Ways to teach modelling—a 50 year study

Abstract

This article describes a sequence of design research projects, some exploratory others more formal, on the teaching of modelling and the analysis of modelling skills. The initial motivation was the author's observation that the teaching of applied mathematics in UK high schools and universities involved no active modelling by students, but was entirely focused on their learning standards models of a restricted range of phenomena, largely from Newtonian mechanics. This did not develop the numeracy/mathematical literacy that was so clearly important for future citizens. Early explorations started with modelling workshops with high school teachers and mathematics undergraduates, observed and analysed-in some case using video. The theoretical basis of this work has been essentially heuristic, though the Shell Centre studies included, for example, a detailed analysis of formulation processes that has not, as so often, been directly replicated. Recent work has focused on developing a formative assessment approach to teaching modelling that has proved both successful and popular. Finally, the system-level challenges in trying to establish modelling as an integral part of mathematics curricula are briefly discussed.

Inquiry and Modeling for Teaching Mathematics in Interdisciplinary Contexts: How Are They Interrelated?

“…Current trends in the teaching of mathematics reveal that the extensive mathematical education community has reached a consensus on how to improve the teaching of the subject. One such trend emphasizes the importance of problem solving and modeling (see, for instance, [1,2]). To "know mathematics" is supposed to include the competence of using mathematics in and applying it to real-life extra-mathematical situations.…”

“…This paper aims at contributing to the understanding of the relationships between both processes, especially when used in an interdisciplinary context, such as archaeology, to develop inquiry and mathematical modeling. With this purpose in mind, the following objectives of this article were established: (1) to analyze the presence of the processes of inquiry and mathematical modeling in the implementation of an interdisciplinary teaching sequence, aiming to look for the coincidences, concatenations and synergies between both processes; and (2) to elaborate an integrated proposal for the joint analysis of both processes in the implementation of teaching sequences in interdisciplinary contexts.…”

Uma Abordagem Didático-Pedagógica Da Modelagem Matemática

“…A matematização da realidade já ocupa um espaço nas discussões relativas à matemática bem como naquelas relativas ao seu ensino e a sua aprendizagem. No que se refere à modelagem, em particular, o estudo de Burkhardt (2018), ao apresentar um panorama de como a modelagem tem sido realizada na sala de aula, destaca que, embora diferentes encaminhamentos para estas atividades tenham sido sugeridos e realizados a partir da década de 1960, todos eles incluem um processo investigativo que implica em associar matemática a situações mediante uma matematização, explicitando interlocuções entre matemática e realidade na sala de aula. Estas interlocuções podem ser teorizadas na modelagem matemática mediante esquemas reconhecidos como ciclos de modelagem matemática.…”

Promoting Active Citizenship in Mathematics and Science Teaching

“…In mathematics education, scholars already discussed the notion of mathematical modeling and bringing extra-mathematical contexts into lessons in the twentieth century (for an overview see, e.g. Burkhardt, 2018 ). In relation to science education, research proposes the engagement of socio-scientific issues (SSI) as one promising path to developing citizenship competences.…”