Error factors: A missing link between cognitive science and classroom practice?

Cognitive scientists are now able to model the errors of learners on simple, well-specified topics such as subtraction. Unfortunately, the associated techniques are too involved, and the analyses too fine-grained, for teachers to apply them to general classroom topics. Deficiencies are also apparent in current curriculum theories, which do not pay sufficient attention to the consequences of untreated errors. The most immediately usable and integrative approach of which I am aware is in terms of Error Factors (EFs)-promoters of underlying confusion in learning. I show here how this framework helps us understand the failure of classical attempts to arrange error-free learning or to provide diagnostic or remedial tests and exercises. Further, anecdotal evidence I present confirms that it is rare for teachers who are peripherally aware of such factors to deal systematically with them; more often, teachers are both ignorant of and unable to recognize typical error factors, whether in their teaching (itself commonly a source of confusion for students) or in their students' learning. Accordingly, this paper provides an overview of the more significant facets of EFs, together with such psychological explanations for their occurrences as exist. It is hoped that a fuller and more cogent appraisal of errors will be seen in classrooms as a result.