Share
Pin it!
Google Plus




Subscriber? Sign in to access.


 

Conceptual Units Analysis of Preservice Elementary School Teachers' Strategies on a Rational-Number-as-Operator Task

Merlyn J. Behr, Helen A. Khoury, Guershon Harel, Thomas Post, Richard Lesh 

January 1997, Volume 28, Issue 1, Page 48

Abstract:
This study explores preservice teachers' understanding of the operator construct of rational number. Three related problems, given in 1-on-1 clinical interviews, consisted of finding 3/4 of a pile of 8 bundles of 4 counting sticks. Problem conditions were suggestive of showing 3/4 of the number of bundles (duplicator/partition-reducer [DPR] subconstruct) and 3/4 of the size of each bundle (stretcher/shrinker [SS] subconstruct). This study provides confirming instances that students use these 2 rational number operator subconstructs. The SS strategies are identified when the rational number, as an operator, is distributed over a uniting operation. With these SS strategies, rational number is conceptualized as a rate. However, the SS strategies were used less often than the DPR strategies. Detailed cognitive models of these strategies in terms of the underlying conceptual units, their structures, and their modifications, were produced, and a "mathematics of quantity" notational system was used as an analytical tool to describe and model the embedded abstractions.

Keywords:
Clinical Interviews
Teacher in Training / Preservice Teacher
Conceptual Development
Higher Education
Fractions / Decimals / Percents / Rational Numbers
Reasoning and Proof