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 whether teaching and learning mathematics using engineering application problems (EAPs) 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 80 first-year engineering students at a University of Technology in South Africa. This study measures whether doing mathematics using EAPs improve students' performance as well as whether students' achievement emotions change as a result of the EAP-tutorial sessions. The data collection involved a mathematics pretest, an intervention (tutorial sessions for the experimental group where they learn mathematics by solving EAPs) and a mathematics posttest. A questionnaire to determine students' achievement emotions pertaining to mathematics (AEQ-M) was completed before the intervention and again after the intervention by both the experimental and control groups. The research design used for this quantitative study is a pretest-posttest control group design. The results indicate a distinct improvement in mathematics performance for the experimental group at the 1% level of significance. The analysis of the AEQ-M questionnaires revealed that the experimental group displayed significantly higher levels of anger towards mathematics after the intervention. The importance of this research rests on its unique connection of cognition (solving mathematical application problems) and reflection regarding mathematics learning related to affective factors (experiences and emotions) in the field of mathematics. These results have implications for the design of modelling activities for tertiary students, for teaching mathematical modelling and for ultimately improving students' modelling abilities.