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ERIC Number: EJ1000868
Record Type: Journal
Publication Date: 2012-Nov
Pages: 9
Abstractor: ERIC
Reference Count: 0
ISSN: ISSN-0025-5769
Using Multiple Representations to Teach Composition of Functions
Steketee, Scott; Scher, Daniel
Mathematics Teacher, v106 n4 p260-268 Nov 2012
Composition of functions is one of the five big ideas identified in NCTM's "Developing Essential Understanding of Functions, Grades 9-12" (Cooney, Beckmann, and Lloyd 2010). Through multiple representations (another big idea) and the use of The Geometer's Sketchpad[R] (GSP), students can directly manipulate variables and thus see dynamic visual images of function behavior. The object is to foster students' deep and flexible understanding of what functions are, how they behave, and how they can be composed--crucial prerequisites for mastery of related topics such as transformations of functions, families of functions, and inverses of functions. Depending on students' previous use of GSP and their familiarity with geometric representations of functions, the five activities described in this article will require from three to five class periods of about forty-five or fifty minutes each. Do not rush students; a thorough and unhurried discussion at the end of each activity is critical. Class discussions allow students to think again about what they have done and observed, to review their use of function notation, to compare and contrast different representations of function composition, and to consolidate their understanding. Although all five activities need not be used, doing so gives students the time and experiences that many need to consolidate and generalize their understanding of this challenging topic. (Contains 11 figures and 3 online resources.)
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:; Web site:
Publication Type: Journal Articles; Reports - Descriptive
Education Level: Grade 10; Grade 11; Grade 12; Grade 9; High Schools
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A