On the Stability of Students'Rules of Operation for Solving Arithmetic Problems

The purpose o f this study was to examine the consistency with which students applied procedural rules for solving signed-number operations across identical items presented in different orders. A test with 64 open-ended items was administered to 161 eighth graders. The test consisted o f two 32-item subtests containing identical items. The items in each subtest were in random order. Students'responses to each subtest were compared with respect to the identified underlying rules o f operation used to solve each problem set. The results indicated that inconsistent rule application was common among students who had not mastered signed-number arithmetic operations. In contrast, mastery level students, those who use the right rules, show a stable pattern o f rule application in signed-number arithmetic. These results are discussed in light of the hypothesis testing approach to the learning process.