Error patterns in the simplification of polynomial expressions

Anderson, Ann Gladys (1982) Error patterns in the simplification of polynomial expressions. Masters thesis, Memorial University of Newfoundland.

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Abstract

The purpose of this study was to investigate whether students made systematic and common errors when simplifying polynomials. In addition to this general question, the study investigated the relationship between the errors made in an algebraic context and a corresponding arithmetic context, whether errors were a function of grade, program, or sex, and whether differences existed between direct and indirect situations. Twenty-five students were randomly selected from eight groups representing a Grade (9 or 10), by Program (Matriculation or Honours), by Sex matrix, resulting in a total sample of 200 students in the analysis. Three tests, an algebra test, an arithmetic test, and a computation test were administered to intact classes within a 40-minute period. The 20-item computation test involved single operations with integers. The 32-item algebra and 20-item arithmetic tests included items involving exponential expressions, the distributive principle and grouping. These tests contained items requiring the same type of skills but the arithmetic test contained no variables. -- The results indicated that 15 common, systematic errors were made in algebra. The common errors were found in the categories of sign errors, wrong operation errors, distribution errors and exponent errors. -- Most students who made common errors did so in one context only, either algebra or arithmetic, but not both. Most common errors arose in the direct mode, where only one step solutions were needed, rather than in the indirect mode, where a series of steps were necessary. The major difference found between grades was in the frequency of errors rather than the types of errors. The same was found when errors made by students in the matriculation programs were compared to those made by students in the honours programs. Only minor differences in performance were found between male and female students. -- Implications for remediation, as well as for teaching in general, were discussed. Recommendations for further research in error analysis were also proposed.

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