ABSTRACT

During the past few years our group has been working on computer systems for diagnosing systematic student errors. These diagnostic systems, BUGGY and more recently DEBUGGY, have been used to analyze thousands of students (Brown & Burton, 1978; Burton, 1981) and have enabled us to construct an extensive catalogue of precisely defined bugs for place-value subtraction. These procedural definitions constitute an extensional, ad hoc theory of bugs. The theory is extensional in that it explains a student’s errors and misconceptions as a combination of some set of prespecified, primitive bugs. It is ad hoc (by design!) in that the language we used to describe the bugs was as open-ended and as powerful as we could find. Although we could have started out using a language restricted by psychological principles, we chose to use a powerful descriptive technique that facilitated our ability to express and experiment with any new bug that was conjectured to exist in the data.