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ERIC Number: ED356973
Record Type: Non-Journal
Publication Date: 1992-Oct
Pages: 29
Abstractor: N/A
Reference Count: N/A
ISBN: N/A
ISSN: N/A
Towards a Stable Diagnostic Representation of Students' Errors in Algebra.
Birenbaum, Menucha; And Others
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' (n=231) errors in algebra with the goal of investigating the relative stability of the diagnoses derived from these approaches. The two approaches utilized were bug analysis and rule-spaced analysis. Bug analysis compares students' answers with entries in a bug matrix constructed from applying students' incorrect procedures (mal-rules) to the test items. Rule-space analysis creates an attribute matrix of solutions strategies for solving test items and compares students' responses on parallel sets of items. Consistent with the findings of recent studies, a relatively large number of bugs were found to be unstable; stable bugs tended to be infrequent. In contrast, the results of the rule-space analysis yielded relatively more stable diagnoses. Four advantages of attribute rule-space analyses over bug analyses are presented: (1) deficient subskills as attributes are known mathematical entities and recognizable to teachers; (2) identified attributes are integral subcomponents of the task enabling failure to be traced to one or more deficiencies in subskills; (3) remedial scripts for subskill deficiencies can be prepared as a consequence of the identified advantages; and (4) teachers and researchers avoid extensive efforts to find mal-rules that are unreliable. A list of 28 references is included. (Author/MDH)
Educational Testing Service, Rosedale Road, Princeton, NJ 08541.
Publication Type: Reports - Research
Education Level: N/A
Audience: Researchers
Language: English
Sponsor: Office of Naval Research, Arlington, VA. Cognitive and Neural Sciences Div.
Authoring Institution: Educational Testing Service, Princeton, NJ.
Identifiers - Location: Israel (Tel Aviv)