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.