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Toward a Stable Diagnostic Representation of Students' Errors in Algebra

Birenbaum, Menucha; Kelly, Anthony E.; Tatsuoka, Kikumi K.
Publication Year:
Report Number:
ETS Research Report
Document Type:
Page Count:
Subject/Key Words:
Office of Naval Research, Algebra, Educational Diagnosis, Error Patterns, Israel, Mathematics, Rule Space Analysis


Diagnoses of students' performance on procedural mathematical tasks need to display a certain level of stability and robustness if they are to be used as the basis for remediation, particularly with computer-delivered instruction. The purpose of this study was to compare two diagnostic approaches for describing students' errors in algebra--a bug analysis and a rule-space analysis--with the goal of investigating the relative stability of the diagnoses derived from these approaches. Consistent with the findings of recent studies, a relatively large number of bugs were unstable; stable bugs tended to be infrequent. In contrast, the results of the rule-space analysis yielded relatively more stable diagnoses. The results were discussed in light of their consequences for designing remediation. (25pp.)

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