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Does our approach to teaching math fail even the smartest kids?

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GreatSchools Blog

By Carol Lloyd

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, multi-faceted problems where the right approach wasn’t immediately apparent.

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. The ones who had only been exposed to traditional math curriculum, the ones who, as Rusczyk puts it, have experienced the “tyranny of 100%” — gave up too easily because they thought if they weren’t getting top scores, they weren’t meant to do math. “Suddenly, a solid B was a 40%, the top grade [was] an 82%, the next 68%, and no one is getting a 100%,” he recalls. “But they didn’t know this.” Rusczyk realized that these kids had been dealt a bad hand: “They were taught [math] is a set of facts, not a process.”

These fundamental ideas — that math isn’t about following rules but about solving problems, that math means fun mental struggle, not boring rote learning — forms the basis of his online math school and curriculum, which currently includes pre-algebra though calculus and one year (third grade) of his new elementary school program, Beast Academy. Unlike traditional math curriculum, The Art of Problem Solving books first give kids problems (not the explanation for how to solve them) and leading questions to get them to struggle with the ideas a little before they are given the foolproof algorithm.

His programs are designed for gifted math students, but he claims his ideas could help all kids, gifted or not. His observations offer a solution for parents who want to help their children keep those STEM doors of opportunity open. To this end, he has a clear message to parents assessing their child’s math experience. What should kids be learning about math? For younger children, it’s important to give them a love for math — just as we try to give kids a love for reading.

"Kids smell fear," he says. "And many elementary school teachers love reading but not math." Once kids get older, don’t be afraid to push your child in a program that challenges him. “It’s supposed to be hard — if you’re getting 98% in a class… it may be too easy.”

He also recommends that parents look outside the classroom to provide the best place to challenge kids. “Math competitions, summer programs, math circles (programs which offer challenging math in non-judgmental environments) — whatever you can find that will give your kids a taste of why math can be fun.”

Finally, and most importantly, Rusczyk wants parents to give kids more time to explore their passions. “It’s terrible. Kids are so overscheduled — there’s AP this AP that — they’re doing all this garbage that doesn’t serve them in the long run.”

Rusczyk cautions that kids who love math and science often end up filling up their time with AP classes that aren’t central to their aspirations but more focused on GPA calculations (like AP Art History), and shortchange themselves when it comes to exploring math and science learning outside the classroom.

In the end, the skills required to solve a complex problem — to break the problem down into smaller parts, to approach it from different angles using different methods, to not getting intimidated or frustrated when the path isn’t obvious — are practical in any field of endeavor — from astrophysics to er, parenting. Ideally, math prepares kids to be better thinkers no matter where they land. For now, parents can use these skills to fill in their children's math deficiencies, one problem at a time.

Next article: 7 ways to get your child excited about math

is the executive editor of GreatSchools and mother to two raucous daughters, ages 9 and 13.

Comments from GreatSchools.org readers

05/1/2012:
"I wonder part of the problem is that most math teachers usually grade assignments and tests based on percentage correct answers. What if they looked more at the process the student uses to set up the equation, draw a diagram the object described, or predict the shape of a graph. Ask students how they chose the steps or procedures they used to get their solution, and explain how an alternate procedure could prove or disprove their answer. Encourage students to think about how they get solutions rather than just checking the bottom line-- or worse, the answer sheet. Yes, I've seen many classrooms where students write only the answers on the assignments and tests turn in. Their teachers don't spend nearly as much time grading papers as the English teachers who read essays, or Social Studies teachers who ask students to explain the significance of events, and their impact on the places where they happened.. It's time to stop rewarding students only for the number of right answers and help them to realize the importance of asking the right questions. "
04/23/2012:
"This speaks to what I see with my SAT & ACT tutoring students. The ACT is gaining popularity at a staggering rate, largely because the question format doesn't require much "outside the box" thinking like the SAT does. "
04/17/2012:
"This article is correct, math education is failing too many students, even the "good ones" And yet, those students are held up as proof that the system works. The US K-12 school system is tough to change. Big systems have a lot of inertia, like the Titanic heading towards the iceberg. But proving that the system is working by showcasing the few students who make it through is like saying that the Titanic was a success because some of the passengers made it to New York. We have to make education work for all kids, not just the survivors. "
04/9/2012:
"This is what we talked ,our kids are not being taught the basics. "
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