tag:theconversation.com,2011:/au/topics/math-problem-16215/articlesMath problem – The Conversation2021-07-29T12:24:04Ztag:theconversation.com,2011:article/1651492021-07-29T12:24:04Z2021-07-29T12:24:04ZBob Moses played critical role in civil rights organizing and math literacy for Black students<figure><img src="https://images.theconversation.com/files/413595/original/file-20210728-13-mlpe5w.jpg?ixlib=rb-1.1.0&rect=14%2C9%2C3244%2C2433&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Civil rights activist Bob Moses founded The Algebra Project to help Black students develop strong math skills.</span> <span class="attribution"><a class="source" href="https://www.flickr.com/photos/princetonpubliclibrary/15627635898">Princeton Public Library/Flickr</a>, <a class="license" href="http://creativecommons.org/licenses/by-nd/4.0/">CC BY-ND</a></span></figcaption></figure><p>As an organizer for the <a href="https://snccdigital.org/inside-sncc/the-story-of-sncc/">Student Nonviolent Coordinating Committee</a> during the 1960s, <a href="https://snccdigital.org/people/bob-moses/">Bob Moses</a> traveled to the most dangerous parts of Mississippi to help African Americans end segregation and secure the right to vote. But it would be tutoring students in math 20 years later at his daughter’s racially mixed middle school in Massachusetts that would lead to his life’s work – The Algebra Project.</p>
<p><a href="https://snccdigital.org/events/bob-moses-begins-algebra-project/">The Algebra Project</a> is a nonprofit dedicated to helping students from historically marginalized communities develop math literacy, which is an individual’s ability to formulate, employ and interpret mathematics in a variety of contexts. Moses founded it in 1982.</p>
<p>After researching Moses’ role in the civil rights movement for my book – <a href="https://nyupress.org/9780814743317/bloody-lowndes/">“Bloody Lowndes: Civil Rights and Black Power in Alabama’s Black Belt”</a> – and later interviewing him for various projects about SNCC, it became abundantly clear that The Algebra Project sprang directly from his civil rights work in Mississippi. That work helped transform Mississippi from a segregationist stronghold into a focal point of the civil rights revolution.</p>
<p>In his book “<a href="https://www.penguinrandomhouse.com/books/206027/radical-equations-by-robert-p-moses/">Radical Equations</a>,” Moses recalls that in 1982 he was surprised to discover that his daughter, Maisha, who was entering the eighth grade at the Dr. Martin Luther King, Jr. School in Cambridge, Massachusetts, would not be taught algebra because the school did not offer it. Without knowledge of algebra, she could not qualify for honors math and science classes in high school.</p>
<h2>Math endeavors</h2>
<p>As explained in his book, Moses had a background in mathematics. In 1957, before joining the civil rights movement, he earned a master’s degree in philosophy at Harvard University and then taught middle school math for a few years in the Bronx, New York, at Horace Mann School, a prestigious private school just north of where he grew up in Harlem. And from 1969 to 1976, he taught algebra in Tanzania before returning stateside to work on a doctorate in the philosophy of math.</p>
<p>Moses asked Maisha’s teacher if he could provide his daughter with supplemental math lessons in class since Maisha refused to be tutored at home – she opposed doing what she called “two maths.” The teacher consented, but on the condition that Moses instruct some of Maisha’s classmates as well, according to his book.</p>
<p>Moses agreed. Like the teacher, he believed that all children, including those from historically marginalized communities, deserved a chance to take advanced math and science classes in high school.</p>
<p>At the end of the school year, Maisha and the three students who studied with her passed the citywide algebra exam. They were the first from their school to do so, according to his book.</p>
<p>Excited by this success, Maisha’s teacher asked Moses to work his math magic with more students. </p>
<p>But it wasn’t magic.</p>
<p>Moses succeeded in teaching algebra to the students who were frequently <a href="https://files.eric.ed.gov/fulltext/EJ1250375.pdf">tracked</a> into less rigorous classes and courses of study because he believed that Black, brown, working-class and poor children could master algebra - or other advanced classes - even at an early age.</p>
<p>He also knew that these same students would be eager to study math if instruction revolved around their lived experiences. Rote memorization would not work; content had to be relatable.</p>
<p>Moses agreed to teach the incoming eighth graders, even though none of his children were in the class. “I was beginning to think I had found my work,” he wrote in “Radical Equations.” And his work was teaching math literacy in the emerging digital age.</p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/413604/original/file-20210728-17-1a4o3t7.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="A Black boy works on a math problem in class." src="https://images.theconversation.com/files/413604/original/file-20210728-17-1a4o3t7.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/413604/original/file-20210728-17-1a4o3t7.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/413604/original/file-20210728-17-1a4o3t7.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/413604/original/file-20210728-17-1a4o3t7.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/413604/original/file-20210728-17-1a4o3t7.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/413604/original/file-20210728-17-1a4o3t7.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/413604/original/file-20210728-17-1a4o3t7.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=503&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Math literacy for African American children was an essential aspect of Moses’ philosophy and work.</span>
<span class="attribution"><a class="source" href="https://www.gettyimages.com/detail/photo/african-american-student-studying-at-desk-in-royalty-free-image/135205410?adppopup=true">Ariel Skelley/DigitalVision via Getty Images</a></span>
</figcaption>
</figure>
<h2>Key to a better life</h2>
<p>Moses believed that math proficiency was a gateway to equality in a post-industrial society. <a href="https://www.npr.org/templates/story/story.php?storyId=7495586">He explained in 2007</a>: “In our society, algebra is the place where we ask students to master a quantitative literacy requirement. And so hence, algebra becomes available as an organizing tool now for educational rights and for economic rights.” In other words, math literacy would provide access to the kinds of computer-driven careers that would enable African Americans, and other historically marginalized youth, to permanently improve their life circumstances and the social and economic conditions of their communities.</p>
<p>But Moses wasn’t interested in teaching just a few students, much as he wasn’t interested in registering just a few Black Mississippians. He wanted to instruct as many young people as possible, in the same way he wanted to organize as many Black people in Mississippi as possible. </p>
<p>Reaching more youth, however, required a dramatic shift in the culture of learning at the school. Expectations regarding when young children from marginalized groups should study algebra had to change, which was no small task considering many children weren’t expected to study algebra at all. </p>
<p>Just as he once organized sharecroppers, he began organizing parents.</p>
<h2>Emphasis on independence</h2>
<p>In the civil rights movement, Moses routinely deferred to the wishes and desires of the people he was organizing, so much so that he left the movement in 1965 when he felt people were turning to him too often for solutions to their problems. This was the approach of his mentor, veteran activist and SNCC adviser <a href="https://uncpress.org/book/9780807856161/ella-baker-and-the-black-freedom-movement/">Ella Baker</a>, who led by asking questions, rather than by providing answers. </p>
<p>Moses talked to parents at the school about the lack of opportunities to take algebra, which, he recalled, led them to initiate a survey that showed that – as explained in his book – “All parents thought their child should do algebra, but not all parents thought that every child should do algebra.” </p>
<p>The parents were shocked and somewhat embarrassed by the survey results, leading to a consensus for allowing any seventh or eighth grader to take algebra. </p>
<p>Only two years after Moses’ daughter passed the citywide exam, the King school offered algebra to students in the seventh and eighth grades, and even provided Saturday classes for parents. </p>
<p>Today, The Algebra Project is fighting to ensure students receive the quality math education they deserve by supporting learning cohorts in dozens of schools across the country where students have historically performed poorly in math on eighth grade state tests. The impact of the project at Mansfield Senior High School in Mansfield, Ohio, is <a href="https://www.mansfieldnewsjournal.com/story/news/local/2016/12/20/students-talk-math-algebra-project-founder/95654378/">illustrative</a>. In the eighth grade, the math proficiency of The Algebra Project cohort was 17%. By the 10th grade, that number had <a href="https://iris.siue.edu/math-literacy-archive/files/original/82b7ceef4d303db77a55e7b34e9b6412.pdf">risen to 82%</a>.</p>
<p>Ella Baker was fond of saying, “Give light and people will find the way.” Few did that better than Bob Moses, who died on July 25, 2021. </p>
<p>[<em>Get the best of The Conversation, every weekend.</em> <a href="https://theconversation.com/us/newsletters/weekly-highlights-61?utm_source=TCUS&utm_medium=inline-link&utm_campaign=newsletter-text&utm_content=weeklybest">Sign up for our weekly newsletter</a>.]</p><img src="https://counter.theconversation.com/content/165149/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Hasan Kwame Jeffries 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>The Algebra Project – a long-standing initiative to teach algebra to Black students who might not otherwise take it – sprang from Bob Moses’ work as a civil rights activist, a historian recounts.Hasan Kwame Jeffries, Associate Professor of History, The Ohio State UniversityLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/825522017-09-12T02:18:56Z2017-09-12T02:18:56ZThese four easy steps can make you a math whiz<figure><img src="https://images.theconversation.com/files/184994/original/file-20170906-9830-3mf2kc.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Can you cut it in this math problem?</span> <span class="attribution"><a class="source" href="https://www.shutterstock.com/image-photo/camembert-cheese-brie-575682340">Sergey Lapin/shutterstock.com</a></span></figcaption></figure><p>Many people find mathematics daunting. If true, this piece is for you. If not, this piece is still for you.</p>
<p>What do you think of when you think about mathematics? Perhaps you think about x’s and y’s, intractable fractions, or nonsensical word problems. The cartoonist Gary Larson once depicted hell’s library as containing only giant tomes of word problems. You know, “If a train leaves New York…” </p>
<p>I was trained as a mathematician, and I will let you in on a trade secret: That is not what mathematics is, nor where it lives. It’s true that learning mathematics often involves solving problems, but it should focus on the joy of solving puzzles, rather than memorizing rules. </p>
<p>I invite you to see yourself as a problem solver and mathematician. And I’d like to introduce you to the man who once invited me to the study of problem solving: George Pólya. </p>
<h1>Math Pólya’s way</h1>
<p>For many reasons, not the least of which is that Pólya <a href="http://articles.latimes.com/1985-09-08/news/mn-2892_1_polya-george-mathematician">died</a> in 1985, you will meet him as I did – through his wildly successful <a href="http://press.princeton.edu/titles/669.html">“How to Solve It</a>.” Penned in 1945, this book went on to sell over one million copies and was translated into 17 languages. </p>
<p>As a mathematician, Pólya worked on a wide range of problems, including the study of heuristics, or how to solve problems. When you read “How to Solve It,” it feels like you’re taking a guided tour of Pólya’s mind. This is because his writing is metacognitive – he writes about how he thinks about thinking. And metacognition is often the heart of problem solving.</p>
<p>Pólya’s problem solving plan breaks down to four simple steps:</p>
<ol>
<li> Make sure you understand the problem.</li>
<li> Make a plan to solve the problem.</li>
<li> Carry out the plan.</li>
<li> Check your work to test your answer.</li>
</ol>
<p>There it is. Problem solving in the palm of your hand – math reduced to four steps.</p>
<p><a href="http://epltt.coe.uga.edu/index.php?title=Situated_Cognition">Here’s a classic problem</a> from research on mathematics education done by Jean Lave. A man, let’s call him John, is making ¾ of a recipe that calls for 2/3 cup of cottage cheese. What do you think John did? What would you do? </p>
<p>If you’re like me, you might immediately dive into calculations, perhaps struggling with what the fractions mean, working to remember the rules for arithmetic. That’s what John seemed to do, at first. But then he had a Eureka! moment.</p>
<p>John measured 2/3 cup of cottage cheese, then dumped it onto a cutting board. He patted the cheese into a circle and drew lines into it, one vertical, one horizontal, dividing the cheese patty into quarters. He then carefully pushed one quarter of the cottage cheese back into its container. Voilá! Three-quarters of 2/3 cup of cottage cheese remained. </p>
<p>John is a mathematician and problem solver. First, he understood the problem: He needed ¾ of what the recipe called for, which was 2/3 cup. Then, he made a plan, most likely visualizing in his head how he would measure and divide the cottage cheese. Finally, he carried out the plan. </p>
<p>Did he check his answer? That remains unclear, but we can check the validity of his work for him. Did he indeed end up with ¾ of 2/3 cup of cottage cheese? Yes, because the full amount was reduced by one-quarter, leaving three-quarters. </p>
<h1>Another approach</h1>
<p>Would this solution work with different foods or serving sizes? So long as a person could divide that serving into quarters, yes, the plan would work. </p>
<p>Could we solve the problem another way with the same result? Sure — there are many ways to solve this problem, and they should all result in the same half-cup answer. Here is one. </p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/185181/original/file-20170907-9603-cugdd3.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/185181/original/file-20170907-9603-cugdd3.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/185181/original/file-20170907-9603-cugdd3.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=265&fit=crop&dpr=1 600w, https://images.theconversation.com/files/185181/original/file-20170907-9603-cugdd3.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=265&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/185181/original/file-20170907-9603-cugdd3.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=265&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/185181/original/file-20170907-9603-cugdd3.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=333&fit=crop&dpr=1 754w, https://images.theconversation.com/files/185181/original/file-20170907-9603-cugdd3.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=333&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/185181/original/file-20170907-9603-cugdd3.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=333&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">How to find ¾ of 2/3.</span>
<span class="attribution"><span class="source">Jennifer Ruef</span>, <a class="license" href="http://creativecommons.org/licenses/by/4.0/">CC BY</a></span>
</figcaption>
</figure>
<p>Notice that this solution uses pictures. <a href="https://www.youcubed.org/downloads/?file_id=1584&file_name=jacmaths-seeing-article&resource_name=visual-math-article-in-journal-of-applied-computational-mathematics">New brain research</a> validates what mathematics educators have been saying for decades: Pictures help us think. Drawing pictures also happens to be another of Pólya’s suggestions.</p>
<p>John probably made use of one of Pólya’s most important suggestions: Can you think of a related problem?</p>
<p>Of course, this is a cheesy problem – sorry, I really didn’t even try to fight that pun – which is a common complaint about story problems. I chose it because it has delighted math researchers for years, and because John is quite clever in his solution. He is also extremely mathematical.</p>
<p>I’ve taught mathematics, and how to teach mathematics, for nearly 30 years. For over a decade, it was my job to convince high school freshmen not only that algebra was meaningful, but that it was meant for them, and they for it. In my work, I’ve met many people who love mathematics and many who find it overwhelming and nonsensical. And so it’s an important part of my work to help people see the beauty and wonder of mathematics, and think of themselves as mathematicians. </p>
<p>These <a href="https://www.youcubed.org/resources/parents-beliefs-math-change-childrens-achievement/">messages</a> are especially important for parents helping children learn mathematics. If you understand the problem you’re trying to solve, you’re well on your way to solving it. And you, yes you, are a problem solver.</p>
<p>We all know it’s not always so simple to solve problems. Pólya did too. That’s the glory of it – the messy, wonderful, powerful adventure.</p><img src="https://counter.theconversation.com/content/82552/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Jennifer Ruef 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>Dreading math class as you head back into school? Never fear: Try these tips from famed mathematician George Pólya.Jennifer Ruef, Assistant Professor of Education Studies, University of OregonLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/714322017-01-20T11:58:07Z2017-01-20T11:58:07ZWhy UPS drivers don’t turn left and you probably shouldn’t either<figure><img src="https://images.theconversation.com/files/153580/original/image-20170120-5260-h8r67a.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">
</span> <span class="attribution"><span class="source">Shutterstock</span></span></figcaption></figure><p>It might seem strange, but UPS delivery vans don’t always take the shortest route between stops. The company gives each driver a specific route to follow and that includes a policy that drivers should <a href="https://priceonomics.com/why-ups-trucks-dont-turn-left/">never turn through oncoming traffic</a> (that’s left in countries where they drive on the right and vice versa) unless absolutely necessary. This means that routes are sometimes longer than they have to be. So, why do they do it?</p>
<p>Every day, along with thousands of other companies, UPS solves versions of the <a href="http://neo.lcc.uma.es/vrp/vehicle-routing-problem/">vehicle routing problem</a>. In these mathematical problems, you are given a set of points and the distances between them, and you have to find the best route(s) to travel through all of them. Best is usually defined as the route with the shortest overall distance. </p>
<p>Vehicle routing problems are used to organise many things, from <a href="https://theconversation.com/more-online-shopping-means-more-delivery-trucks-are-cities-ready-67686">coping with more delivery trucks in cities</a> and <a href="http://dx.doi.org/10.1057/jors.2013.96">hailing taxis</a> to <a href="http://dx.doi.org/%2010.1023/A:1018951218434">catching chickens</a> on a farm. The concept was introduced by <a href="https://dx.doi.org/10.1287%2Fmnsc.6.1.80">George Dantzig</a> in 1959. Over 50 years later, and despite a large body of scientific research, scientists are still looking for new ways to <a href="https://theconversation.com/how-to-teach-deep-blue-to-play-poker-and-deliver-groceries-21707">tackle the problem</a>. </p>
<figure class="align-right ">
<img alt="" src="https://images.theconversation.com/files/153137/original/image-20170117-21167-cehp07.png?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/153137/original/image-20170117-21167-cehp07.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=398&fit=crop&dpr=1 600w, https://images.theconversation.com/files/153137/original/image-20170117-21167-cehp07.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=398&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/153137/original/image-20170117-21167-cehp07.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=398&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/153137/original/image-20170117-21167-cehp07.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=500&fit=crop&dpr=1 754w, https://images.theconversation.com/files/153137/original/image-20170117-21167-cehp07.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=500&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/153137/original/image-20170117-21167-cehp07.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=500&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Vehicle routing problems involve finding the best route between points.</span>
<span class="attribution"><span class="source">Wikipedia Commons</span></span>
</figcaption>
</figure>
<p>UPS have moved away from trying to find the shortest route and now look at other criteria to optimise the journey. One of their methods is to try and avoid turning through oncoming traffic at a junction. Although this might be going in the opposite direction of the final destination, it reduces the chances of an accident and cuts delays caused by waiting for a gap in the traffic, which would also waste fuel. </p>
<p>UPS have designed their vehicle routing software to eliminate as many left-hand turns as possible (in countries with right-hand traffic). Typically, only <a href="http://abcnews.go.com/WNT/story?id=3005890&page=1">10% of the turns are left turns</a>. As a result, the company claims it uses 10m gallons less fuel, emits 20,000 tonnes less carbon dioxide and delivers 350,000 more packages every year. The efficiency of planning routes with its navigation software this way has even helped the firm cut the number of trucks it uses by 1,100, bringing down the company’s total distance travelled by 28.5m miles – despite the longer routes.</p>
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<p>It seems incredible that not turning left can lead to such significant savings. The TV series Mythbusters tested this idea and confirmed that, despite many more turns, the policy of only turning right does save fuel. In their one truck experiment they travelled further, but when you scale this up to a global level, UPS really does <a href="http://abcnews.go.com/WNT/story?id=3005890&page=1">travel fewer miles</a> in total.</p>
<figure>
<iframe width="440" height="260" src="https://www.youtube.com/embed/ppCz4f1L9iU?wmode=transparent&start=0" frameborder="0" allowfullscreen=""></iframe>
</figure>
<p>The success of UPS’s policy raises the question, why don’t we all avoid turning left (or right, depending on what country we’re in), as we drive around cities on our daily commutes? If everyone did it, the carbon savings would be huge and there’d probably be far less congestion.</p>
<p>The problem is that not every journey would be made more efficient by following this strategy, and most people are likely only to change their driving style if they <a href="https://theconversation.com/big-data-shows-how-selfless-driving-could-ease-traffic-congestion-56166">personally benefit</a>.</p>
<h2>Driver’s dilemma</h2>
<p>As with anything related to reducing climate change, if everybody else did it then things would get better and you wouldn’t have to change your lifestyle at all to benefit. But it only needs a few people to not cooperate and the whole system breaks down.</p>
<p>This is a good example of the <a href="https://theconversation.com/the-legacy-of-john-nash-and-his-equilibrium-theory-42343">prisoner’s dilemma</a>, the famous game theory problem. If everybody cooperated then the system as a whole would be much better, but the best thing for an individual when everyone else is cooperating is to be uncooperative and reap the rewards of everybody else’s sacrifices.</p>
<p>So, if you cannot persuade people to always turn right (or left) for the benefit of everyone, it might be down to governments to encourage or even enforce the strategy. For example, we could plan roads that make it more difficult to turn through the traffic. It would take a brave city planner to implement this, but if UPS can save 10m gallons of fuel, how much could a whole city or even a whole country save?</p><img src="https://counter.theconversation.com/content/71432/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Graham Kendall 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>Going round in circles can actually make your journey more efficient.Graham Kendall, Professor of Computer Science and Provost/CEO/PVC, University of NottinghamLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/397392015-04-21T10:25:42Z2015-04-21T10:25:42ZFrom braille to iPad: a new app enables the blind to learn online<figure><img src="https://images.theconversation.com/files/78508/original/image-20150418-3256-1t2enkq.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">A new iPad app is helping blind students learn online.</span> <span class="attribution"><a class="source" href="http://www.shutterstock.com/s/ipad+student/search.html?page=2&thumb_size=mosaic&inline=268455590">iPad image via www.shutterstock.com</a></span></figcaption></figure><p>Imagine you are a sixth grader. </p>
<p>Each of your classmates is going to the computer lab for a math lesson on ratios and proportions. They sit down at their computers, launch the tutoring program and get to work. </p>
<p>Everyone but you – because you can’t see the screen: you’re blind. </p>
<p>You’ve tried screen reading software but it hasn’t worked very well. Your teacher has tried to help but no one in the school really knows how to set up, maintain and trouble-shoot <a href="https://mail.google.com/mail/u/0/#inbox">assistive technologies</a>. </p>
<p>The program isn’t available in braille, so you end up doing some basic worksheets instead of participating with your classmates.</p>
<p>The growth of online learning has thrown up new challenges for those with visual impairment as the learning tools are often not available. It’s also been a challenge for those working on making websites accessible to the visually impaired. It takes extra work and testing. </p>
<p>Now, the <a href="http://awvis.arizona.edu/">Animal Watch Vi Suite (AWViS) project</a> based at The University of Arizona, is developing a math tutoring program for middle school students who have mild, moderate or severe visual impairments. </p>
<p>I am part of a group of researchers combining the software program with more traditional resources such as large print or braille books, to enable visually impaired students access new technology.</p>
<h2>A new app for visually impaired</h2>
<p>We have developed an iPad app that is supplemented with print and braille materials. We decided on an iPad app when we realized that tablet devices were starting to become a potential alternative to the desktop computers that are typically found in schools. </p>
<p>Students who are blind can touch the left side of the iPad screen to hear the math problem, or the right side to hear a description of the picture illustrating the problem. </p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/78511/original/image-20150418-3245-1a7q9z9.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/78511/original/image-20150418-3245-1a7q9z9.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/78511/original/image-20150418-3245-1a7q9z9.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/78511/original/image-20150418-3245-1a7q9z9.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/78511/original/image-20150418-3245-1a7q9z9.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/78511/original/image-20150418-3245-1a7q9z9.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/78511/original/image-20150418-3245-1a7q9z9.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">Problem sets use endangered species for additional learning.</span>
<span class="attribution"><a class="source" href="http://www.shutterstock.com/cat.mhtml?lang=en&language=en&ref_site=photo&search_source=search_form&version=llv1&anyorall=all&safesearch=1&use_local_boost=1&search_tracking_id=xx1I9e5ctvbpBSH55FmqsQ&searchterm=endangered%20animals%20technology&show_color_wheel=1&orient=&commercial_ok=&media_type=images&search_cat=&searchtermx=&photographer_name=&people_gender=&people_age=&people_ethnicity=&people_number=&color=&page=1&inline=186162452">Animal image via www.shutterstock.com</a></span>
</figcaption>
</figure>
<p>The good thing is that most students with visual impairment have some vision. </p>
<p>Students with low vision can double-tap to enlarge the print to the size that is right for them. </p>
<p>The app provides students with support for their math problem solving. Students get three attempts on each word problem. Those with some vision can use an integrated Scratch Pad for working out the solution. </p>
<p>If a student is unable to solve a problem, he or she can watch a screen-capture, fully-narrated video showing the solution, turning a failure point into a learning opportunity. The narrator describes each step so that the explanation can be understood by a student who is blind.</p>
<p>Students always have the option to “give up” on a problem if it is too difficult, but they rarely do.</p>
<h2>Why an animal app works well</h2>
<p>Problem sets involving endangered or invasive species, such as the Snow Leopard, California Condor, Poison Frog and Burmese Python, among others, are used to cover different math topics. The reason we used animals to create word problems is to provide additional science learning.</p>
<p>For example, the module on unit conversion focuses on the Burmese Python. Students learn that these snakes are endangered in their native Asia but are becoming an invasive pest in Florida. </p>
<p>People who bought the snakes as pets because of their beautiful patterned skin often did not realize that the snakes could grow to be the size of telephone poles. When released illegally into the Everglades, the massive snakes thrived, and are displacing native species. </p>
<p>In this unit, students solve word problems about the length and girth of the snakes, the distance that they can travel and the value of their skin for leather goods.</p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/78512/original/image-20150418-3212-15p5pzr.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/78512/original/image-20150418-3212-15p5pzr.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=424&fit=crop&dpr=1 600w, https://images.theconversation.com/files/78512/original/image-20150418-3212-15p5pzr.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=424&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/78512/original/image-20150418-3212-15p5pzr.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=424&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/78512/original/image-20150418-3212-15p5pzr.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=533&fit=crop&dpr=1 754w, https://images.theconversation.com/files/78512/original/image-20150418-3212-15p5pzr.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=533&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/78512/original/image-20150418-3212-15p5pzr.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=533&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Students learn through charts and graphics.</span>
<span class="attribution"><a class="source" href="http://www.shutterstock.com/cat.mhtml?lang=en&language=en&ref_site=photo&search_source=search_form&version=llv1&anyorall=all&safesearch=1&use_local_boost=1&search_tracking_id=tF5vgaky1XQO3_cejJSacA&searchterm=ipad%20charts&show_color_wheel=1&orient=&commercial_ok=&media_type=images&search_cat=&searchtermx=&photographer_name=&people_gender=&people_age=&people_ethnicity=&people_number=&color=&page=1&inline=163535906">Graph image via www.shutterstock.com</a></span>
</figcaption>
</figure>
<p>Providing this background information is especially important for students who do not always have the opportunity to learn about the world through pictures. The animal sounds have proved to be especially popular.</p>
<p>Because math problems with graphics often appear on math achievement tests, we designed 20% of the word problems to involve maps, charts or graphs that contain information the student needs to find in order to solve the problem. </p>
<p>For example, on one problem in the Polar Bear unit, the student must use a line graph to identify the change in sea ice in the summer from 40 years ago to today. Students can view the graphics on the iPad and listen to an audio description by touching the tablet surface, or they can refer to hard copies with embossed lines, textures and print or braille labels. </p>
<p>Many students do find it hard to view the graphics on the tablet screen. Most rely on the hard copies while listening to the audio on the iPad. </p>
<p>Elsewhere too, researchers are developing new tools to fill this emerging need. <a href="http://blog.al.com/breaking/2013/06/uah_professor_helps_blind_visu.html">Ed Summers</a>, who is himself blind, is leading a team of developers at the <a href="http://www.sas.com/en_us/company-information.html">SAS Institute</a> in North Carolina to make software more accessible for the visually impaired. </p>
<p>Derrick Smith at the University of Alabama in Huntsville is leading a <a href="http://blog.al.com/breaking/2013/06/uah_professor_helps_blind_visu.html">project</a> to develop online professional development training to help math teachers understand the needs of students with visual impairment. </p>
<p><a href="http://www.tsbvi.edu/math">Susan Osterhaus</a> at the <a href="http://www.tsbvi.edu/">Texas School for the Blind and Visually Impaired</a>, serves as a national resource for best practices in math instruction for students with visual impairments. </p>
<h2>Students have found the app useful</h2>
<p>Such apps are finding a wide reach. This year, 65 students with visual impairment are using the AWViS materials in their schools in 22 states. Feedback from both students and teachers has been very positive. </p>
<p>One theme is that the technology seems to promote students’ independence. One said, </p>
<blockquote>
<p>“When [I worked on paper] my teacher had to help me once in awhile. When I used the app she didn’t help me as much. With the app I didn’t really have to ask for her to help me.” </p>
</blockquote>
<p>Teachers said students seemed more engaged with the app and less likely to ask for help or reassurance. </p>
<p>Almost every student reported preferring the app to his or her typical learning medium. </p>
<blockquote>
<p>“I liked the app better. I was able to use the hints which you don’t get in the print. It was easy once I figured it out.” </p>
</blockquote>
<p>The scratch pad was really helpful.“ "I used the hints and solution videos. They helped me understand it better.” “I liked knowing if I got the answer right with the app.”</p>
<p>With the growth of new technologies, there is an increasing demand for knowledge. Just recently, the <a href="https://www.edx.org/">online education provider edX</a> <a href="http://www.wandtv.com/story/28710684/national-federation-of-the-blind-applauds-doj-settlement-with-edx">settled</a> with the US Justice Department, agreeing to make its Massive Open Online Courses (MOOCs) accessible to students with disabilities. </p>
<p>There is an urgent need to work on more technologies to ensure that everyone has a way of accessing knowledge.</p><img src="https://counter.theconversation.com/content/39739/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>The research described here has been supported by the U.S. Department of Education’s Institute of Education Sciences (R324A120006). The views expressed here are not necessarily those of the sponsoring agency.</span></em></p>With the emergence of online technologies, the visually impaired can no longer depend on braille alone for their learning needs. App developers are stepping up to the challenge.Carole R Beal, Professor of Education, University of FloridaLicensed as Creative Commons – attribution, no derivatives.