RUME 26
2024
Omaha, Nebraska
Professional Mathematicians' Levels of Understanding and Pseudo-Objectification
Page: 1286
In recent years, research on professional mathematicians' mathematical practices, including how they understand mathematical concepts, has been become more common (e.g., Oehrtman et al., 2019; Shepherd & van de Sande, 2014; Wilkerson-Jerde & Wilensky, 2011). Closely related to understanding is the notion of abstraction. Likely the most prominent theory of abstraction is Piaget’s reflective abstraction and his broader genetic epistemology (Piaget, 1970). Using Piaget's broader theory, this study introduces three different theoretical levels of understanding: pseudo-object-level, process-level, and object-level. With these levels of understanding, this study addresses the following two research questions: (1) In what ways do professional mathematicians operate with highly-abstract, advanced mathematical concepts at different levels of understanding? (2) What factors can influence a professional mathematician’s level of understanding for a given mathematical concept? In this study, I interviewed six professional mathematicians with three distinct semi-structure interviews. Data analysis revealed that mathematicians operate differently depending on their level of understanding for a mathematical concept. Moreover, various factors influence mathematicians' level of understanding for a given mathematical concept, including how the concept is being utilized and certain sociocultural factors.