for the learning of mathematics

an international journal of mathematics education

Rina Zazkis ,  Ami Mamolo - Vol. 29 Num. 3 (2009)
 Sean vs. Cantor: Using mathematical knowledge in ‘experience of disturbance'


Mathematical knowledge used in teaching has attracted the interest of many researchers, but was mainly explored considering teaching at the elementary school level. This paper attends to mathematical knowledge used in teaching at the University level. We present a story about a student suggesting reconsideration of Cantor's diagonal method and the relationship between real and natural numbers. The teacher's response to this unexpected classroom situation and her initiatives to draw on it for further learning are analysed through the lens of ‘knowledge for teaching'. Our contribution is in extending research on teachers' knowledge and on students' struggle with ideas related to infinity.