Using erroneous examples to improve mathematics learning with a web-based tutoring system

• Middle school students learned to solve decimal problems with a web-based tutoring system.
• ExErr group received erroneous examples to correct and explain.
• PS group received problems to solve and explain.
• ExErr group outperformed PS group on a delayed test and on judging answer correctness.
• PS group reported liking the lessons better than the ExErr group.

This study examines whether asking students to critique incorrect solutions to decimal problems based on common misconceptions can help them learn about decimals better than asking them to solve the same problems and receive feedback. In a web-based tutoring system, 208 middle school students either had to identify, explain, and correct errors made by a fictional student (erroneous examples group) or solve isomorphic versions of the problems with feedback (problem-solving group). Although the two groups did not differ significantly on an immediate posttest, students in the erroneous examples group performed significantly better on a delayed posttest administered one week later (d = .62). Students in the erroneous examples group also were more accurate at judging whether their posttest answers were correct (d = .49). Students in the problem-solving group reported higher satisfaction with the materials than those in the erroneous examples group, indicating that liking instructional materials does not equate to learning from them. Overall, practice in identifying, explaining, and correcting errors may help students process decimal problems at a deeper level, and thereby help them overcome misconceptions and build a lasting understanding of decimals.