The Effectiveness of Incorrect Examples and Comparison When Learning About Decimal Magnitude

Abstract

Exposing students to incorrect examples of mathematical procedures can be beneficial for learning. However, it remains unclear how such examples can improve learning. Incorrect examples may be beneficial because students compare them to correct examples or because seeing incorrect examples exposes students to misconceptions. It is also unclear who learns best from incorrect examples. It is possible that students with low prior knowledge could find incorrect examples overwhelming. To examine these questions, 342 fourth- and fifth-grade students learning about decimal magnitude were randomly assigned to one of three conditions: 1) comparing incorrect and correct examples (Incorrect-Compare), 2) studying incorrect and correct examples sequentially (Incorrect-Sequential), or 3) studying only correct examples sequentially (Correct-Sequential). Students studied these examples and answered explanation prompts with a partner in their math class for about two hours. Four ways of measuring students’ misconceptions were explored.

Overall, there were no main effects for condition for conceptual or procedural knowledge, or prevalence of misconception errors. However, the frequency of prior misconception errors moderated the effect of condition for one of the outcomes. Specifically, students with infrequent prior misconceptions had better procedural knowledge in the Incorrect-Sequential condition than in the Incorrect-Compare condition. Students with frequent prior misconception errors performed similarly across conditions. In addition, the intervention was not effective in reducing strongly-held misconceptions, and about 36% of students remained highly confident when making errors after the intervention.

Unlike past research, studying incorrect examples in addition to correct examples did not lead to significantly greater learning than studying only correct examples. Directly comparing incorrect examples to correct ones also did not lead to greater learning than sequential study of incorrect and correct examples, and in one case, comparison was worse than sequential study for some students. These findings highlight that comparison may be overwhelming for some students and that correcting misconceptions is a difficult and gradual process. In addition, it is important to develop multiple measures to assess misconceptions in mathematics. Future research needs to reevaluate these research questions when more instructional guidance is provided.