Symposium on the Occasion
of the 100th Anniversary of ICMI

(Rome, 5–8 March 2008)


Intuition and rigor in mathematics education

Dina Tirosh and Pessia Tsamir (School of Education, Tel-Aviv University)

A perennial theme in mathematics education in general and in the work of ICMI in particular is the balance between, on the one hand, rigor, logic, axiomatic, and formalism and, on the other hand, intuition, insight, common sense, invention and heuristics. This pertains to concept formation and understanding as well as to reasoning and justification in mathematics. The emphasis on either of these two dimensions of mathematics education has varied a lot throughout history, sometimes even taking the form of tension, thus reflecting the difficulty of finding balance. In the first part of our plenary we briefly relate to the development of this issue in the history of ICMI and the way it has been addressed by various communities concerned with mathematics education. In the second part we present one of the seminal works on intuition, rigor and their relationship. The third part presents an example of a possible way of taking account of both the intuition and the rigor dimensions in research in mathematics education. In the last part we raise some issues for further consideration.

Dina Tirosh (Israel) & Pessia Tsamir (Israel); reactor: Aldo Brigaglia (Italy)