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ERIC Number: EJ993622
Record Type: Journal
Publication Date: 2012-Nov
Pages: 6
Abstractor: ERIC
ISBN: N/A
ISSN: ISSN-1072-0839
EISSN: N/A
Get to Know a Circle
Neel-Romine, LeAnn E.; Paul, Sara; Shafer, Kathryn G.
Mathematics Teaching in the Middle School, v18 n4 p222-227 Nov 2012
Middle-grades students have a concept image of a circle, but they lack experience in the act of defining. The structure of definitions needs to include conditions that are necessary and sufficient. Most students are able to identify necessary conditions, but they have trouble determining if sufficient conditions are met. How do teachers engage students in the act of defining, which involves learning the characteristics of a definition? One answer might be to look at a teaching trajectory guided by the van Hiele levels of thought (Hoffer 1983). This teaching trajectory scaffolds the process with specific lesson phases: (1) Inquiry; (2) Directed Orientation; (3) Expliciting; (4) Free Orientation; and (5) Integration. In the authors' experience, learners of all ages typically define a circle by listing traits or properties (that sometimes create something other than a circle). Sara Paul (the second author) taught three classes of sixth-grade mathematics. This article provides a description of what occurred when Paul teamed with a math educator and conducted an activity to develop the definition of a circle. Here, the description of the circle activity is presented within the context of the van Hiele levels of thought. (Contains 4 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: orders@nctm.org; Web site: http://www.nctm.org/publications/
Publication Type: Journal Articles; Reports - Descriptive
Education Level: Middle Schools
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A