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Title: An Alternative Approach for the Learning of (a+b)2=a2+2ab+b2
Authors: Chang, Ching-Kuch;Tsai, Yu-Ling
Contributors: 科學教育研究所
Keywords: (a+b)2=a2+2ab+b2;Combinatorics model;Multiplicative identities
Date: 2005-08
Issue Date: 2012-11-22T07:40:11Z
Abstract: There are two different approaches for the learning of the identity . One is the deductive model, popular in the earlier mathematics curriculum, starting with the definition of distribution law and then introducing the multiplicative identities. The other is geometric model, popular in the new mathematics curriculum, using area calculation to represent the algebraic relationships about the identity . However, according to teacher’s experiences in classroom, about one half of the students would feel useful through geometric mode, and only the one third of the students can learn multiplicative identities through the definition model. Moreover, many of them, are still having difficulties to expand or . In other words, those students have not constructed the mental structure of distribution law yet. Current curriculum reform calls mathematics for all. In order to help more students to learn the algebraic identities to higher levels of understanding, or to enhance students’ facility with symbol manipulation, a professor and a mathematics teacher cooperated to develop instructional modules for the learning of by doing action research in the teacher’s mathematics classroom. The modules were developed by designing a context that involves distributive law concept from the combinatorics activities of the things around daily life in order to assist students to establish their mental structure of the distributive law, and assist students to generalize the concept of the distributive law via the process of progressive mathematizing. Several theories, such as RME and APOS, were used to guide this study. This article describes the alternative approach, called the combinatorics model in this article, for the learning of the identity. The learning activities of the modules would lead students to develop the formal knowledge of multiplicative identities and deal with the problem of polynomial expansions. The effects of the combinatorics model would be discussed in other article.
Relation: The 3rd East Asia Regional Conference on Mathematics Education, Shanghai, Nanjing, and Hangzhou, People's Republic of China
Appears in Collections:[科學教育研究所] 會議論文

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