Toward the Automatic Discovery of Misconceptions

1 Introduction

A misconception is an incorrect understanding of a con­ cept or procedure that results in systematic discrepan­ cies in behavior. Knowledge about the misconceptions of novices or students, when used well, can lead to more effective learning and remediation.

Inferring the misconception(s) of a student from his or her behavior can be viewed as the primary task of a student modeling system. This task is reduced to one of bug detection and look-up when a library of misconcep­ tions already exists; the challenge lies in automatically extending this library, or building it from scratch.

This summary describes a novel approach to gener­ ating misconceptions from behavioral discrepancies in a programming domain. The research problem, proposed work plan, and progress to date are outlined in the sec­ tions that follow.

2 Discovering Programming Misconceptions: Problem and Plan

Previous approaches to learning novel misconceptions understandably dealt with relatively simple behaviors (e.g., numbers, algebraic equations, vectors of nominal values). 1 This research, however, deals with behavior of greater complexity, for which the the single-strategy ap­ proaches of previous systems quickly become inadequate. The goal of this work is, therefore, the development of an effective multistrategic approach to discovering meaning­ ful misconceptions that can account for if not eradicate regularly occurring discrepancies in novice programming behavior.

We propose three steps to achieve the above goal. The first step involves the development of an algorithm for clustering discrepancies in novice programs that not only detects regularities among discrepancies but also estab­ lishes the causal relationships among them. Causal re­ lationships are important for at least two reasons. First, the absence of a causal relationship between subsets of a group of discrepancies indicates the presence of multiple misconceptions and warrants the division of this group into more coherent subgroups. Second, the causative

1 See [Sison and Shimura, 1997] for a discussion.