PROCEEDINGS OF THE 23RD ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2020
Boston, Massachusetts
A potential foundation for trigonometry and calculus: The variable-parts perspective on proportional relationships and geometric similarity
Page: 734
Until recently, the variable-parts perspective on proportional relationships had been overlooked in mathematics education research. We argue that the variable-parts perspective is implicit in contexts of geometric similarity, including trigonometry and the notion of slope, and that it is well-suited to situations involving varying increments of change, as in calculus. We explain how a variable-parts approach to these topics is related to approaches and findings of research on trigonometry, rate of change, and the Fundamental Theorem of Calculus. Our arguments are theoretical, but lead to the empirically testable hypothesis that an explicit focus on the variable-parts perspective could be productive for learning geometric similarity, trigonometry, slope, and calculus.