Title

The effect of presenting a common error with an explanation

Date of Award

1996

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Instructional Design, Development and Evaluation

Advisor(s)

Philip L. Doughty

Keywords

Curricula, Teaching, Mathematics education, algebra, error

Subject Categories

Curriculum and Instruction

Abstract

The purpose of this study was to determine the extent to which presenting a procedure using a common error with an associated explanation reduces errors when writing expressions with exponents in lowest terms for Math 1 algebra students. It would be helpful for math teachers to know whether presenting common errors, the predictable mistakes made by novice learners (Marcone & Reigeluth, 1988), significantly reduces errors when writing expressions with exponents in lowest terms. Mathematic teachers should also know whether presenting students with an explanation of the rule for writing expressions with exponents in lowest terms significantly reduces students' errors.

Two hundred fifteen eighth-grade students from two different schools participated in this study. Each student was randomly assigned to one of four instructional intervention groups. Participants in each of the four instructional intervention groups received instruction on how to write expressions with exponents in lowest terms. However, instruction did not in all cases include common errors and explanations. Group 1, Common Error and an Explanation, received the common errors and explanations of the rules for writing expressions with exponents in lowest terms; Group 2, Common Error Without an Explanation, received only the common errors; Group 3, An Explanation Without a Common Error received only the explanations of the rules for writing expressions with exponents in lowest terms; and Group 4, No Common Error and No Explanation, received neither the common errors nor the explanations of the rules for writing expressions with exponents in lowest terms.

The data collected consisted of student responses on a pretest and a posttest. Each test consisted of 15 expressions with exponents which participants were asked to write in lowest terms. Analysis included a 2 x 2 Analysis of Variance with a blocking factor to determine whether common errors and explanations of the rules were significant as positive instructional strategies.

The results of this study did yield statistical significance for one instructional intervention group, Group 3, An Explanation Without a Common Error. The other three intervention group did not yield statistical significance.

Recommendations for future studies examining the use of common errors and explanations are suggested. Considerations for alternative methodological designs are discussed.

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