RUME 26
2024
Omaha, Nebraska
Students’ Productive Techniques for Approaching Well-Definedness and Everywhere-Definedness
Page: 754
Functions are critical in mathematics but have received limited attention at the advanced level. Research in advanced contexts has primarily focused on students' reasoning about specific types of functions (e.g., isomorphisms) but not on the function concept itself. In this paper, we explore students' productive techniques involving the definitive properties of function: well-defined and everywhere-defined. We found that the techniques students productively employed extended far beyond canonical procedures (like the vertical line test) and largely drew upon function meanings involving coordination of the domain, codomain, and rule, which previous research has highlighted the importance of but stopped short of directly investigating. Two contributions of this work include our focus on productive, successful techniques (rather than challenges and difficulties), and explicit focus on everywhere-defined (which has not received direct attention).