An Analysis of Middle-School Math Errors Across Schools

The little previous research comparing student errors across schools indicates that the distribution of students’ systematic errors in one school does not significantly match those in other schools. We present here data from a set of middle-school mathematics problems, where student errors do seem to be comparable across the three schools studied. We conclude that student errors do seem to transfer for some problems, though not for others. One implication is that tutor remediation based on student performance at one school will likely be useful for students at another school. Introduction The little previous research comparing student errors across schools indicates that the distribution of students’ systematic errors in one school does not significantly match those in other schools. This has been taken by some [1,2] to indicate that student errors do not ever transfer. The issue has practical implications if an intelligent tutor is to provide remediation based on systematic “bugs” in student problem solving [3]. In earlier research [4] we presented empirical data for one middle-school mathematics problem, where there appeared to be significant overlap of student errors across three different schools. In this paper, we present additional data, also from the domain of middle school mathematics. Our initial conclusions are that student errors transfer for some problems in this domain and not for others. We present sample problems in each category, and make some tentative hypotheses as to why this is the case. Previous Research The literature seems to indicate a single study devoted to the study of the transfer of student errors across institutions. Payne and Squibb [5] examined the errors made by 1314 year-old students on algebra problems at three (English) secondary schools. One conclusion they drew (p. 455) is that, “the rules that do the most explanatory work in the three separate groups have surprisingly little overlap.”