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ERIC Number: EJ902124
Record Type: Journal
Publication Date: 2010-Oct
Pages: 6
Abstractor: ERIC
Reference Count: 0
ISSN: ISSN-0025-5769
Teaching Proportional Reasoning through Familiar Biology
Burger, Lance
Mathematics Teacher, v104 n3 p186-191 Oct 2010
Constructivism has constituted a predominant philosophical trend in mathematics education, but its implementation in the classroom has proven to be "far more difficult than the reform community acknowledges". This difficulty may be due in part to administrative cultures that might insist on more procedural types of instruction aimed at testing, in part to the lack of an accessible synthesis of constructivist theory useful for the everyday teacher. Inspired by Jean Piaget, Harel (2000) simplified the technical jargon of constructivism into a simple necessity principle: "For students to learn, they must see an (intellectual, as opposed to social or economic) need for what they are intended to be taught" (p. 185). Often, mathematics activities are not difficult, engaging, or meaningful enough to evoke in students a feeling of needing to solve a problem. Students who see the necessity in the mathematics they learn are more apt to become engaged in and "own" their mathematical problems--a first step for genuinely constructing mathematical knowledge. In this article, the author describes a lesson implemented using the necessity principle to plan engaging content, discussions, and activities meant to promote meaningful student growth in mathematical understanding. He discusses how to teach proportional reasoning through familiar biology and presents an activity that teaches students about the ratio of surface area to volume by exploring the relationships between size and heat loss in dogs.(Contains 5 figures.)
National Council of Teachers of Mathematics. 1906 Association Drive, Reston, VA 20191-1502. Tel: 800-235-7566; Tel: 703-620-3702; Fax: 703-476-2970; e-mail:; Web site:
Publication Type: Journal Articles; Reports - Descriptive
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A