The history of mathematics as a pedagogical tool: exploring learner perspectives with regard to the theorem of pythagoras.

Abstract

This study sought to ascertain whether the inclusion of the history of the Theorem of Pythagoras has any positive influence on learners’ perceptions of the theorem and its applications, on geometry and on mathematics in general. To accomplish this aim, this study had to establish learner perceptions before and after the incorporation of the history of mathematics in the lessons on the Pythagorean Theorem. Changes in perceptions after the inclusion of the history of mathematics were regarded as indicative of the influence of the history of mathematics. The study was informed by the constructivist’s perspective and the genetic approach to teaching and learning. These played a pivotal role in the design of learning materials used during the lessons in which the history of mathematics was incorporated. A case study approach where grade 11 mathematics learners’ perceptions on mathematics, geometry and Pythagoras’ Theorem were sought, was used. Data on learners’ perceptions was collected using qualitative data collection methods, that is, focus group discussions, group interviews and journal entries made by participants after being exposed to lessons in which the history of mathematics was integrated. The collected data was analysed using NVivo software. A qualitative interpretation of analysed results indicated a change in learner perceptions of mathematics, geometry and the theorem of Pythagoras. The change was perceived to have occurred when learners were exposed to learning situations which incorporated the history of mathematics. Notable changes in learner perceptions included affirmations of the increased levels of motivation and claims of preparedness to work hard even in the face of adversity. Despite challenging tasks, learners now regarded mathematics and geometry as challenges that needed to be faced head-on and conquered. It also seemed, from the inclusion of the history of mathematics that learners had learnt that failure is part of the learning process. Learners also confirmed that they had gained confidence in dealing with proofs, enjoyed making their own discoveries and solving mathematical problems in general. Findings from this study were crucial in that they revealed that the history of mathematics has great, yet untapped potential to resolve the challenges of learner apathy and facilitate greater rate of uptake in mathematics at FET phase in South Africa.