To Err Is Human, to Explain and Correct Is Divine: A Study of Interactive Erroneous Examples with Middle School Math Students

Abstract

Erroneous examples are an instructional technique that hold promise to help children learn. In the study reported in this paper, sixth and seventh grade math students were presented with erroneous examples of decimal problems and were asked to explain and correct those examples. The problems were presented as interactive exercises on the Internet, with feedback provided on correctness of the student explanations and corrections. A second (control) group of students were given problems to solve, also with feedback on correctness. With over 100 students per condition, an erroneous example effect was found: students who worked with the interactive erroneous examples did significantly better than the problem solving students on a delayed posttest. While this finding is highly encouraging, our ultimate research question is this: how can erroneous examples be adaptively presented to students, targeted at their most deeply held misconceptions, to best leverage their effectiveness? This paper discusses how the results of the present study will lead us to an adaptive version of the erroneous examples material.