Using geogebra to enhance grade 11 learners' conception of transformations of functions

Abstract

The function concept, which is a central idea in mathematics, is difficult for learners to grasp, nonetheless, transformations of functions aid in this understanding. The purpose of the study was to investigate whether the use of GeoGebra enhances Grade 11 learners’ conception of transformations of functions. A qualitative case study design, as envisaged by Merriam (1998), was used to solicit learner interpretations and reasoning when working with transformations of functions. Participants for the study consisted of 28 mixed ability Grade 11 learners who were purposively and conveniently selected at the researcher’s workplace in Polokwane, South Africa. The APOS theory was put to use as the theoretical framework for the study and the ACE cycle adopted for instructional design. Indicators for APOS theory conception levels were formulated in a genetic decomposition of transformations of functions and used together with deductive thematic analysis of qualitative data to analyse the collected data from learners’ written activities and task-based interviews. The results brought out into the open that Grade 11 learners could not easily recognise transformations on functions and that their mental constructions were based on isolated facts or procedures. The results also conveyed that GeoGebra is an effective tool in supporting conceptual understanding in the learning of transformations of functions. The failure to recognise transformations of functions stemmed from the failure by learners to apply learnt concepts in the solution of new problems and also from giving partial descriptions of transformations of functions. These findings reveal that further research on GeoGebra use is needed so as to explore its capabilities to support retention of knowledge of transformations of functions.