**ERIC Number:**EJ1018174

**Record Type:**Journal

**Publication Date:**2013-Apr

**Pages:**6

**Abstractor:**ERIC

**ISBN:**N/A

**ISSN:**ISSN-0025-5769

**EISSN:**N/A

Geometric Reasoning about a Circle Problem

Gonzalez, Gloriana; DeJarnette, Anna F.

Mathematics Teacher, v106 n8 p586-591 Apr 2013

What does problem-based instruction do for students and teachers? The open-ended geometry problem presented in this article, along with examples of students' work on the problem, illustrates how problem-based instruction can help students develop their mathematical proficiency. Recent studies have shown that students who experience problem-based instruction improve their perceptions about mathematics and about themselves as mathematical learners. In this article, the authors show an example of a problem-based lesson taught in a geometry classroom--the circle problem--and provide evidence of geometry students' reasoning and sense making when working on it. The circle problem provided a context for students to develop competency in the five strands of mathematical proficiency outlined in "Adding It Up": conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition. This analysis of students' work focuses on the latter three competencies, which are less commonly discussed in the literature. "Strategic competence" refers to the ability to formulate, represent, and solve mathematical problems; "adaptive reasoning" is the capacity for logical thought, reflection, explanation, and justification; and "productive disposition" refers to the inclination to see mathematics as worthwhile combined with a belief in diligence and one's own efficacy. By developing insight into how students can build mathematical proficiency through specific problem-based lessons, teachers may become more equipped to teach mathematics through problems.

Descriptors: Mathematical Logic, Mathematics Instruction, Geometry, Geometric Concepts, Problem Based Learning, Problem Solving, Mathematics Skills, Competence, High Schools, Secondary School Mathematics, Teaching Methods

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:**High Schools

**Audience:**Teachers

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A

**Grant or Contract Numbers:**N/A