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But the Poway teen’s mental abilities have no limitations. That’s the glory of it – the messy, wonderful, powerful adventure.For all of his 18 years, Ben Lou’s physical disabilities have made him dependent on others 24 hours a day. We all know it’s not always so simple to solve problems. If you understand the problem you’re trying to solve, you’re well on your way to solving it. These messages are especially important for parents helping children learn mathematics. 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. In my work, I’ve met many people who love mathematics and many who find it overwhelming and nonsensical. 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.
#MATH WHIZ HOW TO#
I’ve taught mathematics, and how to teach mathematics, for nearly 30 years. I chose it because it has delighted math researchers for years, and because John is quite clever in his solution. 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. John probably made use of one of Pólya’s most important suggestions: Can you think of a related problem? Drawing pictures also happens to be another of Pólya’s suggestions. New brain research validates what mathematics educators have been saying for decades: Pictures help us think. 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.Ĭould 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.
#MATH WHIZ FULL#
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. Finally, he carried out the plan.ĭid he check his answer? That remains unclear, but we can check the validity of his work for him. Then, he made a plan, most likely visualizing in his head how he would measure and divide the cottage cheese. First, he understood the problem: He needed ¾ of what the recipe called for, which was 2/3 cup. John is a mathematician and problem solver. Voilá! Three-quarters of 2/3 cup of cottage cheese remained. He then carefully pushed one quarter of the cottage cheese back into its container. He patted the cheese into a circle and drew lines into it, one vertical, one horizontal, dividing the cheese patty into quarters.
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John measured 2/3 cup of cottage cheese, then dumped it onto a cutting board. 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. What do you think John did? What would you do? A man, let’s call him John, is making ¾ of a recipe that calls for 2/3 cup of cottage cheese. Here’s a classic problem from research on mathematics education done by Jean Lave. Problem solving in the palm of your hand – math reduced to four steps. Pólya’s problem solving plan breaks down to four simple steps: And metacognition is often the heart of problem solving. This is because his writing is metacognitive – he writes about how he thinks about thinking.
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When you read “How to Solve It,” it feels like you’re taking a guided tour of Pólya’s mind. For many reasons, not the least of which is that Pólya died in 1985, you will meet him as I did – through his wildly successful “How to Solve It.” Penned in 1945, this book went on to sell over one million copies and was translated into 17 languages.Īs a mathematician, Pólya worked on a wide range of problems, including the study of heuristics, or how to solve problems.