Conclusions and Future Lines of Inquiry in Mathematical Modelling Research in Education

Abstract

This final chapter overviews the 12 contributions to the monograph, organising this along the lines of inquiry suggested by Stillman. Contributors share understanding of mathematical modelling as solving real-world problems. The value and purposes of implementing modelling varies, in part due to local curricula. Theoretical underpinnings of the research include prescriptive modelling, modelling cycles, and modelling competencies. The challenges of engaging in modelling see empirical foci on modellers, teachers, and tasks whilst acknowledging interactions between these. Other important areas of the field, where researchers need to focus in the future include research with experienced student modellers, research on experienced teachers of modelling, and successful mathematisation by modellers. Keywords Modelling tasks • Teachers of modelling • Prescriptive modelling • Affordances 13.1 Mathematical Modelling: What Lines of Inquiry? Defining the bounds of research reported in this monograph is important. This includes the shared understanding by authors as to what mathematical modelling is. Modelling occurs when teachers, students, mathematicians, and others attempt to describe some aspect of the real-world in mathematical terms in order to understand something better or take or recommend actions (e.g. Blum 2015; Blum et al. 2007).

Mathematical Modeling Research Output Impacting New Technological Development: An Axiomatization to Build Novelty

“…Comparing all the group axioms, the central axioms of mathematical modeling research output can be formulized to see on how they impact the development of new technology and the strategy to seek novelty [40] for society use. By constantly comparing [41] four categories of mathematical modeling research output axioms A(X) n , the fundamental axiom modelling output is system theorizing and this can be strategized by inculcating elements of E(T) n which finally impact new technology development as in Table System theorizing of mathematical modeling output [42,43] is the fundamental processes and creates most important general output formulae that can be used for new technological development. Meanwhile, a specific system theorizing modeling output can be derived from the general formulae to produce another new fundamental mathematical research output.…”

Aprendizagem Colaborativa no Contexto de uma Atividade de Modelagem Matemática

“…Embora na literatura encontremos pesquisas que associam o desenvolvimento de atividades de Modelagem em sala de aula e o trabalho colaborativo (ÄRLEBÄCK;DOERR, 2018;IKEDA, 2019;NAFTALIEV, 2017), em geral não é evidenciado metodologicamente como as pesquisas caracterizam a colaboração, o trabalho colaborativo, a aprendizagem colaborativa. A investigação que realizamos está inserida em um projeto de pesquisa que leva em consideração a configuração de um ambiente educacional em que atividades colaborativas se fazem presentes.…”