Teaching induction: Historical perspective and current views

This dissertation first presents an overview of the historical development of mathematical induction. The dissertation surveys literature in this area including papers and texts. Chapter I discusses the importance of induction in modern mathematics, including the NCTM recommendation to incorporate more of the topic in the curriculum. Some material about great mathematicians beginning in the 1500's (Maurolycus) and later (Fermat, Peano, Pascal, Lucas, and DeMorgan) and their contribution to mathematical induction can be found in Chapter II, which includes selected source material including some original correspondence between Fermat and Pascal. Lucas and the Tower of Hanoi, Pascal's Triangle, the Gamblers problem and applications are also discussed in Chapter II. Chapter III reviews the literature on teaching induction and proof by mathematical induction. Chapter IV presents an overview of different college and high school textbooks on teaching mathematical induction, looking at the different methods used to teach mathematical induction (geometric, drawings, verbal description, and formal proof). Appendix A shows an approach to teaching mathematical induction including using history to motivate students as well as some geometrical examples to reinforce the concept. A summary chapter is included which discusses the evolution of mathematical induction in textbooks and papers, and the influence of the new mathematics reform. Conclusions and suggestions for further research on mathematical induction are also included.