Gabriel J. Stylianides and Andreas J. Stylianides

May 2009, Volume 40, Issue 3, Pages 314 - 352

Abstract:
Although students of all levels of education face serious difficulties with proof, there is limited research knowledge about how instruction can help students overcome these difficulties. In this article, the authors discuss the theoretical foundation and implementation of an instructional sequence that aimed to help students begin to realize the limitations of empirical arguments as methods for validating mathematical generalizations and see an intellectual need to learn about secure methods for validation (i.e., proofs). The development of the instructional sequence was part of a 4-year design experiment conducted in an undergraduate mathematics course, prerequisite for admission to an elementary teaching certification program.

Classification:
Patterns
Problem Solving
Reasoning
Proof
Teachers

Additional Keywords:
College/university; Content knowledge; Instructional intervention; Patterns, relationships in mathematics; Problem-solving; Proof; Reasoning; Teacher education