Innovative pedagogy: implications of genetic decompositions for problem solving in management courses

Abstract

Mathematics is a subject on which many business and management courses rely. In this paper the researcher reports on the processes involved in the design of itemised genetic decompositions for certain mathematics tasks. The manner by which this is done may be extended to teaching and learning in management courses in higher education. The researcher used two tasks, one in a high school context from a previously published study and another from a qualitative case study which explored the development of mental constructions of a group of fourth-year pre-service teachers during definition making of certain mathematical concepts in real analysis, at a South African higher education institution. Questionnaires based on two items involving the concept of infinity were administered to those participating pre-service teachers. The pre-service teachers were allowed to respond to these items without lecturer involvement so that a learner-centred learning environment was created. Their mental constructions of these concepts were analysed by using an APOS (Action-Process-Object-Schema) framework. Forty six pre-service teachers, specialising in the teaching of mathematics in the FET school curriculum, participated in the project. It was found that the APOS designed questionnaire generated thick data that led to a modification of the initial genetic decomposition formulated. This modified genetic decomposition has didactical implication for business and management courses taught in higher education. This is illustrated in the recommendations section of this paper.