Ratio and Proportion: Connecting Content and Children's Thinking

Twenty-four sixth-grade children participated in clinical interviews on ratio and proportion before they had received any instruction in the domain. A framework involving problems of four semantic types was used to develop the interview questions, and student thinking was analyzed within the semanti...

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Bibliographic Details
Published in:Journal for research in mathematics education 1993-01, Vol.24 (1), p.41-61
Main Author: Lamon, Susan J.
Format: Article
Language:English
Subjects:
Abstract Reasoning
Balloons
Children
Cognitive Development
Cognitive Style
Denotational semantics
Eggs
Elementary Education
Grade 6
Interviews
Mathematical Concepts
Mathematical problems
Mathematics Education
Pizzas
Problem Solving
Proportional Reasoning
Ratios
Ratios (Mathematics)
Reasoning
Rectangles
Student Evaluation
Thinking Skills
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Summary:Twenty-four sixth-grade children participated in clinical interviews on ratio and proportion before they had received any instruction in the domain. A framework involving problems of four semantic types was used to develop the interview questions, and student thinking was analyzed within the semantic types in terms of mathematical components critical to proportional reasoning. Two components, relative thinking and unitizing, were consistently related to higher levels of sophistication in a student's overall problem-solving ability within a semantic type. Part-part-whole problems failed to elicit any proportional reasoning because they could be solved using less sophisticated methods. Stretcher/shrinker problems were the most difficult because students failed to recognize the multiplicative nature of the problem situations. Student thinking was most sophisticated in the case of associated sets when problems were presented in a concrete pictorial mode.
ISSN:0021-8251
1945-2306
DOI:10.2307/749385