PROCEEDINGS OF THE 20TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2017
San Diego, California
Generalising univalence from single to multivariable settings: The case of Kyle
Page: 562
A function is defined as a mapping from one nonempty set (the domain) to another nonempty set (the co-domain or range) such that each element of the domain maps to exactly one element of the range. Algebra curricula typically include classification tasks in which students determine if a relation violates the univalence criterion – the condition that each element in the domain corresponds to exactly one element of the range. This paper provides a longitudinal case study of how one student generalised the univalence criterion from single- to multivariable functions. For f(x), Kyle primarily thought of univalence in terms of the vertical line test and the variables x and y. He generalised univalence for the multivariable function f(x,y) by thinking about input, output, independence, and dependence. Kyle’s story provides an example of how a student might generalise facets of the function concept in normatively correct ways.