Error patterns: what do they tell us?

Abstract

An analysis of computer diagnostic systems shows that most systems use answer data (product) for their analyses. This process of determining an error pattern, in addition, does little in the way of telling a teacher what should be done to help the child. This two-fold problem, extant in all computerized arithmetic diagnostic systems to date, prompted this study which sought other data sources in order to bring about more accurate computer analyses. A cognitive orientation suggested that the use of clinical diagnostic techniques should be explored as an alternative to error analysis. Essentially, these two approaches were compared. That is, to what extent does error pattern diagnosis (an essentially product oriented approach) and clinical mathematical diagnosis (a process oriented approach) interrelate?

Participants for this study were five, eight year olds from southwest Virginia. These children completed a test that was developed by Van Lehn (1982). This test was analyzed for error patterns and the children were selected on the basis of their error patterns. These children were then tested in a clinical setting using a measure developed for this study in cooperation with a clinical mathematics diagnostician.

The analysis was done on the results of these two measures and the protocols collected during the clinical interviews. The results indicated that there was no clear connection between the two types of diagnosis, but the analysis did yield a broader description of each individual participant. That is, error analysis or clinical mathematics alone does not completely describe an individual's knowledge of mathematics.