Effects of instruction using part-whole concepts with one-step and two-step word problems in grade four.

Abstract

This study grew out of the recognized need to improve performance on problem solving. It determined the effect of teaching word problems using part-whole concepts and meanings of the operations. In the Part-Whole group, classroom teachers used 18 author-designed lessons on one- and two-step word problems using the four operations. Instruction was based on a three-step heuristic: thinking about the problem, representing the problem, and solving the problem. Manipulatives were used by the teachers and students in some lessons. A Practice group did 16 worksheets on the same problems with no explicit instruction. A Control group used their regular curriculum. The subjects were 384 fourth grade students, 99% African-Americans, from seven schools in a large urban school system. They came from families with low- and low-middle income. Data were collected from November to May, 1989-90, from pretests, posttests, retention tests, interviews, and attitude surveys. Achievement data were analyzed with ANCOVA and ANOVA. It was hypothesized that emphasizing conceptual knowledge with connections among the meanings of the operations, models, formal mathematical language (oral and written), and students' everyday experiences would result in superior word problem performance. This hypothesis was verified in all analyses. Achievement was significantly better for the Part-Whole group on addition/subtraction, multiplication/division, and two-step problems on both posttests and retention tests, and on the transfer test for two-step problems. Analyses by ability levels showed similar trends with noteworthy performance of low ability students. Achievement was similar for Practice and Control groups. In interviews at the end of the study, Part-Whole students of all ability levels were able to use their conceptual knowledge to reason through problems. Most Practice and Control group students continued their use of key words and guessing. Part-Whole students tended to maintain the same self-assessment of their ability to solve word problems while the other students lost confidence. Overall, the Part-Whole approach to word problems proved to be highly successful in improving students' performance on word problems, conceptual knowledge of the operations, and ability to express their reasoning verbally.