PROCEEDINGS OF THE 18TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2015
Pittsburgh, Pennsylvania
A discursive approach to support teachers’ development of student thinking about functions
Page: 562
Function is a critical concept for mathematics and related branches of sciences. Despite its centrality in K-12 and undergraduate mathematics, it is one of the most challenging topics to master in school learning due to the various notions associated with the concept (Eisenberg, 1991). Existing research highlights many challenges students face as they learn about functions. Researchers argue that students often associate function with a single algebraic expression or rule (Vinner & Dreyfus, 1989) and have difficulties with piecewise functions (Sfard, 1992). Students also struggle with conceptualizing function both as a process and a mathematical object (Gray & Tall, 1994; Sfard, 1992) and moving flexibly across graphical, algebraic, tabular, and verbal representations of functions (Monk, 1994; Sierpinska, 1992; Tall, 1996). They have difficulties interpreting dynamic representations and information demonstrating the relationship between two variables (Carlson, 1998; Kaput, 1992; Monk, 1994). Given the multiplicity of notions and complexities inherent in the learning of functions, it is important for teachers to address their students’ difficulties in the classrooms. In order to this, teachers need to understand the content and the challenges it presents to students.