PROCEEDINGS OF THE 19TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2016
Pittsburgh, Pennsylvania
What do students attend to when first graphing y = 3 in R^3?
Page: 111
I interviewed 11 differential calculus students as they graphed for the first time in R3. This paper considers how students generalise as they graph y = 3. Some students drew a line, while others drew a plane. In creating their graphs, students attended to equidistance, parallelism, specific (x, y), (y, z), (x, y, z) tuples, and the role of x and z. Students’ use of these ideas was often generalised from thinking about the graphs of y = b equations in R2. A key finding is that the students who thought the graph was a plane always attended to the z variable as free. I discuss this specific result using Harel and Tall’s expansive, reconstructive, and disjunctive generalisations framework. I propose that the expansive and reconstructive categories provide a powerful way to explain and understand the two main ways students generalise from R2 to R3, and why multivariable topics are difficult for learners.