The Effects of a Discrete Covariatonal Approach to Functions Through Computer Programming On Students\u27 Understanding of Rate of Change

Having a broad understanding of functions is paramount to student success in higher math classes, however most students fail to fully develop this concept during their high school years. While the concept of function is multifaceted and a full understanding requires a broad knowledge base, understanding rate of change can be considered a fundamental component of the concept. Unfortunately, even AP Calculus students have difficulty with rate of change (Teuscher & Reys, 2012). The problem may stem from the approach taken in most curricula that focus on the correspondence view of functions rather than the covariational perspective as advocated by researchers and the National Council of Teachers of Mathematics. This qualitative study was a probe into student reasoning about rate of change within the covariational framework developed by Carlson, Jacobs, Coe, Larsen, and Hsu (2002), and the effectiveness of a series of computer programming activities on students\u27 reasoning abilities. The study was conducted at a public urban high school in the southwest United States with 15 student and 2 teacher participants from two ninth grade Algebra I classes. Students were given a pre-assessment prior to completing a series of activities in which they used the VPython programming language to write code that would produce graphs for given data sets and scenarios. Afterwards, the students then completed a post-assessment to measure changes in reasoning. Overall, student participants had an impoverished understanding of rate of change with reasoning at the lowest levels of the covariational framework. In addition, while the activities did not produce a significant change in student reasoning, it appears that they were somewhat effective in improving student reasoning in the context of linear functions and in bringing students\u27 covariational reasoning to the forefront. With subsequent revision and iterations, the lessons may develop into an effective means of teaching rate of change from a covariational perspective