Looking beyond the answer: Strategies used by fifth graders to solve mathematical word problems

This descriptive study observed and described the mathematical problem solving strategies of 10 above-average fifth graders. Each student solved eight problems, two from each of these problem types: Cryptarithms, Geometry, Money, and Number Patterns. Four were solved by the student as an individual and four were solved with a partner. Students were instructed to speak as they solved each problem. Problem-solving sessions were tape recorded and video taped, transcripts were made, work papers collected, and notes were taken by the investigator. In this study a strategy was defined as what a student does to reach a goal. The goal is the solution of mathematical word problems. Analysis of the data resulted in the formation of six major hypotheses, namely: (a) students use a variety of problem solving strategies; (b) students monitor and assess their progress; (c) students react to the problem solving experience; (d) students perceive problem difficulty differently; (e) collaboration results in a more rapid problem solution; (f) students prefer to solve problems with another student rather than alone. Two main categories were identified, Approaches to the Task and Reactions to the Task. Approaches to the Task consisted of spoken linguistic strategies which allowed students to pause and reflect on what they were doing, written linguistic strategies which allowed students to understand, track, and organize their work, and problem-solving strategies which allowed students to plan, monitor, and evaluate their solutions. Reaction to the Task consisted of students\u27 reactions and the investigator\u27s reactions. Students reacted by expressing emotions of confusion, frustration, and joy, and also by making personalizing comments throughout the problem solving process. The investigator reacted by reminding students to speak aloud if they became silent and answered any questions students asked. This study suggests that looking beyond the answer can be a rich and rewarding part of problem solving and assessment. It can also be concluded that students would benefit from solving problems collaboratively under untimed conditions