ERIC Number: ED356973
Record Type: Non-Journal
Publication Date: 1992-Oct
Reference Count: 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)
Descriptors: Algebra, Cognitive Structures, Computer Assisted Instruction, Educational Diagnosis, Equations (Mathematics), Error Patterns, Foreign Countries, Junior High School Students, Junior High Schools, Knowledge Level, Mathematics Education, Mathematics Instruction, Mathematics Skills, Misconceptions, Models, Remedial Instruction, Remedial Mathematics
Educational Testing Service, Rosedale Road, Princeton, NJ 08541.
Publication Type: Reports - Research
Education Level: N/A
Sponsor: Office of Naval Research, Arlington, VA. Cognitive and Neural Sciences Div.
Authoring Institution: Educational Testing Service, Princeton, NJ.
Identifiers - Location: Israel (Tel Aviv)