The principle of mathematical induction (MI) is a prominent proof technique used to justify theorems involving properties of the set of natural numbers. The principle can be stated in different, yet equivalent, versions. The following are two versions common in textbooks:

1. (i) 1 ∈ S.

2. (ii) k ∈ S, then k +1 ∈ S.

1. (i) P(1) is true.

2. (ii) If P(k) is true, then P(k + 1) is true.

Poincaré, among others, viewed the principle of MI as intrinsic to humans' intuition: “Mathematical induction … is … necessarily imposed on us, because it is … the affirmation of a property of the mind itself” (Poincaré, 1952). In fact, historical documents indicate that mathematicians employed this method of proof for at least 200 years before it was explicitly formulated by Peano. Despite its intuitive appeal and its central role within mathematics, research in mathematics education has documented that students have major difficulties understanding MI (Dubinsky, 1986; Fischbein & Engel, 1989; Movshovitz-Hadar, 1993; Reid, 1992; Robert & Schwarzenberger, 1991; Harel, 2001; Brown, 2003).

In this chapter, we explore students' difficulties with MI when taught with the standard instructional treatment and we present results from our teaching experiments, which employed alternative instructional approaches.