Evaluation of Automated Diagnosis and Instruction for Mathematics Problem‐solving

Abstract

ETS and the ETS logo are registered trademarks ofEducational Testing Service (ETS). AbstractThe past several decades have seen numerous approaches toward automated diagnosis and instructional support of students engaged in mathematics problem-solving. These approaches typically involve detailed analysis of potential solution paths for problems, formal representations of correct and incorrect answers, and support in the form of feedback or explanations to students during the process of solving a problem. The approaches of each of a number of representative systems (ACED, ALEKS, Cognitive Tutors, Andes, and Assistments)will be described through a critical evaluation of how they represent content knowledge, their approaches to diagnosis, and their approaches to instructional support. Finally, recommendations are made for new approaches to automated diagnosis and instructional support of mathematics problem-solving.

Approaches to the Design of Diagnostic Item Models

“…In a recent report, Underwood (2007) reviewed six such systems for mathematics problem solving and identified them along several dimensions, including: How knowledge, skills, and abilities (KSAs) were represented, how levels of proficiency for the KSAs were determined, and whether common errors were identified. She found that while all six systems were designed to identify common errors, they varied with respect to how the KSAs were represented and how the KSA proficiency levels were determined.…”