Design principles to consider when student teachers are expected to learn mathematical modelling

Rina Durandt

doi:10.4102/pythagoras.v42i1.618

Abstract

This article sets out design principles to consider when student mathematics teachers are expected to learn mathematical modelling during their formal education. Blum and Leiß’s modelling cycle provided the theoretical framework to explain the modelling process. Learning to teach mathematical modelling, and learning to solve modelling tasks, while simultaneously fostering positive attitudes, is not easy to achieve. The inclusion of real-life examples and applications is regarded as an essential component in mathematics curricula worldwide, but it largely depends on mathematics teachers who are well prepared to teach modelling. The cyclic process of design-based research was implemented to identify key elements that ought to be considered when mathematical modelling is incorporated in formal education. Fifty-five third-year student teachers from a public university in South Africa participated in the study. Three phases were implemented, focusing firstly on relevance (guided by a needs analysis), secondly on consistency and practicality via the design and implementation of two iterations, and lastly on effectiveness by means of reflective analysis and evaluation. Mixed data were collected via a selection of qualitative instruments, and the Attitudes Towards Mathematical Modelling Inventory. Through content analyses students’ progress was monitored. Results analysed through SPSS showed significant positive changes in their enjoyment and motivation towards mathematical modelling. Student teachers require sufficient resources and opportunities through their formal education to participate regularly in mathematical modelling activities, to develop competence in solving modelling tasks, and to augment positive attitudes. This study adds value to the global discussion related to teachers’ professional development regarding mathematical modelling.

Highlights

Student mathematics teachers, who will teach mathematical modelling in their future professional role as teachers, should purposefully and strategically be prepared for this task because both teachers and students find the topic cognitively demanding
Based on data collected from the worksheets, posters and open-ended questions themes were identified reflecting student teachers’ shortcomings and progression in mathematical modelling activities
Teacher competencies describe the preparation work and the facilitation work of participants as they took on the role as teachers of modelling

Summary

Introduction

Student mathematics teachers, who will teach mathematical modelling in their future professional role as teachers, should purposefully and strategically be prepared for this task because both teachers and students find the topic cognitively demanding. A well-prepared teacher should include real-life examples and applications in mathematics teaching as an essential component in mathematics curricula to develop problem-solving and cognitive abilities in learners (Department of Basic Education, 2011), and to help learners to better understand the world, to support mathematics learning (e.g. concept formation), to develop various mathematical competencies and appropriate attitudes, and to contribute to an adequate picture of mathematics (see Blum, 2015; Wessels, 2017). Biccard (2019) confirmed that teachers should be given opportunities to experience tasks in the role both of learner and teacher. One such possibility is to follow a design-based research methodology (compare Biccard, 2019)

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Results

Conclusion