State of the Art on Modelling in Mathematics Education—Lines of Inquiry

Stillman, Gloria

doi:10.1007/978-3-030-14931-4_1

Cited by 29 publications

(19 citation statements)

References 51 publications

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“…What is the effect of digital tools on the spectrum of modelling problems to be worked on? How is teaching culture influenced by the Although these questions need more empirical experimentation, it is necessary to highlight the indispensable role of the calculator or computer in the practice of MM; i.e., here we evidence a dependence on the so-called real problems of the use of those digital tools, which, despite being nonmathematical know-how, work conditioned by mathematical know-how, which distances the gaze of the MM as a strict practice of mathematical know-how, as can make us believe, for example, Niss, Blum, and Galbraith (2007) (apud Stillman, 2019).…”

Section: This Pace Of the Didactic Systems S1 (X1 X3 X4 ₵) And S2 (X2 X5 ₵)mentioning

confidence: 52%

Mathematical Modelling and Didactic Moments

Sodré

2021

Acta Sci.

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Background: from the perspective of mathematics education, an important issue addressed vehemently in international conferences on mathematical modelling teaching, regardless of the theoretical current adopted on the concept, is how we can teach modelling? Objective: to highlight the didactic moments announced by the anthropological theory of the didactic in the process of studying problems in concrete contexts in mathematical modelling. Design: a study and research path was conducted based on theoretical and methodological tools of the anthropological theory of the didactic. Settings and participants: preservice teachers of a degree course of a public institution, who had to solve a problem of application in savings. Data collection and analysis: From an empirical excerpt of a study developed by Sodré (2019) with preservice teachers. Results: the elements found in the empirical research confirm the hypothesis that regardless of the path taken in the modelling process, one or more didactic moments is/are performed. Conclusions: ultimately, the study of problems in concrete contexts, besides highlighting the encounter of teachers with different didactic moments, revealed the remarkable dependence between mathematical and non-mathematical know-how that stimulates us to further investigations.

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Section: This Pace Of the Didactic Systems S1 (X1 X3 X4 ₵) And S2 (X2 X5 ₵)mentioning

confidence: 52%

Mathematical Modelling and Didactic Moments

Sodré

2021

Acta Sci.

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“…There are quite a number of empirical studies on the learning and teaching of mathematical modelling, especially from the last two decades. In the following, we summarise some selected findings on teaching modelling which we consider as particularly relevant for our own study (for a survey about important empirical findings concerning modelling, see Blum, 2015;Kaiser, 2017;Niss & Blum, 2020, chapter 6;Schukajlow et al, 2018;Stillman, 2015Stillman, , 2019. An important general aspect of all those findings is that they have been obtained in certain organisational, societal, and cultural environments, and it must be examined to what extent these findings may be transferred and generalised to other environments.…”

Section: Teaching Of Mathematical Modellingmentioning

confidence: 99%

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

2021

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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 independence-oriented design had the biggest competency growth. In addition, this group exhibited more positive attitudes than the other groups in five of six attitudinal aspects.

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“…Students usually do not follow those steps in linear order when solving modelling tasks, but often 'bounce' between them. Each step can potentially be a cognitive barrier for students (Blum, 2011(Blum, , 2015Stillman, 2019;Stillman, Brown, & Galbraith, 2010). It seems important to develop mathematical modelling competency and sub-competencies related to the subprocesses of the modelling cycle.…”

Section: Learning Mathematical Modellingmentioning

confidence: 99%

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

Durandt

2021

Pythagoras

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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.

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State of the Art on Modelling in Mathematics Education—Lines of Inquiry

Cited by 29 publications

References 51 publications

Mathematical Modelling and Didactic Moments

Mathematical Modelling and Didactic Moments

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

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

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