Rina Durandt

University of Johannesburg, South Africa, Applied Mathematics, Faculty Member

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Address: Johannesburg, Gauteng, South Africa

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Mustafa Cevikbas

Humboldt Universität zu Berlin

Pauline Vos

Western Norway University of Applied Science

Deakin University

University of Münster

Saleh M . Saleh

Arish University

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Books by Rina Durandt

Durandt, R & Lautenbach G. (2020) Pre-service Teachers’ Sense-making of Mathematical Modelling Through a Design-Based Research Strategy

by Rina Durandt and Geoffrey Lautenbach

In: Stillman G., Kaiser G., Lampen C. (eds) Mathematical Modelling Education and Sense-making. International Perspectives on the Teaching and Learning of Mathematical Modelling. pp431-441. Springer, Cham, 2020

This chapter reports on the sense-making of pre-service teachers in and about mathematical modell... more This chapter reports on the sense-making of pre-service teachers in and about mathematical modelling by means of a well-planned design-based research strategy over a period of two iterations. Modelling, and the teaching thereof, is mostly difficult for teachers, but it can be learnt through the development of mathematical, modelling and facilitator competencies of pre-service teachers during their formal education. This study explores how pre-service teachers translate the modelling cycle and develop certain competencies over time through partaking in a series of modelling activities as modellers themselves and as teachers of modelling. Qualitative findings reveal how pre-service teachers improve in their sense-making of the mathematical modelling process, but they disclose some shortcomings that relate to preparing for the teaching of modelling.

Papers by Rina Durandt

Strategic support to students’ competency development in the mathematical modelling process: A qualitative study

Perspectives in Education, 2020

This article reports on third-year mathematics students' competency and sub-competency developmen... more This article reports on third-year mathematics students' competency and sub-competency development through providing intentional support in the learning of mathematical modelling. Students often experience modelling as difficult, and obstructions in the modelling process can lead to a dead end. Literature reports confirm that the modelling task is central in the modelling experience and a carefully planned task, aligned with a suitable activity sheet, can be used as a scaffold in learning mathematical modelling. Hence, this inquiry was conducted to provide a scaffold, as strategic support, for students' mathematical modelling competency development in the early stages of a modelling cycle. Guided by the framework of the Zone of Proximal Development, key elements suggested by the metaphor scaffolding are considered in the learning experience. Based on an analysis of activity sheets collected through group work, an example of a realistic and an unrealistic solution is presented, and students' development of mathematical modelling competencies is argued. Finally, suggestions for intentional support in the modelling process are discussed.

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Student teachers meaningful learning of mathematical modelling via design-based research

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Assessment of tertiary students’ learning of statistical modelling

In this paper, we report on the learning of statistical modelling in a second-year statistics mod... more In this paper, we report on the learning of statistical modelling in a second-year statistics module through the assessment of a problem that required a Monte Carlo simulation. On the forefront of the 4 industrial revolution is science, technology, engineering and mathematics subjects, where mathematical statistics plays a key role in topics such as machine learning and predictive analysis. Students often find statistical modelling difficult, where obstructions in the modelling process could lead towards a dead-end. For this reason, assessment of learning, for learning and as learning in statistics education seems necessary. General pillars of good assessment practice is considered in this study, as well as guidelines for the development of students’ conceptual understanding of the content, such as, statistical reasoning, statistical thinking and statistical literacy. Therefore, this study was conducted to provide educators with information of student achievement of desired student ...

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Learning Mathematics with Technology – a Meaningful Endeavour Involving 2ND Year Education Students

The envisaged relationship between learning mathematics with technology and the achievement of st... more The envisaged relationship between learning mathematics with technology and the achievement of student teachers at the University of Johannesburg (UJ) forms the focus of this research. Since the introduction of a new Faculty of Education programme for Grade 10-12 teachers in 2011, their mathematics lecturer faced several challenges. Most pertinent were inadequate foundational mathematical competency levels of students and their negative attitudes towards the curriculum. In an effort to boost student attitudes, to enhance their intrinsic motivation and more frequent engagement with mathematical content, the second year lecturer integrated an extensive online support programme (Enhanced WebAssign) into the second semester module. The highly constructive effect of this intervention, monitored as research project, can be labelled as almost ‘unlikely’. More encouraging attitudes, amplified confidence levels, a willingness to confront more complex mathematical content and a significant ac...

Investigating the Attitudinal Differences of Students in Service and Mainstream Courses Towards Statistics

Connection between prior knowledge and student achievement in engineering mathematics

In the paper the author reports on connections between first-year engineering mathematics student... more In the paper the author reports on connections between first-year engineering mathematics students’ prior mathematical knowledge and their achievement in an engineering mathematics (year) course in an extended curriculum programme. The importance of links between prior knowledge in learning and performance is widely supported in educational studies, also in learning mathematics. Furthermore, the transition from school to university is a substantial hurdle in the learning trajectory of many students, and particularly in science and engineering courses. The author exposed students to a carefully designed diagnostic entrance test that consists of different content and knowledge components, and correlated these results, by means of regression analysis, with students’ achievement scores at the end of term 1, term 2, and the first semester. The results show a moderate correlation. This research is meant as the beginning of exploring possibilities to predict study success in mathematics by...

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Presenting First Year Mathematics in the Alternative Semester – a Worthy Effort

This paper reports on a worthy effort to improve the throughput rate in first year mathematics at... more This paper reports on a worthy effort to improve the throughput rate in first year mathematics at the University of Johannesburg. Presenting first year mathematics in the alternative semester (introduced in 2010 for the first time) provides students with multiple opportunities; firstly to contribute towards the throughput rate, secondly to improve their mathematical proficiency (knowledge and skills) and thirdly to develop their learning skills. The overarching research aim is to investigate the influence of an alternative semester programme on the mathematical proficiency of a group of first year students and to reflect on the development of students’ self-regulated learning skills by means of the specific mode of teaching. The influence of teaching approaches on students’ mathematical proficiency is highlighted by research (Boaler, 2002; Samuelsson, 2010). Keeping in mind that the mode of teaching seems important for the development of students’ mathematical proficiency, we introd...

Exploring the Initial Convictions and Mindset of Prospective Mathematics Teachers Towards Modelling

Modelling, as a problem solving strategy forms part of the South African mathematics secondary sc... more Modelling, as a problem solving strategy forms part of the South African mathematics secondary school curriculum since 2011. In many instances, mathematics teachers are incapacitated to teach modelling effectively, although literature also reveals the opposite. This study reports on the convictions (beliefs) and mindset (attitude) of prospective mathematics teachers, based on their initial engagement with a modelling task. Significant attitudinal differences emerged between the two genders, and between participants with diverse mathematics competency levels. Participants enjoyed and valued the modelling task, but seemed to lack confidence and motivation in pursuing it in future. In striving to develop the modelling and mathematical proficiency of prospective teachers, a well-planned programme that gradually nurtures participants’ modelling mindsets and confidence is recommended.

Attitudes of Student Teachers Based on Their Maiden Exposure to Mathematical Modelling

This paper reports on the attitudes of mathematics student teachers, based on their maiden exposu... more This paper reports on the attitudes of mathematics student teachers, based on their maiden exposure to a mathematical modelling challenge. The Curriculum and Assessment Policy Statement (CAPS) determines that mathematics learners should develop the ability to identify, investigate and solve problems. The unpreparedness of mathematics teachers to solve and teach modelling activities is acknowledged worldwide. Modelling was thus included for the first time in the programme of a group of third year mathematics student teachers at a South African university. Attitudes are behaviours, feelings or thinking that display someone’s disposition or preferences. The students reported their attitudes towards modelling through an adapted version of the Attitudes towards Mathematics Inventory (ATMI). The nonparametric Mann Whitney test was used to compare the attitudes of the two gender groups, as well as of two groups of students, based on their performance in mathematics in Grade 12. Statistical...

Mathematics Student Teachers’ Approach To, Experience of and Attitudes Towards Mathematical Modelling

This paper interrogates the thinking and planning strategies of Mathematics student teachers, whe... more This paper interrogates the thinking and planning strategies of Mathematics student teachers, when faced with a mathematical modelling challenge for the very first time. Mathematical modelling is the process of generating mathematical representations in attempting to solve real life problems. Modelling has the proven ability to develop learners’ reasoning, communication and problem solving competencies. Literature cautions against the unpreparedness of Mathematics teachers in teaching modelling to learners. The second aim of the Curriculum and Assessment Policy Statement (CAPS, 2011, p. 8) emphasises mathematical modelling as “...an important focal point of the curriculum. Real life problems should be incorporated into all sections whenever appropriate.” A traditional textbook problem was converted into a modelling task and eight groups of third year mathematics student teachers at the University of Johannesburg were confronted with this challenge. The groups’ strategies, nature of ...

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Mathematical Modelling Strategies and Attitudes of Third Year Pre-service Teachers

This chapter reports on the thinking and planning strategies of a group of 38 third year mathemat... more This chapter reports on the thinking and planning strategies of a group of 38 third year mathematics student teachers (preparing to teach Grades 10–12), who were exposed to mathematical modelling for the first time. Participants, in eight comparable groups, attempted a textbook-based traffic flow model-eliciting activity. The open-ended nature of the task, handling intra-group dynamics, construction of appropriate equations and interpretation of findings were the most pressing challenges. Participants’ attitudes towards modelling, attained via a post-questionnaire, were very positive, and all appreciated the mathematics-in-the-real-world exposure. Findings of students’ planning strategies, experiences and attitudes contributed to a set of guidelines aimed at the integration of mathematical modelling into the pre-service education of mathematics teachers.

Pre-service Teachers’ Sense-making of Mathematical Modelling Through a Design-Based Research Strategy

International Perspectives on the Teaching and Learning of Mathematical Modelling

How Does the Teaching Design Influence Engineering Students’ Learning of Mathematical Modelling? A Case Study in a South African Context

International Perspectives on the Teaching and Learning of Mathematical Modelling

This chapter reports on empirical results about the influence of two different teaching designs o... more This chapter reports on empirical results about the influence of two different teaching designs on the development of engineering mathematics students’ modelling competency. 144 first-year students were exposed to a modelling unit (entrance test, pre-test, five lessons with ten tasks, post-test) following two teaching designs, similar to the German DISUM study. One group of participants was offered an independence-oriented teaching style, aiming at a balance between students’ independent work and teacher’s guidance, while two other groups were taught according to a more traditional teacher-guided style. Linear mixed regression models were used to compare pre- and post-test results. The results show that all groups had significant learning progress and that the group taught according to the independence-oriented design had the biggest competency growth.

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

Pythagoras

This article sets out design principles to consider when student mathematics teachers are expecte... more 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 nee...

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Fostering mathematical modelling competency of South African engineering students: which influence does the teaching design have?

This paper reports on empirical results about the influence of two different teaching designs on ... more This paper reports on empirical results about the influence of two different teaching designs on the development of tertiary students’ modelling competency and attitudes towards modelling. A total of 144 first year engineering students were exposed to a diagnostic entrance test, a modelling unit consisting of five lessons with ten tasks, enframed by a pre- and a post-test, and at the end a questionnaire on attitudes towards mathematical modelling. Similar to the German DISUM study, in the modelling unit, one group of participants followed an independence-oriented teaching style, aiming at a balance between students’ independent work and teacher’s guidance, while two other groups were taught according to a more traditional teacher-guided style. Linear mixed regression models were used to compare pre- and post-test results. The results show that all groups had significant learning progress, although there is much room for further improvement, and that the group taught according to the...

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Durandt, R & Lautenbach G. (2020) Pre-service Teachers’ Sense-making of Mathematical Modelling Through a Design-Based Research Strategy

by Rina Durandt and Geoffrey Lautenbach