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Math is about solving problems!

July18

There is a dilemma in Mathematics – the pressure to get students through coursework versus the joy of problem-solving and mathematical investigation. As sure as one plus one equals two, it happens year after year. Kids who have been bringing home A’s in chemistry and acing AP Calculus arrive at college with visions of STEM careers dancing in their heads. Then they hit an invisible, but very painful, wall.

According to research from the University of California, Los Angeles, as many as 60 percent of all college students who intend to study a STEM (science, technology, engineering, math) subject end up transferring out. In an era when politicians and educators are beside themselves with worry over American students’ lagging math and science scores compared to the whiz kids of Shanghai and Japan, this attrition trend so troubles experts it has spawned an entire field of research on “STEM drop-out,” citing reasons from gender and race to GPAs and peer relationships.

So why do even the most accomplished students burn out of STEM programs when they hit college? One recent article in the New York Times explored possible reasons — from the alluring grade inflation in the arts and humanities, to what one engineering professor characterized as the boring, largely theoretical “math-science death march” of first-year requirements.

That may explain the phenomenon, at least in part. But math experts around the country point to another culprit.

Richard Rusczyk, a former Math Olympiad winner and the founder of the online math program Art of Problem Solving,  is part of a group of math educators who sees the mystery of the disappearing STEM major from a different angle. It’s not that kids aren’t getting enough math, they say, but that we’re teaching K-12 math all wrong.

Rusczyk’s insight is based on a phenomenon he witnessed firsthand when he arrived at Princeton University and began studying math alongside kids who had attended the most prestigious high schools in the country. “These were kids who had never gotten anything but 95s and 100s on their tests and suddenly they were struggling and were getting 62s on tests and they decided they weren’t any good [at math],” he explains.

Call it the mathematical reality check. Suddenly, Rusczyk recalls, formerly accomplished students were faced with a new idea: that math required more than rote learning — it required creativity, grit, and strenuous mental gymnastics. “They had been taught that math was a set of destinations and they were taught to follow a set of rules to get to those places,” he recalls. “They were never taught how to read a map, or even that there is a map.”

Indeed, traditional math curriculum is to teach discrete algorithms, a set of rules that elicit a correct answer, like how to do long division, say, or how to use the Pythagorean theorem. Then students “learn” the material by doing a large quantity of similar problems. The result, says Rusczyk, is that students are rarely asked to solve a problem they are not thoroughly familiar with. Instead, they come to think of math as a series of rules to be memorized. The trouble is kids don’t necessarily learn how to attack a new or different kind of equation.

Rusczyk watched many of his fellow students, long accustomed to being “quick studies,” as they soured on math after experiencing what they perceived as failure. They quit — transferring their hopes and dreams to a less numerically challenging field like sociology or graphic design.

Rusczyk, in contrast, felt far more prepared when faced with a problem he didn’t know how to solve. Despite having attended what he characterizes as an average public school without a lot of advanced math classes, he had participated in math clubs and contests. In math clubs, he’d become accustomed to facing harder, multifaceted problems where the right approach wasn’t immediately apparent.

Math as problem solving

Instead of just learning how to follow rules, he explains, “In math competitions, I learned how to solve problems that I hadn’t seen before.” Instead of math becoming something he accomplished in return for a perfect score, he came to see math as problem solving — an exciting pleasure that was a distant relation to the rote drudgery of memorizing algorithms.

When Rusczyk looked around him, he noticed a pattern. His classmates who had experienced this kind of difficult problem solving — usually in after-school math clubs — could survive the transition to college math.

Read the full article here.

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