Exploring Tertiary Students’ Mathematical Modelling Experiences: Insights for Practice

Abstract

The purpose of this study is to investigate tertiary student learning experiences for mathematical modelling. This study is based in New Zealand and involves three different tertiary modelling courses. For students participating in these modelling courses, this was their first time studying modelling at tertiary level. This study uses Interpretive Description as the methodology to look at the student experience with the aim of establishing a better understanding of student experiences with mathematical modelling, the role the lecturer plays in these experiences, and how any new insights can better inform teaching practices.

This study aims: to provide new insights and understandings of the student perspective to inform and advance tertiary teaching practices; to gain a deeper understanding of the lecturer’s role in the student experience; to contribute to the general discussion on how to provide rich student learning experiences in mathematical modelling; and to inform the general discussion for students to be able to contribute to society through mathematical modelling.

One overarching theme and three subthemes were constructed from the data. The overarching theme pushing our boundaries, captures how all students had experiences that are new, unfamiliar, and outside their normal range of experiences with mathematics while mathematically modelling. Subtheme one, moving forward on our own, captures how students needed to learn how to move forward on their own in order to make progress. Moving forward involved taking responsibility, both individually and as a group, to actively find ways forward. Subtheme two, being moved forward, focusses on the use of resources and the lecturer’s role in moving students forward, while also enabling student groups to work independently of the lecturer. Subtheme three, going forward together as a collective, captures the interwoven and collective nature of learning to mathematical model.

This research shows how modelling is a change of culture for students and the lecturer has a role to play. This research presents nuances of the dynamics between independent student work and the lecturer’s role.

The findings of this study suggest students can undertake modelling without the lecturer or teacher being present if they have prepared for the experience beforehand and have access to appropriate resources. Lecturer behaviours that help students to take responsibility for their own modelling process include: providing students with material to refer to; using facilitatory questions/prompts aligned with the modelling process; and creating environments for students to share their thoughts and workings. Lecturer support needs to allow for students to experience struggle, explore, be creative and become self-reliant. Experiencing these key student behaviours allows students to move from being uncertain to finding direction and thus take responsibility and ownership for their own modelling process.

Implications of this research for general mathematics education practices include the suggestion of lecturers and teachers incorporating connecting mathematics to context as a normal part of their teaching practice and develop a learning environment where being uncertain and the need for exploration is a normal part of learning mathematics.