Upcoming SlideShare
×

# Teaching trigonometricfunctionsnctm

333 views

Published on

Teaching trigonometric function

Published in: Education, Technology
0 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

• Be the first to like this

Views
Total views
333
On SlideShare
0
From Embeds
0
Number of Embeds
6
Actions
Shares
0
14
0
Likes
0
Embeds 0
No embeds

No notes for slide

### Teaching trigonometricfunctionsnctm

1. 1. 144 Mathematics Teacher | Vol. 102, No. 2 • September 2008 connecting research to teaching Teaching Trigonometric Functions: Lessons Learned from Research T rigonometry is an important subject in the high school mathematics curriculum. As one of the secondary mathematics topics that are taught early and that link algebraic, geometric, and graphical reasoning, trigonometry can serve as an important precursor to calculus as well as college- level courses relating to Newtonian physics, archi- tecture, surveying, and engineering. Unfortunately, many high school students are not accustomed to these types of reasoning (Blackett and Tall 1991), and learning about trigonometric functions is initially fraught with difficulty. Trigonometry presents many first-time challenges for students: It requires students to relate diagrams of triangles to numerical relationships and manipulate the sym- bols involved in such relationships. Further, trigo- nometric functions are typically among the first functions that students cannot evaluate directly by performing arithmetic operations. Despite the importance of trigonometry and stu- dents’ potential difficulties in learning it, relatively little research has focused on this subject. This arti- cle will present lessons learned from research inves- tigating the learning and teaching of trigonometric functions (Weber 2005). It will report difficulties that students have in understanding trigonometric functions and describe tested instructional strategies to help students overcome their difficulties. TRIGONOMETRIC FUNCTIONS AS RATIOS AND FUNCTIONS What does it mean to understand a trigonometric function? Just as taking a square root or cubing a number can be thought of as operations applied to numbers, the terms sine, cosine, and tangent can be thought of as mathematical operations applied to angles. These trigonometric functions are generally presented in two ways. First, they are presented as ratios that can be applied to labeled right triangles. For instance, students can use a ratio understand- ing of the trigonometric functions to determine that sin A = 3/5, cos A = 4/5, and tan A = 3/4 (see fig. 1). Using calculators, students can use a ratio under- standing of sine and cosine to determine the missing lengths (a and b) of the triangle (see fig. 2). Such an understanding is obviously useful; it is sufficient to solve various types of word problems and perform other tasks. For instance, adding vectors in physics requires this type of trigonometric reasoning. However, a ratio understanding is also limited. Principles and Standards for School Mathematics argues that understanding an operation involves being able to estimate the result of that operation (NCTM 2000, pp. 32–33). For example, under- standing fractions involves knowing that 7/8 + 13/12 should be approximately 2 because each fraction is approximately 1. By itself, a ratio understanding of sine would not permit students to approximate sin 15°, because sin 15° could be This department consists of articles that bring research insights and findings to an audience of teachers and other mathematics educators. Articles must make explicit connections between research and teaching practice. Our conception of research is a broad one; it includes research on student learning, on teacher think- ing, on language in the mathematics classroom, on policy and practice in math- ematics education, on technology in the classroom, on international comparative work, and more. The articles in this department focus on important ideas and include vivid writing that makes research findings come to life for teachers. Our goal is to publish articles that are appropriate for reflection discussions at depart- ment meetings or any other gathering of high school mathematics teachers. For further information, contact the editors. Libby Knott, knott@mso.umt.edu University of Montana, Missoula, MT 59812 Thomas A. Evitts, taevit@ship.edu Shippensburg University, Shippensburg, PA 17257 Keith Weber Copyright © 2008 The National Council of Teachers of Mathematics, Inc. www.nctm.org. All rights reserved. This material may not be copied or distributed electronically or in any other format without written permission from NCTM.