-Cohen’s commentary</a> on autism, ethics and science states his opposition to “preventing” or “curing” autism. But alongside surveys of autistic traits and STEM talent, Cambridge’s Autism Research Centre is also leading research into <a href="https://www.autismresearchcentre.com/project_15_foetaltst">autism and foetal hormones</a> </p>
<p>A publication involving scientists across Europe – including some of those working at Cambridge’s Autism Research Centre – acknowledged in 2015 that prenatal tests for “autism risk” <a href="http://centaur.reading.ac.uk/36984/1/mp201448a.pdf">are not yet possible</a>, but suggest their findings could be used for such research in future. This could inevitably shape some decisions about abortion.</p>
<p>This is why it’s vitally important that there is proper representation of autism in books, film and TV – and society as a whole that embraces the full range of autistic experience and contribution. And it starts with busting the myth that all autistic people are maths geniuses –- because for many, that couldn’t be further from the truth.</p><img src="https://counter.theconversation.com/content/114128/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>James McGrath 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>Autistic and artistic, you can be both.James McGrath, Senior Lecturer in Literature and Cultural Studies, Leeds Beckett UniversityLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1023812018-09-14T08:21:45Z2018-09-14T08:21:45ZMaths quiz: a very problematic game of tennis<figure><img src="https://images.theconversation.com/files/236273/original/file-20180913-177947-l7oqk3.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">One racket of many.</span> <span class="attribution"><a class="source" href="https://www.shutterstock.com/download/success?u=http%3A%2F%2Fdownload.shutterstock.com%2Fgatekeeper%2FW3siZSI6MTUzNjg4NjY0NiwiYyI6Il9waG90b19zZXNzaW9uX2lkIiwiZGMiOiJpZGxfMTE3NDM1MTkzOSIsImsiOiJwaG90by8xMTc0MzUxOTM5L21lZGl1bS5qcGciLCJtIjoxLCJkIjoic2h1dHRlcnN0b2NrLW1lZGlhIn0sIjdXSDZNR0R5YTd3Q2kwMDF3YVdDenBITXFNMCJd%2Fshutterstock_1174351939.jpg&pi=33421636&m=1174351939&src=amBXYY-X-a41abUuJBHm4A-1-48">Shutterstock</a></span></figcaption></figure><p><em>Mathematician Gihan Marasingha specialises in setting devilishly difficult number conundrums, including for BBC Radio 4. Can you solve his latest problem?</em></p>
<p>Each day for a week, a tennis player is to receive a number of tennis rackets as a gift. She knows that she’ll get a different number of rackets on each of the seven days and is told exactly how many she’ll receive in total. Using only this information, she deduces that on at least one day she’ll be presented with at least ten rackets. What is the minimum total number of rackets she could receive for her to know this? </p>
<h2>The solution (spoiler alert)</h2>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/236417/original/file-20180914-177938-r8u2dn.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/236417/original/file-20180914-177938-r8u2dn.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=401&fit=crop&dpr=1 600w, https://images.theconversation.com/files/236417/original/file-20180914-177938-r8u2dn.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=401&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/236417/original/file-20180914-177938-r8u2dn.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=401&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/236417/original/file-20180914-177938-r8u2dn.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=504&fit=crop&dpr=1 754w, https://images.theconversation.com/files/236417/original/file-20180914-177938-r8u2dn.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=504&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/236417/original/file-20180914-177938-r8u2dn.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">It’s all about pigeonholes.</span>
<span class="attribution"><a class="source" href="https://www.shutterstock.com/download/success?u=http%3A%2F%2Fdownload.shutterstock.com%2Fgatekeeper%2FW3siZSI6MTUzNjk0NzUyMywiYyI6Il9waG90b19zZXNzaW9uX2lkIiwiZGMiOiJpZGxfMzExNDQ1ODU3IiwiayI6InBob3RvLzMxMTQ0NTg1Ny9tZWRpdW0uanBnIiwibSI6MSwiZCI6InNodXR0ZXJzdG9jay1tZWRpYSJ9LCJlamEwZEd4cU1OUEFwTm5zR0NkNjhOa3RVcjgiXQ%2Fshutterstock_311445857.jpg&pi=33421636&m=311445857&src=WtfPQuIJUSS_lFrvPXaa-w-1-18">Shutterstock</a></span>
</figcaption>
</figure>
<p>She’ll be given at least 43 rackets. Any fewer and she couldn’t <em>guarantee</em> she would receive ten or more on any one day. For example, if the total was 42, she could receive 9 + 8 + 7 + 6 + 5 + 4 + 3 (= 42) – and not necessarily get ten in one go. </p>
<p>This puzzle is based on the so-called pigeonhole principle. If more than <em>n</em> pigeons are to be placed in <em>n</em> pigeonholes, then at least one pigeonhole must contain at least two pigeons.</p>
<p>The pigeonhole principle has striking consequences. You might wonder, for instance, how likely it is for two people in London to have the same number of hairs on their head. To make the problem interesting, we’ll only consider non-bald Londoners.</p>
<p>There are more than eight million Londoners. These are our “pigeons”. We put each Londoner into a pigeonhole labelled with the number of hairs on his or her head. Humans have 100,000 head hair follicles, on average. The number of follicles are the pigeonholes. Even taking into account variance from the average and bald Londoners, there are vastly more pigeons than pigeonholes. This proves that at least two non-bald Londoners have exactly the same number of hairs on their head.</p>
<hr>
<p><em>Want another puzzle devised by an academic expert?</em></p>
<ul>
<li><em><a href="https://theconversation.com/logic-puzzle-can-you-solve-this-baffling-brexit-conundrum-103850?utm_source=TCUK&utm_medium=linkback&utm_campaign=TCUKengagement&utm_content=UKPuzzle">Logic puzzle: can you solve this baffling Brexit conundrum?</a></em></li>
</ul><img src="https://counter.theconversation.com/content/102381/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Gihan Marasingha 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>Can you outsmart our maths mastermind? The solution’s in.Gihan Marasingha, Senior Lecturer, Mathematics, University of ExeterLicensed 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/999982018-07-19T18:50:26Z2018-07-19T18:50:26ZUniversities can help recruit more science and maths teachers, but they can’t do it alone<figure><img src="https://images.theconversation.com/files/228170/original/file-20180718-142417-1uhqd8i.jpg?ixlib=rb-1.1.0&rect=0%2C0%2C995%2C491&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Encouraging students to study science and maths at university is only one step in a complex pipeline that turns out specialist teachers.</span> <span class="attribution"><a class="source" href="https://www.shutterstock.com/download/success?u=http%3A%2F%2Fdownload.shutterstock.com%2Fgatekeeper%2FW3siZSI6MTUzMTkyNDk5NiwiYyI6Il9waG90b19zZXNzaW9uX2lkIiwiZGMiOiJpZGxfNzAwOTIwMzQzIiwiayI6InBob3RvLzcwMDkyMDM0My9tZWRpdW0uanBnIiwibSI6MSwiZCI6InNodXR0ZXJzdG9jay1tZWRpYSJ9LCJtMXpTNHZQOWRWbnRMRGk5SlpTNTRaVWE5QUUiXQ%2Fshutterstock_700920343.jpg&pi=41133566&m=700920343&src=qL0UHOeGOBa6JWdvd9ukQA-1-65">from www.shutterstock.com</a></span></figcaption></figure><p>Calls for universities to recruit more science and maths students as a way of boosting numbers of specialist school teachers, or risk losing funding, fails to recognise the complexity of the task.</p>
<p>While Education Minister Simon Birmingham’s recent <a href="http://www.abc.net.au/news/2018-07-09/every-high-school-to-get-specialist-maths-science-teachers/9956880">announcement</a> is well-intended, putting the responsibility on universities is unfair.</p>
<p>It fails to consider that the way the teaching profession is portrayed more broadly in society has a significant impact on people’s willingness to enter the profession.</p>
<p>While universities do play a role in boosting specialist teacher numbers, this pressure on universities needs to be part of a <a href="https://research.acer.edu.au/workforce/4/">suite of measures</a> to deal with the shortage.</p>
<h2>Long-standing concerns</h2>
<p>A push for more specialist science and maths teachers follows long-standing <a href="https://research.acer.edu.au/policyinsights/2/">concerns</a> about the <a href="https://research.acer.edu.au/policyinsights/6/">high incidence</a> of maths and science teachers who are not specialists in the subject.</p>
<p>In 2017, the Australian Mathematical Science Institute <a href="https://amsi.org.au/publications/2030-strategic-plan-issues-paper-innovation-science-australia-response/">reported</a> around 30% of year 7-10 maths classes did not have a specialist maths teacher.</p>
<p>The Australian Council for Educational Research’s <a href="https://research.acer.edu.au/policyinsights/6/">analysis</a> of the Staff in Australia’s Schools Survey showed that 30% of maths teachers did not have tertiary level maths. For the sciences, about 20% of chemistry teachers and 30% of physics teachers did not have tertiary level backgrounds in those disciplines. Most alarming is that 37% of all teachers in their first two years of teaching were teaching out-of-field.</p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/too-many-teachers-teaching-outside-their-area-of-expertise-39688">Too many teachers teaching outside their area of expertise</a>
</strong>
</em>
</p>
<hr>
<p>Recruiting more people with science and maths degrees into teaching is an important policy response, given that there are clearly not enough of these teachers in the system, particularly in <a href="https://research.acer.edu.au/policyinsights/6/">rural areas</a>.</p>
<p>But a barrier to recruiting teachers, especially from the sciences and maths, is the continued decline in the number of university graduates in those disciplines. For example, the number of maths graduates has fallen <a href="https://amsi.org.au/publications/2030-strategic-plan-issues-paper-innovation-science-australia-response/">40% since 2003</a>. So attracting more people to study science and maths at university should be a priority. </p>
<p>Another barrier to recruiting teachers is that pay and working conditions in many schools have for some time been <a href="http://www.abc.net.au/news/2011-12-21/australian-students-shun-science/3741316">less attractive</a> than that offered in industry.</p>
<p>These barriers are beyond the control of the university sector. So, any requirement that universities attract more science and maths graduates should be accompanied by discussions about why it is so difficult to attract people to a profession that appears undervalued, underpaid, and constantly criticised.</p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/teachers-who-feel-appreciated-are-less-likely-to-leave-the-profession-89864">Teachers who feel appreciated are less likely to leave the profession</a>
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</em>
</p>
<hr>
<p>Despite this, universities do play a role. Here’s what they can do to recruit more science and maths teachers.</p>
<h2>Closer working relationships</h2>
<p>Closer working relationships between education and science/maths/IT faculties might encourage more young people to teach. This would be through, for example: </p>
<ol>
<li><p>offering education units to science students as tasters. Already in many education degrees, students take discipline-based units offered by other faculties, usually because of accreditation requirements. The same might be promoted through science/maths/IT faculties</p></li>
<li><p>students from science/maths/IT faculties can be used as student ambassadors in schools, or through university outreach, to work with school children, assist teacher innovation, and promote their chosen career pathways. These initiatives can both attract young people to science, technology, engineering and maths – <a href="http://www.invergowrie.org.au/girls-future-our-future-the-invergowrie-foundation-stem-report/">especially girls</a> – and give budding young scientists and mathematicians a taste of working with young people.</p></li>
</ol>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/explainer-whats-the-difference-between-stem-and-steam-95713">Explainer: what's the difference between STEM and STEAM?</a>
</strong>
</em>
</p>
<hr>
<h2>Scholarships and recruitment</h2>
<p>A more costly approach might be to offer scholarships for science and maths graduates entering a graduate education degree. This might be, for example, a scholarship for a global experience program offered as part of an education course, or grants for textbooks.</p>
<p>Universities could work more closely with schools to recruit students into teaching maths and science. This has worked in <a href="http://scholar.google.com.au/scholar_url?url=http://www.academia.edu/download/30369419/sleeter_preparing_teachers_for_culturally_diverse_schools.pdf&hl=en&sa=X&scisig=AAGBfm1aXov4Tk9QpDfpv6bp31sReul80w&nossl=1&oi=scholarr">other countries</a>, especially for recruiting groups within society that might not normally consider <a href="https://www.jstor.org/stable/j.ctt1p0vkh1">teaching as a career</a>.</p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/why-is-it-so-hard-to-recruit-good-maths-and-science-teachers-55697">Why is it so hard to recruit good maths and science teachers?</a>
</strong>
</em>
</p>
<hr>
<h2>Take steps now</h2>
<p>The push to solve the problem of out-of-field teaching by recruiting more science and maths teachers into the system is only part of the solution. It is a long-term one. </p>
<p>More immediate action should be taken to work with current out-of-field maths and science teachers to raise their expertise in these areas through funded retraining, recognised as additional qualifications and rewarded, for example, with increased pay or bonuses. </p>
<p>Preparing out-of-field maths and science teachers as disciplinary experts in these fields should be a priority. An education system in which it becomes standard to assist (that is, fund) teachers to gain additional qualifications places universities at the forefront of maintaining a highly effective teaching workforce. </p>
<h2>Where to now?</h2>
<p>While Birmingham’s announcement is well intended, it fails to recognise the complexity of the recruitment pipeline. Attracting people to the teaching profession is the responsibly of universities, governments, schools, parents, and society generally. </p>
<p>Governments play an important role in promoting public confidence in our education system, so that teaching is seen as a rewarding career in which innovation and creativity is encouraged and not thwarted by <a href="https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0ahUKEwiwkI6GzKjcAhWDsJQKHUJVCmsQFggqMAA&url=https%3A%2F%2Fwww.aitsl.edu.au%2Fdocs%2Fdefault-source%2Fresearch-evidence%2Fspotlight%2Fspotlight---attrition.pdf%3Fsfvrsn%3D40d1ed3c_0&usg=AOvVaw30TKhXlaEpZU7c4K1GVBLe">high workloads and poor support measures</a>.</p>
<p>So, rather than the threat of withholding funding from universities, incentives for universities would provide greater opportunities for thinking differently when considering what they can offer students and new ways of working together.</p><img src="https://counter.theconversation.com/content/99998/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Linda Hobbs has received funding from the Australian Research Council for a Discovery Grant focused on teaching out-of-field. </span></em></p>Recruiting specialist teachers takes more than just encouraging them to study science and maths at university. Governments and wider society needs to come on board too.Linda Hobbs, Associate Professor of Education (Science Education), Deakin UniversityLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/786602017-06-21T10:31:01Z2017-06-21T10:31:01ZChallenging the status quo in mathematics: Teaching for understanding<figure><img src="https://images.theconversation.com/files/174303/original/file-20170618-28772-1vhqkpw.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">How can we change math instruction to meet the needs of today's kids?</span> <span class="attribution"><a class="source" href="https://flic.kr/p/97aGY8">World Bank Photo Collection / flickr</a>, <a class="license" href="http://creativecommons.org/licenses/by-nc-nd/4.0/">CC BY-NC-ND</a></span></figcaption></figure><p>Despite decades of <a href="http://files.eric.ed.gov/fulltext/ED372969.pdf">reform efforts</a>, mathematics teaching in the U.S. <a href="http://www.jstor.org/stable/20405948">has changed little</a> in the last century. As a result, it seems, American students have been left behind, now ranking <a href="https://nces.ed.gov/pubs2017/2017048.pdf#page=31">40th in the world</a> in math literacy. </p>
<p>Several state and national reform efforts have tried to improve things. The most recent <a href="http://www.corestandards.org/Math/">Common Core standards</a> had a great deal of promise with their focus on how to teach mathematics, but after several years, <a href="http://journals.sagepub.com/doi/full/10.3102/0013189X17711899">changes in teaching practices</a> have been minimal. </p>
<p><iframe id="Grc6N" class="tc-infographic-datawrapper" src="https://datawrapper.dwcdn.net/Grc6N/1/" height="400px" width="100%" style="border: none" frameborder="0"></iframe></p>
<p>As an education researcher, I’ve observed teachers trying to implement reforms – often with limited success. They sometimes make changes that are more cosmetic than substantive (e.g., more student discussion and group activity), while failing to get at the heart of the matter: What does it truly mean to teach and learn mathematics?</p>
<h2>Traditional mathematics teaching</h2>
<p>Traditional middle or high school mathematics teaching in the U.S. <a href="http://www.jstor.org/stable/20405948">typically follows this pattern</a>: The teacher demonstrates a set of procedures that can be used to solve a particular kind of problem. A similar problem is then introduced for the class to solve together. Then, the students get a number of exercises to practice on their own.</p>
<figure class="align-right ">
<img alt="" src="https://images.theconversation.com/files/174300/original/file-20170618-28759-1jyothn.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/174300/original/file-20170618-28759-1jyothn.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=686&fit=crop&dpr=1 600w, https://images.theconversation.com/files/174300/original/file-20170618-28759-1jyothn.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=686&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/174300/original/file-20170618-28759-1jyothn.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=686&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/174300/original/file-20170618-28759-1jyothn.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=862&fit=crop&dpr=1 754w, https://images.theconversation.com/files/174300/original/file-20170618-28759-1jyothn.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=862&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/174300/original/file-20170618-28759-1jyothn.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=862&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">The basics of math instruction have changed little since George Eaton taught at Phillips Academy (1880-1930).</span>
<span class="attribution"><a class="source" href="https://flic.kr/p/jKrzFZ">Phillips Academy Archives and Special Collections / flickr</a></span>
</figcaption>
</figure>
<p>For example, when students learn about the area of shapes, they’re given a set of formulas. They put numbers into the correct formula and compute a solution. More complex questions might give the students the area and have them work backwards to find a missing dimension. Students will often learn a different set of formulas each day: perhaps squares and rectangles one day, triangles the next. </p>
<p>Students in these kinds of lessons are learning to follow a rote process to arrive at a solution. This kind of instruction is so common that it’s seldom even questioned. After all, within a particular lesson, it makes the math seem easier, and students who are successful at getting the right answers find this kind of teaching to be very satisfying.</p>
<p>But it turns out that teaching mathematics this way can actually <a href="http://www.jstor.org/stable/3696735">hinder learning</a>. Children can become dependent on <a href="http://www.jstor.org/stable/10.5951/teacchilmath.21.1.0018">tricks and rules</a> that don’t hold true in all situations, making it harder to adapt their knowledge to new situations.</p>
<p>For example, in traditional teaching, children learn that they should distribute a number by multiplying across parentheses and will practice doing so with numerous examples. When they begin learning how to solve equations, they often have trouble realizing that it’s not always needed. To illustrate, take the equation 3(x + 5) = 30. Children are likely to multiply the 3 across the parentheses to make 3x + 15 = 30. They might just as easily have divided both sides by 3 to make x + 5 = 10, but a child who learned the distribution method might have great difficulty recognizing the alternate method – or even that both procedures are equally correct.</p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/174582/original/file-20170619-22075-1mmjc2g.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/174582/original/file-20170619-22075-1mmjc2g.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=320&fit=crop&dpr=1 600w, https://images.theconversation.com/files/174582/original/file-20170619-22075-1mmjc2g.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=320&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/174582/original/file-20170619-22075-1mmjc2g.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=320&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/174582/original/file-20170619-22075-1mmjc2g.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=402&fit=crop&dpr=1 754w, https://images.theconversation.com/files/174582/original/file-20170619-22075-1mmjc2g.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=402&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/174582/original/file-20170619-22075-1mmjc2g.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=402&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Students who learn by rote drilling often have trouble realizing that there are equally valid alternative methods for solving a problem.</span>
<span class="attribution"><span class="source">Kaitlyn Chantry</span></span>
</figcaption>
</figure>
<h2>More than a right answer</h2>
<p>A key missing ingredient in these traditional lessons is conceptual understanding. </p>
<p>Concepts are ideas, meaning and relationships. It’s not just about knowing the procedure (like how to compute the area of a triangle) but also the significance behind the procedure (like what area means). How concepts and procedures are related is important as well, such as how the area of a triangle can be considered half the area of a rectangle and how that relationship can be seen in their area formulas. </p>
<p>Teaching for conceptual understanding has <a href="http://math.coe.uga.edu/Olive/EMAT3500f08/instrumental-relational.pdf">several benefits</a>. Less information has to be memorized, and students can translate their knowledge to new situations more easily. For example, understanding what area means and how areas of different shapes are related can help students understand the concept of volume better. And learning the relationship between area and volume can help students understand how to interpret what the volume means once it’s been calculated.</p>
<p>In short, building relationships between <a href="https://doi.org/10.1007/s10648-015-9302-x">how to solve a problem and why it’s solved that way</a> helps students <a href="https://doi.org/10.1037//0022-0663.91.1.175">use what they already know</a> to solve new problems that they face. Students with a truly conceptual understanding can see how methods emerged from <a href="https://doi.org/10.1037/0022-0663.91.1.175">multiple interconnected ideas</a>; their relationship to the solution goes deeper than rote drilling.</p>
<p>Teaching this way is a critical first step if students are to begin recognizing mathematics as meaningful. Conceptual understanding is a key ingredient to helping people think mathematically and use mathematics outside of a classroom.</p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/174193/original/file-20170616-537-p8ad2j.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/174193/original/file-20170616-537-p8ad2j.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=412&fit=crop&dpr=1 600w, https://images.theconversation.com/files/174193/original/file-20170616-537-p8ad2j.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=412&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/174193/original/file-20170616-537-p8ad2j.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=412&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/174193/original/file-20170616-537-p8ad2j.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=517&fit=crop&dpr=1 754w, https://images.theconversation.com/files/174193/original/file-20170616-537-p8ad2j.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=517&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/174193/original/file-20170616-537-p8ad2j.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=517&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">Procedural learning promotes memorization instead of critical thinking and problem solving.</span>
<span class="attribution"><a class="source" href="https://www.shutterstock.com/image-photo/math-study-exam-set-book-pencil-250606378">m.jrn/shutterstock.com</a></span>
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<h2>The will to change</h2>
<p>Conceptual understanding in mathematics has been recognized as important for <a href="http://www.nctm.org/uploadedFiles/About/President,_Board_and_Committees/Board_Materials/MLarson-SF-NCTM-4-16.pdf">over a century</a> and widely discussed for decades. So why has it not been incorporated into the curriculum, and why does traditional teaching abound? </p>
<p>Learning conceptually can take longer and be more difficult than just presenting formulas. Teaching this way may require additional time commitments both in and outside the classroom. Students may have never been asked to think this way before.</p>
<p>There are systemic obstacles to face as well. A new teacher may face pressure from fellow teachers who teach in traditional ways. The <a href="https://www.thoughtco.com/high-stakes-testing-overtesting-in-americas-public-schools-3194591">culture of overtesting</a> in the last two decades means that students face more pressure than ever to get right answers on tests. </p>
<p>The results of these tests are also being <a href="https://tcta.org/node/13251-issues_with_test_based_value_added_models_of_teacher_assessment">tied to teacher evaluation systems</a>. Many teachers feel pressure to teach to the test, drilling students so that they can regurgitate information accurately.</p>
<p>If we really want to improve America’s mathematics education, we need to rethink both our education system and our teaching methods, and perhaps to <a href="http://www.nea.org/home/40991.htm">consider how other countries approach mathematics instruction</a>. Research has provided evidence that teaching conceptually has <a href="http://www.ascd.org/publications/educational-leadership/feb04/vol61/num05/Improving-Mathematics-Teaching.aspx">benefits</a> not offered by traditional teaching. And students who learn conceptually typically do <a href="https://doi.org/10.3102/0034654310374880">as well or better</a> on achievement tests. </p>
<p>Renowned education expert <a href="https://pasisahlberg.com/">Pasi Sahlberg</a> is a former mathematics and physics teacher from Finland, which is renowned for its world-class education. He <a href="http://www.smithsonianmag.com/innovation/why-are-finlands-schools-successful-49859555/">sums it up</a> well:</p>
<blockquote>
<p>We prepare children to learn how to learn, not how to take a test.</p>
</blockquote><img src="https://counter.theconversation.com/content/78660/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Christopher Rakes receives funding from the National Science Foundation. </span></em></p>Math instruction is stuck in the last century. How can we change teaching methods to move past rote memorization and help students develop a more meaningful understanding – and be better at math?Christopher Rakes, Assistant Professor of Mathematics Education, University of Maryland, Baltimore CountyLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/782532017-06-06T19:23:16Z2017-06-06T19:23:16ZInfographic: Are we making progress on Indigenous education?<figure><img src="https://images.theconversation.com/files/171993/original/file-20170602-22797-9t7cwi.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Northern Territory has the highest proportion of Indigenous school students.</span> <span class="attribution"><span class="source">Neda Vanovac/AAP</span></span></figcaption></figure><p><em>In <a href="https://theconversation.com/au/topics/are-we-making-progress-on-indigenous-education-39329">this series</a>, we’ll discuss whether progress is being made on Indigenous education, looking at various areas including policy, scholarships, school leadership, literacy and much more.</em> </p>
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<img alt="" src="https://images.theconversation.com/files/172654/original/file-20170607-5695-hdi3xl.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/172654/original/file-20170607-5695-hdi3xl.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=8236&fit=crop&dpr=1 600w, https://images.theconversation.com/files/172654/original/file-20170607-5695-hdi3xl.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=8236&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/172654/original/file-20170607-5695-hdi3xl.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=8236&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/172654/original/file-20170607-5695-hdi3xl.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=10350&fit=crop&dpr=1 754w, https://images.theconversation.com/files/172654/original/file-20170607-5695-hdi3xl.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=10350&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/172654/original/file-20170607-5695-hdi3xl.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=10350&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"></span>
<span class="attribution"><span class="source">Various sources/The Conversation</span>, <a class="license" href="http://creativecommons.org/licenses/by-nd/4.0/">CC BY-ND</a></span>
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<hr>
<p><em>• <a href="https://theconversation.com/au/topics/are-we-making-progress-on-indigenous-education-39329">Read more articles</a> in this series.</em></p><img src="https://counter.theconversation.com/content/78253/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Tony Dreise 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>Indigenous students who graduate from university have slightly higher full-time employment prospects than their non-Indigenous peers.Claire Shaw, Education EditorWes Mountain, Social Media + Visual Storytelling EditorJamal Ben Haddou, Editorial internLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/641412016-09-19T15:14:07Z2016-09-19T15:14:07ZWhat’s the point of maths research? It’s the abstract nonsense behind tomorrow’s breakthroughs<figure><img src="https://images.theconversation.com/files/138241/original/image-20160919-11113-1j3jacl.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>Whenever I tell people I’m a mathematical researcher, I’m usually met with some form of bewilderment. Occasionally that’s followed by the immediate end of the conversation. If there is a follow-up question, it’s usually not about the type of research I’m doing or how it’s funded but whether there’s anything left to discover in maths at all.</p>
<p>True, maths rarely makes the headlines and so most people probably don’t think of it as carrying out cutting-edge research. But neither does, say, geology and people don’t assume there’s nothing left to discover in that field. The difference is that everyone is familiar with maths from their schooldays in a way that contrasts vastly from the work of actual mathematicians. In school we learn formulas that are then used to calculate answers to specific problems. The right method correctly calculated will never fail.</p>
<p>Maths research, on the other hand, looks at the myriad problems for which we don’t have such a method. It’s about finding the tools and systems that other subject areas find so useful in formulating their own work. And sometimes it stumbles across <a href="http://mathworld.wolfram.com/RamseyNumber.html">facts about numbers</a> that we have no conceivable use for at the moment but that one day could become vital to the world.</p>
<p>Any mathematical method used at school (or work or anywhere) was figured out at some point by a mathematician. Another mathematician may have proven that it always works. And another may have worked out how to use the method in the real world. Someone else might then have shown that it’s not a very efficient way to solve larger problems and developed a different approach instead.</p>
<p>The method may also have relied on several properties of the underlying number system discovered over a long stretch of time. Others before them will have accomplished the important but unglamorous task of precisely defining that number system, perhaps <a href="http://www-history.mcs.st-and.ac.uk/HistTopics/History_overview.html">a very long time ago</a>.</p>
<h2>Prime purpose</h2>
<p>Research mathematicians essentially still discover similar types of results today. We have simply moved on to different questions that have become important, to new methods for existing questions, to different systems that draw our attention, and to more advanced questions about things that have already been researched.</p>
<p>Here is an example of such a recent result. It deals with the distribution of prime numbers, like 7, 11, 23, or 37, which you cannot divide by another natural number other than 1 or themselves. We’ve found prime numbers as large as <a href="http://www.bbc.co.uk/news/technology-35361090">22m digits</a> long, and researchers are <a href="http://www.mersenne.org">still looking</a>.</p>
<p>If you look at a table of numbers, the prime numbers seem to be almost randomly mixed into the non-prime ones. For a long time, we have been able to describe the <a href="https://primes.utm.edu/howmany.html#better">typical characteristics</a> of prime numbers. As it turns out, prime numbers slowly but steadily appear less frequently – they “thin out” – among the larger numbers. What’s more, we can quantify this process in surprisingly precise terms. </p>
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<img alt="" src="https://images.theconversation.com/files/138242/original/image-20160919-11100-o96axa.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/138242/original/image-20160919-11100-o96axa.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/138242/original/image-20160919-11100-o96axa.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/138242/original/image-20160919-11100-o96axa.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/138242/original/image-20160919-11100-o96axa.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/138242/original/image-20160919-11100-o96axa.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/138242/original/image-20160919-11100-o96axa.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">‘Useless’ number theory turned out to have a very important purpose for modern society.</span>
<span class="attribution"><span class="source">Shutterstock</span></span>
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<p>With the average primes being further and further apart as we look at ever larger numbers, a typical question for maths researchers to ask is whether this process of thinning out also carries over to the smallest gaps between primes. In other words, will all large primes come at increasing distances from each other, or will we always find primes that are close to each other?</p>
<p><a href="http://annals.math.princeton.edu/2014/179-3/p07">A breakthrough result</a> in 2014 showed that no matter how high we go among the numbers, we will always find two primes that are closer to each other than some constant number. That number was initially a whopping 70m. This might not seem very close but the fact that we could identify a finite number was an important breakthrough. Other mathematicians then set out to reduce this value, and the best I am currently aware of is a <a href="http://michaelnielsen.org/polymath1/index.php?title=Bounded_gaps_between_primes">much more manageable 246</a>.</p>
<h2>Real applications – eventually</h2>
<p>You might wonder how solving such abstract problems helps anyone outside of mathematics. First, there is a trickle-down effect. A fundamental result is useful in obtaining other pure mathematical results, which in turn are used to develop applied mathematics, which are then used by non-mathematicians. Second – and more importantly – mathematical theory is often ahead of its time, and the abstract nonsense of yesterday underpins the applied mathematics of today.</p>
<p>For example, number theory is the area that examines, among other items, questions like our prime number example. For many years this was considered the ultimate pure mathematics topic and completely unusable for any purpose other than satisfying human curiosity. The eminent early 20th-century number theorist and pacifist, G.H Hardy, was <a href="http://www.cambridge.org/gb/academic/subjects/mathematics/recreational-mathematics/mathematicians-apology-2?format=PB&isbn=9781107604636">very proud to say</a>: “No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world.” In other words, he was glad his work could not be used for military purposes.</p>
<p>Nowadays, the number theory results that seemed so useless less than a century ago <a href="http://dl.acm.org/citation.cfm?id=359342">are at the heart</a> of the encryption algorithms that let us securely order a product or check our bank accounts online. In a way that would have horrified Hardy, British intelligence services had actually already <a href="http://simonsingh.net/media/articles/maths-and-science/unsung-heroes-of-cryptography/">discovered the same method</a> in secret ahead of their civil colleagues. </p>
<p>When the next technological or scientific breakthrough requires a new type of mathematical model, it is likely that the subject already has the underlying theory in hand, waiting to be adapted to a new setting.</p>
<p>Underlying all of this is one of the fundamental truths about mathematical research. The applications of mathematics might change with scientific progress, making some mathematical topics more useful at times than others. But because mathematical results are based on logical deductions alone, they actually never become wrong, never get obsolete, and never truly get old. They are just waiting for the right application to arrive.</p><img src="https://counter.theconversation.com/content/64141/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Wolfram Bentz does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.</span></em></p>We don’t know what knowledge we’ll need in the future, and that’s where maths research comes in.Wolfram Bentz, Director of Research for Mathematics, University of HullLicensed 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/552372016-02-26T04:02:58Z2016-02-26T04:02:58ZMaths and science are the keys to unlocking Africa’s potential<figure><img src="https://images.theconversation.com/files/112511/original/image-20160223-16447-11f8azp.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">It's time for Africa to produce the technology it needs, rather than being largely a consumer.</span> <span class="attribution"><span class="source">EPA/Nic Bothma</span></span></figcaption></figure><p>Angelina Lutambi was born into a peasant family in Tanzania’s <a href="http://dthd.org/who-we-are/about-tanzania/">Dodoma region</a>, where HIV/AIDS has decimated much of the population. Her future could easily have been bleak – but Angelina had a keen aptitude for maths. She financed her own schooling by selling cold drinks with her siblings and was awarded a grant to study at the University of Dar Es Salaam.</p>
<p>In 2004 she went to the South African <a href="https://www.aims.ac.za/en/about/about-aims">centre</a> of the African Institute for Mathematical Sciences <a href="http://www.nexteinstein.org">(AIMS)</a>. Since then, Angelina has obtained her PhD in epidemiology from the University of Basel in Switzerland. </p>
<p>Today Angelina is a senior research scientist at the Ifakara Health Institute in her native Tanzania. There, she devises mathematical, statistical and computational models to inform and advise public health decisions on HIV/AIDS, tuberculosis and other major diseases.</p>
<p>Africa has many other deep-rooted problems, including poverty, corruption and war. Could these also be tackled through the sort of work that Angelina and her colleagues are doing? Could Africa’s problems be solved through mathematical science?</p>
<h2>Africa must produce its own technology</h2>
<p>Such a proposal might sound outlandish while so many people still lack basic necessities like food, clean water and medicine. In the long view of history, however, mathematics and science have served as the foundation of modern society because they underlie every technology – from plumbing to telecommunications, medicine to satellites. </p>
<p>But the continent has another problem. It is largely a consumer rather than a producer of the technologies it needs. If this doesn’t change, Africa will remain dependent and subject to outside control, its economies dominated by others’ exploitation of its natural resources. Africa will never escape from its reliance on international aid until it builds the capacity to develop itself.</p>
<p>Computers, mobile communications, and medical technologies are the modern engines of commerce, prosperity and public health. Africa will remain sidelined in these areas unless it nurtures its own experts, pioneers, and innovators. </p>
<h2>Attitudes towards maths in Africa</h2>
<p>This is the motivation behind AIMS, a network of training centres across the continent created to empower brilliant young Africans to become agents of change through advanced maths and science.</p>
<p>Our slogan – that the next Einstein should be African – is a signal of how high we are aiming. </p>
<p>It is not an easy task. As a native South African, I have travelled widely in many parts of the continent. Across Africa, maths is often viewed as an ivory tower pursuit, an impractical study with little connection to the real world. University maths departments are often the shabbiest on campus. </p>
<p>Many students only take the subject as a second choice. From primary school onwards, maths is all too often taught by rote learning and memorisation. But it is critical analysis, independent thinking and creativity that are the <a href="http://www.ascd.org/ASCD/pdf/journals/ed_lead/el_196010_mallinson.pdf">real keys</a> to maths and science excellence.</p>
<p>These attitudes linger even beyond school and university. Elsewhere in the world, the most successful companies – Google and Facebook, for example – recruit top maths graduates straight out of university to write the complex codes that define our experience of the digital world. From big data to artificial intelligence to intelligent cities and communities, the gears of prosperity are increasingly powered by mathematical algorithms. </p>
<h2>Bringing African scientists together</h2>
<p>AIMS is a pan-African initiative. There are five centres so far, in Senegal, Cameroon, Ghana, Tanzania and South Africa. Ten more are planned over the next decade, creating a powerful network that will span the continent. </p>
<p>Every centre has a fantastic, highly motivated, pan-African student body. AIMS’ classes are incredibly diverse – a mosaic of languages, ethnicities, languages and religions. More than 30% of the students are women.</p>
<p>Through their common interest in maths, science and the future of Africa, the students are able to transcend the cultural and other differences that have historically divided them. </p>
<p>Over the past decade, AIMS has graduated a thousand students at Masters and PhD level. But its centres don’t just train brilliant young Africans in Africa. They also serve as a magnet attracting those who have studied abroad back to Africa, to work as scientific researchers. </p>
<p>Wilfred Ndifon from Cameroon is one: he took his PhD at Princeton but has returned to AIMS as a junior research chair. Wilfred has just <a href="https://theconversation.com/africas-answer-to-70-year-old-problem-of-how-to-beat-repeat-infections-50920">solved</a> a 70-year-old immunological puzzle called original antigenic sin, which has implications for improving vaccines. </p>
<p>AIMS also brings top international scientists to Africa to share and propagate their knowledge. This international reach is important, because the whole globe has a stake in Africa’s future. </p>
<p>Our globalised, interconnected world means that Africa’s challenges – whether starvation-driven migration or diseases like <a href="https://theconversation.com/why-africa-cant-afford-to-have-an-outbreak-of-the-zika-virus-53738">Zika</a> or <a href="http://www.cdc.gov/chikungunya/">Chikungunya</a> or terrorism – quickly become challenges to all. These problems will only worsen with climate change, population growth, unemployment and insecurity unless Africans are encouraged and empowered to improve their countries’ conditions.</p>
<p>In March 2016, more than 500 bright scientific minds and international leaders will gather in Senegal for the inaugural <a href="http://nef.org/">Next Einstein Forum</a>, organised by AIMS. The three-day summit will highlight emerging scientific and technical talent in Africa and elsewhere, and fuel collaboration which puts this talent to work in the cause of human development. </p>
<p>The summit’s theme is “Connecting Science to Humanity”. It will be an occasion for the most enlightened African and international scientists and leaders to strengthen their commitment to helping young people help Africa.</p>
<p>The problems facing Africa are complex and there are no easy answers. But one of the lessons we’ve learned in science is that the hardest problems are the ones that eventually yield the most important – and the most wonderful – solutions.</p><img src="https://counter.theconversation.com/content/55237/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Neil Turok is affiliated with AIMS – serving as the Chair of its Board of Trustees.</span></em></p>Africa has deep-rooted problems: poverty, disease, corruption and war. Could these be solved through mathematical science?Neil Turok, Director and Niels Bohr Chair, Perimeter Institute for Theoretical PhysicsLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/475592015-10-12T20:11:55Z2015-10-12T20:11:55ZWhy it matters that student participation in maths and science is declining<figure><img src="https://images.theconversation.com/files/95298/original/image-20150918-2529-xwdelm.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Today's students with intentions to study at university do less maths and less science than previous generations.</span> <span class="attribution"><span class="source">AAP/Dan Peled</span></span></figcaption></figure><p>There has been a lot of talk about Australia’s science, technology, engineering and mathematics (STEM) crisis, and new initiatives have been developed to tackle it. There is talk about engaging students with mathematics and science, kindling student interest and transforming the way it is taught. </p>
<p>But the simple fact remains that many students are choosing not to study these subjects at high school. A <a href="http://www.maths.usyd.edu.au/u/SMS/MMW2015.pdf">new report</a>, with my colleague John Mack, confirms that, compared with 15 years ago – in the dark ages of digital technology – recent NSW high school certificate (HSC) graduates are less well prepared to enter STEM courses at university, while 50% of them finish high school with no science study at all. </p>
<p>Unlike many other countries (such as Finland, the US and China), Australia <a href="https://theconversation.com/make-maths-mandatory-and-well-improve-our-international-education-rankings-11663">does not mandate</a> study in mathematics or science for high school graduation. Students get to choose – and in the NSW HSC they have <a href="http://www.boardofstudies.nsw.edu.au/syllabus_hsc/">43 subjects</a> to choose from, not counting the 62 language courses.</p>
<p>More Australian students now complete high school and more go on to university. Yet there are declines and stagnation in mathematics and science study in an era when it is evident that these subjects play an <a href="http://www.letstalkscience.ca/about-us/why-science.html">ever-increasing role</a> in our lives and in <a href="http://www.theguardian.com/science/2015/mar/24/science-and-mathematics-boost-australias-economy-by-145bn-a-year">countries’ economies</a>. </p>
<p>Historical perspectives show just how low current science and maths participation in NSW is.</p>
<iframe src="https://datawrapper.dwcdn.net/giV57/1/" frameborder="0" allowtransparency="true" allowfullscreen="allowfullscreen" webkitallowfullscreen="webkitallowfullscreen" mozallowfullscreen="mozallowfullscreen" oallowfullscreen="oallowfullscreen" msallowfullscreen="msallowfullscreen" width="100%" height="500"></iframe>
<h2>Declining numbers in mathematics</h2>
<p>Prior to the new HSC in 2001, more than 98% of high school graduates studied some sort of mathematics. By 2014, 9.7% of HSC students <a href="http://openjournals.library.usyd.edu.au/index.php/CAL/article/viewFile/7625/8461">did no maths</a>. The proportion of ATAR-eligible boys studying maths had fallen to 90.7%; among girls it was only 78.6%.</p>
<p>The proportions of students studying no mathematics at all for high school graduation in NSW has trebled since 2001. This also occurred among both boys and girls who applied for an ATAR and were planning to go on to university study. </p>
<p>The level of mathematics studies has also fallen. There are <a href="http://openjournals.library.usyd.edu.au/index.php/CAL/article/viewFile/7625/8461">NSW</a> and <a href="http://amsi.org.au/publications/participation-year-12-mathematics-2004-2013/">national declines</a>, with a shift away from intermediate mathematics to more elementary mathematics. In NSW, twice as many students are enrolled in elementary maths as in intermediate maths. </p>
<h2>Illogical declines in science</h2>
<p>Although less dramatic, there are also declines in science participation. Among NSW ATAR-eligible students, science participation was substantially higher in 1991 – biology 35%, chemistry 26%, physics 24% – than in 2014 (biology 30%, chemistry 20%, physics 17%).</p>
<p>These illogical trends come at a time when there is increasing recognition of the important role these subjects play in educating <a href="http://www.aigroup.com.au/portal/binary/com.epicentric.contentmanagement.servlet.ContentDeliveryServlet/LIVE_CONTENT/Publications/Reports/2013/Ai_Group_Skills_Survey_2012-STEM_FINAL_PRINTED.pdf">future workforces</a>.</p>
<p>Since the new HSC in 2001, the proportion of ATAR-eligible students undertaking no science study is stagnant, but at high levels – around 45%. So, nearly one in two university students went science-free in HSC.</p>
<p>The biggest subject in HSC science is biology. More than one-third of ATAR-eligible girls take biology. Only 16% now take a science subject other than biology.</p>
<p><a href="http://eprints.qut.edu.au/73153/1/Continuing_decline_of_science_proof.pdf">National surveys</a> of science participation also show declines despite rising numbers of students completing high school. </p>
<p>When we compare these statistics to international practice the levels are low. Most countries mandate mathematics study for high school. Many of the high-attaining countries also <a href="http://www.businessinsider.com.au/pisa-rankings-2013-12">require science study</a> – even for students who take arts-based streams. England is playing catch-up and now <a href="http://www.dailymail.co.uk/news/article-2571276/Labour-reveal-plan-make-teenagers-study-maths-English-age-18-education-chief-says-arent-teachers.html">plans to</a> require maths study up to 18 years of age. </p>
<h2>Declining university preparation</h2>
<p>Science and mathematics subject combinations are particularly important preparation for many university degrees. Yet <a href="http://www.maths.usyd.edu.au/u/SMS/MMW2015.pdf">levels of participation</a> are low in various maths and science subject combinations among HSC and ATAR groups, especially among girls. </p>
<p>In 2001, 19.7% of boys and 16.8% of girls from the corresponding Year 8 cohort went on to study a maths-science combination in the HSC. By 2014, only 19% of boys and 14.1% of girls went on to study such maths-science combinations in the HSC. </p>
<p>The magnitude of these declines could be considered marginal. However, the 2001 HSC retention rates from Year 8 for males and females were 63% and 74% respectively, while in 2014 they were 71% and 80% respectively. </p>
<p>One might assume that increased upper secondary and tertiary participation would lead to greater participation in mathematics and science – but this is not the case. </p>
<h2>What does this mean?</h2>
<p>John Mack points out that the rising numbers of students with no maths means that:</p>
<blockquote>
<p>Some 50% of the entire HSC cohort is now ill-prepared to understand any argument presented to them that depends on an understanding of rates of change in scientific data.</p>
</blockquote>
<p>The problem is also broader and deeper. The performance of Australian 15-year-olds is <a href="https://theconversation.com/six-ways-australias-education-system-is-failing-our-kids-32958">falling</a> in the international assessment of mathematics and science literacy (PISA). Australia’s mean scores and international rankings have declined since 2000. </p>
<p>Many students opt out of science and mathematics after the age of 16 – even among those intending to study at university (some in STEM-related degrees). This places Australia in a precarious position in the world’s <a href="http://www.theworkfoundation.com/downloadpublication/report/41_41_ke_life_of_nations.pdf">competitive knowledge economy</a>.</p>
<p>Our <a href="http://www.maths.usyd.edu.au/u/SMS/MMW2015.pdf">report</a> suggests that today’s students with intentions to study at university do less maths and less science than previous generations. And they do much less science and maths than their peers around the world. If these trends continue, Australians can no longer think of themselves as belonging to the clever country.</p>
<hr>
<p><em>Amendment: a reference to the UK was changed to say England</em></p><img src="https://counter.theconversation.com/content/47559/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Rachel Wilson 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>School leavers are less well prepared to enter STEM courses at university, while many finish high school with no science study at all.Rachel Wilson, Senior Lecturer - Research Methodology / Educational Assessment & Evaluation, University of SydneyLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/440162015-07-09T20:07:01Z2015-07-09T20:07:01ZKids prefer maths when you let them figure out the answer for themselves<figure><img src="https://images.theconversation.com/files/86784/original/image-20150630-9056-j7udzd.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">New research for primary and junior secondary schools shows kids prefer to nut out maths problems without the teacher's help. </span> <span class="attribution"><span class="source">from www.shutterstock.com</span></span></figcaption></figure><p>A common view is that students learn maths best when teachers give clear explanations of mathematical concepts, usually in isolation from other concepts, and students are then given opportunities to practise what they have been shown. </p>
<p>I’ve recently undertaken research at primary and junior secondary levels exploring a different approach. This approach involves posing questions like the following and expecting (in this case, primary level) students to work out their own approaches to the task for themselves prior to any instruction from the teacher:</p>
<blockquote>
<p>The minute hand of a clock is on two, and the hands make an acute angle. What might be the time?</p>
</blockquote>
<p>There are three ways that this question is different from conventional questions. First, it focuses on two aspect of mathematics together, time and angles. Contrasting two concepts helps students see connections and move beyond approaching mathematics as a collection of isolated facts. </p>
<figure class="align-left ">
<img alt="" src="https://images.theconversation.com/files/86791/original/image-20150630-9090-1qt7nzc.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/86791/original/image-20150630-9090-1qt7nzc.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/86791/original/image-20150630-9090-1qt7nzc.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/86791/original/image-20150630-9090-1qt7nzc.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/86791/original/image-20150630-9090-1qt7nzc.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/86791/original/image-20150630-9090-1qt7nzc.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/86791/original/image-20150630-9090-1qt7nzc.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">Questions posed to students as part of the research are different to conventional math problems.</span>
<span class="attribution"><span class="source">from www.shutterstock.com</span></span>
</figcaption>
</figure>
<p>Second, the question has more than one correct answer. Having more than one correct answer means students have opportunities to make decisions about their own answer and then have something unique to contribute to discussions with other students. </p>
<p>Third, students can respond at different levels of sophistication: some students might find just one answer, while other students might find all of the possibilities and formulate generalisations.</p>
<p>The task is what is described as appropriately challenging. The solutions and solution pathways are not immediately obvious for middle primary students but the task draws on ideas with which they are familiar. An explicit advantage of posing such challenging tasks is that the need for students to apply themselves and persist is obvious to the students, even if the task seems daunting at first.</p>
<p>After the students have worked on the task for a time, the teacher manages a discussion in which students share their insights and solutions. This is an important opportunity for students to see what other students have found, and especially to realise that in many cases there are multiple ways of solving mathematics problems. </p>
<p>It is suggested to teachers that they use a data projector or similar technology to project students’ actual work. This saves time rewriting the work, presents the students’ work authentically and illustrates to students the benefits of writing clearly and explaining thinking fully.</p>
<p>Subsequently, the teacher poses a further task in which some aspects are kept the same and some aspects changed, such as:</p>
<blockquote>
<p>The minute hand of a clock is on eight, and the hands make an obtuse angle. What might be the time?</p>
</blockquote>
<figure class="align-right ">
<img alt="" src="https://images.theconversation.com/files/86793/original/image-20150630-9062-1n5cj6w.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/86793/original/image-20150630-9062-1n5cj6w.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/86793/original/image-20150630-9062-1n5cj6w.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/86793/original/image-20150630-9062-1n5cj6w.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/86793/original/image-20150630-9062-1n5cj6w.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/86793/original/image-20150630-9062-1n5cj6w.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/86793/original/image-20150630-9062-1n5cj6w.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">The tasks given to students are appropriately challenging.</span>
<span class="attribution"><span class="source">from www.shutterstock.com</span></span>
</figcaption>
</figure>
<p>The intention is that students learn from the thinking activated by working on the first task and from the class discussion, then apply that learning to the second task.</p>
<p>The research aims to identify tasks that not only are appropriately challenging but can be adapted to suit the needs of particular students. For example, there may be some students for whom the first task is too difficult. Those students might be asked to work on a question like:</p>
<blockquote>
<p>What is a time at which the hands of a clock make an acute angle?</p>
</blockquote>
<p>The intention is that those students then have more chance of engaging with the original task. Of course, there are also students who can find answers quickly and are then ready for further challenges. Those students might be posed questions like:</p>
<blockquote>
<p>With the minute hand on two, why are there six times for which the hands make an acute angle? Is there a number to which the minute hand might point for which there are not six possibilities?</p>
</blockquote>
<p>There might even be advanced students who could be asked:</p>
<blockquote>
<p>What are some times for which the hands on a clock make a right angle?</p>
</blockquote>
<p>The combination of the students’ own engagement with the problem and the different levels of prompts means the students’ work contains rich and useful information about what the students know. Teachers can use this not only to give the students feedback but also to plan subsequent teaching.</p>
<h2>Students welcomed the challenge</h2>
<figure class="align-left ">
<img alt="" src="https://images.theconversation.com/files/86786/original/image-20150630-9102-1rd26jj.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/86786/original/image-20150630-9102-1rd26jj.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/86786/original/image-20150630-9102-1rd26jj.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/86786/original/image-20150630-9102-1rd26jj.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/86786/original/image-20150630-9102-1rd26jj.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/86786/original/image-20150630-9102-1rd26jj.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/86786/original/image-20150630-9102-1rd26jj.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">The project found that students prefer to work out solutions and representations by themselves or with other students.</span>
<span class="attribution"><span class="source">from www.shutterstock.com</span></span>
</figcaption>
</figure>
<p>The project found that, contrary to the preconceptions of some teachers, many students do not fear challenges in mathematics but welcome them. Rather than preferring teachers to instruct them on solution methods, many students prefer to work out solutions by themselves or by working with other students. </p>
<p>The project also established that students learn substantive mathematics content from working on challenging tasks and are willing and able to develop ways of articulating their reasoning.</p><img src="https://counter.theconversation.com/content/44016/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Peter Sullivan receives funding from The Australian Research Council.
The Australian Research Council funding the research from which the article is drawn. There is no conflict of interest between the ARC and this article.</span></em></p>Rather than having teachers instruct students on solution methods, many students prefer to work out solutions by themselves or by working with other students.Peter Sullivan, Professor of Science, Mathematics and Technology Education, Monash UniversityLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/326022014-10-09T03:59:38Z2014-10-09T03:59:38ZMaximising ATARs: why studying maths doesn’t add up<figure><img src="https://images.theconversation.com/files/61200/original/33jsrymy-1412811908.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Less students are choosing to undertake more complex maths subjects because they want to maximise their tertiary admission score.</span> <span class="attribution"><a class="source" href="http://www.shutterstock.com/downloading_tips.mhtml?code=&id=131548352&size=huge&image_format=jpg&method=download&super_url=http%3A%2F%2Fdownload.shutterstock.com%2Fgatekeeper%2FW3siZSI6MTQxMjg0MDYzNywiYyI6Il9waG90b19zZXNzaW9uX2lkIiwiZGMiOiJpZGxfMTMxNTQ4MzUyIiwicCI6InYxfDEwMTI3NTg4fDEzMTU0ODM1MiIsImsiOiJwaG90by8xMzE1NDgzNTIvaHVnZS5qcGciLCJtIjoiMSIsImQiOiJzaHV0dGVyc3RvY2stbWVkaWEifSwiNktuMXkrYS9FR0FUS05zYTNPdFlrMGJ0SFZZIl0%2Fshutterstock_131548352.jpg&racksite_id=ny&chosen_subscription=1&license=standard&src=qiTkFfZiFsFqx1ou23SuwQ-1-53">Shutterstock</a></span></figcaption></figure><p>The percentage of students taking intermediate or advanced mathematics at school has <a href="http://www.smh.com.au/technology/sci-tech/20year-decline-in-year-12-science-and-maths-participation-study-finds-20141006-10qvq2.html">declined significantly</a>. Why is this happening and why does it matter?</p>
<h2>Why the decline?</h2>
<p><a href="http://www.gsu.uts.edu.au/academicboard/cabs/082/papers/082-item6-1.pdf">Some factors</a> that influence whether students choose to study maths and, if so, which subject(s), are:</p>
<figure class="align-right zoomable">
<a href="https://images.theconversation.com/files/61201/original/56mczvrm-1412812098.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/61201/original/56mczvrm-1412812098.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/61201/original/56mczvrm-1412812098.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/61201/original/56mczvrm-1412812098.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/61201/original/56mczvrm-1412812098.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/61201/original/56mczvrm-1412812098.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/61201/original/56mczvrm-1412812098.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/61201/original/56mczvrm-1412812098.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">Some kids just don’t think they’re very good at maths, or don’t see how it applies to the real world.</span>
<span class="attribution"><span class="source">Shutterstock</span></span>
</figcaption>
</figure>
<ul>
<li><p>how good they think they are at maths</p></li>
<li><p>whether they have an interest in and appreciation of higher-level maths</p></li>
<li><p>how difficult they think the different maths subjects are</p></li>
<li><p>their past grades</p></li>
<li><p>their perception of how useful maths will be in real life</p></li>
<li><p>their cultural background and the <a href="http://ses.library.usyd.edu.au/bitstream/2123/5142/1/Farid%20Awad%20Honours%20Thesis.pdf">influence of their parents</a></p></li>
<li><p>the removal of intermediate and advanced high-school <a href="https://www.austms.org.au/Publ/Gazette/2014/Sep14/Monitoring.pdf">maths subjects as prerequisites</a> to get into university courses.</p></li>
</ul>
<p>However, one of the most influential reasons students choose whether to study maths or not has to do with their ATAR, or tertiary admission rank. In a 2013 survey <a href="http://www.mansw.nsw.edu.au/resources/public-resources/2013-secondary-mathematics-teacher-survey-report">by the Mathematics Association of NSW</a>, teachers said many competent students chose the most basic “entry level” senior mathematics courses, rather than the more challenging calculus-based subjects in an attempt to maximise their ATAR score.</p>
<p>Ironically, it seems that the choice of proficient high-school students to turn away from higher-level maths subjects to more basic ones is a strategic decision, which can be explained through mathematics itself.</p>
<figure class="align-left zoomable">
<a href="https://images.theconversation.com/files/61202/original/rcwn83kc-1412812206.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/61202/original/rcwn83kc-1412812206.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/61202/original/rcwn83kc-1412812206.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/61202/original/rcwn83kc-1412812206.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/61202/original/rcwn83kc-1412812206.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/61202/original/rcwn83kc-1412812206.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/61202/original/rcwn83kc-1412812206.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/61202/original/rcwn83kc-1412812206.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>
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<span class="caption">The drop in students choosing maths can be explained by … maths.</span>
<span class="attribution"><span class="source">Shutterstock</span></span>
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<p>“Mathematical optimisation” involves a strategic choice of “best” elements that lead to the optimal outcome. Here the “optimal” outcome in the minds of many students is achieving the highest ATAR they can, as a higher ATAR brings greater tertiary entry opportunities. The strategic choice involves selecting the particular maths subject that they believe will boost their ATAR as much as possible.</p>
<p>Accomplished students have the potential to perform well in the more basic senior maths subjects, as they will be less challenged by the depth and breadth of material. It also allows them to devote more time to other subjects that will contribute to their ATAR.</p>
<p>The potential effectiveness of this ATAR-optimisation strategy was <a href="http://www.mansw.nsw.edu.au/documents/item/70">proven when the Mathematics Association of NSW</a> analysed university admissions data. It found that in 2013 a student who took “entry level” General Mathematics (no calculus) on the 90th percentile scored a higher study score than the median student in the (calculus-based) 2 Unit maths course and was likely to gain an additional <em>ten</em> ATAR points for making this choice.</p>
<h2>Does it matter if fewer kids study maths?</h2>
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<a href="https://images.theconversation.com/files/61203/original/xkwtj5ft-1412812373.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/61203/original/xkwtj5ft-1412812373.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/61203/original/xkwtj5ft-1412812373.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=401&fit=crop&dpr=1 600w, https://images.theconversation.com/files/61203/original/xkwtj5ft-1412812373.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=401&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/61203/original/xkwtj5ft-1412812373.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=401&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/61203/original/xkwtj5ft-1412812373.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=504&fit=crop&dpr=1 754w, https://images.theconversation.com/files/61203/original/xkwtj5ft-1412812373.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=504&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/61203/original/xkwtj5ft-1412812373.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"></a>
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<span class="caption">Engineers and scientists make the world go round.</span>
<span class="attribution"><span class="source">Shutterstock</span></span>
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<p>Graduates with strong maths skills drive the science, technology and innovation that are essential for increasing productivity; creating jobs; enhancing competitiveness; and growing an economy. <a href="http://www.maths.unsw.edu.au/news/2013-04/employer-attitudes-towards-mathematical-skills">Pilot studies</a> at the University of New South Wales have revealed that employers highly value job applicants with strong maths skills.</p>
<p>Universities need incoming students with strong quantitative abilities. This will ensure Australian universities remain globally competitive in the quality of education that they provide to students in programs such as science and engineering.</p>
<h2>How can we fix it?</h2>
<p>We need to inspire students with the beauty and relevance of maths throughout school. Instilling a curiosity and fascination within students will make them more likely to continue with their maths studies to higher levels.</p>
<p>Universities can help the problem of declining maths students by reinstating entry prerequisites. Replacing the current practice of “assumed knowledge” with firm entry prerequisites will send a clear message to potential students that the intermediate and advanced calculus-based maths subjects are necessary for a successful transition to university subjects like science and engineering.</p><img src="https://counter.theconversation.com/content/32602/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Chris Tisdell has received funding from The Australian Research Council and The Australian Academy of Science.</span></em></p>The percentage of students taking intermediate or advanced mathematics at school has declined significantly. Why is this happening and why does it matter? Why the decline? Some factors that influence whether…Chris Tisdell, Associate Dean of Science, UNSW SydneyLicensed as Creative Commons – attribution, no derivatives.