tag:theconversation.com,2011:/us/topics/math-teaching-48882/articlesMath teaching – The Conversation2023-08-17T12:34:54Ztag:theconversation.com,2011:article/2111712023-08-17T12:34:54Z2023-08-17T12:34:54Z3 reasons we use graphic novels to teach math and physics<figure><img src="https://images.theconversation.com/files/542875/original/file-20230815-20-jxi8dm.jpg?ixlib=rb-4.1.0&rect=10%2C0%2C2393%2C1061&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Graphic novels can help make math and physics more accessible for students, parents or teachers in training.</span> <span class="attribution"><a class="source" href="https://www.gettyimages.com/detail/photo/education-concept-science-technology-reading-books-royalty-free-image/1201355144?adppopup=true">Metamorworks/iStock via Getty Images</a></span></figcaption></figure><p>Post-pandemic, some educators are trying to reengage students with technology – like videos, <a href="https://theconversation.com/video-gaming-can-bolster-classroom-learning-but-not-without-teacher-support-190483">computer gaming</a> or artificial intelligence, just to name a few. But integrating these approaches in the classroom can be an uphill battle. Teachers using these tools often struggle to retain students’ attention, competing with the latest social media phenomenon, and can feel limited by using short video clips to get concepts across. </p>
<p>Graphic novels – offering visual information married with text – provide a means to engage students without losing all of the rigor of textbooks. As two educators <a href="https://www.sarahklanderman.com/">in math</a> <a href="https://www.joshaho.com/">and physics</a>, we have found graphic novels to be effective at teaching students of all ability levels. We’ve used graphic novels in our own classes, and we’ve also inspired and encouraged other teachers to use them. And we’re not alone: Other teachers are rejuvenating this analog medium with a <a href="https://doi.org/10.1353/jeu.2014.0018">high level of success</a>.</p>
<p>In addition to <a href="https://gnclassroom.com/">covering a wide range of topics and audiences</a>, graphic novels can explain tough topics without alienating student averse to STEM – science, technology, engineering and math. Even for students who already like math and physics, graphic novels provide a way to dive into topics beyond what is possible in a time-constrained class. In our book “<a href="http://bloomsbury.com/uk/using-graphic-novels-in-the-stem-classroom-9781350279186/">Using Graphic Novels in the STEM Classroom</a>,” we discuss the many reasons why graphic novels have a unique place in math and physics education. Here are three of those reasons:</p>
<h2>Explaining complex concepts with rigor and fun</h2>
<p>Increasingly, schools are <a href="https://theconversation.com/textbooks-in-the-digital-world-78299">moving away from textbooks</a>, even though studies show that students learn better <a href="https://theconversation.com/the-enduring-power-of-print-for-learning-in-a-digital-world-84352">using print rather than digital formats</a>. Graphic novels offer the best of both worlds: a hybrid between modern and traditional media.</p>
<p>This integration of text with images and diagrams is especially <a href="https://theconversation.com/heroes-villains-biology-3-reasons-comic-books-are-great-science-teachers-143251">useful in STEM disciplines</a> that require quantitative reading and data analysis skills, like math and physics.</p>
<p>For example, our collaborator <a href="https://www.dordt.edu/people/jason-ho">Jason Ho, an assistant professor at Dordt University</a>, uses “<a href="https://maxthedemon.com">Max the Demon Vs Entropy of Doom</a>” to teach his physics students about entropy. This topic can be particularly difficult for students because it’s one of the first times when they can’t physically touch something in physics. Instead, students have to rely on math and diagrams to fill in their knowledge.</p>
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<p>Rather than stressing over equations, Ho’s students focus on understanding the subject more conceptually. This approach helps build their intuition before diving into the algebra. They get a feeling for the fundamentals before they have to worry about equations.</p>
<p>After having taken Ho’s class, more than <a href="https://acmsonline.org/wp-content/uploads/2023/05/journal-and-proceedings-2023.pdf">85% of his students agreed</a> that they would recommend using graphic novels in STEM classes, and <a href="https://acmsonline.org/conferences/">90% found this particular use</a> of “Max the Demon” helpful for their learning. When strategically used, graphic novels can create a dynamic, engaging teaching environment even with nuanced, quantitative topics.</p>
<h2>Combating quantitative anxiety</h2>
<p>Students learning math and physics today are surrounded by <a href="https://theconversation.com/think-youre-bad-at-math-you-may-suffer-from-math-trauma-104209">math anxiety and trauma</a>, which often lead to their own negative associations with math. A student’s perception of math can be influenced by the attitudes of the role models around them – whether it’s <a href="https://theconversation.com/when-parents-with-high-math-anxiety-help-with-homework-children-learn-less-46841">a parent who is “not a math person”</a> or <a href="https://doi.org/10.20429/ijsotl.2021.150213">a teacher with a high level of math anxiety</a>.</p>
<p>Graphic novels can help make math more accessible not only for students themselves, but also for parents or students learning to be teachers.</p>
<p>In a geometry course one of us (Sarah) teaches, secondary education students don’t memorize formulas and fill out problem sheets. Instead, students read “<a href="https://gnclassroom.com/graphic-novel/who-killed-professor-x/">Who Killed Professor X?</a>”, a murder mystery in which all of the suspects are famous mathematicians. The suspects’ alibis are justified through problems from geometry, algebra and pre-calculus.</p>
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<iframe width="440" height="260" src="https://www.youtube.com/embed/vATkt9xuA44?wmode=transparent&start=27" frameborder="0" allowfullscreen=""></iframe>
<figcaption><span class="caption">A peak inside the mathematical graphic novel ‘Who Killed Professor X?’.</span></figcaption>
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<p>While trying to understand the hidden geometry of suspect relationships, students often forget that they are doing math – focusing instead on poring over secret hints and notes needed to solve the mystery. </p>
<p>Although this is just one experience for these students, it can help change the narrative for students experiencing mathematical anxiety. It boosts their confidence and shows them how math can be fun – a lesson they can then impart to the next generation of students.</p>
<h2>Helping students learn and readers dream big</h2>
<p>In addition to being viewed favorably by students, graphic novels can enhance student learning by improving <a href="http://repository.unej.ac.id/handle/123456789/97529">written communication skills</a>, <a href="http://dx.doi.org/10.1002/jaal.666">reading comprehension</a> and <a href="https://doi.org/10.1598/JAAL.53.2.5">critical literacy skills</a>. And even outside the classroom, graphic novels support long-term memory for those who have diagnoses like <a href="https://doi.org/10.1080/21504857.2019.1635175">dyslexia</a>. </p>
<p>Pause and think about your own experience – how do you learn about something new in science? </p>
<p>If you’re handed a textbook, it’s extremely unlikely that you’d read it cover to cover. And although the internet offers an enormous amount of math and physics content, it can be overwhelming to sift through hours and hours of videos to find the perfect one to get the “aha!” moment in learning.</p>
<p>Graphic novels provide a starting point for such <a href="https://gnclassroom.com/">a broad range of niche topics</a> that it’s impossible for anyone to be experts in them all. Want to learn about programming? Try the “<a href="https://gnclassroom.com/graphic-novel/secret-coders/">Secret Coders</a>” series. Want to understand more about quantum physics? Dive into “<a href="https://gnclassroom.com/graphic-novel/suspended-in-language/">Suspended in Language: Niels Bohr’s life, discoveries, and the century he shaped</a>.” Searching for more female role models in science? “<a href="https://gnclassroom.com/graphic-novel/astronauts-women-on-the-final-frontier/">Astronauts: Women on the Final Frontier</a>” could be just what you’re looking for.</p>
<p>With all that they offer, graphic novels provide a compelling list of topics and narratives that can capture the attention of students today. We believe that the right set of graphic novels can inspire the next generation of scientists as much as any single individual can.</p><img src="https://counter.theconversation.com/content/211171/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>Graphic novels pair text and images to explain complex topics – from thermodynamics to abstract math – without alienating STEM-averse students.Sarah Klanderman, Assistant Professor of Mathematics, Marian UniversityJosha Ho, Adjunct Professor of Mathematics and Computer Science, Marian 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-4.1.0&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>
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<img alt="Three seashells are shown under the words " src="https://images.theconversation.com/files/518209/original/file-20230329-24-bfj94q.png?ixlib=rb-4.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/518209/original/file-20230329-24-bfj94q.png?ixlib=rb-4.1.0&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-4.1.0&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-4.1.0&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-4.1.0&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-4.1.0&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-4.1.0&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/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-4.1.0&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>
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<img alt="" src="https://images.theconversation.com/files/332071/original/file-20200501-42942-wr4tlc.jpg?ixlib=rb-4.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/332071/original/file-20200501-42942-wr4tlc.jpg?ixlib=rb-4.1.0&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-4.1.0&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-4.1.0&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-4.1.0&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-4.1.0&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-4.1.0&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">In today’s mathematics classrooms, discussion is important.</span>
<span class="attribution"><span class="source">(Shutterstock)</span></span>
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<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>
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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>
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</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-4.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/332073/original/file-20200501-42951-pxpcn5.jpg?ixlib=rb-4.1.0&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-4.1.0&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-4.1.0&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-4.1.0&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-4.1.0&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-4.1.0&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-4.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/327316/original/file-20200412-10562-6mjs1u.jpg?ixlib=rb-4.1.0&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-4.1.0&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-4.1.0&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-4.1.0&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-4.1.0&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-4.1.0&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/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-4.1.0&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-4.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/245588/original/file-20181114-172710-10g65c6.jpg?ixlib=rb-4.1.0&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-4.1.0&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-4.1.0&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-4.1.0&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-4.1.0&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-4.1.0&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/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-4.1.0&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-4.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/202946/original/file-20180123-182948-15himt5.jpg?ixlib=rb-4.1.0&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-4.1.0&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-4.1.0&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-4.1.0&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-4.1.0&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-4.1.0&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-4.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/203087/original/file-20180123-33567-9160bw.jpg?ixlib=rb-4.1.0&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-4.1.0&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-4.1.0&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-4.1.0&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-4.1.0&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-4.1.0&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-4.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/203088/original/file-20180123-33560-1cwtroz.jpg?ixlib=rb-4.1.0&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-4.1.0&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-4.1.0&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-4.1.0&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-4.1.0&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-4.1.0&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-4.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/203089/original/file-20180123-33551-1jxqjqc.jpg?ixlib=rb-4.1.0&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-4.1.0&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-4.1.0&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-4.1.0&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-4.1.0&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-4.1.0&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-4.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/202954/original/file-20180123-182976-1a65eqk.jpg?ixlib=rb-4.1.0&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-4.1.0&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-4.1.0&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-4.1.0&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-4.1.0&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-4.1.0&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-4.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/202955/original/file-20180123-182962-1ibfvb5.jpg?ixlib=rb-4.1.0&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-4.1.0&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-4.1.0&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-4.1.0&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-4.1.0&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-4.1.0&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-4.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/202956/original/file-20180123-182941-8l3vjq.jpg?ixlib=rb-4.1.0&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-4.1.0&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-4.1.0&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-4.1.0&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-4.1.0&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-4.1.0&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.