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When does a way of working become a methodology? (2000)
Journal Article
Duffin, J., & Simpson, A. (2000). When does a way of working become a methodology?. Journal of Mathematical Behavior, 19(2), 175-188. https://doi.org/10.1016/s0732-3123%2800%2900043-2

We discuss the question of how to determine what are valid methodologies in mathematics education and the problems associated with developing new ways of working into acceptable research methods. We develop the idea of a two-stage validation process... Read More about When does a way of working become a methodology?.

A search for understanding (2000)
Journal Article
Duffin, J., & Simpson, A. (2000). A search for understanding. Journal of Mathematical Behavior, 18(4), 415-427. https://doi.org/10.1016/s0732-3123%2800%2900028-6

We discuss an important breakthrough for us in our search for a technical meaning of “understanding” in mathematics education. In this article, we describe the background to this discovery, the catalyst for the breakthrough, and a concise explanation... Read More about A search for understanding.