**ERIC Number:**EJ1044591

**Record Type:**Journal

**Publication Date:**2014-Feb

**Pages:**6

**Abstractor:**ERIC

**Reference Count:**15

**ISBN:**N/A

**ISSN:**ISSN-0025-5769

Cultivating Deductive Thinking with Angle Chasing

Edwards, Michael todd; Quinlan, James; Harper, Suzanne R.; Cox, Dana C.; Phelps, Steve

Mathematics Teacher, v107 n6 p426-431 Feb 2014

Despite Common Core State Standards for Mathematics (CCSSI 2010) recommendations, too often students' introduction to proof consists of the study of formal axiomatic systems--for example, triangle congruence proofs--typically in an introductory geometry course with no connection back to previous work in earlier algebra courses. Van Hiele notes that students must pass through lower levels of geometric thought before meaningful study of formal proof is possible (Crowley 1987). Premature study of formal proof leads students to memorize theorems with little understanding of their purpose (Battista and Clements 1995). Before their formal study of axiomatic systems, students need opportunities to formulate deductive arguments in developmentally appropriate ways. Research suggests that increased emphasis on informal deduction fosters stronger understanding of formal proof in subsequent instruction (Bell 1976; NCTM 1938). Recreational puzzles (Wanko 2010), dynamic geometry software (Sinclair and Crespo 2006; Furner and Marinas 2007), and image analysis (Maher and Martino 1996) have been put forth as possible methods for promoting deductive thought before study of formal proof in introductory geometry courses. In this article, the authors present angle chasing as another such vehicle. Angle chasing, a process of determining measures of angles using deductive logic, provides students with an engaging way to explore fundamental properties of angles. It requires students to "use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure" (CCSSI 2010, p. 50). Instructional assumptions, a three-step approach (deductive-inductive-deductive) to teaching angle chasing, and fostering student reflection are discussed.

Descriptors: Mathematics Instruction, Logical Thinking, Validity, Secondary School Mathematics, Geometry, Geometric Concepts, High Schools, Mathematics Skills, 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:**Secondary Education; High Schools

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A