Experimental Approaches to Theoretical Thinking: Artefacts and Proofs

Ferdinando Arzarello*, Maria Giuseppina Bartolini Bussi, Allen Y L Leung, Maria Alessandra Mariotti, Ian Stevenson

*Corresponding author for this work

Research output: Chapter in book/report/conference proceedingChapterpeer-review

17 Citations (Scopus)


This chapter 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 Judy-anne Osborn.

Original languageEnglish
Title of host publicationProof and Proving in Mathematics Education
Subtitle of host publicationThe 19th ICMI Study
EditorsGila Hanna, Michael de Villiers
PublisherSpringer, Dordrecht
Number of pages47
ISBN (Electronic)9789400721296
ISBN (Print)9789400721289, 9789401780667
Publication statusPublished - 11 Feb 2012

Publication series

NameNew ICMI Study Series
ISSN (Print)1387-6872
ISSN (Electronic)2215-1745

Scopus Subject Areas

  • Mathematics (miscellaneous)
  • Education

User-Defined Keywords

  • Deductive Nature
  • Dynamic Tension
  • Euclidean Geometry
  • Indirect Proof
  • Instrument Action


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