In my talk I will discuss the meaning of ‘mathematical explanation’ from an enactivist perspective. Enactivism was so named by Varela, Thompson and Rosch (1991) and has its origins in Maturana’s Biology of Cognition (Maturana, 1970/1980; Maturana & Varela, 1992; Maturana, & Poerksen, 2004). A central principle is the observation, derived from the biological study of perception, that living beings do not directly perceive features of an external world. This means in the current context that I must abandon the question, “What is a ‘mathematical explanation’?” and ask instead, “What happens in me when I say that I see something as a ‘mathematical explanation’?”. Hence it is this latter question that I will explore. I will make reference to the feelings of certainty and ‘knowing why’ that I experience in connection with proving and explaining. Along the way, I will also make connections with the ways ‘mathematical explanation’ has previously been characterised in the mathematics education literature, and discuss some implication of this perspective for teaching.

Sources:

Maturana, H. & Varela, F. (1992). The Tree of Knowledge: The biological roots of human understanding. Shambhala.

Maturana, H. R., & Poerksen, B. (2004). From being to doing: The origins of the biology of cognition. Carl-Auer Verlag.

Maturana, H. (1980). Biology of cognition. In Maturana, H. & Varela, F. (Eds.) Autopoiesis and Cognition: The Realization of the Living (pp. 5–58). Reidel. Originally published in 1970 by the Biological Computer Laboratory, Department of Electrical Engineering, University of Illinois.

Varela, F., Thompson, E. & Rosch, E. (1991). The Embodied Mind: Cognitive Science and Human Experience. MIT Press.