What do students attend to when first graphing planes in R3?

This talk considers what students attend to as they first encounter R3 coordinate axes and are asked to graph y = 3. Graphs are critical representations in single and multivariable calculus, yet findings from research indicate that students struggle with graphing functions of more than one variable. We found that some students thought y = 3 in R3 would be a line, while others thought it would be a plane. In creating their graphs, students attended to equidistance, parallelism, specific points, 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.