Researching how professional mathematicians construct new mathematical definitions: a case study

• Published in: International journal of mathematical education in science and technology Vol. 49; no. 7; pp. 1069 - 1082
• Main Authors: Martín-Molina, Verónica, González-Regaña, Alfonso J., Gavilán-Izquierdo, José María
• Format: Journal Article
• Language: English
• Published: London Taylor & Francis 03.10.2018; Taylor & Francis Ltd
• Subjects: Case studies; Defining; Definitions; Differential geometry; Foreign Countries; generalizing; Geometry; Graduate studies; Graduate Study; Mathematical analysis; Mathematicians; Mathematics; Mathematics Activities; Mathematics Instruction; Professional Personnel; Qualitative analysis; Qualitative research; Researchers; Undergraduate Study; Spain
• ISSN: 0020-739X; 1464-5211
• DOI: 10.1080/0020739X.2018.1426795

In this work, we study the mathematical practice of defining by mathematics researchers. Since research is an important part of many professional mathematicians, understanding how they do research is a necessary step before thinking about future researchers' undergraduate and postgraduate education. We focus on the defining process associated with the generalization of existing definitions as a way of constructing new ones. Data of this qualitative study come from a case study whose subject is a mathematics researcher in the area of differential geometry. We have interviewed this researcher and collected her research documents. From our analysis of the data, we have identified four phases in the defining process (Finding an opportunity to generalize an existing concept, Proposing a new definition, Justifying that the new definition is valid and Continuing the chain of definitions), which we will describe in detail in Section 4.