Multi-Relation Strategy in Students’ Use of a Representation for Proportional Reasoning
Kazuhiko Nunokawa 1 *
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1 Joetsu University of Education, JAPAN* Corresponding Author


The purpose of this paper is to analyze in detail the process in which a 5th grade student learned proportion and percent using double number lines and to obtain insights into how his use of those representations supported his learning. A series of lessons were designed and conducted in a class and the whole learning process of one student was videorecorded. The analysis showed that he used double number lines to search for various multiplicative relationships in problem situations and their consistent pictures, rather than to make necessary numerical expressions systematically. The analysis also showed that such uses of number lines made it possible for him to control his proportional reasoning and develop his understanding of proportion and percent.


This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, 2012, Volume 8, Issue 4, 233-248

Publication date: 12 Jan 2012

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