Fibonacci sequence II (helping students become active learners through guided mathematical investigations)

Abstract

Elementary number theory provides a variety of topics suitable for guided investigation in mathematics (the scheme of investigation is diagramed). We demonstrate this with the help of non-traditional and fascinating topic - the Fibonacci sequence. We present here two general strategies of investigation: the strategy of “accepting the given” and the strategy of “not accepting the given”. (In our case, the first strategy leads to the investigation of the Fibonacci sequence and the second strategy to the investigation of different kinds of sequences which are closely related to Fibonacci sequence, such as pseudo-Fibonacci sequences and the Tribonacci sequences.) This article also demonstrates the method of guided investigations through several mini-investigations.