sealPurdue News

December 1998

New equation can overcome math phobia

WEST LAFAYETTE, Ind. -- Tunnel-vision teaching and traditional testing methods are multiplying the problem of students who "can't do math" -- and adults who suffer from the same math phobia.

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One of this country's leading mathematics educators has a formula for solving the problem: Recognize that basic calculation skills and rules are only about one-fourth of what students need to know, even though those are the easiest skills to measure.

"We must broaden the definition of what constitutes good mathematical skills and create new ways to measure them," says Richard Lesh, the new director of Purdue University's School Mathematics and Science Center. "Educators seem to be stuck on this notion that we have to choose between emphasizing the basic calculation skills measured by standardized tests and the global problem-solving skills that allow youngsters to understand and analyze complex systems. Students, though, need instruction in both to be successful in the 21st century."

Lesh says that instruction should include powerful language models and metaphors that encourage children to think about complex systems.

"The world today is full of complex systems, and mathematics is the subject that's supposed to provide models, frameworks and metaphors for thinking quantitatively about those things," Lesh says. "Calculation and rule-following only make up a small part of the big picture in terms of what students need to know, but because they are the easiest skills to measure, that's what schools emphasize. And children who don't grasp it right away or don't enjoy doing it often end up fearful of all math."

Lesh, the Robert B. Kane Distinguished Professor of Education in Purdue's School of Education, is internationally recognized for his groundbreaking research into how people solve problems in real-life situations and how children learn those abilities. One of the major goals of his research is to find ways of recognizing and rewarding a much broader range of abilities, and that's going to require a fundamental change in priorities among educators.

"If we're going to be equitable, and if we're going to get kids over math phobia, then how much do we really care about the math that's been portrayed on standardized tests?" Lesh asks. "That's really a pretty narrow, low-level view of mathematics, and who cares if you don't like that to some degree?"

A large body of Lesh's work involves developing methods for teaching mathematical concepts to students who have been identified as deficient in math skills. In one popular exercise, students read a newspaper article about a summer concession business in which the owner cannot afford to rehire all the workers from the previous year. The article contains tables showing the number of hours each employee worked and the amount of money he or she took in during that time. The tables also indicate the overall level of activity in the amusement park where the vendors were operating.

"The assignment asks students to evaluate how well each vendor performed and then write a letter to the business owner with recommendations on who she should hire for the upcoming season," Lesh explains. "We're finding that kids who really struggle with working through a traditional math problem can come up some very creative ways of solving this employment dilemma. They will often create a graph describing trends, and that's precisely the kind of quantitative thinking that math is supposed to teach."

Lesh says this method of instruction is far more effective than the typical story problem, which basically asks the student to pull mathematical data from text and plug it into the appropriate calculation.

"You can ask a youngster to figure out where and when the train leaving New York City will meet up with the train leaving Los Angeles, but chances are pretty good that he's not going to care too much about the answer because it doesn't have a lot of meaning in his world," Lesh explains. "The case studies being used in professional and graduate schools are far more appropriate models for the concepts we want children to grasp."

Lesh says the way we use math in our everyday lives has changed radically over the past 10 years because of advancing technology and how we use information, so math instruction needs to change as well.

"If we ask for an answer that isn't necessarily just a number, and combine that with the use of technology in an interesting way, kids will often invent better ideas than anyone has ever tried to teach them. It's another way to enlist their thinking in the service of doing something mathematical -- and everybody wins."

Source: Richard Lesh, (765) 496-3673;

Writer: Sharon Bowker, (765) 494-2077;

Purdue News Service: (765) 494-2096; e-mail,

This quilt pattern and accompanying measurements are one example of math concepts being used in real-life activities. (Reprinted by permission of the Educational Testing Service, the copyright owner)
Color graphic, electronic transmission, and Web and ftp download available. Graphic ID: Lesh.mathphobia
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