**ERIC Number:**EJ1044573

**Record Type:**Journal

**Publication Date:**2014-Apr

**Pages:**8

**Abstractor:**ERIC

**Reference Count:**11

**ISBN:**N/A

**ISSN:**ISSN-0025-5769

The Circle Approach to Trigonometry

Moore, Kevin c.; LaForest, Kevin R.

Mathematics Teacher, v107 n8 p617-623 Apr 2014

How do students think about an angle measure of ninety degrees? How do they think about ratios and values on the unit circle? How might angle measure be used to connect right-triangle trigonometry and circular functions? And why might asking these questions be important when introducing trigonometric functions to students? When teaching trigonometric functions, most teachers would agree that students have difficulty using trigonometric functions to relate quantities in circle and right-triangle contexts. If students are to use trigonometric functions productively, they must understand angle measure, the unit circle, and right triangles in ways that let them see trigonometric functions as relations between two quantities. In addition, trigonometry instruction should adhere to the Common Core State Standards for Mathematics' emphasis on students' quantitative reasoning (CCSSI 2010). In this article, Kevin Moore and Kevin LaForest draw from recent research on student learning in trigonometry to illustrate a connected introduction of angle measure and the sine function that entails quantitative reasoning. To demonstrate these ideas in practice, they provide examples of precalculus students' solutions to various trigonometry problems. The ideas presented here also outline nuances involved in increasing student learning during a sequence of activities like that presented by Landers (2013). In particular, they draw attention to reasoning about varying quantities in the context of graphing and how issues of measurement help students understand the unit circle and ratios.

Descriptors: Trigonometry, Mathematics Instruction, Mathematical Concepts, Mathematical Logic, Logical Thinking, Measurement, Secondary School Mathematics, Graphs, Geometric Concepts, Problem Solving

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

**Audience:**Teachers

**Language:**English

**Sponsor:**National Science Foundation

**Authoring Institution:**N/A

**IES Grant or Contract Numbers:**EHR-0412537