PROCEEDINGS OF THE 23RD ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2020
Boston, Massachusetts
Multivariate functions, physical representations, and real world connections
Page: 892
Understanding functions of two variables is difficult even for students who have studied multivariate calculus. The eight participants in this study, prospective middle and high school mathematics teachers, constructed physical models of functions of two variables by creating and assembling sets of transparencies representing cross-sectional planes. The models provided “chunky” representations of surfaces defined by function rules of two variables. This study reports ways in which students with the experience of constructing these models interpreted and operated on a real-world example of multivariate functions (wind chill index) that was reported in a national newspaper. Participants were confronted with potential cognitive conflicts in that the article contained typographical errors that eliminated a variable from the function rule and omitted essential graphical information. First rounds of analysis suggest the importance of focusing on what is being represented rather than solely on the form of the representation.