tag:theconversation.com,2011:/us/topics/math-education-48883/articlesMath education – The Conversation2023-08-08T12:29:05Ztag:theconversation.com,2011:article/2092982023-08-08T12:29:05Z2023-08-08T12:29:05ZRhyme and reason – why a university professor uses poetry to teach math<figure><img src="https://images.theconversation.com/files/537945/original/file-20230718-29-l0wtv9.jpg?ixlib=rb-1.1.0&rect=29%2C65%2C3971%2C3737&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Math problems take on new meaning in this class that combines rhymes and verse with math instruction.</span> <span class="attribution"><a class="source" href="https://www.gettyimages.com/detail/photo/books-on-vintage-background-with-math-formulas-royalty-free-image/1170503197?phrase=poetry+and+math&adppopup=true">ra2studio via Getty Images</a></span></figcaption></figure><figure class="align-right ">
<img alt="Text saying: Uncommon Courses, from The Conversation" src="https://images.theconversation.com/files/499014/original/file-20221205-17-kcwec8.png?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/499014/original/file-20221205-17-kcwec8.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=375&fit=crop&dpr=1 600w, https://images.theconversation.com/files/499014/original/file-20221205-17-kcwec8.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=375&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/499014/original/file-20221205-17-kcwec8.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=375&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/499014/original/file-20221205-17-kcwec8.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=471&fit=crop&dpr=1 754w, https://images.theconversation.com/files/499014/original/file-20221205-17-kcwec8.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=471&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/499014/original/file-20221205-17-kcwec8.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=471&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
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<p><em><a href="https://theconversation.com/topics/uncommon-courses-130908">Uncommon Courses</a> is an occasional series from The Conversation U.S. highlighting unconventional approaches to teaching.</em> </p>
<h2>Title of course:</h2>
<p>The Ways Math and Poetry Can Open Your Eyes to the World</p>
<h2>What prompted the idea for the course?</h2>
<p>I have always enjoyed writing poetry. As a high school mathematics teacher, I recall telling my students that everything is and can be connected to math, even creative writing. Then, as a graduate student, I read about people using <a href="https://www.nga.gov/content/dam/ngaweb/Education/learning-resources/lessons-activities/self-portraits/i-am-poem.pdf">“I am” poem templates</a> for young people to express who they are through a series of “I am” statements, and I thought to myself, where is the “I am” math poem template? So I <a href="https://drive.google.com/file/d/1QSYyTAv0DcVYTQnITsECYAkvgwn24xcO/view">created one</a>.</p>
<p>I then started working on what I call problem-posing poetry, which are poems connected to a social issue and that can be used as alternatives to traditional math word problems. Working with <a href="https://theconversation.com/profiles/yousef-kara-1454971/news">Yousef Kara</a>, who is a poet studying to become a teacher, we learned to see poetry as a way to understand the real world before connecting to math learning. We also began to use poetry to reflect on prior math learning. After using math poetry with high schoolers and teachers, it became apparent it should be a part of my math methods courses for future teachers.</p>
<h2>What does the course explore?</h2>
<p>The course explores the idea of poetry as a rich experience before, during and after math learning connected to real-world issues.</p>
<p>The <a href="https://drive.google.com/file/d/1QSYyTAv0DcVYTQnITsECYAkvgwn24xcO/view?usp=sharing">“I am” math poem template</a> is an example of poetry before math. The prompts used in the template allow the teacher to incorporate students’ interests when learning math in the future. For example, the last prompt shows what students are passionate about, and teachers should use that interest in their teaching of math. </p>
<p>Problem-posing poems like <a href="https://docs.google.com/document/d/16c5lFhePvWUZws1yyYxgtgK2FBZ1-ZjwJG6K-bFJ2WU/edit?usp=sharing">“Number Sense,”</a> written by Ricardo Martinez, show how a poem can use actual data to become a math problem for students to solve. Poetry after math learning can best be captured by Yousef’s poem <a href="https://docs.google.com/document/d/1v590OpScLOECC6su6LvPEbhNVgggn-kZLf4Wpou9qPM/edit?usp=sharing">“The Wrong Bathroom, Continuously,”</a> a reflection on trans identity related to functions that model relationships between two quantities.</p>
<p>This poem demonstrates concepts of math through exploring different types of continuous functions in calculus. Functions that oscillate, approach opposite infinities and disjointed functions, all of which make it impossible to find the exact value of a limit. Hence the line, “You cannot pin me down to a single point.”</p>
<p>Here is an excerpt from the poem:</p>
<p><em>I am a continuous function.</em> </p>
<p><em>I oscillate</em>
<em>My gender, in constant motion,</em>
<em>And I don’t care if I am unrecognizable to you</em></p>
<p><em>I approach both infinities</em>
<em>From the left and the right</em>
<em>Expanding with each self discovery.</em>
<em>Expanding far beyond your comprehension</em></p>
<p><em>I am disjointed</em>
<em>Deconstructed and decolonized.</em>
<em>I teleport between and beyond genders</em>
<em>You cannot pin me down to a single point</em></p>
<p>It shows how learning more about math expands our vocabulary and understanding of what we experience. </p>
<h2>Why is this course relevant now?</h2>
<p>The beauty of using poetry is that it makes math more exciting and allows it to connect to any topic or idea. Math poetry becomes even more critical today as people need an outlet to communicate their truths about societal injustices like trans people’s rights, bans on Black history or Islamophobia. Math and poetry create new metaphors that allow people to better understand societal issues along with themselves and others.</p>
<h2>What’s a critical lesson from the course?</h2>
<p>A key takeaway from the course is that math is a vital part of each person, and poetry can help people see that math is all around us.</p>
<h2>What will the course prepare students to do?</h2>
<p>By exploring math and poetry, I believe they, as aspiring teachers, will begin to question how they were taught – for example, the use of timed tests and learning with no real-world connections. A lot of people say they don’t like math, when, in truth, they have never knowingly experienced math connected to their culture, values, desires and dreams. Math and poetry work to reclaim how we all see, experience and live with math every day.</p><img src="https://counter.theconversation.com/content/209298/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Ricardo Martinez does not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.</span></em></p>A math professor explains how he prepares future teachers to use poetry in their math instruction.Ricardo Martinez, Assistant Professor of Mathematics Education, Penn StateLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/2052842023-07-07T12:28:53Z2023-07-07T12:28:53ZWhy putting off college math can be a good idea<figure><img src="https://images.theconversation.com/files/536324/original/file-20230707-17-tn5432.jpg?ixlib=rb-1.1.0&rect=9%2C63%2C4944%2C3944&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Research shows that at least 17% of the population experiences high levels of math anxiety.
</span> <span class="attribution"><a class="source" href="https://www.gettyimages.com/detail/photo/student-solving-math-problems-royalty-free-image/695513286?phrase=college+math&adppopup=true">Emilija Manevska/Moment via Getty Images </a></span></figcaption></figure><p><em>The <a href="https://theconversation.com/us/topics/research-brief-83231">Research Brief</a> is a short take about interesting academic work.</em> </p>
<h2>The big idea</h2>
<p>Putting off college math could improve the likelihood that students remain in college. But that may only be true as long as students don’t procrastinate more than one year. This is what colleagues and I found in a <a href="https://doi.org/10.1177/1521025120973949">study published in 2023</a> of 1,119 students at a public university for whom no remedial coursework was required during their first year. </p>
<p>Enrolling in a math course during the first semester of college resulted in students being four times more likely to drop out. Although delayed enrollment in a math course had benefits in the first year, its advantages vanished by the end of the second year. In our study, almost 40% of students who postponed the course beyond a year did not attempt it at all and failed to obtain a degree within six years. </p>
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<img alt="A student working on math equations with their calculator." src="https://images.theconversation.com/files/533575/original/file-20230622-21-rc9pbc.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/533575/original/file-20230622-21-rc9pbc.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/533575/original/file-20230622-21-rc9pbc.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/533575/original/file-20230622-21-rc9pbc.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/533575/original/file-20230622-21-rc9pbc.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/533575/original/file-20230622-21-rc9pbc.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/533575/original/file-20230622-21-rc9pbc.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">Math anxiety and procrastination can affect students’ decisions on taking math during their first year.</span>
<span class="attribution"><a class="source" href="https://www.gettyimages.com/detail/photo/person-solving-math-equations-on-paper-with-royalty-free-image/1434696653?phrase=math&adppopup=true">Alex Walker/Moment via Getty Images</a></span>
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<h2>Why it matters</h2>
<p>Nearly 1.7 million students who recently graduated from high school will <a href="https://nces.ed.gov/programs/coe/indicator/cpa/immediate-college-enrollment-rate">immediately enroll in college</a>. Math is a requirement for most degrees, but students aren’t always ready to do college-level math. By putting off college math for a year, it gives students time to adjust to college and prepare for more challenging coursework. </p>
<p>Approximately <a href="https://doi.org/10.7916/D8MD0BD8">40% of four-year college students</a> must first take a remedial math course. This can <a href="https://www2.ed.gov/about/offices/list/opepd/education-strategies.pdf">extend the time it takes to graduate</a> and increase the likelihood of dropping out. Our study did not apply to students who need remedial math. </p>
<p>For students who do not require remedial courses, some delay can be beneficial, but students’ past experiences in math can lead to avoidance of math courses. Many students experience <a href="https://doi.org/10.1186/s40359-021-00537-2">math anxiety</a>. Procrastination can be an <a href="https://www.fastcompany.com/90357248/procrastination-is-an-emotional-problem">avoidance strategy</a> for managing fears about math. The fear of math for students may be a more significant barrier than their performance. </p>
<p>It is estimated that <a href="https://www.usnews.com/education/k12/articles/tackling-math-anxiety">at least 17%</a> of the population will likely experience high levels of math anxiety. Math anxiety can lead to a <a href="https://doi.org/10.1177/0734282908330580">drop in math performance</a>. It can also lead to avoiding majors and career paths involving math. </p>
<p>Our study fills the void in research on the effects of how soon students take college-level math courses. It also supports prior evidence that students benefit from a <a href="https://sc.edu/about/offices_and_divisions/national_resource_center/publications/search/details.php?id=2408onnect.com">mix of coursework</a> that is challenging yet not overwhelming as they transition to college. </p>
<h2>What still isn’t known</h2>
<p>We believe colleges need to better promote student confidence in math by examining how <a href="https://www.bestcolleges.com/blog/why-take-a-first-year-seminar/">student success courses</a> can reduce math anxiety. Student success courses provide students with study skills, note-taking skills, goal setting, time management and stress management, as well as career and financial decision making to support the transition to college. Although student success courses are a <a href="https://www.aacu.org/trending-topics/high-impact">proven practice</a> that help students stick with college, rarely do these courses address students’ fear of math. </p>
<p>Students are at the greatest risk of <a href="https://searchworks.stanford.edu/view/11883667">dropping out</a> of college during their first year. <a href="https://blog.ed.gov/2022/08/the-importance-of-academic-advising-in-higher-education/">Advisors</a> play a crucial role in providing students with resources for success. This includes recommendations on what courses to take and when to take them. More research is also needed about how advisors can effectively communicate the impact of when math is taken by students.</p><img src="https://counter.theconversation.com/content/205284/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Forrest Lane has received funding from the Greater Texas Foundation. </span></em></p>College students can benefit from not taking math courses in their freshman year, new research shows.Forrest Lane, Associate Dean and Professor of Educational Research, Sam Houston State UniversityLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/2057332023-06-19T20:48:59Z2023-06-19T20:48:59ZHow Canadian and Chinese teachers’ reciprocal learning can benefit students<figure><img src="https://images.theconversation.com/files/532467/original/file-20230616-17-nw47xo.jpg?ixlib=rb-1.1.0&rect=30%2C814%2C5673%2C3420&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Working to understand and appreciate differences between western and Chinese approaches to education could contribute to the cross-cultural understanding we need to address global crises.</span> <span class="attribution"><span class="source">(Shutterstock)</span></span></figcaption></figure><p>What makes a good elementary teacher, and how can teaching systems support this?</p>
<p>Ontario has a generalist teaching model at the elementary level, meaning elementary teachers have a foundational understanding of most subjects. A 2014 report commissioned by the Elementary Teachers’ Federation of Ontario noted there was “<a href="https://www.etfo.ca/getmedia/dcdb69d0-fb8c-44bb-9f93-d8875e90b24f/161123_ReviewSpecTeacher.pdf">increasing pressure on public elementary teachers to be generalist practitioners in all areas of a highly specialized and progressively complex elementary curriculum</a>.”</p>
<p>In April, Ontario’s minister of education announced <a href="https://news.ontario.ca/en/release/1002937/ontario-launches-plan-to-boost-math-writing-and-reading-skills">funding to “boost math skills”</a> by hiring more school math coaches in classrooms, identifying a math lead per board and “enhancing skills of new teachers.”</p>
<p><a href="https://www.oecd.org/china/Education-in-China-a-snapshot.pdf">China’s elementary teachers are primarily specialist teachers</a> with expert understanding in specific fields. Chinese teachers are trained to focus on content knowledge and basic skills, and around <a href="https://www.semanticscholar.org/paper/The-Cross-national-Comparison-of-Pre-service-and-Chen-Mu/ab343d162d286f763515bab5bac23740555e620e">60 per cent of their post-secondary study courses are subject knowledge courses</a>. </p>
<p>However, Naiqing Song, an education scholar, proposes that <a href="https://chn.oversea.cnki.net/KCMS/detail/detail.aspx?dbcode=CJFD&dbname=CJFDLAST2022&filename=JIJX202204001&uniplatform=OVERSEA&v=GUJP9vbvq0OBy-kCTHOiuvGbfilvZKJHWrVDlBKS8bHGdqQrhq9O2pfJrn3-rS-f">more than 90 per cent of Chinese elementary teachers should be trained as generalist teachers</a> in the next decade. </p>
<p>It is essential to understand generalist and specialist models of teaching through reciprocal learning. These approaches need not be treated as dichotomized or opposed to each other.</p>
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<img alt="A teacher and students outdoors." src="https://images.theconversation.com/files/532457/original/file-20230616-11631-7qstn.jpg?ixlib=rb-1.1.0&rect=0%2C58%2C3000%2C1854&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/532457/original/file-20230616-11631-7qstn.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=433&fit=crop&dpr=1 600w, https://images.theconversation.com/files/532457/original/file-20230616-11631-7qstn.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=433&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/532457/original/file-20230616-11631-7qstn.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=433&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/532457/original/file-20230616-11631-7qstn.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=544&fit=crop&dpr=1 754w, https://images.theconversation.com/files/532457/original/file-20230616-11631-7qstn.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=544&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/532457/original/file-20230616-11631-7qstn.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=544&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">Varied approaches to teaching need not be treated as opposed to each other. Kindergarten teachers and children outdoors at the Ritan Park in Beijing in 2012.</span>
<span class="attribution"><span class="source">(AP Photo/Andy Wong)</span></span>
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<h2>Reciprocal learning</h2>
<p>Shijing Xu, Canada Research Chair in International and Intercultural Reciprocal Learning, and one of the authors of this story, and Michael Connelly, an education professor emeritus at Ontario Institute for Studies in Education, research reciprocal learning. This is “<a href="https://doi.org/10.1007/978-3-030-59533-3_37-1">a concept and an approach for international and cross-cultural teacher education and school education for bridging the West-East dichotomy…</a>.”</p>
<p>Their research has addressed harmonizing eastern learning and western knowledge with mutual respect and appreciation, and determining what generalist and specialist teachers can reciprocally learn from each other. A book series, <a href="https://link.springer.com/series/15114"><em>Intercultural Reciprocal Learning in Chinese and Western Education</em></a>, shares findings from this work.</p>
<p>Chenkai Chi, the lead author of this story, is doing doctoral research as part of Xu and Connelly’s research project, titled <a href="https://www.reciprocal-learning.ca/pages/">Reciprocal Learning in Teacher Education and School Education Between Canada and China</a>. </p>
<p>This research is based on intensive six-year fieldwork in <a href="https://reciprocal-learning.ca/show/sisterSchool-W-C.html">a Windsor primary school and a Chongqing primary school, a Canada-China sister school pair that is part of the larger study</a>. </p>
<h2>Sharing learning</h2>
<p>Policymakers sometimes stress essential differences in curricular and teaching approaches, depending on the policy paradigms they embrace: <a href="https://interdisciplinarystudies.org/docs/Vol28_2010/28_OntarioSchools.pdf">“accountability” paradigms (often using language of “back to basics”) or student-centred paradigms</a>. Some scholars highlight that such framings <a href="https://theconversation.com/6-changes-in-ontarios-not-so-basic-new-elementary-math-curriculum-148878">may exaggerate differences</a> in curriculum or what teachers actually do.</p>
<p>Still, there are lessons that teachers and teaching systems can share. One important lesson that Canadian generalist teachers can learn from specialist teachers in China is teachers’ collaboration with each other, seen, for example, in collective lesson planning. </p>
<p>Education researcher <a href="https://cies2023.org/program/keynote/">Linda Darling-Hammond</a> has outlined some examples of what she observed in Shanghai about teacher collective lesson plans, and has highlighted the importance of teacher mutual support. </p>
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<figcaption><span class="caption">‘Transforming Education for a More Equitable World,’ featuring education researcher Linda Darling-Hammond.</span></figcaption>
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<p>Specialist teachers in China should also learn how Canadian generalist teachers develop the whole child. This approach focuses on priorities such as children’s <a href="https://www.ontario.ca/document/health-and-physical-education-grades-1-8/social-emotional-learning-sel-skills">social emotional learning needs</a>, developing a <a href="https://www.ontariovirtualschool.ca/understanding-developing-growth-mindset/">growth mindset</a>, and the importance of <a href="https://doi.org/10.20935/AL387">transdisciplinary thinking</a>. </p>
<h2>Trust and collaboration</h2>
<p>Generalist and specialist teaching both have advantages and disadvantages. Mutual and appreciative learning and sharing should be based on trust.</p>
<p>Educators need to uphold the spirit of <a href="https://doi.org/10.1080/13540602.2019.1601077">reciprocal learning</a>. We need educators who can dedicate themselves towards harnessing diversity in a variety of academic disciplines.</p>
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<figcaption><span class="caption">Catherine Febria of the Great Lakes Institute for Environmental Research presents as part of Asian Heritage Month 2023 on the subject of harnessing diversity in freshwater science.</span></figcaption>
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<p>By highlighting appreciative learning, educators can gain insights across cultures to understand how to focus on <a href="https://sdgs.un.org/goals">urgent issues of today for sustainable development</a>.</p>
<p>As education scholars Yishin Khoo and Jing Lin argue, <a href="https://doi.org/10.1007/s12564-023-09827-3">people need to see themselves as citizens of Earth to solve the issues with “we-togetherness” thinking</a>. </p>
<p>We human beings should think beyond anthropocentrism, and our own comfortable cultural frameworks, and act collaboratively in a harmonious way. In so doing, together we can find ways <a href="https://www.youtube.com/watch?v=AbuaU6IYV2I&t=44s">to address climate change</a>, <a href="https://www.youtube.com/watch?v=FEwzoairmQk">racism and prejudice</a>, <a href="https://www.uwindsor.ca/vp-equity-diversity-inclusion">and equity, diversity and inclusion</a>. We can then significantly positively impact people’s lives and the next generations.</p>
<p>With mutual appreciation and through relationships, school teachers, teacher educators and policymakers can work collaboratively to build an education system that is holistic, inclusive, reciprocal and equitable.</p><img src="https://counter.theconversation.com/content/205733/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Chenkai Chi is a research assistant in Xu and Connelly's SSHRC Partnership Grant Project and has received a SSHRC Doctoral Fellowship and an Ontario Graduate Scholarship.</span></em></p><p class="fine-print"><em><span>Shijing Xu has received research funding from SSHRC Partnership Grant and Canada Research Chair Program for research in international and intercultural reciprocal learning in education. </span></em></p>Teachers in Ontario elementary schools can learn from how teachers in China approach collaboration as subject area specialists, while Chinese teachers can learn about developing the whole child.Chenkai Chi, PhD candidate, Faculty of Education, University of WindsorShijing Xu, Canada Research Chair, Faculty of Education, University of WindsorLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/2029212023-05-02T12:13:53Z2023-05-02T12:13:53ZMath teachers hold a bias against girls when the teachers think gender equality has been achieved<figure><img src="https://images.theconversation.com/files/523481/original/file-20230428-22-ygf772.jpg?ixlib=rb-1.1.0&rect=0%2C92%2C7744%2C5143&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Effects of biases can snowball over time.</span> <span class="attribution"><a class="source" href="https://www.gettyimages.com/detail/photo/shot-of-a-little-girl-doing-maths-on-a-board-in-a-royalty-free-image/1391720645?phrase=girls+math&adppopup=true">PeopleImages via Getty Images</a></span></figcaption></figure><p><em>The <a href="https://theconversation.com/us/topics/research-brief-83231">Research Brief</a> is a short take about interesting academic work.</em> </p>
<h2>The big idea</h2>
<p>Math teachers who believe women no longer face discrimination tend to be biased against girls’ ability in math. This is what we found through an <a href="https://doi.org/10.1186/s40594-023-00420-z">experiment we conducted</a> with over 400 elementary and middle school math teachers across the United States. Our findings were published in a peer-reviewed article that appeared in April 2023 in the International Journal of STEM Education.</p>
<p>For our experiment, we asked teachers to evaluate a set of student solutions to math problems. The teachers didn’t know that gender- and race-specific names, such as Tanisha and Connor, had been randomly assigned to the solutions. We did this so that if they evaluated identical student work differently, it would be because of the gender- and race-specific names they saw, not the differences in student work. The idea was to see if the teachers had any unconscious biases.</p>
<p>After the teachers evaluated the student solutions, we asked a series of questions about their beliefs and experiences. We asked if they felt society had achieved gender equality. We asked them whether they felt anxious about doing math. We asked whether they felt students’ ability in math was fixed or could be improved. We also asked teachers to think about their own experience as math students and to report how frequently they experienced feelings of unequal treatment because of their race or gender.</p>
<p>We then investigated if these beliefs and experiences were related to how they evaluated the math ability of students of different genders or racial groups. </p>
<p>Consistent with our <a href="https://doi.org/10.3102/0013189X19890577">prior work</a>, we found that implicit bias against girls arises in ambiguous situations — in this case, when student solutions were not completely correct.</p>
<p>Further, for teachers who believed that U.S. society had achieved gender equality, they tended to rate a student’s ability higher when they saw a male student name than when they saw a female student name for the same student work.</p>
<h2>Why it matters</h2>
<p>Teachers’ unconscious <a href="https://doi.org/10.1016/j.compedu.2022.104627">gender biases</a> in math classes have been documented repeatedly.</p>
<p>Our study identifies factors that underlie such biases; namely, that biases are stronger among teachers who believe that gender discrimination is not a problem in the United States. Understanding the relationship between teachers’ beliefs and biases can help teacher educators create effective and targeted interventions to remove such biases from classrooms. </p>
<p>Our findings also shed light on potential reasons that <a href="https://doi.org/10.1016/j.lindif.2016.01.002">males tend to have higher confidence in math</a> and <a href="https://doi.org/10.1126/science.aba7377">stick with math-intensive college majors</a> even when they’re not high performers.</p>
<h2>What still isn’t known</h2>
<p>One big remaining question is how to create targeted interventions to help teachers overcome such biases. Evidence suggests that unconscious biases <a href="https://doi.org/10.1177/17456916211057565">come into play in situations where stereotypes might emerge</a>. Further, research suggests that these unconscious biases can be suppressed only when people are aware of them and motivated to restrain them.</p>
<p>Since bias may take on different forms in different fields, a one-time, one-size-fits-all anti-bias training <a href="https://doi.org/10.1037/pspa0000160">may not have a lasting effect</a>. We think it’s worthwhile to investigate if it’s more effective to provide implicit bias training programs that are specific to the areas where bias is revealed.</p><img src="https://counter.theconversation.com/content/202921/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Joseph Cimpian receives funding from the U.S. Department of Education Institute of Education Sciences and the National Science Foundation. </span></em></p><p class="fine-print"><em><span>Ian Thacker and Yasemin Copur-Gencturk do not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and have disclosed no relevant affiliations beyond their academic appointment.</span></em></p>Teachers judged the same math work differently based on whether the work was associated with male or female names.Yasemin Copur-Gencturk, Associate Professor of Education, University of Southern CaliforniaIan Thacker, Assistant Professor of Educational Psychology, The University of Texas at San AntonioJoseph Cimpian, Professor of Economics and Education Policy, New York UniversityLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/2026912023-03-31T18:15:47Z2023-03-31T18:15:47ZDeclines in math readiness underscore the urgency of math awareness<figure><img src="https://images.theconversation.com/files/518595/original/file-20230330-1139-7yolln.jpg?ixlib=rb-1.1.0&rect=0%2C73%2C6134%2C4000&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Math scores plummeted during the COVID-19 pandemic. What will it take to raise them back up?</span> <span class="attribution"><a class="source" href="https://www.gettyimages.com/detail/photo/girl-solving-mathematical-addition-royalty-free-image/950609102?phrase=math%20classroom&adppopup=true">Ridofranz / iStock / Getty Images Plus</a></span></figcaption></figure><p>When President Ronald Reagan <a href="https://ww2.amstat.org/mam/98/what.is.maw.html">proclaimed the first National Math Awareness Week</a> in April 1986, one of the problems he cited was that too few students were devoted to the study of math.</p>
<p>“Despite the increasing importance of mathematics to the progress of our economy and society, enrollment in mathematics programs has been declining at all levels of the American educational system,” Reagan wrote in his proclamation.</p>
<p>Nearly 40 years later, the problem that Reagan lamented during the first National Math Awareness Week – which has since evolved to become “<a href="https://ww2.amstat.org/mathstatmonth/aboutmathstatmonth.html">Mathematics and Statistics Awareness Month</a>” – not only remains but has gotten worse.</p>
<p>Whereas 1.63%, or about <a href="https://nces.ed.gov/programs/digest/d21/tables/dt21_325.65.asp">16,000</a>, of the <a href="https://nces.ed.gov/programs/digest/d12/tables/dt12_310.asp">nearly 1 million</a> bachelor’s degrees awarded in the U.S. in the 1985-1986 school year went to math majors, in 2020, just 1.4%, or about <a href="https://nces.ed.gov/programs/digest/d21/tables/dt21_325.65.asp">27,000</a>, of the <a href="https://nces.ed.gov/programs/digest/d12/tables/dt12_310.asp">1.9 million</a> bachelor’s degrees were awarded in the field of math – a small but significant decrease in the proportion.</p>
<p>Post-pandemic data suggests the number of students majoring in math in the U.S. is likely to decrease in the future.</p>
<p>A key factor is the <a href="https://www.nytimes.com/2022/10/24/us/math-reading-scores-pandemic.html">dramatic decline in math learning</a> that took place during the lockdown. For instance, whereas 34% of eighth graders were proficient in math in 2019, test data shows the percentage <a href="https://www.nytimes.com/2022/10/24/us/math-reading-scores-pandemic.html">dropped to 26% after the pandemic</a>.</p>
<p>These declines will undoubtedly affect how much math U.S. students can do at the college level. For instance, in 2022, only <a href="https://www.act.org/content/dam/act/unsecured/documents/2022/2022-National-ACT-Profile-Report.pdf">31% of graduating high school seniors were ready for college-level math</a> – down from 39% in 2019.</p>
<p>These declines will also affect how many U.S. students are able to take advantage of the growing number of <a href="https://www.bls.gov/ooh/math/home.htm">high-paying math occupations</a>, such as <a href="https://www.bls.gov/ooh/math/data-scientists.htm">data scientists</a> and <a href="https://www.bls.gov/ooh/math/actuaries.htm">actuaries</a>. Employment in math occupations is projected to <a href="https://www.bls.gov/ooh/math/home.htm">increase by 29%</a> in the period from 2021 to 2031.</p>
<p>About <a href="https://www.bls.gov/ooh/math/home.htm">30,600 math jobs</a> are expected to open up per year from growth and replacement needs. That exceeds the 27,000 or so math graduates being produced each year – and <a href="https://www.bls.gov/ooh/field-of-degree/mathematics/mathematics-field-of-degree.htm">not all math degree holders</a> go into math fields. Shortages will also arise in several other areas, since math is a gateway to many STEM fields.</p>
<p>For all of these reasons and more, as a <a href="https://manilsuri.umbc.edu/">mathematician</a> who thinks deeply about the <a href="https://wwnorton.com/books/9781324007036">importance of math</a> and what it means to our world – and even to <a href="https://scholar.google.com/citations?view_op=view_citation&hl=en&user=lFWFsSkAAAAJ&sortby=pubdate&citation_for_view=lFWFsSkAAAAJ:j3f4tGmQtD8C">our existence as human beings</a> – I believe this year, and probably for the foreseeable future, educators, policymakers and employers need to take Mathematics and Statistics Awareness Month more seriously than ever before.</p>
<h2>Struggles with mastery</h2>
<p>Subpar math achievement has been endemic in the U.S. for a long time. </p>
<p>Data from the National Assessment of Educational Progress shows that <a href="https://www.nationsreportcard.gov/mathematics/nation/achievement/?grade=12">no more than 26% of 12th graders</a> have been rated proficient in math since 2005.</p>
<p>The pandemic <a href="https://www.nationsreportcard.gov/mathematics/nation/groups/?grade=4#nation-gaps-gaps">disproportionately affected</a> racially and economically disadvantaged groups. During the lockdown, these groups had <a href="https://www.nationsreportcard.gov/highlights/mathematics/2022/#student-experiences">less access to the internet and quiet studying spaces</a> than their peers. So securing Wi-Fi and places to study are key parts of the battle to improve math learning.</p>
<p>Some people believe math teaching techniques need to be revamped, as they were through the <a href="https://www.vox.com/2014/4/20/5625086/the-common-core-makes-simple-math-more-complicated-heres-why">Common Core</a>, a new set of educational standards that stressed alternative ways to solve math problems. Others want a return to more traditional methods. Advocates also argue there is a need for colleges to <a href="https://www.nctq.org/publications/Teacher-Prep-Review:-Building-Content-Knowledge">produce better-prepared teachers</a>.</p>
<p>Other observers believe the problem lies with the “<a href="https://www.penguinrandomhouse.com/books/44330/mindset-by-carol-s-dweck-phd/">fixed mindset</a>” many students have – where failure leads to the conviction that they can’t do math – and say the solution is to foster a <a href="https://www.frontiersin.org/articles/10.3389/feduc.2021.784393/full#B21">“growth” mindset</a> – by which failure spurs students to try harder.</p>
<p>Although all these factors are relevant, none address what in my opinion is a root cause of math underachievement: our nation’s ambivalent relationship with mathematics.</p>
<h2>Low visibility</h2>
<p>Many observers worry about how U.S. children fare in <a href="https://data.oecd.org/pisa/mathematics-performance-pisa.htm">international rankings</a>, even though math anxiety makes <a href="https://files.eric.ed.gov/fulltext/ED536509.pdf">many adults in the U.S.</a> steer clear of the subject themselves.</p>
<p>Mathematics is not like art or music, which people regularly enjoy all over the country by visiting museums or attending concerts. It’s true that there is a National Museum of Mathematics in New York, and some science centers in the U.S. devote exhibit space to mathematics, but these can be geographically inaccessible for many.</p>
<p>A 2020 study on media portrayals of math <a href="https://doi.org/10.29333/iejme/8260">found an overall “invisibility of mathematics</a>” in popular culture. Other findings were that math is presented as being irrelevant to the real world and of little interest to most people, while mathematicians are stereotyped to be singular geniuses or socially inept nerds, and white and male. </p>
<p>Math is tough and typically takes much discipline and perseverance to succeed in. It also calls for a <a href="https://doi.org/10.1088/1742-6596/947/1/012029">cumulative learning approach</a> – you need to master lessons at each level because you’re going to need them later. </p>
<p>While research in neuroscience shows almost everyone’s brain is <a href="https://blogs.ams.org/matheducation/2019/02/01/everyone-can-learn-mathematics-to-high-levels-the-evidence-from-neuroscience-that-should-change-our-teaching/">equipped to take up the challenge</a>, many students balk at putting in the effort when they don’t score well on tests. The <a href="https://www.frontiersin.org/articles/10.3389/feduc.2018.00026/full#B6">myth that math is just about procedures and memorization</a> can make it easier for students to give up. So can <a href="https://files.eric.ed.gov/fulltext/EJ1304392.pdf">negative opinions</a> about math ability conveyed by peers and parents, such as declarations of not being “<a href="https://www.nytimes.com/2017/04/24/well/family/fending-off-math-anxiety.html">a math person</a>.”</p>
<h2>A positive experience</h2>
<p>Here’s the good news. A 2017 Pew poll found that despite the bad rap the subject gets, <a href="https://www.pewresearch.org/social-trends/2018/01/09/many-americans-say-they-liked-math-and-science-in-school-thought-about-a-stem-career/">58% of U.S. adults enjoyed their school math classes</a>. It’s members of this legion who would make excellent recruits to help promote April’s math awareness. The initial charge is simple: Think of something you liked about math – a topic, a <a href="https://www.mathsisfun.com/puzzles/">puzzle</a>, a fun fact – and go over it with someone. It could be a child, a student, or just one of the many adults who have left school with a negative view of math.</p>
<figure class="align-center ">
<img alt="Three seashells are shown under the words " src="https://images.theconversation.com/files/518209/original/file-20230329-24-bfj94q.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/518209/original/file-20230329-24-bfj94q.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=430&fit=crop&dpr=1 600w, https://images.theconversation.com/files/518209/original/file-20230329-24-bfj94q.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=430&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/518209/original/file-20230329-24-bfj94q.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=430&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/518209/original/file-20230329-24-bfj94q.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=540&fit=crop&dpr=1 754w, https://images.theconversation.com/files/518209/original/file-20230329-24-bfj94q.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=540&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/518209/original/file-20230329-24-bfj94q.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=540&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Math exercise for shells can be downloaded at https://www.manilsuri.com/assets/shell_patterns.pptx.</span>
<span class="attribution"><span class="source">Manil Suri</span>, <span class="license">Author provided</span></span>
</figcaption>
</figure>
<p>Can something that sounds so simplistic make a difference? Based on my years of experience as a mathematician, I believe it can – if nothing else, for the person you talk to. The goal is to stimulate curiosity and convey that mathematics is much more about <a href="https://theconversation.com/pi-gets-all-the-fanfare-but-other-numbers-also-deserve-their-own-math-holidays-200046">exhilarating ideas that inform our universe</a> than it is about the school homework-type calculations so many dread.</p>
<p>Raising math awareness is a first step toward making sure people possess the basic math skills required not only for employment, but also to understand math-related issues – such as gerrymandering or climate change – well enough to be an informed and participating citizen. However, it’s not something that can be done in one month.</p>
<p>Given the decline in both math scores and the percentage of students studying math, it may take many years before America realizes the stronger relationship with math that President Reagan’s proclamation called for during the first National Math Awareness Week in 1986.</p><img src="https://counter.theconversation.com/content/202691/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Manil Suri does not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.</span></em></p>Nearly four decades after President Ronald Reagan proclaimed the first National Math Awareness Week, math readiness and enrollment in college math programs continue to decline.Manil Suri, Professor of Mathematics and Statistics, University of Maryland, Baltimore CountyLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1931242022-11-02T12:27:44Z2022-11-02T12:27:44ZFormer math teacher explains why some students are ‘good’ at math and others lag behind<figure><img src="https://images.theconversation.com/files/492832/original/file-20221101-25191-esequq.jpg?ixlib=rb-1.1.0&rect=0%2C0%2C5590%2C3707&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Math proficiency scores fell during the pandemic. </span> <span class="attribution"><a class="source" href="https://www.gettyimages.com/detail/photo/students-teacher-math-classroom-technology-digital-royalty-free-image/155387240?phrase=middle%20school%20math%20students&adppopup=true">fstop123 via Getty Images</a></span></figcaption></figure><p><em>When Frances E. Anderson saw <a href="https://www.nationsreportcard.gov/highlights/mathematics/2022/">2022 math scores</a> for America’s fourth- and eighth-graders, she was hardly surprised that they had dropped. Until recently – including the period of remote instruction during the pandemic – Anderson taught high school math to students at all levels.“ Now she is a researcher seeking to change how people understand children’s math ability. In the following Q&A, <a href="https://scholar.google.com/citations?hl=en&user=zwfRnAMAAAAJ">Anderson</a> explains what makes some kids "good” at math and what it will take to catch up those who have fallen behind.</em></p>
<h2>What was the hardest part about teaching during the pandemic?</h2>
<p>Seeing students who already struggled not be able to get <a href="https://www.nctm.org/uploadedFiles/Standards_and_Positions/PtAExecutiveSummary.pdf">what they needed during that time</a>. Before the pandemic, I could work with students one on one, have students work in pairs, or have students in more advanced classes come tutor students in entry-level classes. During the pandemic, all of this was taken away because we didn’t share the room with our students and – at least in the initial stages of the pandemic – many of us didn’t have the skills to use comparable teaching strategies online.</p>
<h2>How do you explain the recent drop in math scores?</h2>
<p>Once schools shifted to remote learning during the pandemic, teachers didn’t have as many ways to keep students engaged. It was difficult to do hands-on activities and project-based learning, which are <a href="https://doi.org/10.1080/00220671.2014.979911">better for students who struggle in math</a>. </p>
<p>Math teachers had to tell students what to do in mathematics, but this kind of direct instruction <a href="https://www.td.org/insights/debunk-this-people-remember-10-percent-of-what-they-read">works for only about 20% of students</a>. A lot of teaching math is <a href="https://www.youcubed.org/wp-content/uploads/2017/04/JACmaths-seeing-article.pdf">visual</a>. You need so much more space than just one screen. Teachers might use their words, hand gestures, whiteboards, graphs, diagrams, objects, physical movements, student work examples and more. These actions and items build a comprehensive experience and <a href="https://www.worldcat.org/title/48544780">build more of the skills that math students need</a> since the students can look at several of these teaching aids at once. Online, the teacher is limited only to what can be seen on their screen or on one student’s screen at a time, which is vastly different.</p>
<p>In addition to being visual, <a href="https://www.worldcat.org/title/703623758">teaching math is a lot about what is said</a> during class. In fact, one of the most important functions of effective math teaching is how the teacher engages in conversations with students about mathematics. This conversation, known as classroom discourse, <a href="https://www.worldcat.org/title/703623758">has great power to help students learn</a>. When every student is muted so that they can hear the teacher, it’s impossible to hear the students speak about mathematics. </p>
<h2>Why are some students ‘good’ at math and others can’t solve basic problems?</h2>
<p>It’s not true that some kids are good at math and others aren’t. It comes down to what kind of <a href="https://www.researchgate.net/publication/281065932_America%27s_Children_Providing_early_exposure_to_STEM_Science_Technology_Engineering_Math_Initiatives">exposure and experiences</a> children have early in their lives. Some parents see to it that their kids do more with numbers than others. They do more at home, they do more in social events, and they do more in school. These routine exposures make them appear good at math. It isn’t that they’re good so much as it is that they had more time to work with mathematics.</p>
<h2>Why did you leave teaching?</h2>
<p><a href="https://www.unomaha.edu/college-of-education-health-and-human-sciences/teacher-education/about-us/directory/frances-anderson.php">I still teach today</a>, only I teach a different set of students: future teachers. As a schoolteacher, my impact was limited to the 180 students that I had each year. But now I am in a position where I can impact about 100 future teachers every year. That means each of those 100 future teachers can turn around and impact 180 students themselves every single year. In my position now, I can help so many more students in education than I ever could being a classroom teacher. </p>
<h2>What is the focus of your research?</h2>
<p>The purpose of my research is to change how people think about math ability and inability, which means a lot of my time is spent reading about mathematics teaching and learning. One of the most compelling articles that I’ve read explained that the brains of math experts, such as people who are mathematicians, compared to nonexperts <a href="https://doi.org/10.1111/mbe.12179">are no different</a>. Then, watching Jo Boaler, a widely respected math education researcher, explain how <a href="https://www.youtube.com/watch?v=7FjZ_JW2WCw">plastic the brain is, even through adulthood</a>, has made me realize that math is not an innate ability; it is a learned skill, just like a lot of things. The goal of my research is to find enough convincing evidence for everyone to believe this as well.</p>
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<figcaption><span class="caption">Video on brain growth.</span></figcaption>
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<h2>What’s the best way for students to catch up?</h2>
<p>More time.</p>
<p>Students who have fallen behind should have <a href="https://eric.ed.gov/?id=ED591888">twice as much instruction</a> to engage in grade-level mathematics. And the time spent in math should be organic, rich, task-based teaching and learning. What this means is meaningful, personal experiences need to happen every day in math class. For example, a hands-on activity in math class, a story problem that is relevant to every student, or the students creating their own story problem with a teacher asking <a href="https://arxiv.org/pdf/2208.04715.pdf">different types of questions</a> to challenge the learners.
All students need to <a href="https://files.eric.ed.gov/fulltext/ED503746.pdf#page=341">see themselves as mathematicians</a> so that they develop a personal connection to mathematics learning.</p><img src="https://counter.theconversation.com/content/193124/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Frances E. Anderson receives funding from the Nebraska Math Omaha Noyce Partnership, authorized under the National Science Foundation (NSF). Funding does not directly support the work of this article nor do the words of the author directly reflect the NOYCE project or the NSF.</span></em></p>A former math teacher explains what’s behind the recent drop in math scores for the nation’s fourth and eighth graders.Frances E. Anderson, Faculty Member in Teacher Education, University of Nebraska OmahaLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1792662022-05-27T12:33:01Z2022-05-27T12:33:01ZStudents are often segregated within the same schools, not just by being sent to different ones<figure><img src="https://images.theconversation.com/files/465073/original/file-20220524-22-jiazkf.jpg?ixlib=rb-1.1.0&rect=9%2C27%2C6029%2C3983&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Classmates in grades 3, 4 and 5 are more likely to come from diverse economic backgrounds than their schoolmates in grades 6, 7 and 8.</span> <span class="attribution"><a class="source" href="https://www.gettyimages.com/detail/news-photo/students-pass-a-beach-ball-to-the-next-person-on-the-list-news-photo/1334723214">Paul Bersebach, MediaNews Group/Orange County Register via Getty Images</a></span></figcaption></figure><p><em>The <a href="https://theconversation.com/us/topics/research-brief-83231">Research Brief</a> is a short take about interesting academic work.</em> </p>
<h2>The big idea</h2>
<p>Children from low-income households are <a href="https://doi.org/10.3102/0013189X221081853">increasingly being segregated into different classrooms</a> from their peers from higher-income households, according to recent research <a href="https://scholar.google.com/citations?user=NOT4bMEAAAAJ&hl=en&oi=ao">I</a> have conducted with education policy scholar <a href="https://www.american.edu/spa/faculty/marcotte.cfm">Dave E. Marcotte</a>.</p>
<p>From 2007 to 2014, we tracked all North Carolina public school students statewide, from third through eighth grades, observing how the students were grouped into math and English language arts classes by each school’s process for creating class groups.</p>
<p>We used course enrollment data to figure out how many students in each classroom were from families whose incomes are at or below 185% of the federal poverty threshold – and how many were not. We found that those economically disadvantaged students were increasingly likely to be concentrated in a subset of classrooms rather than spread out relatively evenly throughout the school. </p>
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<h2>Why it matters</h2>
<p>Often school segregation is thought about as Black and white students being forced to attend <a href="https://doi.org/10.1111/tsq.12010">different schools</a>. This makes sense given the <a href="https://library.law.howard.edu/civilrightshistory/blackrights/jimcrow">history of Jim Crow</a> – a 19th- and 20th-century legal system meant to <a href="https://www.ferris.edu/HTMLS/news/jimcrow/what.htm">relegate Black people to second-class status</a> in white society – and <a href="https://doi.org/10.1146/annurev-soc-071913-043152">court orders to desegregate schools</a>. </p>
<p>Another aspect of this issue is how students are sorted into classrooms within schools. A 2021 study found that more racially diverse schools are <a href="https://doi.org/10.1007/s12552-020-09309-w">more likely to have classrooms that are more segregated</a> than schools that are less diverse overall.</p>
<p>Researchers have recently begun to identify <a href="https://doi.org/10.3102/0002831216652722">rising levels of segregation between schools</a> based not just on race, but also on household income.</p>
<p>Students from wealthier households are more likely than their less-well-off peers to have <a href="https://www.russellsage.org/publications/whither-opportunity">higher academic achievement as measured by test scores</a> and to <a href="https://doi.org/10.1177/2332858416645834">attend and complete college</a>.</p>
<p>Efforts to provide equitable opportunities for all students often focus on comparing funding and staffing between schools. Indeed, lower levels of school funding lead to <a href="https://doi.org/10.1093/qje/qjv036">lower educational attainment and lower wages in adulthood</a>.</p>
<p>However, resources can also be distributed inequitably within schools, on a classroom-by-classroom basis. For instance, <a href="https://doi.org/10.1016/j.jpubeco.2010.11.009">more experienced teachers raise student test scores more than novice teachers, on average</a>. However, novice teachers are <a href="https://doi.org/10.3102/0013189X13495087">frequently assigned to classrooms with more low-income students</a>. Therefore, the more students are separated along lines of household income, the more likely poorer students are to fall behind academically.</p>
<h2>What still isn’t known</h2>
<p>We aren’t sure why there is an increase in segregation within schools by household income. One potential reason could be an increase in what is called “<a href="https://doi.org/10.1207/s15430421tip4501_2">academic tracking</a>,” which is the process of grouping students into classes based on their prior achievement, such as performance on standardized tests. </p>
<p>If <a href="https://doi.org/10.1257/aer.102.5.1927">low-income students perform worse on standardized tests than their peers</a>, they may be placed in lower tracks. However, standardized test scores may not accurately reflect ability for low-income students, since <a href="https://doi.org/10.1016/j.appdev.2003.09.002">students from marginalized groups perform disproportionately worse</a> on assessments.</p>
<p>If in fact test scores do accurately reflect ability, there may be <a href="https://doi.org/10.1257/aer.101.5.1739">some educational advantages</a> to track students into certain classes. However, researchers have long argued that <a href="https://doi.org/10.1177%2F019263658506948430">tracking perpetuates inequalities between low- and high-tracked students</a>. For example, students who are placed on lower tracks than their peers <a href="https://doi.org/10.1002/berj.3172">suffer from lower self-esteem</a> and are <a href="https://doi.org/10.1177/0895904816681526">not as well prepared for college success</a> as higher-tracked students with similar test scores.</p>
<p>The <a href="https://www.axios.com/2021/09/22/charter-school-pandemic-enrollment-growth">growth in charter school enrollments</a> over the past two decades could also contribute to the increases in within-school segregation by income that we find. Public school principals who fear their students may depart for charters may attempt to retain them <a href="https://doi.org/10.3102/0162373715577447">by introducing specialized curricula or expanding gifted and talented programs</a>. If these programs continue to primarily serve students from families with higher incomes, that could increase income segregation within schools. This is a possibility we are exploring.</p><img src="https://counter.theconversation.com/content/179266/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Kari Dalane and Dave Marcotte received funding from the Smith Richardson Foundation.</span></em></p>In middle school classes, students from lower-income families tended to be concentrated in just a few classrooms, new research from North Carolina has found.Kari Dalane, Ph.D. Candidate in Public Administration and Policy, American University School of Public AffairsLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1693342021-12-22T13:09:28Z2021-12-22T13:09:28ZSports card explosion holds promise for keeping kids engaged in math<figure><img src="https://images.theconversation.com/files/438758/original/file-20211221-21-19r1mkw.jpg?ixlib=rb-1.1.0&rect=36%2C0%2C6002%2C4019&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Sports trading cards can be used as teaching tools. </span> <span class="attribution"><a class="source" href="https://www.gettyimages.com/detail/news-photo/sports-cards-at-mile-high-card-company-in-castle-rock-news-photo/1351167297?adppopup=true">Hyoung Chang/MediaNews Group/The Denver Post via Getty Images</a></span></figcaption></figure><p>When it comes to collecting sports cards, people often <a href="https://www.boston.com/sports/mlb/2021/08/29/sports-card-collecting-boom-panini/">focus on the cards’ financial worth</a>. And understandably so.</p>
<p>After all, when a small piece of cardboard that originally cost just dollars or even cents is suddenly worth more than a million bucks after the featured player rises to fame, it’s hard to ignore the kind of massive wealth that certain sports cards can command.</p>
<p>For instance, a 1952 Mickey Mantle card <a href="https://www.espn.com/mlb/story/_/id/30709705/mickey-mantle-baseball-card-shatters-all-record-sells-52-million">sold for a then-record US$5.2 million</a> in January 2021. A 2003-2004 LeBron James card <a href="https://www.usatoday.com/story/sports/nba/2021/04/27/lebron-james-rookie-basketball-card-sells-record/7395964002/">also sold for $5.2 million</a> in April 2021.</p>
<p>The highest-selling sports card in history is one that features Honus Wagner, which <a href="https://www.cbssports.com/mlb/news/honus-wagner-card-sells-for-record-6-6m-becomes-most-valuable-sports-card-of-all-time/">sold for $6.6 million in August 2021</a>.</p>
<p>As a business professor who focuses on sports, I would never knock the trading of sports cards as a way to make an extra buck or as a hobby, or even just to pocket a piece or two of sports memorabilia – or just for the nostalgia of it all. But as an educator, I see another purpose for sports cards that goes well beyond memorabilia and their monetary worth.</p>
<p>And that is, I believe sports cards – just like sports in general – can be <a href="https://baseballhall.org/discover-more/education/batter-up">integrated into the classroom</a> as a way to stimulate students’ interest in math, probability, statistics and other related subjects they might otherwise dread.</p>
<p>This can be done at the college level, which I have done. But more importantly, I believe it should be done at the K-12 level as well. Integrating sports into the classroom is what <a href="https://csm.rowan.edu/departments/math/facultystaff/adjuncts/kautz-natalie.html">math curriculum specialist Natalie Kautz</a> of Rowan University and her colleague Michelle Kowalsky argue in a <a href="https://www.igi-global.com/chapter/using-sports-to-motivate-math-learners/265066">book about using pop culture to reach K-12 students</a>.</p>
<p>“The rich variety of numbers generated by all types of sports, as well as connections to popular culture extensions, naturally provides opportunities for exploration in numerical literacy,” Kautz and Kowalksy wrote in a chapter about using sports as a way to foster numerical literacy among students. “Using real sports data, students can perform operations and calculations, do statistical analyses, and create charts or graphs to enhance their learning of both basic and advanced operations.”</p>
<p>They go on to say that “nearly every concept taught in a K-12 mathematics curriculum” lends itself to a sport-based lesson of some sort.</p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/438751/original/file-20211221-27-1vx65q7.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="A family stands at a trading card booth." src="https://images.theconversation.com/files/438751/original/file-20211221-27-1vx65q7.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/438751/original/file-20211221-27-1vx65q7.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/438751/original/file-20211221-27-1vx65q7.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/438751/original/file-20211221-27-1vx65q7.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/438751/original/file-20211221-27-1vx65q7.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=502&fit=crop&dpr=1 754w, https://images.theconversation.com/files/438751/original/file-20211221-27-1vx65q7.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=502&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/438751/original/file-20211221-27-1vx65q7.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">Trading cards are on the rise again.</span>
<span class="attribution"><a class="source" href="https://www.gettyimages.com/detail/news-photo/guests-look-at-buy-it-now-display-with-collectibles-and-news-photo/1345383541?adppopup=true">Bryan Bedder/Getty Images for ReedPop</a></span>
</figcaption>
</figure>
<h2>Resurgent interest</h2>
<p>Now is a particularly good time to use sports cards in the classroom. Trading cards have grown quite <a href="https://www.boston.com/sports/mlb/2021/08/29/sports-card-collecting-boom-panini/">popular</a> as of late due to the pandemic.</p>
<p>For example, in 2020, interest in sports card collecting <a href="https://www.si.com/mlb/2020/05/04/breaking-the-fall-sports-cards-and-the-pandemic">grew as sports games were canceled due to COVID-19</a>. Such a scenario may be slowly unfolding anew as new variants of the coronavirus have begun to cause officials to <a href="https://abcnews.go.com/Health/major-sports-entertainment-events-canceled-rescheduled-due-rising/story?id=81819770">postpone or cancel sports contests</a> once again in late 2021 going into 2022.</p>
<h2>Cards in the classroom</h2>
<p>Using sports as a teaching tool is not an abstract concept for me. Back in 2017 and 2018 at Florida State University, I used baseball and basketball cards to teach a class about sports analytics, which is essentially the use of data analytics in the world of sports.</p>
<p>Sports analytics – which is expected to become a <a href="https://www.prnewswire.com/news-releases/global-sports-analytics-market-report-2021-301379531.html">$3.44 billion industry globally by 2028</a> – is playing an increasingly vital role in sports. For instance, some colleges use it to <a href="https://www.si.com/college/2021/08/23/wazzu-basketball-kyle-smith-moneyball">recruit athletic talent</a>. Professional sports teams, such as the the Golden State Warriors, have used analytics as the “<a href="https://chartio.com/blog/how-analytics-drives-the-golden-state-warriors/">secret sauce to championship success</a>.”</p>
<p>The class I taught attracted mostly sport management majors but was open to other students as well. And sports trading cards played a prominent role in my class.</p>
<figure class="align-left zoomable">
<a href="https://images.theconversation.com/files/438709/original/file-20211221-21-614sml.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="A boy places a trading card in a binder." src="https://images.theconversation.com/files/438709/original/file-20211221-21-614sml.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/438709/original/file-20211221-21-614sml.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=899&fit=crop&dpr=1 600w, https://images.theconversation.com/files/438709/original/file-20211221-21-614sml.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=899&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/438709/original/file-20211221-21-614sml.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=899&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/438709/original/file-20211221-21-614sml.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=1130&fit=crop&dpr=1 754w, https://images.theconversation.com/files/438709/original/file-20211221-21-614sml.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=1130&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/438709/original/file-20211221-21-614sml.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=1130&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Students can learn mathematics skills with trading cards.</span>
<span class="attribution"><a class="source" href="https://www.gettyimages.com/detail/photo/year-old-boy-pasting-soccer-trading-cards-into-his-royalty-free-image/535750070?adppopup=true">EThamPhoto/Getty Images</a></span>
</figcaption>
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<p>For instance, to teach the <a href="https://www.baseball-reference.com/bullpen/Pythagorean_Theorem_of_Baseball">“Pythagorean Theorem of Baseball,”</a>, which <a href="https://sabr.org/sabermetrics#:%7E:text=As%20originally%20defined%20by%20Bill,Society%20for%20American%20Baseball%20Research.">baseball analytics guru Bill James</a> developed to estimate how many games a team will win, I would have students “draft” players by randomly picking cards from packs. Then, using statistics from the same year for the selected players, I would have students tally the runs scored for the hitters and the runs allowed for the pitchers. Once students collect those two numbers, all that remains is putting them into the formula of Runs Scored squared divided by Runs Scored squared plus Runs Allowed squared. This formula then produces a winning percentage estimate.</p>
<p>Within the context of sports analytics, the idea is to show students that various statistics, when looked at collectively, can be used to predict certain outcomes. But such an exercise can also be used just to get students comfortable with statistics and using them in different ways.</p>
<p>Students have enjoyed seeing how their teams performed using something like a <a href="https://www.espn.com/mlb/standings">standings page</a> that they might see on ESPN.</p>
<p>I did a similar exercise using packs of basketball cards I bought online. I would have students select of pack of cards and then rank the players using economics professor David Berri’s <a href="https://www.nbastuffer.com/analytics101/win-score/">“Win Score” formula</a>. The simple formula requires students to add a player’s points, rebounds and steals from one season together, then add half of their assists and half of their blocked shots. Students then subtract a player’s field goal attempts, turnovers and half of their free throw attempts – again, from the same season – along with half of the player’s personal fouls. This enables a person to develop a snapshot of a player’s performance. But it also shows students how they can use statistics to analyze a player’s performance in different ways.</p>
<h2>At all levels</h2>
<p>One of the best things about using sports cards is that they can be used at any grade level. For example, in preschool, you can use the cards to help kids learn and remember numbers by having them read the <a href="https://simpleplayideas.com/play-with-jersey-numbers">numbers on players’ jerseys</a>. </p>
<p>In elementary school, students can use the information on the back of baseball cards to learn division. Simple exercises like dividing a player’s number of hits by their total number of times at bat produces the player’s batting average – a key statistic in baseball.</p>
<p>Sports trading cards lend themselves to all sorts of fun and lively lessons. For instance, in 2020, the Topps trading card company put forth a <a href="https://www.mlb.com/news/topps-of-the-class-posts-teaching-lessons">series of lessons</a> that teachers could do using sports trading cards. In one lesson, the company invited teachers to ask students to find the average age of five players in their card collection. Another lesson called for students to organize 10 cards based on a player’s weight from heaviest to lightest as fast as students could.</p>
<p>[<em>You’re smart and curious about the world. So are The Conversation’s authors and editors.</em> <a href="https://memberservices.theconversation.com/newsletters/?source=inline-youresmart">You can read us daily by subscribing to our newsletter</a>.]</p>
<h2>Flipping the cards</h2>
<p>The use of sports cards in the classroom could serve as a way to help maintain interest in math – a subject in which students’ skills have <a href="https://www.washingtonpost.com/lifestyle/2021/02/16/kids-math-skills-have-taken-hit-during-pandemic-heres-how-parents-can-help/">taken a hit during the pandemic</a>. Interest in a subject is key for <a href="https://www.kqed.org/mindshift/32503/how-the-power-of-interest-drives-learning">learning the subject</a> and <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5839644/">succeeding at it</a>.</p>
<p>For all these reasons, instead of focusing on the photographs on the face of sports cards, I believe the time has come for educators to start making better use of the statistics on the backs of the cards. While the photos on the front tend to generate the most attention, the statistics on the back of the card provide multiple ways to engage students in math using a sport they love or an athlete that they admire.</p><img src="https://counter.theconversation.com/content/169334/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>John Holden does not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.</span></em></p>Student math skills dropped during the pandemic. A business professor believes using sports cards in class could help turn that around.John Holden, Assistant Professor of Legal Studies, Oklahoma State UniversityLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1703502021-10-28T17:47:40Z2021-10-28T17:47:40Z5 ways sorting Halloween candy can help children develop mathematics skills<figure><img src="https://images.theconversation.com/files/428858/original/file-20211027-21-12r3u3k.jpg?ixlib=rb-1.1.0&rect=0%2C120%2C6720%2C4335&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Whatever costume you wear, put on your 'sorting hat' after trick-or-treating to help children lay the foundation for higher-level mathematics.</span> <span class="attribution"><span class="source">(Shutterstock)</span></span></figcaption></figure><p>Thinking back on Halloween, were you a “dump all your candy into one bowl” child? Or did you enjoy meticulously sorting your treats into a post-Halloween candy store and trading with others? </p>
<p>If you were the sorting and arranging type, whether you realized it or not, you took advantage of the many informal and unintentional mathematics learning opportunities Halloween provides. These opportunities likely have <a href="https://doi.org/10.1007/s10643-009-0340-1">important long-term benefits for children’s mathematical knowledge and confidence</a>. </p>
<p>Math <a href="https://doi.org/10.1016/j.cogdev.2014.11.002">talk at home can promote early math learning</a>. Our research has consistently shown that <a href="https://doi.org/10.1016/j.jecp.2013.11.006">early exposure to math content at home predicts children’s school mathematics outcomes</a>. In our latest work with <a href="https://carleton.ca/cmi/about/">colleagues who are part of a language learning and mathematics achievement research group</a>, we are learning that when children are involved in second or additional-language learning, gaining math vocabulary <a href="http://dx.doi.org/10.1037/edu0000673">in the additional language is also important</a>.</p>
<p>Counting and sorting Halloween treats — and other forms of household sorting that caregivers could lead, like sorting socks in the laundry — allows children to learn important skills that lay the foundation for higher-level mathematics. </p>
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<iframe width="440" height="260" src="https://www.youtube.com/embed/eaGMItI8osA?wmode=transparent&start=0" frameborder="0" allowfullscreen=""></iframe>
<figcaption><span class="caption">Early years teacher and parent Sarah Melo sorts Halloween treats with children.</span></figcaption>
</figure>
<h2>Every day early learning opportunities</h2>
<p>Because of the strong relationship between early home learning and child outcomes, a group of researchers, community educators, high school and university students, founded <a href="https://www.toyboxmanitoba.ca/">ToyBox, an educational resource</a>. This work started at the University of Winnipeg and now engages collaborators from across Canada. </p>
<p>ToyBox provides fun and easy-to-use ideas <a href="https://www.toyboxmanitoba.ca/copy-of-literacy-activities">about numbers</a>, <a href="https://www.toyboxmanitoba.ca/servicesmagazine-1">language</a> <a href="https://www.toyboxmanitoba.ca/copy-of-numeracy-activities">and wellness</a> that are based on child development research for caregivers and their children aged two to eight years. The resource offers learning activities for beginner, intermediate and advanced learners to capture the interests and developmental capabilities of young minds. Each activity also contains an explanation about why the idea is important for learning. Student collaborators created characters who accompany each strategy, to keep the learning fun.</p>
<p>One focus of ToyBox is helping caregivers to <a href="https://doi.org/10.1177/0956797615592630">use math every day to help increase math knowledge, which may also have benefits to keep the math learning positive</a>. Opportunities to highlight math in everyday lives could mean <a href="https://www.toyboxmanitoba.ca/copy-of-let-s-sort">talking about money</a> <a href="https://www.toyboxmanitoba.ca/copy-of-storytelling-2">or time</a> — or using Halloween candy to highlight math concepts.</p>
<h2>Sorting: An important math concept</h2>
<p>Sorting is part of the early school math curricula. <a href="https://doi.org/10.5951/TCM.12.5.0236">By sorting, children gain</a> <a href="https://doi.org/10.1080/03004430.2019.1608193">deep understandings</a>, including the attributes of objects and inferences about them. They learn about sameness or difference, and improve how thoughts are organized in their memories. </p>
<p>Sorting tasks encourage children to focus on categorizing objects by attributes such as size, shape, colour or brand. The roots of algebra and geometry are embedded in these problem-solving opportunities that present naturally in homes.</p>
<p>Caregivers can base discussions on what their children know and are ready to learn. Caregivers’ involvement and approach may differ depending on the unique interests and capabilities of each child. Children’s interests <a href="https://doi.org/10.1007/s10643-013-0604-7">and caregiver involvement support learning</a>. Have the conversation, and your child will surprise you!</p>
<h2>Ways to sort candy with children</h2>
<p><strong>1. Involve children</strong> as you discuss categories. Children can sort however they want, and it is fun! </p>
<p>For the little ones, caregivers could ask children to “find the orange ones,” and then count them. Preschool children can be asked to count and sort by conventional candy type (chocolate bars, chips, gum). School-aged children can generate their own categories like “my favourites,” “Dad’s favourites” or “peanut free.” </p>
<p>Caregivers can ask children about their ideas for how to sort, or start them out with ideas: For example, sort by size.</p>
<p><strong>2. Encourage mathematics vocabulary and number and shape words:</strong> Caregivers can introduce or reiterate number words, or count in an additional language. Comparative words like bigger or smaller, or superlative words like largest or smallest; or words representing sizes such as tiny, mini or bite-size can be used to expand vocabulary. </p>
<p>Caregivers can be strategic and creative, using key vocabulary denoting shapes, but also in using words like long, fat, thin and round. They can talk about what math education experts call number magnitudes, like the concept of “which has more.” Children can learn measurement terms such as grams, millilitres, centimetres — or even money and unit costs. </p>
<p><strong>3. Encourage children to <a href="https://doi.org/10.1016/j.cogdev.2017.07.003">make patterns</a></strong> with the sorted candy as this activity also has learning benefits. </p>
<p><strong>4. With older children, graph results</strong> to show patterns in the data derived from sorting. You do not need graph paper! In a YouTube example, one of our collaborators, early years teacher and parent <a href="https://youtu.be/uaDxFaXL4Gc">Sarah Melo shows how children can draw a graph</a> on plain or lined paper showing a simple list of categories. For instance, list different brands of candy, and then, across the top of the page, create lines to segment different boxes where children can show “how many” in each category. Melo’s website, <a href="https://melomath4kids.ca">MeloMath4Kids</a> has great further resources. </p>
<p><strong>5. <a href="https://doi.org/10.1111/cdev.13199">Talk about fractions</a>:</strong> For example: “one-third of the treats are chocolate bars.”</p>
<h2>More ideas for home learning</h2>
<p>For more ideas about early learning at home, we invite caregivers to consult the ToyBox website. Or you can <a href="https://www.toyboxmanitoba.ca/copy-of-sign-me-up">sign up to receive regular</a> activities about language, numbers or wellness. We also continue to seek participants for our research.</p>
<p>Happy counting and sorting this Halloween and beyond!</p><img src="https://counter.theconversation.com/content/170350/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Sheri-Lynn Skwarchuk receives funding from the Social Sciences and Humanities Research Council. She is also a board member at Oak Street Nursery School and the Project Director of the ToyBox project.</span></em></p><p class="fine-print"><em><span>Erin A Maloney receives funding from the Social Sciences and Humanities Research Council.</span></em></p><p class="fine-print"><em><span>Heather P. Douglas 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>Early exposure to everyday math at home predicts children’s school mathematics outcomes.Sheri-Lynn Skwarchuk, Full Professor, Faculty of Education, University of WinnipegErin A Maloney, Assistant professor, School of Psychology, L’Université d’Ottawa/University of OttawaHeather P. Douglas, Adjunct professor, Department of Cognitive Science, Carleton UniversityLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1672592021-10-21T14:19:50Z2021-10-21T14:19:50Z4 moves to make math visible with kids, using counters<figure><img src="https://images.theconversation.com/files/425751/original/file-20211011-25-1dnzapk.jpg?ixlib=rb-1.1.0&rect=0%2C135%2C4751%2C3003&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">If we each get to choose four colourful candies, my four includes three orange and one blue. Yours? </span> <span class="attribution"><span class="source">(Shutterstock)</span></span></figcaption></figure><p>Let’s say you’re a parent helping a Grade 1 child with their math, and they’re subtracting eight from 17, using small items — counters — like Smarties, multicoloured Rocket candies or Lego pieces.</p>
<p>The child counts out 17 items. Then, they count eight of those items to take away. Finally, they start counting the remaining items. </p>
<p>Here is where parents who haven’t revisited math instruction for decades <a href="https://theconversation.com/the-new-math-how-to-support-your-child-in-elementary-school-87479">get confused and want to show their child what they believe</a> is a faster or better way: by picking up a pencil and paper to stack the 17 on top of the eight.</p>
<p>Don’t be surprised if your child brings home a few unfamiliar strategies. Many classrooms today embrace “<a href="http://www.meaningfulmathmoments.com/number-talks.html">number talks</a>” — what math educator Sherry Parish defines as discussions about computation problems “<a href="https://books.google.ca/books/about/Number_Talks.html?id=p4B9F1u2T4kC">designed to elicit specific strategies that focus on number relationships and number theory</a>.” </p>
<h2>Making math thinking visible</h2>
<p>In the example above that involves subtracting eight from 17, parents may be thinking the next step in teaching a child is relaying the rule that you never take a bigger number from a smaller one. </p>
<p>They may want to tell the child: “You can’t take eight away from seven, so you borrow a 10 from the tens column …” That’s when the parent and child both realize they are exactly where they started, subtracting eight from 17. Yikes!</p>
<p>Instead of falling into the trap of showing and telling your preferred method for subtracting, mathematics educators recommend <a href="https://theconversation.com/4-things-weve-learned-about-math-success-that-might-surprise-parents-135114">listening to learners and talking about what they already know</a>. </p>
<p>What the child says and does can be a resource for understanding subtraction. </p>
<p>Here are ways parents or teachers could support a learner’s strategy by helping make their thinking visible.</p>
<figure class="align-center ">
<img alt="Six wooden rounds organized into two rows with a wooden figure six on top." src="https://images.theconversation.com/files/426303/original/file-20211013-15-51qber.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/426303/original/file-20211013-15-51qber.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/426303/original/file-20211013-15-51qber.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/426303/original/file-20211013-15-51qber.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/426303/original/file-20211013-15-51qber.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/426303/original/file-20211013-15-51qber.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/426303/original/file-20211013-15-51qber.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">It’s important for kids to learn to quickly see how many without counting, through quick visual recognition.</span>
<span class="attribution"><span class="source">(Shutterstock)</span></span>
</figcaption>
</figure>
<h2>Move No. 1: Make arrangements</h2>
<p>Talking about numbers involves understanding “how muchness” — for instance: how 17 is 20 less three, or how it’s 15 and two more. Math educators talk about the importance of learning to “subitze” — learning to quickly see how many without counting, through quick visual recognition. </p>
<p>Using counters helps students see quantities. This can be done by making specific arrangements with counters, like grouping counters into circles, rows or clusters of threes, fours and fives. For example, if the number 17 is arranged into subitized images of five, a child might say they see three fives and two remaining single units.</p>
<figure class="align-left zoomable">
<a href="https://images.theconversation.com/files/425928/original/file-20211012-23-91b1wh.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="17 dots arranged into clusters of three fives and a two." src="https://images.theconversation.com/files/425928/original/file-20211012-23-91b1wh.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/425928/original/file-20211012-23-91b1wh.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=382&fit=crop&dpr=1 600w, https://images.theconversation.com/files/425928/original/file-20211012-23-91b1wh.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=382&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/425928/original/file-20211012-23-91b1wh.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=382&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/425928/original/file-20211012-23-91b1wh.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=480&fit=crop&dpr=1 754w, https://images.theconversation.com/files/425928/original/file-20211012-23-91b1wh.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=480&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/425928/original/file-20211012-23-91b1wh.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=480&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Seventeen seen as five, five, five and two. How would you subtract eight?</span>
<span class="attribution"><span class="source">(Marc Husband)</span></span>
</figcaption>
</figure>
<p>Prompting them to subtract eight might provoke a strategy where the child takes away five, and then another three. Depending on where the child starts taking away (from left to right versus right to left), they could be left with different subitized images: for example, two, five and two; or five and four. </p>
<p>Such processes of “decomposing” numbers — breaking down the eight into five, two and one — builds what’s called <a href="https://www.stenhouse.com/content/number-sense-routines-grades-k-3">number sense</a> (understanding how numbers are related).</p>
<h2>Move No. 2: Colour code</h2>
<figure class="align-left zoomable">
<a href="https://images.theconversation.com/files/425929/original/file-20211012-23-17syhnb.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="17 dots shown with ten of the dots blue, and seven of them in green." src="https://images.theconversation.com/files/425929/original/file-20211012-23-17syhnb.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/425929/original/file-20211012-23-17syhnb.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=438&fit=crop&dpr=1 600w, https://images.theconversation.com/files/425929/original/file-20211012-23-17syhnb.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=438&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/425929/original/file-20211012-23-17syhnb.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=438&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/425929/original/file-20211012-23-17syhnb.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=550&fit=crop&dpr=1 754w, https://images.theconversation.com/files/425929/original/file-20211012-23-17syhnb.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=550&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/425929/original/file-20211012-23-17syhnb.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=550&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Using different colours can help kids see numbers within numbers.</span>
<span class="attribution"><span class="source">(Marc Husband)</span></span>
</figcaption>
</figure>
<p>Using two different colour counters can enhance a learner’s ability to see activities <a href="https://doi.org/10.1007/s10857-006-9005-9">that are happening in their minds</a>. </p>
<p>Supposing the child says, in subtracting eight from 17, they want to subtract seven first. You can then lay out seven green counters and 10 blue ones, and then remove seven green and one blue. Coding numbers with colours helps students to see numbers within numbers (that seven and one make eight).</p>
<h2>Move No. 3: Show the action</h2>
<p>When learners subtract, they’re doing a mental action. Seeing this action with counters supports understanding the concept of “taking away.” </p>
<p>Let’s continue with our example of 17 minus eight with the 17 organized into subitized images of five and two. If the child says that they want to subtract the seven first, a parent or teacher can illustrate this by pulling (in a downwards motion) the arrangements of seven, followed by one from the remaining 10. </p>
<figure class="align-left zoomable">
<a href="https://images.theconversation.com/files/425931/original/file-20211012-21-1lrxtez.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="Eight dots with arrows are shown moving away from a cluser of 17 dots." src="https://images.theconversation.com/files/425931/original/file-20211012-21-1lrxtez.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/425931/original/file-20211012-21-1lrxtez.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=530&fit=crop&dpr=1 600w, https://images.theconversation.com/files/425931/original/file-20211012-21-1lrxtez.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=530&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/425931/original/file-20211012-21-1lrxtez.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=530&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/425931/original/file-20211012-21-1lrxtez.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=666&fit=crop&dpr=1 754w, https://images.theconversation.com/files/425931/original/file-20211012-21-1lrxtez.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=666&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/425931/original/file-20211012-21-1lrxtez.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=666&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Moving the counters demonstrates what thinking processes are happening.</span>
<span class="attribution"><span class="source">(Marc Husband)</span></span>
</figcaption>
</figure>
<p>Emphasizing the mental activities by doing and recording is beneficial for all learners. It may in particular also be a way for educators to seek to engage Indigenous learners. As math researcher and educator Lisa Lunney Borden writes, in a case <a href="https://eric.ed.gov/?id=EJ961339">study of Mi'kmaw students in Atlantic Canada learning math, most Indigenous languages in Canada have verb-based origins, and language generates world views</a> and cultural ways of knowing. From this perspective, emphasizing process and action in math may help engage Indigenous learners and affirm their identity formation whether or not they currently speak their ancestral language.</p>
<h2>Move No. 4: Check-in repeatedly</h2>
<p>While you’re arranging counters, colour coding and showing actions to make ideas visible, you can support a two-way conversation by checking in multiple times with kids. Consider the following questions or prompts: </p>
<p><strong>“Can you say it again?”</strong>: If you’re unsure what they did, don’t be afraid to ask them to repeat it. Taking time to figure out what they did values their thinking and can be engaging for everyone, including the parent or educator.</p>
<p><strong>Gesture</strong>: When you move counters to make a learner’s thinking visible, gesture by making a circle with a finger over the counters they say they’re seeing. While colour coding, you might ask: “What numbers do you see now? Show me the 10. Where’s the seven? The one?” Take turns gesturing over the counters to seek agreement on what you’re recording. </p>
<p><strong>Go slowly</strong>: Students’ thinking can happen fast, so slowing down what’s happening in their head is a good thing. To support slowing down, ask questions like: “What did you do first?”</p>
<p><strong>Let the learner take the lead</strong>: If the learner says their strategy is: “I subtracted seven first, then one more,” pull seven counters down and ask them which counter (from the remaining 10) should be pulled down to make the eight. The learner might choose a counter different than you. There is no correct answer here — pulling the middle counter down, for example, might make it easier for them to see the remaining nine. </p>
<p>We would love to hear how these moves support talking about math!</p><img src="https://counter.theconversation.com/content/167259/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>Math educators share four ways parents can use counters, like candies or lego pieces, to lead ‘number talks’ that help kids develop an understanding of how numbers are related.Marc Husband, Assistant Professor, School of Education, St. Francis Xavier UniversityHeather Bourrie, PhD Candidate, Mathematics Education, York University, CanadaLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1577382021-04-02T12:16:02Z2021-04-02T12:16:02Z5 ways parents can help children with the ‘new’ math<figure><img src="https://images.theconversation.com/files/392345/original/file-20210329-23-yt4yl6.jpg?ixlib=rb-1.1.0&rect=60%2C0%2C6720%2C4456&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Many parents have had to play the role of a substitute math teacher during the pandemic.</span> <span class="attribution"><a class="source" href="https://www.gettyimages.com/detail/photo/teenage-boy-having-problems-in-finishing-homework-royalty-free-image/1033164818?adppopup=true">damircudic/E+ via Getty Images</a></span></figcaption></figure><p>In his <a href="https://www.youtube.com/watch?v=-tg3C4bhhz4">March 2021 Netflix special</a>, comedian Nate Bargatze complains about having to teach his kids a confusing <a href="https://www.washingtonpost.com/lifestyle/2021/03/19/parents-confused-common-core-math/">“new math”</a> based on standards known as the Common Core.</p>
<p>“The goal of Common Core is to use one sheet of paper for every problem,” Bargatze jokes. He observes that this new math requires people to “keep breaking the problem down.”</p>
<p>“You put the problem at the top, and it just keeps going,” Bargatze says. “And then what’s funnier is you see old math in the middle of it. As you break it down, old math gets in there and you’re like, ‘Oh, just do that at the top.’ I don’t even know what we’re doing.”</p>
<figure>
<iframe width="440" height="260" src="https://www.youtube.com/embed/-tg3C4bhhz4?wmode=transparent&start=0" frameborder="0" allowfullscreen=""></iframe>
<figcaption><span class="caption">Comedian Nate Bargatze tells a joke about Common Core math during his comedy special.</span></figcaption>
</figure>
<h2>Math worries</h2>
<p>Bargatze is by no means alone in his frustration. Since many schools went largely remote during the COVID-19 pandemic, countless parents, <a href="http://www.clarissathompson.com">me</a> included, are becoming <a href="https://www.nytimes.com/2020/05/13/parenting/coronavirus-remote-learning-burn-out.html">burnt out</a> as we find ourselves thrust into the role of <a href="https://www.usnews.com/news/health-news/articles/2020-12-22/parents-feel-the-strain-as-pandemic-adds-new-role-teacher">substitute math teacher</a>.</p>
<p>Why does this so-called new math – which has actually been around for over a decade – draw so much <a href="https://slate.com/business/2014/07/common-core-math-questions-show-why-parents-are-upset-about-its-methods.html">scorn</a> from parents?</p>
<p>This new math is based on a <a href="http://www.corestandards.org/Math/">list of standards</a> that students should master within each grade. It’s different from “old math” in that the standards focus not only on the step-by-step procedures to solve math problems, but also on <a href="https://www.nctm.org/Standards-and-Positions/Common-Core-State-Standards/Teaching-and-Learning-Mathematics-with-the-Common-Core/">why those procedures work</a> in the first place. The idea is to teach the procedures in such a way that children can apply this knowledge to <a href="http://www.corestandards.org/Math/Practice/">future math problems that they encounter</a> – both at school and in real-life contexts. </p>
<p>For instance, in solving the multiplication problem, 312 x 23, parents historically might line the problem up and start multiplying from right to left. We were told that we had to include the 0 on the right under 936, but I don’t recall ever being told why. But under the Common Core standards, students are encouraged to break the problem down into hundreds, tens and ones. This newfangled way to do the math makes it more transparent where the answer, 7,176, and that mystery 0 come from.</p>
<p><div data-react-class="Tweet" data-react-props="{"tweetId":"1248106005868744709"}"></div></p>
<h2>Overcoming math anxiety</h2>
<p>As Bergatze’s stand-up bit points out, this new math has triggered some parents’ “<a href="https://doi.org/10.1111/1467-8721.00196">math anxiety</a>” – a common apprehension that can <a href="https://doi.org/10.1080/13546783.2018.1475303">impair math performance</a>, <a href="https://doi.org/10.1037/bul0000307">many studies show</a>.</p>
<p>Researchers haven’t completely figured out how to <a href="https://doi.org/10.1080/00461520.2018.1447384">eliminate math anxiety</a>. But as a researcher who studies why people <a href="https://doi.org/10.1080/00220973.2019.1653815">hate math</a>, I believe there are steps parents can take to combat any negative attitudes they may have toward math and to improve children’s math understanding. Five of those steps are listed below.</p>
<h2>1. Point out math in everyday life</h2>
<p>Math learning doesn’t happen just in classrooms. Parents can draw children’s attention to <a href="https://playfullearninglandscapes.com/">math all around them</a>. They can talk about math in the <a href="https://doi.org/10.1111/mbe.12195">grocery store</a> or at the <a href="https://doi.org/10.1080/15248372.2019.1673753">bus stop</a>. One idea is to incorporate positive <a href="http://bedtimemath.org/apps/">math talk</a> while reading books with our children, even if <a href="https://doi.org/10.3389/fpsyg.2017.02242">the books don’t inherently include numbers</a>. For example, even though the classic children’s book “<a href="https://www.worldcat.org/title/very-hungry-caterpillar-la-oruga-muy-hambrienta/oclc/1196094219&referer=brief_results">The Very Hungry Caterpillar</a>” doesn’t include counting or comparing how much the caterpillar eats each day, parents can insert guiding scenarios like “The very hungry caterpillar ate 4 strawberries. Let’s count them. 1-2-3-4. Did the caterpillar eat more plums or strawberries?” This is a “two-for-one deal” that could help time-strapped parents promote literacy and numeracy.</p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/392346/original/file-20210329-15-1czm3ua.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="A group of children gather to play Chutes and Ladders on the floor." src="https://images.theconversation.com/files/392346/original/file-20210329-15-1czm3ua.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/392346/original/file-20210329-15-1czm3ua.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=405&fit=crop&dpr=1 600w, https://images.theconversation.com/files/392346/original/file-20210329-15-1czm3ua.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=405&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/392346/original/file-20210329-15-1czm3ua.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=405&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/392346/original/file-20210329-15-1czm3ua.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=509&fit=crop&dpr=1 754w, https://images.theconversation.com/files/392346/original/file-20210329-15-1czm3ua.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=509&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/392346/original/file-20210329-15-1czm3ua.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=509&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Playing Chutes and Ladders can help children learn to identify, compare and estimate numbers.</span>
<span class="attribution"><a class="source" href="https://www.gettyimages.com/detail/news-photo/october-2008-credit-katherine-frey-twp-bluemont-va-the-news-photo/97161275?adppopup=true">Katherine Frey/The Washington Post via Getty Images</a></span>
</figcaption>
</figure>
<h2>2. Play board games and card games</h2>
<p>Children can learn about math as they play fun board <a href="https://doi.org/10.1111/j.1467-7687.2008.00714.x">games</a>, such as Chutes and Ladders, and card <a href="https://doi.org/10.1111/j.1751-228X.2012.01149.x">games</a>, like war. Research has shown that playing board games pays off. One study found that while low-income families played board games <a href="https://doi.org/10.1111/j.1467-8624.2007.01131.x">less at home</a> than middle-income families, even one hour of board-game play across a period of two weeks increased low-income children’s math performance to the level of their middle-income peers. </p>
<h2>3. Break math down step by step</h2>
<p>To help kids avoid the <a href="https://www.edweek.org/teaching-learning/kids-are-behind-in-math-because-of-covid-19-heres-what-research-says-could-help/2020/12">COVID slide</a>, a major dip in math performance occurring during the pandemic, parents can <a href="https://doi.org/10.5951/mathteacmiddscho.21.1.0026">break down math problems step by step</a>. As they learn the procedure at <a href="https://doi.org/10.1002/acp.3663">each step</a> children can then better understand how to get to the correct answer, or where they made a mistake along the way.</p>
<h2>4. Draw connections to more familiar and well-liked math</h2>
<p>Parents can also help children understand more difficult math concepts, such as fractions, by drawing connections to more familiar, well-liked and less anxiety-provoking math, <a href="https://doi.org/10.1016/j.cedpsych.2019.03.011">such as whole numbers or percentages</a>. For instance, parents can show that ¾ – that is, three-fourths – <a href="https://doi.org/10.1016/j.cogpsych.2011.03.001">is the same as</a> 75 out of 100, or 75%. Parents can draw a connection to money, too. There are four quarters in a dollar. Each quarter is worth 25 cents. That means that three out of four quarters is worth 75 cents. </p>
<h2>5. Avoid negative math attitudes</h2>
<p>This recommendation goes hand in hand with our first recommendation. Parents should seek out opportunities to talk about math at every chance they get, but they should avoid negative math talk. Many an American will freely admit to being <a href="https://osf.io/hcqst">“not a math person”</a>. These off-the-cuff remarks can have serious consequences for children, who <a href="http://doi.org/10.1126/science.274.5294.1926">soak up information in their environments</a>. </p>
<p>Math-anxious teachers and parents can <a href="https://doi.org/10.1073/pnas.0910967107">transmit their anxiety to children, especially girls</a>. Girls and women have <a href="http://doi.org/10.1186/1744-9081-8-33">higher math anxiety</a>, which could be one reason they have <a href="https://doi.org/10.1007/11409.1556-1631">lower math performance and less confidence when estimating numbers</a> and are less likely than men to pursue <a href="https://doi.org/10.1177/1529100614541236">STEM careers</a>.</p>
<p>I hope parents embrace their new role as math tutors, because it seems as if home schooling <a href="https://info.burbio.com/school-tracker-update-feb-22/">will continue throughout the spring for many students</a>. It shouldn’t go unmentioned that kids aren’t all that enamored with their home-school teachers either. Some may even hope they won’t have the same teacher next year.</p>
<p>[<em><a href="https://theconversation.com/us/newsletters/the-daily-3?utm_source=TCUS&utm_medium=inline-link&utm_campaign=newsletter-text&utm_content=experts">Expertise in your inbox. Sign up for The Conversation’s newsletter and get expert takes on today’s news, every day.</a></em>]</p><img src="https://counter.theconversation.com/content/157738/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Clarissa A. Thompson receives funding from the U.S. Department of Education (Institute of Education Sciences). </span></em></p><p class="fine-print"><em><span>Marta Mielicki receives funding from the U.S. Department of Education (Institute of Education Sciences). </span></em></p><p class="fine-print"><em><span>Charles J. Fitzsimmons, Daniel A. Scheibe, and Lauren K. Schiller do not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and have disclosed no relevant affiliations beyond their academic appointment.</span></em></p>Parents thrust into the role of math teacher can take simple steps to help their children understand math better and dread it less.Clarissa A. Thompson, Associate Professor of Cognitive Psychology, Kent State University Lauren K. Schiller, Adjunct assistant professor, Teachers College, Columbia UniversityMarta Mielicki, Postdoctoral research associate, Kent State University Licensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1424482020-09-17T11:24:42Z2020-09-17T11:24:42ZFuture teachers often think memorization is the best way to teach math and science – until they learn a different way<figure><img src="https://images.theconversation.com/files/354411/original/file-20200824-16-1pl70q7.jpg?ixlib=rb-1.1.0&rect=140%2C0%2C6569%2C4476&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Problem-solving is key to math and science instruction.</span> <span class="attribution"><a class="source" href="https://www.gettyimages.com/detail/photo/writing-mathematical-formulas-on-transparent-wipe-royalty-free-image/925114826?adppopup=true">Pekic/Getty Images</a></span></figcaption></figure><p><em>The <a href="https://theconversation.com/us/topics/research-brief-83231">Research Brief</a> is a short take about interesting academic work.</em></p>
<h2>The big idea</h2>
<p><a href="https://doi.org/10.1080/02635143.2020.1784126">I found</a> that college students who are taking courses to become teachers can change their beliefs of how science and mathematics should be taught to and learned by K-12 students.</p>
<p>Most of these future teachers tell me when they start my course, they believe that K-12 students must memorize science and mathematics knowledge to learn it. They also believe that students cannot acquire knowledge through a process used by scientists and mathematicians called <a href="https://www.nextgenscience.org/sites/default/files/Appendix%20F%20%20Science%20and%20Engineering%20Practices%20in%20the%20NGSS%20-%20FINAL%20060513.pdf">problem</a>-<a href="http://www.corestandards.org/Math/Practice/">solving</a>. Problem-solving asks students to <a href="https://link.springer.com/article/10.1007/s10763-016-9755-5">solve engaging and challenging problems</a> that are provided without a strategy or solution. It also involves group work and a time to present and justify their strategies and solutions to the class. </p>
<p>To challenge my students’ beliefs, I ask future teachers to teach science and mathematics to students with problem-solving. At first they often resist because they believe that their students can only memorize science and mathematics knowledge. However, after they have asked the students to use problem-solving and find it successful, they discover that <a href="https://doi.org/10.1111/ssm.12374">students can learn like scientists and mathematicians</a> The evidence and experiences start to change their beliefs.</p>
<p>The way I reached these conclusions was by studying future teachers over the course of four years. I studied 113 future teachers’ beliefs in 10 sections of a course that I taught on how to teach science and mathematics. Throughout the course, I asked the future teachers to discover science and mathematics knowledge with problem-solving. I also had the future teachers teach students at a local school by asking them to learn with problem-solving.</p>
<p>To measure changes in future teachers’ beliefs following completion of the class, I asked them to complete a survey at the start and end of the course. At the end, the findings showed that the future teachers were significantly more likely to teach in a way that reflected how scientists and mathematicians solve problems.</p>
<p>It also appeared that their teaching of science with problem-solving encouraged their use of the method when they taught mathematics. Conversely, their teaching of mathematics with problem-solving encouraged their use of the method when they taught science.</p>
<h2>Why it matters</h2>
<p>This study matters because a <a href="https://doi.org/10.1093/acrefore/9780190264093.013.747">teacher’s beliefs</a> – their personal philosophy about teaching and learning – often determine how they will teach and what students will learn. And because problem-solving is necessary for scientific and mathematical literacy, students need teachers who will expose them to problem-solving. </p>
<p>This study also matters because college professors who work with future teachers can employ similar strategies. They can place future educators in situations in which they must confront their beliefs about teaching and learning with evidence and experiences that <a href="https://doi.org/10.1037/13274-019">contradict</a> their <a href="https://doi.org/10.1080/0950069022000070261">beliefs</a>.</p>
<h2>What other research is being done?</h2>
<p>Those who do similar research are trying to figure out how to assure future teachers use problem-solving in their future classrooms. I have taught many education students who did quite well in my course, and successfully used science and mathematics problem-solving with their students. However, former students that I ran into years later often told me that they do not use problem-solving as teachers. Instead, they reverted to simply asking students to memorize science and mathematics information. They told me the reason for this is that teachers in their present schools do not use problem-solving. I find this troubling.</p>
<h2>What’s next</h2>
<p>It may be that one way to solidify beliefs about teaching through problem-solving instead of memorization would be for science and mathematics faculty to use problem-solving in their college classrooms. Research shows that <a href="https://doi.org/10.1080/00220272.2015.1124145">similarities</a> and <a href="https://doi.org/10.1080/00220270500391589">coherence</a> between college courses may increase the likelihood that future teachers will believe in the value of problem-solving. If so, then my students may become less likely to abandon the methods learned in their courses. In turn, they may be more likely to help make their future students more adept at mathematics and science.</p>
<p>[<em>Deep knowledge, daily.</em> <a href="https://theconversation.com/us/newsletters/the-daily-3?utm_source=TCUS&utm_medium=inline-link&utm_campaign=newsletter-text&utm_content=deepknowledge">Sign up for The Conversation’s newsletter</a>.]</p><img src="https://counter.theconversation.com/content/142448/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Peter C. Cormas does not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.</span></em></p>Teachers in training can be taught to teach their students to tackle problems like mathematicians and scientists. But will they stick with that approach once they get their own class?Peter C. Cormas, Associate Professor of Science Education, California University of PennsylvaniaLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1321372020-07-27T20:03:22Z2020-07-27T20:03:22ZRacist stereotyping of Asians as good at math masks inequities and harms students<figure><img src="https://images.theconversation.com/files/348406/original/file-20200720-63094-1gyfffl.jpg?ixlib=rb-1.1.0&rect=387%2C27%2C3170%2C3053&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">The myth of Asians being good at math both encourages a “blame-the-victim” approach to math failure and imposes significant psycho-social pressure on high-achieving students. </span> <span class="attribution"><span class="source">(Chuttersnap/Unsplash) </span>, <a class="license" href="http://creativecommons.org/licenses/by/4.0/">CC BY</a></span></figcaption></figure><p>Some people stereotype Asian students as the “model minority” in math achievement: they <a href="https://theconversation.com/asians-are-good-at-math-why-dressing-up-racism-as-a-compliment-just-doesnt-add-up-128731">generalize attributes of a so-called “minority” (racialized) community in a way that just perpetuates racism disguised as a compliment</a>. </p>
<p>It is clear, however, that not all students identified as Asian are good at math. The word <a href="https://www.taylorfrancis.com/books/e/9781315658438/chapters/10.4324/9781315658438-15">“Asian” is a category used to represent human beings who are, in fact, diverse and their differences are lost by their inclusion in the term</a>. “Asian” includes <a href="https://doi.org/10.1080/13613320500490630">50 or so ethnic groups</a> in a huge diversity of linguistic, socio-economic, political and cultural settings. Making judgments based on categories often leads to faulty or erroneous implications. </p>
<p><a href="https://books.google.ca/books/about/Model_Minority_Myth_Revisited.html?id=G2jHy9gv3M0C&redir_esc=y">Both scholars</a> and cultural commentators have highlighted the problem that the “model minority” label is sometimes used politically to divide those who are held up as so-called “model” groups and those who are not. Reporter Kat Chow notes that some white people have talked about <a href="https://www.npr.org/sections/codeswitch/2017/04/19/524571669/model-minority-myth-again-used-as-a-racial-wedge-between-asians-and-blacks">Asians in North America in ways that positions Asians’ so-called “success” as a “racial wedge</a>” that separates Asians from Black people or other racialized groups. Such framing distracts from necessary <a href="https://cjc-rcc.ucalgary.ca/index.php/ajer/article/view/55221">conversations about racism and structural inequalities</a>. </p>
<p>We are involved in a study launched in 2018, “Behind the Model Minority Mask,” that seeks <a href="https://languagesciences.ubc.ca/news-events/announcement-research-news-story/jun-12-2019-looking-behind-model-minority-mask-help">to understand divergent literacy and academic trajectories of Cantonese- and Mandarin-speaking children in Canada</a>. We wanted to explore how early factors such as home and classroom environments and larger cultural myths surrounding “Asian academic achievement” may be affecting children’s academic results.</p>
<p>Our research has found that holding up a “model minority” stereotype leads to destructive emotional stress for students. The “model minority” myth both encourages blaming students for failure, obscures the socio-economic factors that influence student academic achievement and also imposes significant psychosocial pressure on high-achieving students. </p>
<h2>Breaking down the meaning of ‘ESL’</h2>
<p>Our research into Asian students in Vancouver schools also revealed that there are also problems with the generalized use of terms such as “English as a Second Language” (ESL) learners and “English Language Learners” (ELL).</p>
<p>For example, we learned through a series of studies of about <a href="https://www.routledge.com/English-Only-Instruction-and-Immigrant-Students-in-Secondary-Schools-A/Gunderson/p/book/9780805825145">25,000 immigrant students</a> aged six to 19 who were categorized as “ESL” that a small number were in fact non-ESL. They were raised in families where they learned another language in addition to English from birth.</p>
<p>Of the students who did learn English after another language, there was a wide range of English-language skills, from those who spoke only a little bit of English to those who were fluently bilingual. The group included immigrants and refugees and those who were from low to high socio-economic backgrounds, and included speakers of 150 first languages and dialects. </p>
<p>The “ESL” or “ELL” labels, like the “Asian” label, however, are sometimes also used in ways that can misrepresent achievement, influence or realities of individuals. Some right-wing media commentators use <a href="http://www.vancouversun.com/life/trouble+with+schools/10203596/story.html">the “ESL” label, for example, to argue that ESL students are responsible for a “strain on the system,” and “lowering” education</a>. </p>
<p>Such reprehensible commentary is facilitated by studies or news reports that <a href="https://books.google.ca/books?id=AuuXY3tbLMoC&dq=August+Shanahan+%22Report+of+the+National+Literacy+Panel%22&hl=en&sa=X&ved=2ahUKEwjzgZyC8NnqAhUtJTQIHaHJBrQQ6AEwAXoECAIQAg">rely on generalized categories</a> and pay <a href="https://www.cambridge.org/core/journals/language-teaching/article/emergent-bilingual-students-in-secondary-school-along-the-academic-language-and-literacy-continuum/A1550CE4E703D1B7FA693EF2C61DD9B7">insufficient attention to variables</a>. </p>
<figure class="align-center ">
<img alt="A group of teens with school books and bags walk outside" src="https://images.theconversation.com/files/348413/original/file-20200720-63094-w2ycob.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/348413/original/file-20200720-63094-w2ycob.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/348413/original/file-20200720-63094-w2ycob.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/348413/original/file-20200720-63094-w2ycob.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/348413/original/file-20200720-63094-w2ycob.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/348413/original/file-20200720-63094-w2ycob.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/348413/original/file-20200720-63094-w2ycob.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">Holding up a ‘model minority’ stereotype leads to destructive emotional stress for students.</span>
<span class="attribution"><span class="source">(Shutterstock)</span></span>
</figcaption>
</figure>
<h2>Roots of achievement patterns</h2>
<p>In part of our study, Lee Gunderson recorded science, math, English and social studies academic achievement of 5,000 randomly selected students from grades 8 to 12 in 18 Vancouver secondary schools including Asian students. ESL students scored significantly higher than native English speakers in all academic areas except English and social studies in Grade 12. Mandarin speakers’ academic achievement was also significantly higher than that of Cantonese, Korean, Spanish, Tagalog, Vietnamese and other language groups. </p>
<p>While there were high achievers among this diverse group of Asians, many Asian students (even among the Chinese subgroups) also reported struggling academically and socio-emotionally in school. </p>
<p>Socio-economic status <a href="https://books.google.ca/books/about/English_Only_Instruction_And_Immigrant_S.html?id=dm4UkTp8BNcC&redir_esc=y">was also found to be an important variable: Mandarin-speaking immigrants were from more affluent families than the other ethno-linguistic groups</a>. Mandarin-speaking families employed more tutors to bolster their children’s academic work than other groups. Indeed, among this group, some Mandarin-speaking university students worked as academic tutors. </p>
<figure class="align-center ">
<img alt="A mother is helping her teenage son do homework" src="https://images.theconversation.com/files/348409/original/file-20200720-18366-1cr72k7.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/348409/original/file-20200720-18366-1cr72k7.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=316&fit=crop&dpr=1 600w, https://images.theconversation.com/files/348409/original/file-20200720-18366-1cr72k7.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=316&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/348409/original/file-20200720-18366-1cr72k7.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=316&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/348409/original/file-20200720-18366-1cr72k7.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=397&fit=crop&dpr=1 754w, https://images.theconversation.com/files/348409/original/file-20200720-18366-1cr72k7.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=397&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/348409/original/file-20200720-18366-1cr72k7.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=397&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Mandarin-speaking families were more affluent and employed more tutors to bolster academic achievement.</span>
<span class="attribution"><span class="source">(Shutterstock)</span></span>
</figcaption>
</figure>
<p>The sample of native-English speaking students included a wide-range of families from a range of socio-economic backgrounds. By contrast, the Mandarin sample, as a result of immigration patterns, included more high economic status families than other groups. </p>
<p>When high economic status native English speakers were selected they scored significantly higher in all academic areas than Mandarin speakers at all grades. Socio-economic status is related to school success. </p>
<h2>Early beginnings</h2>
<p>With this same set of students, initial assessment results in the early grades revealed no significant differences in achievement between young Cantonese and Mandarin speakers. However, by Grade 12 there were differences with Mandarin speakers having significantly <a href="https://www.researchgate.net/publication/286868016_High_School_May_Not_Be_Enough_An_Investigation_of_Asian_Students'_Eligibility_for_Post-secondary_Education">higher</a> grades. </p>
<p>Mandarin-speaking girls were four times more like to be eligible for university than <a href="https://teslcanadajournal.ca/index.php/tesl/article/view/1114">Cantonese-speaking boys</a>. About two-thirds of the Cantonese boys did not have grades sufficient for admission to university. Cantonese boys were at-risk students. The other Asian groups scored lower than Mandarin speakers in all academic areas.</p>
<h2>Understanding differences</h2>
<p>The two largest groups of Asian immigrants, the Cantonese and Mandarin speakers, were from Hong Kong, Taiwan and China. The language of instruction in their communities was not English, so we expected these children’s English skills would be nascent when they immigrated to Canada.</p>
<p>As researchers, we did not expect that these students’ achievement would differ at the end of their public school careers. We also didn’t expect to see gender differences in academic achievement when this difference wasn’t present when these children first entered Canada. Nor did we expect to see differences among the Cantonese and Mandarin speakers. </p>
<p>As our research continues, we predict the findings will provide critical knowledge that educators need to improve the learning of Cantonese-speaking boys or others who we find to be at risk academically or socio-emotionally in Canadian schools. </p>
<p>We also hope we will identify characteristics of supportive ESL environments and inform early intervention through effective ESL program design and teacher professional development. Our hope is to provide information that informs parents about how to effectively support their children in school and at home in their early years.</p><img src="https://counter.theconversation.com/content/132137/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Lee Gunderson receives funding from SSHRC. </span></em></p><p class="fine-print"><em><span>Guofang Li receives funding from SSHRC Insight Grants, Canada.</span></em></p>A Vancouver study found Mandarin-speaking girls were more likely to be eligible for university than Cantonese-speaking boys. High-achieving students were from wealthier families who had tutors.Lee Gunderson, Professor, Department of Language and Literacy Education, University of British ColumbiaGuofang Li, Professor + Canada Research Chair (Tier 1) in Transnational/Global Perspectives of Language and Literacy Education of Children and Youth, University of British ColumbiaLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1404892020-06-16T11:52:34Z2020-06-16T11:52:34Z‘Telepresence’ can help bring advanced courses to schools that don’t offer them<figure><img src="https://images.theconversation.com/files/341508/original/file-20200612-153812-n2d08y.jpg?ixlib=rb-1.1.0&rect=1%2C0%2C528%2C352&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Remote learning can be used for more than just education at home.</span> <span class="attribution"><a class="source" href="https://www.gettyimages.com/detail/news-photo/students-alexander-leith-left-and-amelie-jamanka-right-sit-news-photo/1202322657?adppopup=true">Suzanne Kreiter/The Boston Globe via Getty Images</a></span></figcaption></figure><p><em>The Research Brief is a short take on interesting academic work</em>.</p>
<h2>The big idea</h2>
<p>In schools where students want to take an advanced course that the school doesn’t offer, <a href="https://doi.org/10.3102%2F0013189X20932461">the telepresence model</a>, which enables students in one school to use <a href="https://www.cisco.com/c/en/us/solutions/industries/education/case-studies.html#%7Etab-one">videoconferencing</a> to take a course offered at another school, is an effective alternative that can keep students learning and engaged.</p>
<p>To reach this conclusion, which we published in a recent <a href="https://doi.org/10.3102/0013189X20932461">study</a>, we looked at the use of the telepresence model at the public school system in <a href="https://mps.milwaukee.k12.wi.us/en/District/About-MPS/Departments/Office-of-Innovation-Information/Innovation-Development/Instructional-Technology--Personalized-Learning.htm#:%7E:text=The%20telepresence%20program%20in%20Milwaukee,physically%20in%20the%20same%20school">Milwaukee</a>. Beyond videoconferencing equipment, the telepresence model uses smartboards, an online learning platform, and video and text chat to bring students from schools throughout the city together into a virtual classroom.</p>
<h2>Why it matters</h2>
<p>Using telepresence enables schools to offer students advanced courses they wouldn’t otherwise be able to take. By providing more students with advanced coursework, it makes them more <a href="https://doi.org/10.3102/0162373707313409">ready for college</a>.</p>
<p>Telepresence can be particularly useful in school districts that don’t offer many Advanced Placement courses, more commonly known as AP courses. While approximately <a href="https://nces.ed.gov/pubs2019/2019430.pdf">92% of schools offer AP</a> or <a href="https://www.accreditedschoolsonline.org/resources/international-baccalaureate/">International Baccalaureate</a> courses, which are college-level courses that students can take in high school, research has found that AP courses are <a href="https://doi.org/10.3102%2F0034654318787268">offered less frequently</a> at schools that serve primarily low-income students of color. </p>
<p>In our research, we found telepresence allowed students attending 10 schools across Milwaukee to learn in a single virtual classroom. Teachers facilitated learning from a classroom at the host high school. Normally, there has to be an minimum number of students enrolled in an advanced course in order for a school to justify offering the course. Telepresence bypasses the need for an individual school to meet this requirement.</p>
<p>The approach appears to be effective. We found that participating students enrolled in one to two more AP courses than otherwise predicted. Students participating remotely also attended three more days of school than in prior school years. Students participating at both the host and remote schools scored two to three points higher on the ACT college entrance exam than students from similar backgrounds and of similar academic standing. In a survey of 499 students, 93% agreed or strongly agreed that the teacher encouraged them to participate in class. Eighty-six percent of the students agreed or strongly agreed that the telepresence technology provided many chances for student input throughout the course.</p>
<p>A teaching assistant at each remote site ensured engagement by helping the teacher get a read on whether students were paying attention. In some instances, students in a particular class took field trips or did weekend study sessions together.</p>
<h2>What’s next</h2>
<p>These findings show that you can keep students engaged and learning together even when they are not located in the same classroom or even the same school.</p>
<p>This will be particularly important now and in the future since the recent COVID-19 crisis pushed many of America’s school to transition to virtual learning – something that is <a href="https://www.forbes.com/sites/kerrymcdonald/2020/05/11/four-k-12-education-models-that-may-gain-popularity-during-covid-19/#5e5afd116b77">likely to continue</a> in various forms into the coming school year and beyond. For this reason, educators need to know what approaches are effective.</p>
<p>Telepresence by itself is not what makes it work. For instance, teachers stressed the need to refer to remote classmates by name in order to make the social atmosphere more like a regular classroom. Teachers also facilitated interaction by using text and video chat for group work. Teachers shared these successful strategies with each other online and through regular meetings.</p>
<p>The coming school year provides a chance to study the use of telepresence across more classrooms. There may also be the potential for partnerships between school districts in, say, rural and urban districts, to ensure that more students have access to quality advanced courses.</p>
<p>[<em>You’re smart and curious about the world. So are The Conversation’s authors and editors.</em> <a href="https://theconversation.com/us/newsletters/weekly-highlights-61?utm_source=TCUS&utm_medium=inline-link&utm_campaign=newsletter-text&utm_content=weeklysmart">You can get our highlights each weekend</a>.]</p><img src="https://counter.theconversation.com/content/140489/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Jennifer Darling-Aduana received funding from the William T. Grant Foundation to support this research.</span></em></p><p class="fine-print"><em><span>Carolyn Heinrich received funding from the William T. Grant Foundation to support this research.</span></em></p>If a high school doesn’t offer advanced coursework, having students take such a class remotely offers a promising alternative.Jennifer Darling-Aduana, Assistant Professor of Learning Technologies, Vanderbilt UniversityCarolyn Heinrich, Patricia and Rodes Hart Professor of Public Policy, Education and Economics, Vanderbilt UniversityLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1351142020-05-05T13:43:05Z2020-05-05T13:43:05Z4 things we’ve learned about math success that might surprise parents<figure><img src="https://images.theconversation.com/files/332066/original/file-20200501-42942-go7fsv.jpg?ixlib=rb-1.1.0&rect=47%2C228%2C5272%2C3133&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">The good news: your child can use their fingers and you can too. </span> <span class="attribution"><span class="source">(Shutterstock)</span></span></figcaption></figure><p>School <a href="https://www.theguardian.com/world/2020/apr/30/coronavirus-scientists-caution-against-reopening-schools">closures due to conronavirus</a> have put parents in the challenging position of home-schooling their children.</p>
<p>In mathematics education programs for future math teachers, we often discuss the <a href="https://link.springer.com/article/10.1007/s10857-012-9208-1">traditional classroom</a> that those studying to become teachers are familiar with. We’re interested in how their own experiences as students can influence their teaching.</p>
<p>Traditional modes of instruction have emphasized that math is best learned through <a href="https://www.jstor.org/stable/40247978">studying and memorizing alone, with the teacher demonstrating procedures and then checking students’ answers</a>.</p>
<p>If parents grew up with this style of instruction, their ideal home-math classroom might look like strict scheduling, workbooks, a child working alone in silence and parents telling children how to solve problems. But if parents enforce this approach, there could be conflicts and maybe even some crying. </p>
<p>But parents, like future educators, can also learn from newer approaches. Here are some practical tips for a different form of home learning. </p>
<h2>1. Talking about math</h2>
<p>Gone are the days of students sitting quietly while the math teacher does all the talking at the chalkboard. <a href="https://www.jstor.org/stable/749877">Discussion</a> is important in the mathematics classroom. </p>
<p>Parents should be explicit. Tell your child “we learn by sharing ideas and listening to each other.”</p>
<p>Model active listening skills. Show your child that you are listening by asking questions about what they said to clarify your understanding of their idea. Try saying “tell me more …” or asking “how do you know that?”</p>
<p>Try setting aside your own idea(s) so you can listen and build on their ideas. Instead of saying “yes, but …,” use “<a href="https://link.springer.com/chapter/10.1007/978-3-319-78928-6_3">yes, and …</a>” to help children feel that they’re not being judged and their ideas are important.</p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/332071/original/file-20200501-42942-wr4tlc.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/332071/original/file-20200501-42942-wr4tlc.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/332071/original/file-20200501-42942-wr4tlc.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/332071/original/file-20200501-42942-wr4tlc.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/332071/original/file-20200501-42942-wr4tlc.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/332071/original/file-20200501-42942-wr4tlc.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/332071/original/file-20200501-42942-wr4tlc.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">In today’s mathematics classrooms, discussion is important.</span>
<span class="attribution"><span class="source">(Shutterstock)</span></span>
</figcaption>
</figure>
<h2>2. Attitude</h2>
<p>Researchers have identified <a href="https://link.springer.com/article/10.1007/s10857-009-9134-z?shared-article-renderer">three underlying interconnected aspects of childrens’ relationships</a> with math that impact how they engage with math: emotional disposition (“I like math”), perceived competence (“I am good at math”) and their vision of math: whether math is about problem solving and understanding or math is about memorization and regurgitation.</p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/mathematics-is-about-wonder-creativity-and-fun-so-lets-teach-it-that-way-120133">Mathematics is about wonder, creativity and fun, so let's teach it that way</a>
</strong>
</em>
</p>
<hr>
<p>Parents can set a positive attitude for children by being mindful not to say things like “I don’t like math” or “I’m not a math person.” Your child might think they don’t have a chance because <a href="https://www.researchgate.net/publication/249054114_A_Quantitative_and_Qualitative_Study_of_Math_Anxiety_Among_Preservice_Teachers">you didn’t pass on a math mind</a>. </p>
<p>Academics have debunked common beliefs about the “<a href="https://www.ams.org/journals/notices/200102/rev-devlin.pdf">math gene</a>” and explain that there’s <a href="https://books.google.ca/books?hl=en&lr=&id=K1Ld7FgOdtoC&oi=fnd&pg=PT17&dq=%22math+gene%22+parent&ots=Bxk5UApbwY&sig=dMLYhCKH%20K7mHhHOvfy8SOEc_es&redir_esc=y#v=onepage&q=%22math%20gene%22%20parent&f=false">lots involved in being good at math</a>. Celebrate the process and not just the final answer. Give high fives for sharing solution strategies, developing a plan to tackle the problem and for not giving up.</p>
<p>Make it clear that <a href="https://books.google.ca/books?hl=en&lr=&id=bOGHDQAAQBAJ&oi=fnd&pg=PR9&dq=dweck+mindset+mistakes&ots=YMX--knDci&sig=y07leb0VLednZ4ZhScAAYsKCkyE#v=onepage&q=dweck%20mindset%20mistakes&f=false">making mistakes</a> is OK and can even be a good thing. Many highly successful people see mistakes as learning opportunities and an indication that learning is happening.</p>
<h2>3. Working in partnership</h2>
<p><a href="https://www.advance-he.ac.uk/knowledge-hub/engagement-through-partnership-students-partners-learning-and-teaching-higher">A partnership</a> is about working together and can include seeing the <a href="https://www.semanticscholar.org/paper/We-are-the-Process%3A-Reflections-on-the-of-Power-in-Kehler-Verwoord/aeecc3e2e8e352474a24ce4ccd407f62629d6f56">teacher as a learner and the student as a teacher</a>. It isn’t about the teacher being “all-knowing” and making all the decisions. </p>
<p>Traditional math teaching, where the teacher assumes an authoritative role, is a major cause of <a href="https://doi.org/10.1177/1365480214521457">math anxiety</a>. Researchers have found that not all <a href="https://doi.org/10.1016/j.cedpsych.2019.101784">math homework help</a> is beneficial. There is a difference between parents being controlling and being supportive.</p>
<p>With this in mind, wait for your child to ask for help. Try not to control everything. Focus on asking questions about their decisions that will help them figure out possible limitations and benefits of their decisions. </p>
<p>Let children fail. Failure can <a href="https://books.google.ca/books?id=q0VZwEZoniUC&lpg=PP1&dq=The%20Optimistic%20Child%3A%20A%20Proven%20Program%20to%20Safeguard%20Children%20Against%20Depression%20and%20Build%20Lifelong%20Resilience&lr&pg=PP1#v=onepage&q&f=false">build confidence</a>. Confidence can come from mastery; mastery can come from <a href="https://www.jstor.org/stable/40248303">practice</a>. Good practice includes analyzing what went wrong and what went right.</p>
<p>Don’t worry about being the expert. Be honest and say “I’m not sure. Let’s figure it out together.” </p>
<p>Start with <a href="https://books.google.ca/books?id=Irq913lEZ1QC&lpg=PR13&lr&pg=PP1#v=onepage&q&f=false">what children already know</a>. When your child is stuck, ask them to talk through what they are doing.</p>
<p>Take turns doing questions and talking about solution strategies.</p>
<p>Follow your child’s interests <a href="https://theconversation.com/eight-ways-to-keep-your-kids-smart-over-the-summer-break-100132">and ideas</a>. Let them take the lead, even if you think your approach is better.</p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/332073/original/file-20200501-42951-pxpcn5.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/332073/original/file-20200501-42951-pxpcn5.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/332073/original/file-20200501-42951-pxpcn5.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/332073/original/file-20200501-42951-pxpcn5.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/332073/original/file-20200501-42951-pxpcn5.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/332073/original/file-20200501-42951-pxpcn5.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/332073/original/file-20200501-42951-pxpcn5.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">Focus on asking your child questions that will help them figure out possible limitations and benefits of their decisions.</span>
<span class="attribution"><span class="source">(Shutterstock)</span></span>
</figcaption>
</figure>
<h2>4. Basic math skills</h2>
<p>If you grew up with traditional math instruction and haven’t thought about math since your school days, it might surprise you to learn that there are multiple ways to solve problems.</p>
<p>You could ask your child to share their way of solving the problem and also share your way. </p>
<p>For instance: What is 24 x 6? </p>
<p>It’s OK if you’re looking for a pencil to do this: </p>
<p> 24<br>
<u>x 6</u><br>
144</p>
<p>But what are some other ways you might you figure it out? </p>
<p>Multiply 20 x 6 to get 120. Now multiply 4 x 6 to get 24. Add the two figures: 120 + 24 = 144.</p>
<p>Another way would be to focus on 25 x 6 to get 150. Now subtract 6 and you’ve got 144. </p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/the-new-math-how-to-support-your-child-in-elementary-school-87479">The 'new math': How to support your child in elementary school</a>
</strong>
</em>
</p>
<hr>
<p>In all math problems (including addition or subtraction), your child can use their fingers and you can too. </p>
<figure class="align-right ">
<img alt="" src="https://images.theconversation.com/files/327316/original/file-20200412-10562-6mjs1u.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/327316/original/file-20200412-10562-6mjs1u.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=450&fit=crop&dpr=1 600w, https://images.theconversation.com/files/327316/original/file-20200412-10562-6mjs1u.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=450&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/327316/original/file-20200412-10562-6mjs1u.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=450&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/327316/original/file-20200412-10562-6mjs1u.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=566&fit=crop&dpr=1 754w, https://images.theconversation.com/files/327316/original/file-20200412-10562-6mjs1u.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=566&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/327316/original/file-20200412-10562-6mjs1u.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">
<figcaption>
<span class="caption">Author Tina Rapke finds an occasion for everyday math in making cookies.</span>
<span class="attribution"><span class="source">(Shutterstock)</span></span>
</figcaption>
</figure>
<p>You can also look for opportunities to highlight math in daily activities. </p>
<p>One fun way is through baking. Arrange three rows of cookie dough with four cookies in each row. Ask how many cookies per batch or how many each family member will get if they share equally. </p>
<p>Being successful at <a href="https://www.jstor.org/stable/10.5951/mathteacher.108.7.0543?casa_token=53fYsdfs758AAAAA:iROqe6Bs17ufC1uUB1x_ToGBlxgh-LgCEmMqSXgYT9cfbcLkdq0BdhWUjkxEfmYM5aLT__nM3eJ2CBiRa7EIwNPcR9W5BhbYspgB1oC4YDJaM2LWdp4#metadata_info_tab_contents">mental math</a> (like the arithmetic you do at the store) happens gradually over time. </p>
<p>Try focusing on basic math skills with your child for 10 minutes or less, every other day. </p>
<h2>The takeaway</h2>
<p>Think of quality over quantity. </p>
<p>If you want to support math learning at home based on math research: talk with your child, see learning as a partnership and make sure to celebrate their ideas. Your child may teach you something new. </p>
<p>We’d love to hear about how math has provoked families to slow down, have fun, go with the flow and connect.</p><img src="https://counter.theconversation.com/content/135114/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Tina Rapke received funding from SSHRC: Partnership Engage Grants. </span></em></p><p class="fine-print"><em><span>Cristina De Simone 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>Your cheat sheet for best practices in teaching math at home. Keep it positive and mask your shock when your child tells you there are many ways to multiply numbers.Tina Rapke, Associate Professor of Mathematics Education, York University, CanadaCristina De Simone, Middle School Teacher. PhD Mathematics Education Student, York University, CanadaLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1138952019-09-30T11:23:30Z2019-09-30T11:23:30ZWhy I’m teaching kids science through the sport of rowing<figure><img src="https://images.theconversation.com/files/286051/original/file-20190729-43118-1km76kx.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">The math behind the movement.</span> <span class="attribution"><a class="source" href="https://www.shutterstock.com/image-photo/womens-rowing-team-on-blue-water-794460844?src=oJfmTCHjKkAT1h9nwY_EpQ-1-0&studio=1">Dmitrydesign/Shutterstock.com</a></span></figcaption></figure><p>I didn’t know what the world looked like at 5:00 a.m. until my son began rowing for the <a href="https://www.detroitboatclubcrew.com/">Detroit Boat Club Crew</a>, the oldest continuous rowing program in North America. </p>
<p>The sight of young rowers slicing through the water in unison in narrow sculling boats, against the backdrop of dawn on the Detroit River, is simply awe-inspiring. </p>
<p>This year, I am working with the Detroit Boat Club Crew, overseen by the nonprofit Friends of Detroit Rowing, to combine the sport of rowing with a new curriculum that teaches middle and high school students science and mathematical concepts.</p>
<p>The innovative approach is tackling two areas of concern for Detroit youths: promoting physically active lifestyles and preparing youth for successful careers in scientific and technological fields. </p>
<h2>Knowledge gap</h2>
<p>Over the next 10 years, <a href="https://www.nms.org/Portals/0/Docs/Why%20Stem%20Education%20Matters.pdf">STEM job creation</a> – jobs in science, technology, engineering and mathematics – will outpace non-STEM jobs significantly.</p>
<p>Across the nation, STEM jobs are predicted to grow 17%, as compared to 9.8% for non-STEM positions.</p>
<p>STEM figures largely in occupations with the fastest expected growth in the coming years – such as biomedical engineers, network systems and data communications analysts, medical scientists, computer programmers and app developers.</p>
<p><a href="https://www.usinnovation.org/state/pdf_cvd/ASTRA-STEM-on-the-Hill-Michigan2019.pdf">People in STEM fields</a> can expect to earn 26% more money on average per year and are less likely to experience job loss in Michigan.</p>
<p>Yet, Michigan is <a href="https://www.mistempartnership.com/about/why-stem-is-important.html">failing to produce enough skilled STEM workers</a> to meet the needs of employers now and may fail to meet them in the future. According to <a href="https://www.nms.org/Portals/0/Docs/Why%20Stem%20Education%20Matters.pdf">the National Commission on Mathematics and Science for the Twenty-first Century</a>, 61% of the new jobs that will open in the 21st century will require skills possessed by only 20% of the current workforce. </p>
<p>What’s more, youth in southeast Michigan are not active enough. The Centers for Diseases Control and Prevention recommends one hour of daily physical activity, but <a href="http://www.ralphcwilsonjrfoundation.org/wp-content/uploads/2017/06/State_Of_Play_Michigan_RWJF.pdf">only 13% of southeast Michigan kids under 18 are engaged at that level</a>. According to the Sports and Fitness Industry Association, 17% of U.S. children ages 6 to 12 engage in no physical activities. </p>
<h2>Rowing curriculum</h2>
<p>Over the next school year, our group has scheduled rowing and classroom sessions with Detroit youth between the ages of 11 and 15. </p>
<p>Practice for each cohort of 30 students, over the eight-week session, will include experiences on land as well as on the water. </p>
<p>Our curriculum, which aligns with content standards of the state of Michigan, aims to enhance knowledge and skills of rowing techniques.</p>
<p>The basic principles of rowing appear quite simple, but in reality, <a href="https://www.durhamboat.com/2017/08/05/analyzing-the-rowing-movement/">rowing success is complex</a>. Momentum is transferred to the water by pulling on the oar and pushing with the legs, which causes the seat to slide backwards. The oars pivot on a “lock-pin assembly,” which levers the water backwards. The motion of the boat is complicated by the movement of the rowers within the boat, the current of the water and wind speed. </p>
<p>Rowing leans heavily on STEM concepts commonly found in the fields of mathematics, physics and kinesiology. Through the sport, our curriculum covers works from the famous Greek mathematician Archimedes up through NASA engineer Katherine Johnson.</p>
<p>For example, potential and kinetic energy, boat velocity and rowers’ mass are strategies for teaching essential concepts. </p>
<h2>Looking ahead</h2>
<p>We are continuing to look for new ways for students to learn complex concepts through rowing.</p>
<p>For example, we are raising money for an indoor rowing tank to provide instantaneous analysis of rowing force data, creating a year-round rowing physics lab. Youth will sit in a boat in the indoor tank and simulate rowing actions. We hope that this will ultimately facilitate students’ analyses of their own and teammates’ activity data.</p>
<p>Promoting critical thinking skills, problem-solving and innovation through STEM education is necessary for job creation and retention for youth in the 21st century. Physical activity and participation in sports such as rowing is essential for mental and physical health and well-being.</p>
<p>We hope that fusing the components of STEM and rowing will result in an engaging educational experience, healthier youth and future careers in high-demand fields. </p>
<p>[ <em>You’re smart and curious about the world. So are The Conversation’s authors and editors.</em> <a href="https://theconversation.com/us/newsletters?utm_source=TCUS&utm_medium=inline-link&utm_campaign=newsletter-text&utm_content=youresmart">You can read us daily by subscribing to our newsletter</a>. ]</p><img src="https://counter.theconversation.com/content/113895/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Community Foundation for Southeast Michigan is the primary funder for the work described in this article. Private donors granted to Friends of Detroit Rowing also supported the efforts. </span></em></p>A new project for Detroit middle and high schoolers combines athletics and mathematical concepts.Elizabeth A. Barton, Associate Professor of Research, Wayne State UniversityLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1114882019-07-21T11:02:29Z2019-07-21T11:02:29ZMath challenges? A school psychologist could help<figure><img src="https://images.theconversation.com/files/284396/original/file-20190716-173338-1t35tue.jpg?ixlib=rb-1.1.0&rect=0%2C80%2C1000%2C431&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">There are many daily ways math can be relevant to children – from using money to matching or counting cards.
</span> <span class="attribution"><span class="source">(Shutterstock)</span></span></figcaption></figure><p>Statistically speaking, <a href="https://www.researchgate.net/profile/Thomas_Faulkenberry/publication/259582384_The_Cognitive_Origins_of_Mathematics_Learning_Disability_A_Review/links/004635304e90067673000000.pdf">five to eight per cent</a> of children meet the criteria for a mathematics learning disability. </p>
<p>Kids who have challenges with math at a young age also tend to experience these challenges throughout their education. Identifying these children and providing them with appropriate supports early on is therefore crucial.</p>
<p>When people think about who is involved in supporting math learning, the interactions between teachers, children and parents come quickly to mind. They may picture a tutor, grandparent or a classmate’s support as well. However, there may be another key player for those students experiencing the greatest challenges — the school psychologist. </p>
<p>In my doctoral studies, I am training to become a school psychologist. </p>
<p>I am also exploring how school psychologists’ math knowledge and “number sense” relates to their potential to support math. Math educators define number sense as being <a href="https://www.mnd.su.se/english/research/mathematics-education/research-projects/fons/fons-publications/foundational-number-sense-summarising-the-development-of-an-analytical-framework-1.317241">about awareness of number and quantity, counting, estimation and number patterns</a> or, more broadly, <a href="https://www.gsacrd.ab.ca/download/10268">flexibly thinking with numbers</a>. </p>
<h2>Extreme math feelings</h2>
<p>The good news is that children seem to have a positive outlook towards math upon starting school. However, by Grade 2, students’ feelings about math become largely <a href="https://cjc-rcc.ucalgary.ca/index.php/ajer/article/view/56197">influenced by their perceived skill level</a>. </p>
<p>Simply put, for most kids if they think they’re good at math, they like it, and if they think they’re bad at it, they don’t. </p>
<p>This good-or-bad mentality is reflected in their views of seeing math as either easy or hard. Usually, once students develop their opinion on the subject, that perception follows them throughout their education and even afterwards. By <a href="https://link.springer.com/article/10.1007/s10763-015-9621-x">grades 3 to 6</a> some students experience extreme negative feelings about math including hatred or even feeling sick. </p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/284400/original/file-20190716-173325-ssebvv.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/284400/original/file-20190716-173325-ssebvv.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=398&fit=crop&dpr=1 600w, https://images.theconversation.com/files/284400/original/file-20190716-173325-ssebvv.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=398&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/284400/original/file-20190716-173325-ssebvv.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=398&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/284400/original/file-20190716-173325-ssebvv.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=501&fit=crop&dpr=1 754w, https://images.theconversation.com/files/284400/original/file-20190716-173325-ssebvv.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=501&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/284400/original/file-20190716-173325-ssebvv.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=501&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Once students develop a perception about their math abilities, this tends to persist.</span>
<span class="attribution"><span class="source">(Shutterstock)</span></span>
</figcaption>
</figure>
<p>With children’s perspectives on math developing so young and with such <a href="https://www.tandfonline.com/doi/abs/10.1080/14794802.2018.1477058">longstanding effects</a>, this means that educators or families are encouraged to do their best to support those struggling with math learning, or those with negative attitudes towards math, while promoting positive engagement with the subject. </p>
<p>Educator math knowledge is associated with <a href="https://eric.ed.gov/?id=EJ986708">increased effectiveness of math instruction</a> and <a href="https://doi.org/10.3102/0002831210387916">student math outcomes</a>. </p>
<h2>School psychologists as math supports</h2>
<p>School psychologists’ <a href="https://cpa.ca/cpasite/UserFiles/Documents/publications/CPA%20Practice%20Guide.pdf">roles and responsibilities</a> include assessment, consultation and intervention. They can work with students, families, teachers or consult about systems. </p>
<p>The requirements to <a href="https://cpa.ca/docs/File/Sections/EDsection/School%20Psychology%20in%20Canada%20-%20Roles,%20Training,%20and%20Prospects.pdf">receive a designation as a school psychologist</a> varies between provinces in Canada, with the majority of provinces either requiring, or moving towards requiring, PhD-level credentials.</p>
<p>Generally speaking, <a href="https://www.nasponline.org/about-school-psychology/who-are-school-psychologists">children can be referred</a>, often by parents or teachers, to see a school psychologist when they are experiencing learning, social-emotional or behavioural challenges. </p>
<p>If math learning is posing big challenges, school psychologist involvement can be helpful given that a one-size fits all approach does not apply to math learning. Skills are not developed in a bubble without outside influences: children have thoughts, feelings, behaviour, knowledge, skills and experiences that shape their classroom engagement.</p>
<h2>Whole-child approach</h2>
<p>School psychologists are <a href="https://cpa.ca/cpasite/UserFiles/Documents/publications/CPA%20Practice%20Guide.pdf">trained to take a whole-child approach</a> to understanding how various factors — such as cognitive, emotional or behavioral ones — come together to influence a student’s functioning. </p>
<p>They can act as a kind of detective, where they investigate what child-specific and contextual factors may be interacting and influencing a child’s learning. With this information, psychologists can <a href="http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.180.1317&rep=rep1&type=pdf">target and tailor math support to a specific child’s needs</a>.</p>
<p>In my preliminary research, I have found that many school psychologists have high levels of math knowledge, and are thus potentially well-positioned to support students who are struggling with math. </p>
<p>That said, school psychologists typically serve as generalists, much like family doctors, so it is likely that their level of math expertise varies according to personal interest and specialization. They are also often in high demand so accessing their services can involve a long wait time. </p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/284402/original/file-20190716-173355-t1x0d6.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/284402/original/file-20190716-173355-t1x0d6.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/284402/original/file-20190716-173355-t1x0d6.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/284402/original/file-20190716-173355-t1x0d6.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/284402/original/file-20190716-173355-t1x0d6.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/284402/original/file-20190716-173355-t1x0d6.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/284402/original/file-20190716-173355-t1x0d6.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">Look for the little moments to discuss comparison, measurement, subtraction, addition.</span>
</figcaption>
</figure>
<h2>Math experiences at home</h2>
<p>The good news is that creating <a href="https://www.tandfonline.com/doi/abs/10.1080/09669761003693926">math experiences with children at home</a> is beneficial and parental involvement is a contributor to numeracy development. </p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/the-new-math-how-to-support-your-child-in-elementary-school-87479">The 'new math': How to support your child in elementary school</a>
</strong>
</em>
</p>
<hr>
<p>Here are some strategies that can be used at home:</p>
<h2><em>1. Keep it positive and make it fun</em>:</h2>
<p>Within a field called positive psychology, there is something known as the “<a href="https://psycnet.apa.org/doiLanding?doi=10.1037%2F0003-066X.56.3.218">broaden and build theory</a>” which proposes that when people experience positive emotions, including interest, it builds a person’s ability to succeed by promoting more divergent thinking, creativity and engagement. Over time, this facilitates skill development. Playing fun games that have math content can be one way to quickly engage children and build positive feelings that allow them to be more available for learning. </p>
<h2><em>2. Make it relevant and practical</em>:</h2>
<p>There are many daily ways math can be relevant to children – from using money to measuring hockey sticks to see if they’ll fit in the car. Other examples can include thinking about activities: If I want to make cookies, how do I get half a cup of butter? If I’m playing a game of cards and I accidentally handed out eight cards instead of five, how many do I need to take back? Or if I am choosing a spoon to eat my ice cream with, which spoon is largest? Look for the little moments to discuss comparison, measurement, subtraction and addition. </p>
<h2><em>3. Praise the effort and process, not the result</em>:</h2>
<p>Learning is hard work. Praising kids for their efforts and the process of solving problems is more important than the end result. Praise can help encourage kids to keep trying rather than feeling disheartened for being “wrong.”</p><img src="https://counter.theconversation.com/content/111488/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Kelsey Gould receives funding from The Social Sciences and Humanities Research Council of Canada</span></em></p>Children’s perspectives on math develop at a very young age and have longstanding effects, so it matters that families and teachers promote positive engagement with math skills.Kelsey Gould, PhD student, School and Applied Child Psychology, University of CalgaryLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1201332019-07-17T23:02:50Z2019-07-17T23:02:50ZMathematics is about wonder, creativity and fun, so let’s teach it that way<figure><img src="https://images.theconversation.com/files/284141/original/file-20190715-173355-10cjyhl.jpg?ixlib=rb-1.1.0&rect=2%2C79%2C994%2C534&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Why don't students say math is imaginative? Here, the White Rabbit character originally from Alice's Adventures in Wonderland, written under mathematician Charles Lutwidge Dodgson's pen name, Lewis Carroll. </span> <span class="attribution"><span class="source">(Shutterstock)</span></span></figcaption></figure><p>Alice in Wonderland enthusiasts recently celebrated the story’s anniversary with creative events like playing with <a href="https://www.storymuseum.org.uk/about-us/what-we-do/alices-day/">puzzles and time</a> — and future Alice <a href="https://londonist.com/london/museums-and-galleries/alice-in-wonderland-exhibition-v-and-a-2020">exhibits are in the works</a>. The original 1865 children’s book <em>Alice’s Adventures in Wonderland</em>, sprung from a mathematician’s imagination, continues to inspire exploration and fun. </p>
<p>But is a connection between math and creativity captured in schools? Much discussion across the western world from both experts and the public has emphasized the need to <a href="https://www.nctm.org/Store/Products/Catalyzing-Change-in-High-School-Mathematics/">revitalize high school mathematics</a>: critics say the experience is <a href="https://www.nytimes.com/2019/03/30/opinion/sunday/fix-high-school-education.html">boring</a> or <a href="https://qz.com/377742/this-school-in-norway-abandoned-teaching-subjects-40-years-ago/">not meaningful to most students</a>. Experts concerned with the public interest and decision-making say students need skills in <a href="https://cca-reports.ca/reports/some-assembly-required-stem-skills-and-canadas-economic-productivity/">critical thinking, creativity, communication and collaboration</a>. </p>
<p>Mathematicians, philosophers and educators are also concerned with the excitement and energy of creative expression, with invention, <a href="https://www.jstor.org/stable/40248373">with wonder</a> and even with what might be called <a href="https://education.stateuniversity.com/pages/2548/Whitehead-Alfred-North-1861-1947.html">the romance of learning</a>. </p>
<p>Mathematics has all the attributes of the paragraph above, and so it seems to me that <a href="https://doi.org/10.3390/educsci8020056">what’s missing from high school math is mathematics itself</a>.</p>
<p>I am now working with colleagues at Queen’s University and the University of Ottawa to develop <a href="http://www.rabbitmath.ca">RabbitMath,</a> a senior level high-school math curriculum designed to enable students to work together creatively with a high level of personal engagement. My preparation for this has been 40 years of working with teachers in high-school classrooms. </p>
<p>In partnership with grades 11 and 12 math teachers, we will be piloting this curriculum over the next few years.</p>
<h2>Mathematical novels</h2>
<p>When students study literature, drama or the creative arts in high school, the curriculum centres on what can be called sophisticated works of art, created in response to life’s struggles and triumphs. </p>
<p>But currently in school mathematics, this is rarely the case: students are not connected to the larger imaginative projects through which professional mathematicians confront the world’s problems or explore the world’s mysteries. </p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/284191/original/file-20190715-173351-drn82p.JPG?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/284191/original/file-20190715-173351-drn82p.JPG?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=450&fit=crop&dpr=1 600w, https://images.theconversation.com/files/284191/original/file-20190715-173351-drn82p.JPG?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=450&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/284191/original/file-20190715-173351-drn82p.JPG?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=450&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/284191/original/file-20190715-173351-drn82p.JPG?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=566&fit=crop&dpr=1 754w, https://images.theconversation.com/files/284191/original/file-20190715-173351-drn82p.JPG?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=566&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/284191/original/file-20190715-173351-drn82p.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">
<figcaption>
<span class="caption">The author, Peter Taylor, right, at a Lisgar Collegiate Institute Grade 11 math classroom in Ottawa, 2018.</span>
<span class="attribution"><span class="source">(Ann Arden)</span>, <span class="license">Author provided</span></span>
</figcaption>
</figure>
<p>Mathematician Jo Boaler from the Stanford Graduate School of Education says that a <a href="https://www.wiley.com/en-ca/Mathematical+Mindsets%3A+Unleashing+Students%27+Potential+through+Creative+Math%2C+Inspiring+Messages+and+Innovative+Teaching-p-9780470894521">“wide gulf between real mathematics and school mathematics is at the heart of the math problems we face in school education.”</a></p>
<p>Of the subject of mathematics, Boaler notes that:</p>
<blockquote>
<p>“Students will typically say it is a subject of calculations, procedures, or rules. But when we ask mathematicians what math is, they will say it is the study of patterns that is an aesthetic, creative, and beautiful subject. Why are these descriptions so different?” </p>
</blockquote>
<p>She points out the same gulf isn’t seen if people ask students and English-literature professors what literature is about. </p>
<p>In the process of constructing the RabbitMath curriculum, problems or activities are included when team members find them engaging and a challenge to their intellect and imagination. Following the analogy with literature, we call the models we are working with mathematical novels. </p>
<p>For example, one project invites students to work with ocean tides. It would hard to find a dramatic cycle as majestic as the effect of that sublime distant moon on the powerful tidal action in the Bay of Fundy.</p>
<h2>Student engagement</h2>
<p>In the 1970s, the extraordinary mathematician and computer scientist at Massachusetts Institute of Technology, Seymour Papert, noticed that in art class, students, just as mature artists, are involved in <a href="https://doi.org/10.1080/0020739700030306">personally meaningful work</a>. Papert’s objective was to be able to say the same of a mathematics student.</p>
<p>I had a parallel experience in 2013 when I was the internal reviewer for the Drama program at Queen’s. I marvelled at students’ creative passion as they prepared to stage a performance. And they weren’t all actors: they were singers, musicians, writers, composers, directors and technicians.</p>
<p>In Papert’s curriculum model, students with diverse abilities and interests <a href="https://flm-journal.org/index.php?do=details&lang=en&vol=37&num=2&pages=25-29&ArtID=1146">work together on projects</a>, whereby they collaborate on problems, strategies and outcomes. </p>
<p>As a pioneering computer scientist, Papert understood that students could directly access the processes of design and construction through digital technology. Papert used his computer system LOGO for this technical interface. LOGO was limited in its scope, but Papert’s idea was way ahead of its time. </p>
<p>Students in the RabbitMath classroom will work together using the programming language Python to construct diagrams and animations to better understand their experiments with springs and tires, mirrors and music. They will produce videos that can explain to their classmates the workings of a sophisticated structure.</p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/284162/original/file-20190715-173342-15mge07.PNG?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/284162/original/file-20190715-173342-15mge07.PNG?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=228&fit=crop&dpr=1 600w, https://images.theconversation.com/files/284162/original/file-20190715-173342-15mge07.PNG?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=228&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/284162/original/file-20190715-173342-15mge07.PNG?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=228&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/284162/original/file-20190715-173342-15mge07.PNG?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=286&fit=crop&dpr=1 754w, https://images.theconversation.com/files/284162/original/file-20190715-173342-15mge07.PNG?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=286&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/284162/original/file-20190715-173342-15mge07.PNG?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=286&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">RabbitMath focuses on the analysis of complex structures. Students studying the curriculum will be involved presenting mathematical ‘stories.’</span>
<span class="attribution"><span class="source">(RabbitMath image by Skyepaphora)</span>, <span class="license">Author provided</span></span>
</figcaption>
</figure>
<p>Today, technology, the internet, computer algebra systems and mathematical programming provide possibilities for immediate engagement in processes of design and construction — exactly what Papert wanted. The platform for RabbitMath is the <a href="https://jupyter.org/">Jupyter Notebook</a>, a direct descendant of LOGO.</p>
<h2>Technical skill</h2>
<p>For too many years, real progress in school mathematics education has been hamstrung by a ridiculous confrontation between so-called “traditional” and “discovery” math. The former is concerned with technical facility and the latter is about skills of inquiry and investigation.</p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/ontario-math-has-always-covered-the-basics-115445">Ontario math has always covered 'the basics'</a>
</strong>
</em>
</p>
<hr>
<p>There is no conflict between the two; in fact they support each other rather well. Every sophisticated human endeavour, from conducting a symphony orchestra to putting a satellite into orbit, understands the complementary nature of technical facility and creative investigation. </p>
<p>Stanford University Graduate School of Education mathematician Keith Devlin advises parents to ensure their child has mastery of what he calls number sense, “<a href="https://www.edge.org/response-detail/27097">fluidity and flexibility with numbers, a sense of what numbers mean, and an ability to use mental mathematics to negotiate the world and make comparisons</a>.” But for students embarking on careers in science, technology or engineering, that is not enough, he says. They need a deep understanding of both those procedures and the concepts they rely on — the capacity to analyze and work with complex systems.</p>
<p>A high-school math class is a rich ecosystem of differing abilities, capacities, objectives and temperaments. </p>
<p>The educator’s goal must be to enable a diverse mix of students to work together in a math class as creatively and intensely as students in the drama program, or to bring the same personal passion as they might to writing fiction.</p><img src="https://counter.theconversation.com/content/120133/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Peter Taylor receives funding from: The Mathematics Knowledge Network; The Fields Institute;The Canadian Mathematical Society; The Social Sciences and Humanities Research Council of Canada.
</span></em></p>Mathematician Peter Taylor taught high school math to prepare to develop a new ‘RabbitMath’ curriculum that emphasizes collaborative creativity and learning to work with complex systems.Peter Taylor, Professor, Queen's University, OntarioLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1154452019-05-02T21:54:22Z2019-05-02T21:54:22ZOntario math has always covered ‘the basics’<figure><img src="https://images.theconversation.com/files/272086/original/file-20190501-113830-1stfftu.jpg?ixlib=rb-1.1.0&rect=54%2C108%2C5090%2C2560&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Provincial leaders' portrayal of developments in math education over the past 20-plus years has been disturbingly poor. </span> <span class="attribution"><span class="source">(Shutterstock)</span></span></figcaption></figure><p>Some disturbing statements have been made recently about Ontario’s student math achievement and curriculum. Premier Doug Ford told the media that “<a href="https://globalnews.ca/news/5173501/ontario-students-lowest-math-scores-canada/">Grade 6 students are the lowest math scores in the entire country</a>” — this is false — and Minister of Education Lisa Thompson has described Ontario’s math curriculum as “<a href="https://globalnews.ca/news/4416177/ontario-elementary-school-math-scores-down/">failed experimental curriculum</a>.” </p>
<p>We are mathematics education faculty members who also also have extensive years of experience classroom teaching in Ontario. We have researched <a href="http://www.fields.utoronto.ca/journalarchive/FMEJ/53.html">math curriculum in Ontario</a> and we spend much of our time working with future Ontario teachers and observing current teachers in classrooms. </p>
<p>We feel our provincial leaders’ portrayal of teachers’ efforts, and the developments in mathematics education over the past 20-plus years, has been disturbingly poor. Here’s why.</p>
<h2>The myth of ‘discovery math’</h2>
<p>During his campaign, Ford said many times that <a href="https://www.cbc.ca/news/canada/toronto/ford-math-free-speech-1.4654966">he wanted to get rid of the “discovery math” curriculum</a>, and before this school year the minister of education issued a <a href="https://news.ontario.ca/edu/en/2018/08/statement-by-education-minister-on-eqao-results.html?_ga=2.61762409.410064977.1555452822-1319607232.1555117882">news release citing the end of “discovery math” in Ontario</a>. </p>
<p>The current curriculum is not, and never has been, based on “discovery.” <em>Discovery</em> is not one of the verbs used in the curriculum to describe the actions of students in math classes. </p>
<p>If you do a word search on the Ontario math Grades 1 to 8 curriculum document, The words “discover” or “discovery” are <em>not contained in the learning or process expectations</em>. One sentence states students will “discover” <a href="http://www.edu.gov.on.ca/eng/curriculum/elementary/math18curr.pdf">a connection between effort and achievement on page 4</a>.</p>
<p>The current curriculum advocates for the development of <em>understanding</em>, along with fluency. What <em>are</em> in the curriculum are words like “investigate,” “determine” and “explore” <a href="https://thelearningexchange.ca/videos/dr-christine-surrtamm-a-balanced-approach/">to explain students need to do mathematical thinking, not just compute formulas</a>.</p>
<h2>Curriculum already covers ‘basics’</h2>
<p>A more recent news release from the minister of education called for “<a href="https://news.ontario.ca/edu/en/2019/03/back-to-basics-math-curriculum-renewed-focus-on-skilled-trades-and-cellphone-ban-in-the-classroom-co.html?_ga=2.51267113.1846165903.1555117882-1319607232.1555117882">back-to-basics</a>” with math. </p>
<p>This statement overlooks the fact that the “basics” are not omitted in the current curriculum and never have been. Understanding the four fundamental operations (addition, subtraction, division and multiplication) and developing fluency with them is front and centre. </p>
<p>In fact, the Ontario Ministry of Education released a document early this school year, <a href="http://www.edu.gov.on.ca/eng/curriculum/elementary/math.html"><em>Focusing on the Fundamentals of Math: A Teacher’s Guide</em></a>, showing how this learning has always been part of the current curriculum. </p>
<p>While he was campaigning, Ford also blamed the previous Kathleen Wynne government for alleged failures in math, stating that he intended to replace her “<a href="http://www.fordnationlive.ca/watch_doug_s_plan_to_fix_ontario_s_education_system_by_respecting_parents_and_getting_back_to_basics">ideological ‘discovery math’.</a>” Reality check: the previous government didn’t create the math curriculum. The research behind Ontario’s math curriculum did not even begin in Canada. The current curriculum is based on decades of worldwide research.</p>
<p>The <a href="https://www.nctm.org/store/Products/Curriculum-and-Evaluation-Standards-for-School-Mathematics--Executive-Summary/">National Council of Teachers of Mathematics</a> is a U.S.-based math education organization that <a href="https://www.nctm.org/About/">advocates for high-quality math teaching and learning</a> and is the largest math organization in the United States or Canada. It also <a href="https://www.nctm.org/Standards-and-Positions/Principles-and-Standards/">issues math principles and standards documents</a>. </p>
<p>This council released a document in 1989 that described many of the principles that have guided Ontario’s current math curriculum since it was first launched in 2005 (a slight revision of a 1997 version) — that when children are doing math, they should create <a href="https://theconversation.com/why-your-child-will-benefit-from-inquiry-based-learning-97245">math understanding through investigating and exploring</a>. These ideas are <a href="https://journals.sagepub.com/doi/abs/10.3102/00028312026004499">based on solid research, and they have been around for decades</a>. </p>
<h2>Ontario math scores ranked 2nd in Canada</h2>
<p>When you play the video in a recent animated tweet by Ford, it’s alleged that Ontario students haven’t been properly taught math “because of a program brought in by the Wynne Liberals called discovery math.” </p>
<p><div data-react-class="Tweet" data-react-props="{"tweetId":"1106591888033742849"}"></div></p>
<p>The tweet also suggests the standardized provincial test, the <a href="http://www.eqao.com/Pages/launch.aspx">EQAO</a> is a “basic math test” — a comment that shows no grasp of what the EQAO assesses and also insults teachers’ hard work. Don’t take our word on it, look at the types of <a href="http://www.eqao.com/en/assessments/examples-of-the-assessments/Pages/default.aspx">questions</a> asked. If you look at the image below, you can see that simply memorizing formulas will not help kids do better on this test. </p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/271858/original/file-20190430-136787-s0omfh.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/271858/original/file-20190430-136787-s0omfh.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=739&fit=crop&dpr=1 600w, https://images.theconversation.com/files/271858/original/file-20190430-136787-s0omfh.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=739&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/271858/original/file-20190430-136787-s0omfh.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=739&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/271858/original/file-20190430-136787-s0omfh.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=929&fit=crop&dpr=1 754w, https://images.theconversation.com/files/271858/original/file-20190430-136787-s0omfh.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=929&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/271858/original/file-20190430-136787-s0omfh.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=929&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Sample EQAO question.</span>
<span class="attribution"><span class="source">(Jennifer Holm)</span>, <span class="license">Author provided</span></span>
</figcaption>
</figure>
<p>There is another problem with the premier’s tweet. The video voiceover states that “over half of Grade 6 students are failing to meet the provincial standards in math.” It might sound like half of Grade 6 students are <em>failing</em>. In fact, this statement refers to the fact that 51 per cent of Grade 6 students did not get a “B” level or higher (which the Ontario Ministry translates to a 70 per cent or over) on the EQAO. Put differently — about <em>half of Grade 6s (49 per cent) are scoring higher than “B.</em>” </p>
<p>According to <a href="http://www.eqao.com/en/assessments/results/assessment-docs-elementary/provincial-report-junior-achievement-results-2018.pdf">the EQAO</a>, an additional 31 per cent of students are approaching the provincial standard (which translates to 60 per cent to 69 per cent). </p>
<p>Indeed, if you consider the 2015 <a href="http://www.oecd.org/pisa/">Program for International Student Assessment (PISA)</a> scores, Ontario is doing quite well in the world in terms of math. Québec is the only Canadian province statistically ahead of Ontario. It’s worth noting that Québec does not use a “back-to-basics” curriculum characterized exclusively or largely by learning formulas instead of mathematical thinking.</p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/271852/original/file-20190430-136810-17wdqkj.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/271852/original/file-20190430-136810-17wdqkj.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=715&fit=crop&dpr=1 600w, https://images.theconversation.com/files/271852/original/file-20190430-136810-17wdqkj.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=715&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/271852/original/file-20190430-136810-17wdqkj.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=715&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/271852/original/file-20190430-136810-17wdqkj.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=898&fit=crop&dpr=1 754w, https://images.theconversation.com/files/271852/original/file-20190430-136810-17wdqkj.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=898&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/271852/original/file-20190430-136810-17wdqkj.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=898&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Where Ontario sits with PISA scores.</span>
<span class="attribution"><span class="source">(Jennifer Holm)</span>, <span class="license">Author provided</span></span>
</figcaption>
</figure>
<h2>Reasonable criticisms of Ontario’s math</h2>
<p>Having said all this, there is room for improvement in how Ontario teaches math. Ontario teachers were never universally given the professional development that should have accompanied the new curriculum released in 1997. </p>
<p>We teach people who are studying to be teachers, who are mostly products of Ontario’s educational system over the last 20 years. In our data on over 1,000 future teachers amassed over more than the last decade, we note most are still learning through memorizing formulas and procedures. In other words, very few have been taught using the current curriculum as it was meant to be taught since 2005. </p>
<p>After students spend a year “re-learning” math in our courses, using the mandates of the current curriculum <em>as intended</em>, the overwhelming response is they wished they had <a href="https://www.tandfonline.com/doi/abs/10.1080/14926156.2012.649055?journalCode=ucjs20">learned math like this before</a>. </p>
<p>We propose that Ontario should provide significant and ongoing professional development and resources to teachers so that they can support students in truly learning math. </p>
<p>Let’s stop letting our leaders sell teachers short and instead hold them accountable for what they say.</p><img src="https://counter.theconversation.com/content/115445/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Ann Kajander receives funding from the Ministry of Education Mathematics Knowledge Network. </span></em></p><p class="fine-print"><em><span>Jennifer Holm 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>Two math professors set the record straight on Ontario math curriculum and achievement.Jennifer Holm, Assistant Professor, Faculty of Education, Wilfrid Laurier UniversityAnn Kajander, Associate Professor of mathematics education, Lakehead UniversityLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1127402019-04-25T10:46:56Z2019-04-25T10:46:56ZWhy Facebook belongs in the math classroom<figure><img src="https://images.theconversation.com/files/268885/original/file-20190411-44805-1ks0135.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">What can you learn from your connections on social media?</span> <span class="attribution"><a class="source" href="https://www.shutterstock.com/image-photo/teenager-boy-folds-cubes-logo-popular-624195410?src=T90wIqtBDkl5KJK9pZUCTQ-1-21">AlesiaKan/shutterstock.com</a></span></figcaption></figure><p>Take a close look at your Facebook friends. </p>
<p>Some of your friends are also friends with each other, while others are not. It’s quite likely that you can find a “clique” who are all friends with each other.</p>
<p>It’s also possible you may have a group of Facebook friends who are all mutual strangers, where nobody is friends with anybody else in the group; let’s call such a group an “anti-clique.” </p>
<p>It wouldn’t take long to find a clique or anti-clique of at least three people. In fact, among any six people, there will be a group of three that forms either a clique or an anti-clique. </p>
<p>This exercise might seem frivolous, but there’s an underlying structure here that serves as an effective illustration of certain advanced mathematics. I use examples like these in the classroom to engage undergraduates in mathematical reasoning without detailed computations.</p>
<h2>Graphing cliques</h2>
<p>Let’s return to the problem of finding a clique or anti-clique. Consider a girl called Alice who is spending time with five people. Among these five, Alice must see either more friends or more strangers. </p>
<p>If Alice sees more friends than strangers, that means there are at least three people who are all friends with Alice. If any pair within these three people are friends, then they form a clique of three people with Alice. If none of these three are friends, then we have found an anti-clique of three people. </p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/269677/original/file-20190416-147518-ptunbz.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/269677/original/file-20190416-147518-ptunbz.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/269677/original/file-20190416-147518-ptunbz.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=242&fit=crop&dpr=1 600w, https://images.theconversation.com/files/269677/original/file-20190416-147518-ptunbz.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=242&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/269677/original/file-20190416-147518-ptunbz.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=242&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/269677/original/file-20190416-147518-ptunbz.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=304&fit=crop&dpr=1 754w, https://images.theconversation.com/files/269677/original/file-20190416-147518-ptunbz.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=304&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/269677/original/file-20190416-147518-ptunbz.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=304&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Left: Alice sees three friends and two strangers; Center: If any pair of Alice’s friends are also friends, then they form a clique with Alice; Right: If none of Alice’s friends knows each other, the three form an anti-clique.</span>
<span class="attribution"><span class="source">Jonathan Hulgan</span>, <a class="license" href="http://creativecommons.org/licenses/by-sa/4.0/">CC BY-SA</a></span>
</figcaption>
</figure>
<p>The same situation would work if you assumed Alice saw more strangers than friends.</p>
<p>This argument is a relatively simple result from the area of pure mathematics known as <a href="https://en.wikipedia.org/wiki/Graph_theory">graph theory</a>. </p>
<p>In mathematics, graphs sometimes refer to the graphical representation of functions, such as lines, parabolas and other curves. Graph theory studies something different. It focuses on the properties of mathematical structures that abstractly model relationships between objects. The objects can be represented by points, called vertices; related objects would have their corresponding vertices connected by a line called an edge.</p>
<p>In the Facebook example, a graph theorist would consider a graph whose vertices represent the collection of friends. An edge would connect each pair of individuals who were Facebook friends with each other. </p>
<p>Precisely speaking, when a graph is defined by a relation on some collection of objects, as is the case here, it is called a “network.” So Facebook truly describes a “social network.”</p>
<h2>Asking more questions</h2>
<figure class="align-right zoomable">
<a href="https://images.theconversation.com/files/269638/original/file-20190416-147508-1a4i03c.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/269638/original/file-20190416-147508-1a4i03c.png?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/269638/original/file-20190416-147508-1a4i03c.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=575&fit=crop&dpr=1 600w, https://images.theconversation.com/files/269638/original/file-20190416-147508-1a4i03c.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=575&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/269638/original/file-20190416-147508-1a4i03c.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=575&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/269638/original/file-20190416-147508-1a4i03c.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=723&fit=crop&dpr=1 754w, https://images.theconversation.com/files/269638/original/file-20190416-147508-1a4i03c.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=723&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/269638/original/file-20190416-147508-1a4i03c.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=723&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">A Petersen graph, a common example used in graph theory problems.</span>
<span class="attribution"><a class="source" href="https://commons.wikimedia.org/wiki/File:Petersen_graph_3-coloring.svg">Wikimedia</a></span>
</figcaption>
</figure>
<p>Most students I encounter have never studied graph theory; it’s rare for it to appear in high school or a lower-level math course.</p>
<p>This is unfortunate, as I feel that graph theory provides a perfect setting for practicing mathematical arguments without requiring tedious calculations – just as in the example with Alice and her Facebook friends.</p>
<p>What’s more, graph theory lends itself nicely to the development of questions of real mathematical substance. My simple demonstration of the presence of a three-person clique or anti-clique in any group of six people can motivate further questions from the curious observer: When can you guarantee a four-person clique or anti-clique? If three relationships are possible between individuals – for instance, friends, strangers and acquaintances – when would you be guaranteed to see a three-person clique, anti-clique or “pseudo-clique” of mere acquaintances? </p>
<p>These and similar questions were answered in 1955 by mathematicians <a href="https://doi.org/10.4153/CJM-1955-001-4">Robert Greenwood and Andrew Gleason</a>. The mathematical contributions of Greenwood and Gleason are profound and numerous. However, no mathematical expertise is required to develop such questions, nor is it needed to enjoy the pursuit of a complete solution.</p>
<figure>
<iframe width="440" height="260" src="https://www.youtube.com/embed/SC5CX8drAtU?wmode=transparent&start=0" frameborder="0" allowfullscreen=""></iframe>
<figcaption><span class="caption">The traveling salesman problem comes up in graph theory.</span></figcaption>
</figure>
<h2>Teaching graph theory</h2>
<p>This August, <a href="http://oxford.emory.edu/academics/discovery-seminar.html">I will teach a course</a> entitled “Graph Theory: Problems, Proofs and Conjectures,” specifically geared toward incoming first-year students. Using concepts from graph theory, my course will introduce students to the process by which knowledge is developed and discovered in mathematics.</p>
<p>Many math courses focus on developing the tools for demonstrating the logical truth of mathematical statements. While my seminar will include a healthy dose of this – including fundamentals of writing formal mathematical proof – it will also require students to develop novel mathematical statements for which it is unknown whether its outcome is true or false. </p>
<p>One of the first problems we will examine is the Facebook friends problem described earlier. I will not bring up Greenwood and Gleason’s work, but I expect at least one or two students will pose some variation of the problems they considered.</p>
<p>Just as graph theory is one area among many within the larger field of mathematics, the types of problems presented here represent only one sort of question considered by graph theorists. My seminar will investigate questions from other parts of graph theory, including the famous traveling salesman problem – for which there exist a number of <a href="http://www.math.uwaterloo.ca/tsp/poke/index.html">curious applications</a> – and graph coloring problems, which are <a href="https://doi.org/10.1016/j.disc.2008.06.002">my particular interest</a>.</p>
<p>In my view, graph theory illuminates an underlying nature of mathematics that can often seem hidden behind the numbers and computations of algebra and calculus. Introducing questions such as these in the classroom can let students see a side of mathematics they might not have considered before.</p><img src="https://counter.theconversation.com/content/112740/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Jonathan Hulgan does not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.</span></em></p>Simple math reveals some surprising facts about the underlying structure of Facebook and other social networks.Jonathan Hulgan, Assistant Professor of Mathematics, Emory UniversityLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1117302019-02-14T22:14:22Z2019-02-14T22:14:22ZReduce children’s test anxiety with these tips — and a re-think of what testing means<figure><img src="https://images.theconversation.com/files/258814/original/file-20190213-181593-1hezl5o.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Parents can assure children that anxiety is a natural feeling they can learn to manage. </span> <span class="attribution"><span class="source">(Shutterstock)</span></span></figcaption></figure><p>The term “test anxiety” typically conjures up images of a high school or university student obsessing over an upcoming exam. </p>
<p>Certainly, older students have been the focus of more than a half a century of research examining test and assessment anxiety and its impact on grades. Researchers know that such test anxiety generally has <a href="https://psycnet.apa.org/doiLanding?doi=10.1037%2Fh0043012">a negative impact on academic achievement</a>. </p>
<p>Yet we also know schools and parents are recognizing <a href="https://www.cmho.org/education-resources/facts-figures">anxiety in younger children</a>. Researchers have probed how, in particular, a rise in test anxiety in schools <a href="https://onlinelibrary.wiley.com/doi/abs/10.1002/pits.21689">corresponds to an increase in the use of standardized testing</a> increasingly mandated for accountability and evaluation purposes. </p>
<p>Coupled <a href="https://smh-assist.ca/wp-content/uploads/Info-Sheets-Supporting-Minds-Anxiety-1.pdf">with growing awareness of responding to mental health challenges in schools</a>, educators and policy-makers need to understand how to confront and minimize the effects of testing on students’ anxiety.</p>
<p>In the big picture, current assessment methods must adapt to reflect contemporary knowledge of both children’s diverse cultural contexts and a more nuanced understanding of developmental competencies. </p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/culturally-responsive-teaching-in-a-globalized-world-109881">Culturally responsive teaching in a globalized world</a>
</strong>
</em>
</p>
<hr>
<p>In the day-to-day, parents and teachers can empower themselves to be better prepared to support student well-being by re-thinking their own approaches to tests, and what adults are modelling. </p>
<h2>What is test anxiety?</h2>
<p>Test anxiety is generally regarded as a “nervous feeling” that is excessive and interferes with student performance. Symptoms of <a href="https://www.anxietycanada.com/sites/default/files/Test_Anxiety_Booklet.pdf">test anxiety may fall into four broad physical, emotional, behavioural and cognitive categories</a>. </p>
<p>Children could exhibit physical symptoms such as headaches, nausea, sweating and shortness of breath or feelings of fear, depression and helplessness. Behaviours might include fidgeting, pacing and avoidance. Cognitive disruptions could look like “going blank,” racing thoughts and negative self-talk. </p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/259107/original/file-20190214-1736-1elo0ex.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/259107/original/file-20190214-1736-1elo0ex.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=389&fit=crop&dpr=1 600w, https://images.theconversation.com/files/259107/original/file-20190214-1736-1elo0ex.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=389&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/259107/original/file-20190214-1736-1elo0ex.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=389&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/259107/original/file-20190214-1736-1elo0ex.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=488&fit=crop&dpr=1 754w, https://images.theconversation.com/files/259107/original/file-20190214-1736-1elo0ex.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=488&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/259107/original/file-20190214-1736-1elo0ex.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=488&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Left prolonged or unattended, test anxiety can lead to negative outcomes.</span>
<span class="attribution"><span class="source">(Shutterstock)</span></span>
</figcaption>
</figure>
<p>Although not all students experience each of these problems, the impact of one or more of these symptoms can be debilitating. Left unacknowledged or unaddressed, in time such symptoms may lead to personal negative outcomes or harm, and difficulties at school. </p>
<h2>The trouble with testing policy</h2>
<p>Our research in Canada and abroad has consistently found
that when policy-makers seek school reform, there is an ensuing emphasis on testing for accountability. </p>
<p>In these contexts, teachers and school administrators will <a href="https://www.springer.com/gp/book/9789400740945">focus classroom and school instruction on select areas and ultimately undermine a more holistic approach to children’s education</a>. Standardized testing for accountability is also associated with heightened educator and student stress. </p>
<p>A narrow sense of “achievement” — such as is measured via standardized tests in select subject areas — is inadequate to capture key knowledge, skills and dispositions children need to be successful in contemporary schooling and life. </p>
<p>For these reasons, policy-makers would be wise to consider multi-dimensional approaches to holding schools accountable. For example, educational reforms <a href="https://www.edcan.ca/wp-content/uploads/EdCan-2007-v47-n1-Volante.pdf">are more likely to be successful when they use collective processes that incorporate perspectives of educators and communities</a>. </p>
<h2>What parents and teachers can do</h2>
<p>In the context of these systemic and long-term issues, parents and teachers can intervene to reduce test anxiety for young children in the following ways: </p>
<h2><em>1. Offer positive messaging</em></h2>
<p>One of the simplest and most effective ways parents can combat test anxiety is through positive messaging. </p>
<p>For example, research demonstrates positive benefits when <a href="https://eric.ed.gov/?id=EJ885222">parents encourage positive self-talk, offer relaxation techniques</a> and reassure children that anxiety is a natural feeling. Parents should know that psychological research suggests a certain amount of <a href="https://hbr.org/2016/04/are-you-too-stressed-to-be-productive-or-not-stressed-enough">heightened arousal is necessary to perform well, a state of balance-in-tension</a>. </p>
<h2><em>2. Keep communication open</em></h2>
<p>Parents also need to maintain open lines of communication with their child’s teachers — particularly since students do not necessarily exhibit test anxiety in all subjects.</p>
<h2><em>3. Lower the stakes</em></h2>
<p>Too often parent expectations increase the perceived “stakes” of the tests for students, assigning additional consequences or judging a child’s merit and ability on the outcome of a single test. </p>
<p>Instead, it is important for parents to understand and also convey to their child that tests are one indicator of their performance in a subject. No test is a perfect reflection of what a student knows or is able to do. </p>
<p>Seeing tests as one piece of information about how a child is progressing, and seeking out additional information as needed, will help parents gain perspective. </p>
<h2><em>4. Take care of yoursef</em></h2>
<p>Ironically, one key issue both parents and teachers need to consider when attempting to assist students with test anxiety is to first take care of themselves. </p>
<p>Just as parents must be aware of what messsages they send, teachers also need to attend to their own well-being and avoid inadvertently transmitting their own anxieties to students. </p>
<p>For example, the relationship <a href="https://nationalpost.com/pmn/news-pmn/canada-news-pmn/trying-to-tackle-the-math-bogeyman-anxiety-in-students-teachers-and-parents">between teachers’ math anxiety and student math anxiety is well-established</a> prompting some researchers to explore ways of breaking a <a href="https://link.springer.com/article/10.1007/s10649-010-9260-7">mathematics anxiety cycle</a>. </p>
<p>Similarly, teacher worry about large-scale test results, such as provincial or state-wide assessments, can transfer to students. </p>
<p>Thankfully, a positive development to emerge from some of these troubling findings is that there is a <a href="https://www.edcan.ca/articles/teach-resiliency/">growing recognition of the relationship between teacher and student well-being</a>. </p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/259109/original/file-20190214-1717-vw8wgm.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/259109/original/file-20190214-1717-vw8wgm.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=396&fit=crop&dpr=1 600w, https://images.theconversation.com/files/259109/original/file-20190214-1717-vw8wgm.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=396&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/259109/original/file-20190214-1717-vw8wgm.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=396&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/259109/original/file-20190214-1717-vw8wgm.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=497&fit=crop&dpr=1 754w, https://images.theconversation.com/files/259109/original/file-20190214-1717-vw8wgm.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=497&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/259109/original/file-20190214-1717-vw8wgm.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=497&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Teacher and student well-being is connected.</span>
<span class="attribution"><span class="source">(Shutterstock)</span></span>
</figcaption>
</figure>
<h2><em>5. Emphasize test skills, not drilling</em></h2>
<p>Teachers can also help students combat test concerns by offering test-preparation skill development and reviews before important assessments. </p>
<p>The latter should not be confused with <a href="https://journalhosting.ucalgary.ca/index.php/cjeap/article/view/42715">“teaching to the test,” which both narrows curriculum and may relentlessly drill test content</a>. </p>
<p>Rather, practicing strategies such as re-reading difficult questions, writing brief outlines beside short answer questions and managing time during tests will be helpful.</p>
<p>Preparing students to write tests effectively also includes teaching students about test structures — question formats, the rationale of scoring schemes and common pitfalls with different question types. </p>
<p>Collectively, these skills can be applied to any curriculum or test. Students who have been prepared in both content and skills tend to have lower levels of test anxiety and are more capable of managing their time and responses. </p>
<p>Not surprisingly, these types of strategies are more effective when they are supported by parents and caregivers.</p>
<p>Optimally, parents, teachers and policymakers can work in their various roles to support children’s success while learning about possibilities for more <a href="https://www.routledge.com/Testing-Times-The-Uses-and-Abuses-of-Assessment-1st-Edition/Stobart/p/book/9780415404754">complex and intelligent forms of accountability</a>. </p>
<p>Overall, we need to re-think what matters in schools and what’s worth measuring.</p><img src="https://counter.theconversation.com/content/111730/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Louis Volante receives funding from the Social Sciences and Humanities Research Council of Canada (SSHRC) </span></em></p><p class="fine-print"><em><span>Christopher DeLuca receives funding from the Social Sciences and Humanities Research Council of Canada.</span></em></p>Educational experts offer tips for parents and teachers to help children manage test anxiety but find that overall, policy-makers need to re-think what matters in schools and what’s worth measuring.Louis Volante, Professor of Education, Brock UniversityChristopher DeLuca, Associate Dean, School of Graduate Studies & Associate Professor, Faculty of Education, Queen's University, OntarioLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1064332018-11-14T23:50:38Z2018-11-14T23:50:38ZFor the sake of kids, embrace math<figure><img src="https://images.theconversation.com/files/244827/original/file-20181109-36763-19zhz42.jpg?ixlib=rb-1.1.0&rect=64%2C64%2C5277%2C3224&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Parents have a responsibility for their children’s math development too. </span> <span class="attribution"><span class="source">Shutterstock </span></span></figcaption></figure><p>Mathematics is causing headaches in schools across Canada, Australia and many other parts of the world. Teachers in both Canada and Australia feel neither competent nor confident in math and, frankly, they are the first to admit it. </p>
<p>As researchers, educators and authors who have advised globally about best practices for improving learning and achievement, we have had opportunities to notice common trends and <a href="https://www.theguardian.com/australia-news/2018/jan/07/pasi-sahlberg-finland-teach-australian-schools-education">obstacles</a>, and notable gains, in math education. </p>
<p>Up close, we’ve heard from teachers in <a href="https://news.ontario.ca/edu/en/2017/08/ontario-appoints-new-advisors-to-guide-transformation-in-education-system.html">Ontario</a>, Canada, and in <a href="https://pasisahlberg.com/news/gonski-2-0-a-conversation-with-pasi-sahlberg-and-adrian-piccoli/">Australia</a> and we’ve considered how people can best <a href="http://www.clri.com.au/article/collaborative-professionalism/research">collaborate</a> to protect and grow students’ love of learning. </p>
<p>We’ve seen that some math improvement efforts get bogged down by fears of the unknown. Others get an initial spark but soon lose energy.</p>
<p>Let’s start with the bad news. </p>
<h2>‘Way more effective?’</h2>
<p>In response to a year-on-year decline in math scores, Ontario, for example, has started to give math achievement high priority. An underlying principle of the Ontario mathematics curriculum is to “<a href="http://www.edu.gov.on.ca/eng/curriculum/elementary/math18curr.pdf">investigate ideas and concepts through problem solving</a>.” A September report from Canadian think tank The Institute for Competitiveness and Prosperity pointed out that inquiry-based approaches to mathematics <a href="https://www.competeprosper.ca/uploads/2018_WP33_Teaching_for_tomorrow.pdf">actually get better results than more “basic” alternatives</a>. </p>
<p>But many parents and some educators remain skeptical, if not downright hostile, towards <a href="https://theconversation.com/the-new-math-how-to-support-your-child-in-elementary-school-87479">unfamiliar math strategies</a>. </p>
<p>In Australia, critics of inquiry-based mathematics curricula have suggested a change of course. In a recent story in the <em>Sydney Morning Herald</em>, with the headline “There is a better way of teaching bored Australian students,” a research fellow at Australian think tank the Centre for Independent Studies lamented that “explicit, direct instruction across the board is <a href="https://www.smh.com.au/national/there-is-a-better-way-of-teaching-bored-australian-students-20181030-p50csj.html">way more effective</a> in achieving higher student outcomes.” One could not help but wonder how many parents might have been nodding their heads over their coffee. </p>
<p>But while we can’t resolve the math problem simply by getting “back to basics,” we can revive good ideas about math education. </p>
<h2>More oxygen please</h2>
<p>From the early 2000s, Ontario’s government pledged to improve achievement in literacy and math (or numeracy, as it was then called). The government invested significant resources and established a Literacy and Numeracy Secretariat to spearhead the effort. </p>
<p>Principals made literacy their top priority. Expert coaches worked alongside classroom teachers, demonstrating effective strategies and giving teachers feedback on how to use them with students. </p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/245588/original/file-20181114-172710-10g65c6.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/245588/original/file-20181114-172710-10g65c6.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/245588/original/file-20181114-172710-10g65c6.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/245588/original/file-20181114-172710-10g65c6.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/245588/original/file-20181114-172710-10g65c6.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/245588/original/file-20181114-172710-10g65c6.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/245588/original/file-20181114-172710-10g65c6.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">We can revive good ideas about math education such as addressing how comfortable and competent elementary teachers feel about math.</span>
<span class="attribution"><a class="source" href="https://www.shutterstock.com/image-photo/teacher-helping-pupils-studying-desks-classroom-139406252">www.shutterstock.com</a></span>
</figcaption>
</figure>
<p>The gains in literacy were impressive and are now <a href="https://www.wiley.com/en-ca/Empowered+Educators+in+Canada%3A+How+High+Performing+Systems+Shape+Teaching+Quality-p-9781119369622">the envy of the world</a>.</p>
<p>But, like in a number of other countries, the literacy strategy consumed all the attention and left math with too little oxygen. It’s almost impossible to reform literacy and math all at once — the scope is too great, so the effort either <a href="http://www.washingtonpost.com/blogs/answer-sheet/wp/2014/09/26/why-we-cant-reform-literacy-and-math-all-at-once/">leaves one of them to fall by the wayside by default</a> or just burns teachers out. </p>
<p>It’s time to give math reform the same treatment as literacy. But math reform has to confront an obstacle that literacy reform didn’t: Almost every primary and elementary teacher in many countries, including Canada and Australia, loves reading, writing and books, as do many of the kids. </p>
<p>Literacy reform had a lot to build on. This is not the case with math. </p>
<p>In interviews one of us conducted last year with more than 200 Ontario educators, teachers would say things like:</p>
<blockquote>
<p><a href="http://ccsli.ca/downloads/2018-Leading_From_the_Middle_Final-EN.pdf">“I’m not a math person.”</a> </p>
</blockquote>
<p>One principal reflected how they had all been “amazing readers and writers.” But she also wondered:</p>
<blockquote>
<p>“Did we share that similar passion and appetite for numeracy?” </p>
</blockquote>
<h2>Fear of math vs. higher salary</h2>
<p>Compared to literacy, there is a shortage of teachers who feel competent in math and confident enough to teach students what mathematics is and what mathematicians do. Many schools also have shortages of colleagues with the expertise to help them. </p>
<p>Some of the current answers to this problem — such as more hours allocated to how to teach math during elementary teacher training, or assigning professional development days to improving math teaching — won’t do any harm. But we must also address how confident and comfortable, and not just minimally competent, elementary teachers need to feel about math. </p>
<p>In Ontario, for example, <a href="https://www.competeprosper.ca/blog/why-are-elementary-school-math-scores-declining-in-ontario">80 per cent of elementary teachers have no university qualification in math</a>. However, in Finland, one of the world’s leading performers in mathematics, around half of elementary teachers <a href="http://www.finland.org/Public/default.aspx?contentid=238689&nodeid=35833&contentlan=2">have studied math or science and how to teach them effectively during their university degrees</a>. </p>
<p>Second, in Singapore, the world’s No. 1 performer in math, elementary teachers are paid as much as engineers when they start teaching. This means students who are good at math choose teaching based on their mission and purpose in life, <a href="https://www.nie.edu.sg/news-detail/learning-from-singapore-the-power-of-paradoxes-by-ng-pak-tee">not on salary differentials</a>. Perhaps Canada and Australia need to think harder about how to attract more people with math and science backgrounds into elementary teaching. </p>
<h2>Teacher and parent aid</h2>
<p>Third, improving teaching mathematics should be built on collaboration between experienced teachers and those with less confidence in schools. This coaching should focus not just on how to teach math but also on teachers’ relationship to math generally. </p>
<p>Intensive coaching was a big factor in raising literacy achievement. Because math expertise is now thinner, teachers need more resources and resourcefulness in classrooms. </p>
<p>Last, parents have a responsibility for their children’s math development too. But two-thirds of surveyed Ontario parents <a href="https://www.competeprosper.ca/uploads/2018_WP33_Teaching_for_tomorrow.pdf">don’t know how to help their elementary-aged children with mathematics</a>. </p>
<p>Supporting school interventions known as family math that help parents <a href="https://www.edu.gov.on.ca/eng/literacynumeracy/parentGuideNumEn.pdf">converse about numbers and shapes with their children as easily as they might about words could do a lot to rectify this</a>.</p>
<p>We need to make math as much a priority now as literacy has been. We need to get teachers in primary or elementary schools just as comfortable as well as competent with math and how to teach it successfully to all children as they are with reading in their lives as well as in their classes. </p>
<p>If we avoid falling for simplistic solutions, then eventually, the words “I am not a math person” may become a thing of the past.</p><img src="https://counter.theconversation.com/content/106433/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Andy Hargreaves has received funding from the Council of Directors of Education for Ontario (CODE) - the report of this research is cited in this article. </span></em></p><p class="fine-print"><em><span>Pasi Sahlberg 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>Instead of getting “back to basics” to improve math skills, we should make math literacy a priority by developing, attracting and supporting skilled teachers, and improving math literacy at home.Andy Hargreaves, Research Professor in Education, Boston CollegePasi Sahlberg, Professor of Education Policy, UNSW SydneyLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/943782018-05-15T10:26:19Z2018-05-15T10:26:19ZMaria Agnesi, the greatest female mathematician you’ve never heard of<figure><img src="https://images.theconversation.com/files/218462/original/file-20180510-34038-s8x19d.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Agnesi was the first woman to write a mathematics textbook.</span> <span class="attribution"><span class="source">AlexeyMaltsev/shutterstock.com</span></span></figcaption></figure><p>The outmoded gender stereotype that women lack mathematical ability suffered a major blow in 2014, when <a href="https://news.stanford.edu/2017/07/15/maryam-mirzakhani-stanford-mathematician-and-fields-medal-winner-dies/">Maryam Mirzakhani</a> became the first woman to receive the Fields Medal, math’s most prestigious award.</p>
<p>An equally important blow was struck by an Italian mathematician <a href="https://jhupbooks.press.jhu.edu/content/world-maria-gaetana-agnesi-mathematician-god">Maria Gaetana Agnesi</a> in the 18th century. Agnesi was the first woman to write a mathematics textbook and to be appointed to a university chair in math, yet her life was marked by paradox.</p>
<p>Though brilliant, rich and famous, she eventually opted for a life of poverty and service to the poor. Her remarkable story serves as a source for mathematical inspiration even today.</p>
<h2>Early years</h2>
<p>Born May 16, 1718 in Milan, Agnesi was the eldest of her wealthy silk merchant father’s 21 children. By age 5 she could speak French, and by 11 she was known to Milanese society as the “seven-tongued orator” for her mastery of modern and classical languages. In part to give Agensi the best education possible, her father invited leading intellectuals of the day to the family’s home, where his daughter’s gifts shone.</p>
<p>When Agnesi was 9, she recited from memory a <a href="http://chicago.universitypressscholarship.com/view/10.7208/chicago/9780226010564.001.0001/upso-9780226010540-chapter-6">Latin oration</a>, likely composed by one of her tutors. The oration decried the widespread prejudice against educating women in the arts and sciences, which had been grounded in the view that a life of managing a household would require no such learning. Agnesi presented a clear and convincing argument that women should be free to pursue any kind of knowledge available to men. </p>
<p>Agnesi eventually became tired of displaying her intellect and expressed a desire to enter a convent. When her father’s second wife died, however, she assumed responsibility for his household and the education of her many younger siblings. </p>
<p>Through this role, she recognized that teachers and students needed a comprehensive mathematics textbook to introduce Italian students to the many recent Enlightenment-era mathematical discoveries. </p>
<h2>Agnesi’s textbook</h2>
<figure class="align-right zoomable">
<a href="https://images.theconversation.com/files/218459/original/file-20180510-184630-1b2owug.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/218459/original/file-20180510-184630-1b2owug.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/218459/original/file-20180510-184630-1b2owug.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=698&fit=crop&dpr=1 600w, https://images.theconversation.com/files/218459/original/file-20180510-184630-1b2owug.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=698&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/218459/original/file-20180510-184630-1b2owug.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=698&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/218459/original/file-20180510-184630-1b2owug.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=877&fit=crop&dpr=1 754w, https://images.theconversation.com/files/218459/original/file-20180510-184630-1b2owug.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=877&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/218459/original/file-20180510-184630-1b2owug.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=877&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Portrait of Maria Agnesi by an unknown artist.</span>
<span class="attribution"><a class="source" href="https://en.wikipedia.org/wiki/File:Maria_Gaetana_Agnesi.jpg">Wikimedia</a></span>
</figcaption>
</figure>
<p>Agnesi found a special appeal in mathematics. Most knowledge derived from experience, she believed, is fallible and open to dispute. From mathematics, however, come truths that are wholly certain, the contemplation of which brings particularly great joy. In <a href="http://users.metu.edu.tr/e128415/project/maria.htm">writing her textbook</a>, she was not only teaching a useful skill, but opening to her students the door to such contemplation.</p>
<p>Published in two volumes in 1748, Agnesi’s work was entitled the “<a href="https://books.google.com/books?id=o54AAAAAMAAJ&pg=PR3#v=onepage&q&f=false">Basic Principles of Analysis</a>.” It was composed not in Latin, as was the custom for great mathematicians such as Newton and Euler, but Italian vernacular, to make it more accessible to students.</p>
<p>Hers represented one of the first textbooks in the relatively new field of calculus. It helped to shape the education of mathematics students for several generations that followed. Beyond Italy, <a href="https://en.wikisource.org/wiki/1911_Encyclop%C3%A6dia_Britannica/Agnesi,_Maria_Gaetana">contemporary scholars</a> in Paris and Cambridge translated the textbook for use in their university classrooms. </p>
<p>Agnesi’s textbook was praised in 1749 by the <a href="http://home.adelphi.edu/%7Ebradley/HOMSIGMAA/agnesi.pdf">French Academy</a>: “It took much skill and sagacity to reduce to almost uniform methods discoveries scattered among the works of many mathematicians very different from each other. Order, clarity, and precision reign in all parts of this work. … We regard it as the most complete and best made treatise.”</p>
<p>In offering similarly fine words of praise, another contemporary mathematician, <a href="http://web.calstatela.edu/sgray/Agnesi/Nun/Nun.html">Jean-Etienne Montucla</a>, also revealed some of the mathematical sexism that persists down to the present day. He wrote: “We cannot but behold with the greatest astonishment how a person of a sex that seems so little fitted to tread the thorny paths of these abstract sciences penetrates so deeply as she has done into all the branches of algebra.”</p>
<p>Agnesi dedicated the “Basic Principles” to Empress <a href="http://www.dw.com/en/what-made-austrias-maria-theresa-a-one-of-a-kind-ruler/a-37935974">Maria Theresa of Austria</a>, who acknowledged the favor with a letter of thanks and a diamond-bearing box and ring. Pope Benedict XIV praised the work and predicted that it would enhance the reputation of the Italians. He also appointed her to the chair of mathematics at the University of Bologna, though she never traveled there to accept it.</p>
<h2>A life of service</h2>
<p>A passionate advocate for the education of women and the poor, Agnesi believed that the natural sciences and math should play an important role in an educational curriculum. As a person of deep religious faith, however, she also believed that scientific and mathematical studies must be viewed in the larger context of God’s plan for creation.</p>
<p>When Maria’s father died in 1752, she was free to answer a religious calling and devote herself to her other great passion: service to the poor, sick and homeless. She began by founding a small hospital in her home. She eventually gave away her wealth, including the gifts she had received from the empress. When she died at age 80, she was buried in a <a href="https://jhupbooks.press.jhu.edu/content/world-maria-gaetana-agnesi-mathematician-god">pauper’s grave</a>. </p>
<p>To this day, some mathematicians express surprise at Maria’s apparent turn from learning and mathematics to a religious vocation. To her, however, it made perfect sense. In her view, human beings are capable of both knowing and loving, and while it is important for the mind to marvel at many truths, it’s ultimately even more important for the heart to be moved by love.</p>
<p>“Man always acts to achieve goals; the goal of the Christian is the glory of God,” she <a href="http://www.vofoundation.org/faith-and-science/maria-gaetana-agnesi-mathematics-making-catholic-enlightenment/">wrote</a>. “I hope my studies have brought glory to God, as there were useful to others, and derived from obedience, because that was my father’s will. Now I have found better ways and means to serve God, and to be useful to others.”</p>
<p>Though few remember Agnesi today, her pioneering role in the history of mathematics serves as an inspiring story of triumph over gender stereotypes. She helped to blaze a trail for women in math and science for generations to follow. Agnesi excelled at math, but she also loved it, perceiving in its mastery an opportunity to serve both her fellow human beings and a higher order.</p><img src="https://counter.theconversation.com/content/94378/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 organization that would benefit from this article, and have disclosed no relevant affiliations beyond their academic appointment.</span></em></p>May 16 marks the 300th anniversary of the first woman to write a mathematics textbook.Richard Gunderman, Chancellor's Professor of Medicine, Liberal Arts, and Philanthropy, Indiana UniversityDavid Gunderman, Lillian Gilbreth Postdoctoral Fellow, Purdue UniversityLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/898992018-01-24T23:47:22Z2018-01-24T23:47:22ZWhy all children must learn their times tables — and fun ways to teach them<figure><img src="https://images.theconversation.com/files/203009/original/file-20180123-182973-17niiyh.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">To break down the "math barrier" that has been shown to limit success in school, career and life, all children must learn their times tables. </span> <span class="attribution"><span class="source">(Shutterstock)</span></span></figcaption></figure><p>Recently, I was asked by a parent how old children should be to learn how to multiply numbers. He was shocked when I said that children in kindergarten may be experts in multiplication. </p>
<p>It’s not uncommon for young children to recite preliminary “times tables” as they “skip count” aloud. “Two, four, six, eight, 10” and “three, six, nine, 12” are among the first steps in learning about multiples. </p>
<p>In fact, adults can support skip counting by using two tools found in every home: A calculator and a clock. </p>
<p>Your child can “teach” the calculator to skip count by four, for example, simply by entering “4” on the calculator, next pressing “+” and “4” and then pressing the equal sign repeatedly. </p>
<p>You can follow along as the display changes from four to eight to 12 to 16 to 20, representing the multiples of four in the four times table. To count by six (or any other number), just change the starting number and the first addition number. </p>
<p>Alternately, you and your child can discover the five times table on the face of an analog clock. It’s easy because the clock has five minute increments and is numbered from one to 12. The number of minutes correspond to the multiplication fact, so, for example, <em>5 X 5 = 25</em>. This also helps children learn to read time.</p>
<h2>Creating muscle memory in the brain</h2>
<p>These “kitchen table” family math activities are examples of strategies that offer repeated practice while making the task of learning the times tables more fun and engaging. </p>
<figure class="align-right ">
<img alt="" src="https://images.theconversation.com/files/202946/original/file-20180123-182948-15himt5.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/202946/original/file-20180123-182948-15himt5.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=581&fit=crop&dpr=1 600w, https://images.theconversation.com/files/202946/original/file-20180123-182948-15himt5.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=581&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/202946/original/file-20180123-182948-15himt5.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=581&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/202946/original/file-20180123-182948-15himt5.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=730&fit=crop&dpr=1 754w, https://images.theconversation.com/files/202946/original/file-20180123-182948-15himt5.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=730&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/202946/original/file-20180123-182948-15himt5.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=730&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Parents can help their children discover the five times tables using an analogue clock.</span>
</figcaption>
</figure>
<p>More importantly, these and other “Let’s Play Math” fact games serve to <a href="https://mathmo.co.nz/2014/05/05/automaticity-times-tables/">create “muscle memory” in the brain</a>, simultaneously making it possible for students to retain their number facts and laying the groundwork for more complicated computations and applications down the road.</p>
<p>Familiarity and proficiency with the basic times tables are an essential building block in math. </p>
<p>It opens the door to multi-digit multiplication and demystifies processes like long division and simplifying fractions. It lays the foundation for algebra.</p>
<h2>‘Math makes sense’ approach</h2>
<p>At workshops, I often ask teachers and parents to look at the following examples of student work from <a href="https://deborahloewenbergball.com/projects-intro/">education scholar Deborah Ball</a>. I ask them to identify which of these students would they judge to be using a method that could be used to multiply ANY two numbers and explain why.</p>
<figure class="align-right ">
<img alt="" src="https://images.theconversation.com/files/203087/original/file-20180123-33567-9160bw.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/203087/original/file-20180123-33567-9160bw.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=465&fit=crop&dpr=1 600w, https://images.theconversation.com/files/203087/original/file-20180123-33567-9160bw.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=465&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/203087/original/file-20180123-33567-9160bw.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=465&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/203087/original/file-20180123-33567-9160bw.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=584&fit=crop&dpr=1 754w, https://images.theconversation.com/files/203087/original/file-20180123-33567-9160bw.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=584&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/203087/original/file-20180123-33567-9160bw.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=584&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption"></span>
</figcaption>
</figure>
<p>In the first case, <em>Student A</em> multiplies from the top down, from right to left: </p>
<p><em>5 X 25 = 125</em> and <em>3(0) X 25 = 75(0)</em>. </p>
<p>Fortunately, the student gets the right answer, largely due in part to the simple multiplications (students relate multiplying <em>25</em> to using 25 cent coins) and because she positioned the <em>75</em> correctly. </p>
<figure class="align-right ">
<img alt="" src="https://images.theconversation.com/files/203088/original/file-20180123-33560-1cwtroz.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/203088/original/file-20180123-33560-1cwtroz.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=465&fit=crop&dpr=1 600w, https://images.theconversation.com/files/203088/original/file-20180123-33560-1cwtroz.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=465&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/203088/original/file-20180123-33560-1cwtroz.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=465&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/203088/original/file-20180123-33560-1cwtroz.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=584&fit=crop&dpr=1 754w, https://images.theconversation.com/files/203088/original/file-20180123-33560-1cwtroz.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=584&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/203088/original/file-20180123-33560-1cwtroz.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=584&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption"></span>
</figcaption>
</figure>
<p><em>Student B</em> multiplies from right to left: </p>
<p><em>5 X 35</em> (mentally calculating <em>2 X 35 = 70</em>, so <em>4 X 35 = 140</em>, so <em>5 X 35 = 140 + 35 or 175</em>) and <em>20 X 35 (getting 700)</em> then adds the partial sums together to get the final product. </p>
<p>The strategy produces a “right answer” but the student’s “work” is not transparent.</p>
<figure class="align-right ">
<img alt="" src="https://images.theconversation.com/files/203089/original/file-20180123-33551-1jxqjqc.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/203089/original/file-20180123-33551-1jxqjqc.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=624&fit=crop&dpr=1 600w, https://images.theconversation.com/files/203089/original/file-20180123-33551-1jxqjqc.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=624&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/203089/original/file-20180123-33551-1jxqjqc.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=624&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/203089/original/file-20180123-33551-1jxqjqc.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=785&fit=crop&dpr=1 754w, https://images.theconversation.com/files/203089/original/file-20180123-33551-1jxqjqc.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=785&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/203089/original/file-20180123-33551-1jxqjqc.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=785&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption"></span>
</figcaption>
</figure>
<p><em>Student C</em> uses a step-by-step place value process that will ALWAYS work: </p>
<p>The student multiplies <em>5 X 5</em>, then <em>5 X 30</em>, then <em>20 X 5</em> and <em>20 X 30</em> to get <em>25 + 150 + 100 + 600</em> which sums to <em>875</em>.</p>
<p>This “math makes sense” approach to multi-digit multiplication (also called the “partial products method”) appeals to students because it values their prior learning by putting their basic number facts to use, logically and efficiently. </p>
<p>It does not require any unnecessary “carry the one and move to the left, adding zeroes as place holders” line-by-line rules, and it is universal. </p>
<p>It works for numbers of any magnitude because of its mathematical simplicity, elegance and, most importantly, generalizability. </p>
<h2>Eyes on the future</h2>
<figure class="align-right ">
<img alt="" src="https://images.theconversation.com/files/202954/original/file-20180123-182976-1a65eqk.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/202954/original/file-20180123-182976-1a65eqk.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=444&fit=crop&dpr=1 600w, https://images.theconversation.com/files/202954/original/file-20180123-182976-1a65eqk.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=444&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/202954/original/file-20180123-182976-1a65eqk.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=444&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/202954/original/file-20180123-182976-1a65eqk.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=558&fit=crop&dpr=1 754w, https://images.theconversation.com/files/202954/original/file-20180123-182976-1a65eqk.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=558&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/202954/original/file-20180123-182976-1a65eqk.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=558&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Table.</span>
</figcaption>
</figure>
<figure class="align-right ">
<img alt="" src="https://images.theconversation.com/files/202955/original/file-20180123-182962-1ibfvb5.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/202955/original/file-20180123-182962-1ibfvb5.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=340&fit=crop&dpr=1 600w, https://images.theconversation.com/files/202955/original/file-20180123-182962-1ibfvb5.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=340&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/202955/original/file-20180123-182962-1ibfvb5.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=340&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/202955/original/file-20180123-182962-1ibfvb5.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=428&fit=crop&dpr=1 754w, https://images.theconversation.com/files/202955/original/file-20180123-182962-1ibfvb5.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=428&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/202955/original/file-20180123-182962-1ibfvb5.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=428&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Grid.</span>
</figcaption>
</figure>
<figure class="align-right ">
<img alt="" src="https://images.theconversation.com/files/202956/original/file-20180123-182941-8l3vjq.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/202956/original/file-20180123-182941-8l3vjq.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=509&fit=crop&dpr=1 600w, https://images.theconversation.com/files/202956/original/file-20180123-182941-8l3vjq.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=509&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/202956/original/file-20180123-182941-8l3vjq.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=509&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/202956/original/file-20180123-182941-8l3vjq.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=640&fit=crop&dpr=1 754w, https://images.theconversation.com/files/202956/original/file-20180123-182941-8l3vjq.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=640&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/202956/original/file-20180123-182941-8l3vjq.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=640&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Algebra.</span>
</figcaption>
</figure>
<p>The mathematicians and education researchers who have helped classroom teachers to implement this straightforward computational procedure are eager to emphasize that their enthusiasm is due, in part, to their “eyes on the future” — focused on secondary and post-secondary mathematics.</p>
<p>The “place value” model for multi-digit multiplication (which works left to right or right to left) can be represented visually using the “area” model of multiplication.</p>
<p>As students move through the grades, the “area” model of multiplication becomes increasingly important.</p>
<p>The transition from … </p>
<ol>
<li><p>Table [<em>(100 + 40 + 3) X (20 + 7)</em>] to </p></li>
<li><p>Grid [<em>(40 + 8) X (20 + 6)</em>] to </p></li>
<li><p>Algebra [<em>(x + 3) X (x + 2)</em>] </p></li>
</ol>
<p>… follows a natural progression with respect to mathematical sophistication.</p>
<h2>Breaking the math barrier</h2>
<p>Recently, we have seen many “pro” mathematics movements across the continent and the globe: For example, <a href="https://www.amazon.com/gp/withmathican">With Math I Can</a> and <a href="https://www.theglobalmathproject.org/">The Global Math Project</a>. </p>
<p>In these, we have seen a renewed emphasis for efforts to support ALL children to be successful mathematics learners, and, by so doing, <a href="http://www.dreambox.com/blog/the-math-barrier-an-unfortunate-reality">break down the math barrier that has been shown to limit success in school, career and life</a>.</p>
<p>For that to be possible, all children must learn their times tables. </p>
<p>Being able to recall basic facts efficiently is a necessary first step in the development of more advanced skills for computational fluency with larger numbers and algebraic expressions. </p>
<p>Diagrams, charts, procedural models and representations using concrete materials like algebra tiles (which are the visual and concrete descriptions of the multiplication of multidigit numbers and algebraic terms) are only possible when place value applications as well as number properties and patterns can be put into operation (figuratively and literally) by students. </p>
<p>And that requires students to understand connections by appreciating the meaning, significance and application of even the simplest number fact in computing a correct calculation. </p>
<p>And that means that elementary school multiplication is anything but elementary.</p><img src="https://counter.theconversation.com/content/89899/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Lynda Colgan receives funding from The Ministry of Education for the Province of Ontario and The Mathematics Knowledge Network (KNAER). </span></em></p>Parents can teach very young children to “skip count” at the kitchen table, and it will set them up to be successful math learners throughout their secondary and post-secondary education.Lynda Colgan, Professor of Elementary Mathematics, Queen's University, OntarioLicensed as Creative Commons – attribution, no derivatives.