TEACHING AND LEARNING MATHEMATICS WITHIN A MODEL AND MODELLING PERSPECTIVE

The main purpose of this research study is to explore from within a models and modelling perspective (MMP) whether teaching and learning mathematics using engineering application problems (EAPs) (the intervention) improve students’ understanding of and performance in mathematics. The study also aims to determine the achievement emotions that are present during mathematics learning and whether these emotions change as a result of doing mathematics through EAPs. The participants for this study are 200 first-year engineering students at a University of Technology in South Africa. This study has a quantitative component (measuring whether doing mathematics using EAPs improve students’ performance, and whether students’ achievement emotions change as a result of the EAP-tutorial sessions) as well as a qualitative component (establishing students’ experiences about learning mathematics through EAPs). Hence the study falls within the field of a mixed methods research design. The quantitative data collection consists of a mathematics pretest, and emotions pretest (before the intervention) and mathematics posttest and emotions posttest (after the intervention). Because two independent group scores are compared on their average score on a quantitative variable (performance in mathematics tests) a t-test will be used to analyse the quantitative data. Within-group variance for the experimental group, and between-group variance between the experimental and control groups will be considered. All the qualitative data sources (video-recordings, interviews and questionnaires) were transcribed verbatim and analysed to develop themes, patterns and categories that identify and describe the participants’ experiences while working on the EAPs. This study may lead to the design of mathematics lessons at university level using a MMP. Most studies on emotion and achievement regarding mathematics focus on negative emotions, such as anxiety. If using a MMP in mathematics results in positive changes in emotion, this could have implications for the development of improved mathematics curricula. The importance of this research rests on its unique connection of cognition (solving complex mathematical problems using EAPs) and reflection relating to affective factors in the field of mathematics.