Students' Constructive Uses of Mathematical Errors: A Taxonomy

The purpose of this study is to contribute to an understanding of how errors could be employed in mathematics instruction so that the students use them constructively in support of their learning of mathematics. A teaching experiment was designed to create an ideal context in which the pedagogical approach to errors as springboards could be applied constantly. The teaching experiment was organized as 10 lessons on mathematical definitions for two 11th-grade female students. Twenty mathematical errors were recorded and analyzed. The error activities identified and described are different from learning goals and outcomes. A taxonomy of constructive uses of errors was developed based on level of mathematics discourse and stance of learning. Eight potential benefits associated with errors as springboards were generated from the analysis of error activities. (YP)