Treatments of trigonometric functions during reforms in the United States
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Textbooks and reform documents provide a multiple source of descriptions of what it is to treat trigonometric functions as a school subject during three periods. Trigonometric functions in schools are introduced and developed in three major mathematical frames over the course of three reform periods in the United States – unified mathematics, new math, and standards-based instruction. Those frames are triangle, circle, and vector. They are used to explain the variations in textbooks’ treatments of trigonometry as a phenomenon during and across reforms. Using phenomenology, I focused on ideas of trigonometric functions as a school subject manifested in textbooks and reform documents during reform periods. I used Schubring’s methodology of historical textbook analysis to develop a history of interpretations of trigonometric functions as a school subject. I described the appearances and changes in the treatments of the trigonometric functions for each frame along the course of three reform periods from selected textbooks and reform documents.