CONTACT: STEPHEN PRADARELLI
100 Old Public Library
Iowa City IA 52242
(319) 384-0007; fax (319) 384-0024
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
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
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.
"It becomes especially difficult for students and teachers right there
in middle school, where you have the transition to algebra," Moore said.