An exploration of pre-service science and mathematics teachers' use of visualisation in a problem solving context : a case study at a South African university.

Abstract

The poor performance of learners in Science and Mathematics in South Africa is a persistent cause for concern to stakeholders in education, and to society at large. Teacher training institutes form crucial stakeholders in Science and Mathematics education. This has been the underlying motivation for this case study, which is based on an exploration of pre-service Science and Mathematics teachers’ use of visualisation within a problem solving context. The study is grounded in the interpretivist paradigm. The purpose of this study stems from anecdotal evidence that has showed teachers’ reluctance to teach problem solving because they are unequipped and/or not confident in solving problems. The exploration of pre-service Science and Mathematics teachers’ use of visualisation in a problem solving context revolved around the following critical questions: 1. What do pre-service Science and Mathematics teachers understand by problem solving within a visualisation context? 2. Why do pre-service Science and Mathematics teachers choose to use the visualisation strategies they use when teaching problem solving? 3. How do pre-service Science and Mathematics teachers plan the use of visualisation when preparing their lessons? The framework used to guide this study falls within the interpretivist paradigm and the theory used is the metacognition theory. This theory refers to a higher order of thinking and, simply put, thinking about thinking. In this study, it was analysed how pre-service teachers view their teaching and what their understanding of visualisation is within a problem solving context. The pilot group comprised five pre-service Science and Mathematics teachers at a South African teacher training institute who were registered for two modules, namely Natural Science Method Two, and Mathematics Method Two. These modules include the teaching of problem solving. A purposive sample population of eighty pre-service teachers were invited to participate in this project, and twelve completed part of the project, while five pre-service teachers participated until the conclusion of the project. A qualitative methodological approach was used and pre-service teachers participated in four stages of data collection. Firstly, a semi-structured questionnaire was used to collect the biographical data of the participating pre-service teachers, and their understanding of problem

solving and visualisation. Secondly, a task sheet was administered, which included a Science as well as a Mathematics selection of problems for the pre-service teachers to solve. All problems were purposively selected because visualisation methods could have been used to solve them. This tool was used to decipher what visualisation strategies pre-service teachers use when solving problems and why they use these strategies. Thirdly, a lesson plan was developed by participants to enable an exploration of how they taught problem solving using visualisation, as well as what cognitive processes they used to incorporate visualisation into problem solving. The fourth stage involved engaging participants in individual, face-to-face interviews. Semi structured interview schedules were used for both interviews. All responses were analysed and focused on the three research questions. The findings revealed that the majority of the pre-service teachers understood visualisation as a set of teaching aids that made solving problems easier. The majority of participating pre-service teachers solved Mathematics problems accurately when they used a combination of diagrams and formulae. The responses to the Science problems revealed that the majority of participating pre-service teachers used formulae instead of diagrams to solve them. However, the opposite scenario was presented by these participants when they generated their lesson plans. A greater variety of visualisation strategies were used in the Science lesson plans than in the Mathematics lesson plans. The findings show that the use of visualisation in problem solving helped pre-service teachers solve Science and Mathematics problems successfully. It is anticipated that the pre-service teachers will take this finding and make use of it in their classes in the near future, which should in turn develop more competent problem solvers at schooling level.