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Release: Dec. 21, 1999

UI's Moore to study math reasoning, use of symbols in middle schools

IOWA CITY, Iowa -- Understanding symbols is essential to understanding math, particularly higher forms of mathematics. But not everyone easily makes the transition from pluses and minuses to more abstract statistical representations.

Using a $450,000 grant from the National Science Foundation, University of Iowa Assistant Professor Joyce Moore and a colleague from Vanderbilt University will study middle-school classrooms to find out why symbols prove so vexing for some students and to develop a style of instruction to make them less so. The three-year grant begins in January.

Moore, a specialist in cognition and learning in the UI College of Education's Educational Psychology program, said one reason many children have difficulty comprehending and using mathematical representations is that they don't understand the work a given representation -- or symbol -- is designed to do.

"They tend to view symbolic formulas as rules that make life harder, not easier," Moore said.

Moore will study sixth, seventh and eight-grade classrooms in the Iowa City area, exploring such mathematical concepts as variability, including average and standard deviation.

"The basic idea is that we give students situations and ask them to create their own procedures or formulisms to distinguish them," she said. "The first part is they invent their own notations, which we assume will be very limited -- we don't expect them to come up with conventional notations like mathematicians do. Then we'll give them another set of situations and see if their notations work, and they probably won't, and we will repeat the process. The goal is for them to determine the point of a notation and the quantitative properties those notations are useful for, or what situations they're used in."

After several cycles of inventing, testing, and revising, the students will be taught how to use conventional approaches to variability. The goal is to help students notice important quantitative properties, and to prepare them to learn how conventional representational solutions elegantly capture those properties.

Moore said her motivation for conducting the study comes from two main sources. The National Council of Teachers of Mathematics has recommended that statistical instruction begin in middle school, but to date Moore says there aren't many strong instructional models to accomplish that. Second, there's general concern about the state of mathematics instruction -- and comprehension -- in U.S. schools.

"It becomes especially difficult for students and teachers right there in middle school, where you have the transition to algebra," Moore said.