2021 Research in Undergraduate Mathematics Education Reports
2021
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The Presentation of Composition Across the Curriculum
Page: 124
Research has shown that college students struggle to understand the operation of composition and the compositive structure of functions. A study of the treatment of composition in written US curricula identified the opportunities that were provided to teachers and students. This report presents the types of functions and representations used to communicate composition in mathematics curricula across the transition from secondary mathematics to college calculus. The presentation of composition was overwhelmingly algebraic and less than four percent involved multiple representations. The results also revealed that composition was mainly presented with linear binomials, monomials, and the inverse cancellation of transcendental functions. The opportunities in written curricula were similar to the types of tasks on which researchers have reported students being successful. Diversifying textbook problems and examples has potential to increase student and teacher knowledge on composition and the compositive structure of functions.