On Linear Functions and Their Graphs: Refining the Cartesian Connection
- PDF / 1,631,407 Bytes
- 20 Pages / 439.37 x 666.142 pts Page_size
- 76 Downloads / 252 Views
On Linear Functions and Their Graphs: Refining the Cartesian Connection Leslie Glen 1 & Rina Zazkis 1 Received: 9 August 2019 / Accepted: 6 July 2020/ # Ministry of Science and Technology, Taiwan 2020
Abstract This study focuses on connections between linear functions and their graphs that were made by tertiary remedial algebra students. In particular, we describe students’ work on a Task designed to examine the connection between points on a graph and the equation of a line. The data consist of 63 responses to a written questionnaire and individual interviews with three participants. The results indicate that visual approaches impede students’ solutions and point to incomplete connections between algebraic and graphical representation. While algebraic approaches point to various connections used in approaching the Task, students’ ability to work with algebraic representation did not necessarily result in capitalizing on these connections. Furthermore, interpretations of the graph based on visual inspection appeared most useful when used in support of the algebraic approach. Keywords Cartesian connection . Community college . Linear functions . Graphical
representation It is critical that students understand connections between algebraic and graphical representations of functions. The goal of our study is to investigate connections between the graph and the equation of a linear function, made by tertiary students in a remedial algebra course. Our focus is on student work related to one of these connections: the connection between the coordinates of a point and its location on a particular line. This is what Moschkovich, Schoenfeld, and Arcavi (1993) refer to as “the Cartesian Connection”: “A point is on the graph of the line L if and only if its coordinates satisfy the equation of L” (p. 73). In what follows we start with a brief overview of research literature on linear functions. Next, we elaborate on the Cartesian Connection, which is a theoretical
* Rina Zazkis [email protected]
1
Faculty of Education, Simon Fraser University, 8888 University Drive, Burnaby, BC V5A 1S6, Canada
L. Glen, R. Zazkis
construct that guided our investigation. We then present the detailed account of our study.
Brief Overview of Related Literature on Linear Functions Research in mathematics education has pointed to students’ difficulties in learning the algebra of linear functions in general (e.g. Leinhardt, Zaslavsky, & Stein, 1990) and in comprehending various components of the topic in particular (e.g. Hattikudur et al., 2012; Pierce, Stacey, & Bardini, 2010). Prior studies examined various teaching strategies that support student learning (Pierce et al., 2010) and the impact of the use of technology on students’ work (e.g. Bardini, Pierce, & Stacey, 2004). Difficulties described in the literature are numerous and diverse, but they can, for the most part, be broadly sorted into a few categories. These difficulties are related to graphing linear equations (e.g. Davis, 2007; Hattikudur et al., 2012), to the function notation and t
Data Loading...
