PROCEEDINGS OF THE 21ST ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2018
San Diego, California
Identifying Subtleties in Preservice Secondary Mathematics Teachers’ Distinctions Between Functions and Equations
Page: 1562
For more than thirty years, the secondary school mathematics curriculum has seen a shift to functions-based approaches to algebra. Advancing comprehension of the equals sign as an equivalence relation is critical for beginning algebra students studying equations, and developing understanding of functions is foundational as a gateway to courses required of science, technology, engineering, and mathematics majors. This study explores the ways in which mathematics majors seeking secondary mathematics teaching certification distinguish between the concepts of function and equation. Participants (n=24) completed a ten-item pre- and post-assessment on functions and equations. Open coding techniques were used to identify emerging categories that describe participants’ distinctions between the concepts. After a mathematics course experience with an eight-week unit on functions, the participants’ concept image for functions focused primarily on input and output whereas their concept image for equations centered broadly on the equivalence of two quantities.