An approach to mathematical induction — starting from the early stages of teaching mathematics ⁄
Margita Pavleković · University of Zagreb University Computing Centre (SRCE) · 1998
It is well-known that the method of proof by mathematical induction often creates serious problems to students who encounter these proofs in secondary schools. It is Therefore important to prepare the stu- dents for understanding and the application of the method of mathematical induction. For this purpose, our students should develop the abilities to notice, compare, generalize, conjecture by analogy and conjecture by induc- tive reasoning. On the other hand, the examples showing that conjectures suggested by inductive reasoning could be incorrect, should be pointed out at early stages. In that way, we show the students the need of proving the conjectures as well as finding the methods for proving. In this paper we mention a number of such examples through which the students at early stages of teaching mathematics are induced to inductive reasoning, but we also mention examples which illustrate how cautious one has to be when accepting hypotheses obtained by inductive reasoning.