Facilitating the Transition from Empirical Arguments to Proof

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.