Evoking Learning by Examples through Reducing Misconceptions and Highlighting Procedures

Abstract

Prior research highlights a positive effect of incorrect worked examples on mathematics learning. Yet the mechanisms underlying these benefits are unclear. To investigate potential mechanisms of the benefits of various worked example types, we examined process data from a previously published classroom-based experiment. More specifically, we analyzed students’ explanations made while explaining worked examples in three varying example conditions as well as students’ problem-solving errors made when solving problems. These data operationalize two potential mechanisms: a reduction of misconceptions (i.e., fewer targeted conceptual errors), and an increase in principled algebra knowledge (i.e., explanations focusing on principles underlying procedures). Mediation analyses revealed both as important mechanisms of varying effects. A reduction of misconceptions explained greater benefits of all three worked example conditions, compared to a problem-solving control, on an algebra concepts posttest. More principled explanations of procedures explained the benefits of incorrect worked examples on problem-solving at posttest compared to the two other example conditions. These findings help explain differential findings in prior work by example type and may elucidate potential avenues for errorful instruction.