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ERIC Number: ED547720
Record Type: Non-Journal
Publication Date: 2012
Pages: 152
Abstractor: As Provided
Reference Count: N/A
ISBN: 978-1-2674-6893-2
ISSN: N/A
The Treatment of Composition in Secondary and Early Collegiate Mathematics Curricula
Horvath, Aladar Karoly
ProQuest LLC, Ph.D. Dissertation, Michigan State University
Composition has been described as essential for understanding functions (Carlson, Oehrtman, & Engelke, 2010; Cooney, Beckmann, & Lloyd, 2010). Studies of students' understanding of function composition have shown that students use multiplication and other operations in place of composition (Carlson et al., 2010; Horvath, 2010). While there have been studies of students' knowledge of composition, the teaching of and curricular development of composition has not received as much attention. This dissertation attempted to fill this void by examining the treatment of composition in secondary and early collegiate mathematics curricula. By examining the definitions, explanations, and uses of composition, I was able to describe the kinds of explicit and implicit opportunities that textbooks provide to students with respect to the concept of composition. This analysis of textbooks of high school algebra 1 and 2, geometry, and precalculus and collegiate precalculus and calculus textbooks utilized multiple frameworks. Mathematically, composition can be viewed as an operation on objects (e.g., functions or relations) or as a recursive sequence of processes where the output of the nth process is the input of the n+1st process. A framework of procedural, conceptual, and conventional knowledge was used to describe the ways that textbooks define, explain, and perform composition. The representation (e.g., algebraic, graphical, tabular) and type of function, relation, or transformation (e.g., polynomial, reflection) is also included in the coding scheme of this study. The results indicated that composition appeared throughout the secondary and early collegiate curriculum and utilized functions as both objects and processes. Composition content was predominately presented using the algebraic representation and the use of compositive structure in transcendental functions was largely implicit. This examination provided background information for existing studies of student knowledge of composition and provides a framework for future studies of the teaching and learning of composition. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]
ProQuest LLC. 789 East Eisenhower Parkway, P.O. Box 1346, Ann Arbor, MI 48106. Tel: 800-521-0600; Web site: http://www.proquest.com/en-US/products/dissertations/individuals.shtml
Publication Type: Dissertations/Theses - Doctoral Dissertations
Education Level: Secondary Education; Higher Education; Postsecondary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A