The Effects of Curricula on Students' Ability to Analyze and Solve Problems in Algebra

Abstract

The purpose of this study was to compare students two different curricula on two problem solving in abilities, the ability to identify the underlying mathematical structure in a problem and the ability to solve problems. The two curricula were the Algebra with Computers project materials and the algebra 1 curriculum normally taught in the schools where the Algebra with Computers materials, which sought to give an existence proof for a computer-intense algebra curriculum, were being field tested. The experimental and control classes were at two sites in the Middle Atlantic region. At both sites, control and experimental students were given two researcher-designed tasks. The Problem Solving Test contained ten problems typical of algebra 1 which students were asked to solve in any way known to them. The Triads Task consisted of 24 groups of three problems each. Students were asked to identify which pair of each triad would be solved in the same manner. The results of the two tasks were analyzed using analysis of covariance with each site and each task being analyzed separately. The covariates, taken from the eighth grade scores on the California Achievement Test, were total reading, mathematical concepts and mathematical computation. sex was used as a blocking variable. The ANCOVA results were significant in favor of the experimental groups for both Site One (at the .OS level) and Site Two (at the .01 level) on the Problem Solving Test and at Site Two ( at the .01 level ) for the Triads Task. The Site One Triads Task results were not significant. There were no significant differences between the performances of males and females at both sites on the Problem Solving Test or at Site Two on the Triads Task. At Site One there was a significant difference in favor of the females on the Triads Task. There were no significant interactions between sex and treatment. The students using the Algebra with Computers materials were better problem solvers in three of the four analyses. This study has shown that as measured by the two tasks given, the Algebra with Computers curriculum does produce better problem solvers.