Physics Colloquium - Fall 2006 - The Implications of an "Aha!" moment: Some examples from reasoning about first-order differential equations
Dept of Physics & Astronomy
University of Maine, Orono, Maine
Presents
John E. Donovan
Assistant Professor of Mathematics
Dept. of Mathematics, University of Maine
The Implications of an "Aha!" moment: Some examples from reasoning about first-order differential equations
I can best describe my experience of doing mathematics in terms of entering a dark mansion. One goes into the first room and it's dark, completely dark. One stumbles around bumping into the furniture. Gradually you learn where each piece of furniture is. And finally you find the light switch, you turn it on and suddenly it's all illuminated, you can see exactly where you were.
-Andrew Wyles, mathematician who proved Fermat's last theorem (i.e. there are no whole number solutions to the equation x^n + y^n = z^n, n>2)
The experience that Wyles describes is familiar; we have all experienced it in mathematics although the scales of our discoveries vary significantly. These moments are important because they are often accompanied by a mental compression, or reification. The step-by-step processes and algorithms in essence get "filed away" so they can be recalled easily and used in other processes. The theory of reification is a theory about learning mathematics that describes the characteristics of this process and shows it importance for the development of subsequent concepts. In this talk I will use examples from my research on students' understanding of first-order differential equations to illustrate important aspects of this theory and explain sharp differences in two case studies.
Friday, December 8, 2006
3:10 pm
140 Bennett Hall
Refreshments will follow in Rm. 114, Bennett Hall
Back to Physics Colloquium - Fall 2006
