
06083900
a
2012e.00495
Arzarello, Ferdinando
Bartolini Bussi, Maria Giuseppina
Leung, Allen Yuk Lun
Mariotti, Maria Alessandra
Stevenson, Ian
Experimental approaches to theoretical thinking: artefacts and proofs. With a response by Jonathan M. Borwein and Judyanne Osborn.
Hanna, Gila (ed.) et al., Proof and proving in mathematics education. The 19th ICMI study. Berlin: Springer (ISBN 9789400721289/hbk; 9789400721296/ebook). New ICMI Study Series 15, 97143 (2012).
2012
Berlin: Springer
EN
E50
R20
U50
D40
experimental mathematics
ancient examples
historical examples
use of mathematical tools
use of new technologies
mathematics classroom
indirect proofs
the logic of `not'
doi:10.1007/9789400721296_5
Summary: This article discusses some strands of experimental mathematics from both an epistemological and a didactical point of view. We introduce some ancient and recent historical examples in Western and Eastern cultures in order to illustrate how the use of mathematical tools has driven the genesis of many abstract mathematical concepts. We show how the interaction between concrete tools and abstract ideas introduces an ``experimental'' dimension in mathematics and a dynamic tension between the empirical nature of the activities with the tools and the deductive nature of the discipline. We then discuss how the heavy use of the new technology in mathematics teaching gives new dynamism to this dialectic, specifically through students' proving activities in digital electronic environments. Finally, we introduce some theoretical frameworks to examine and interpret students' thoughts and actions whilst the students work in such environments to explore problematic situations, formulate conjectures and logically prove them. The chapter is followed by a response by Jonathan Borwein and Judyanne Osborn.