STUDENTS’ REVERSIBLE REASONING ON FUNCTION COMPOSITION PROBLEM: REVERSIBLE ON FUNCTION AND SUBSTITUTION

Abstract

In this paper we report students’ reversible reasoning types on function composition problem. Reversible reasoning can be observed according to operation and structural correlation among input, process, and result.  There are seven students participate in doing function composition related to structural correlation in (f∘g)(x)=h(x), The researchers assume that there are four types of reversible reasoning in composition problem, namely: (1) reversible on composition; (2) reversible on function; (3) reversible on substitution; (4) reversible on variables. However, there are only two appearing reversible reasoning, they are: reversible on function and reversible on substitution. Each type were selected a subject to be interviewed for 25 minutes and asked to do the Function Composition Task (FCT). Subject with reversible on function type identifies structural correlation among input, source and result as well as involving inverse in input with permissibility (f(y)) to produce basic function (f(x)). Meanwhile, subject with reversible on substitution type, constructs result based on the input, identifies structural similarity and generalizes from the structural similarity to produce basic function.