Abstract
This is a commentary on the ESM 2021 Special Issue on Innovations in Measuring and Fostering Mathematical Modelling Competencies. We have grouped the ten studies into three themes: competencies, fostering, and measuring. The first theme and the papers therein provide a platform to discuss the cognitivist backgrounds to the different conceptualizations of mathematical modelling competencies, based on the modelling cycle. We suggest theoretical widening through a competence continuum and enriching of the modelling cycle with overarching, analytic dimensions for creativity, tool use, metacognition, and so forth. The second theme and the papers therein showcase innovative ideas on fostering and on the definition and analysis thereof. These reveal the need for a social turn in modelling research in order to capture aspects of student collaboration and agency, as well as tensions in fostering when tasks are derived from real-world scenarios, but socio-mathematical norms come from the (pure) mathematics classroom. The third theme, measuring, and the papers therein offer insights into the challenges of positivist research that aims to develop innovative measurement instruments that are both reliable and valid, particularly in light of student group work, cultural background, and other socio-cultural aspects. Drawing on the three discussions, we go on to make recommendations for further research.
Highlights
This is a commentary on the ESM Special Issue (SI) on Innovations in Measuring and Fostering Mathematical Modelling Competencies
The major finding of this study is that the classroom culture is a matter of negotiations between the participants involved in the activity, which means that the fostering of mathematical modelling competencies does not depend solely on well-designed tasks and competent teachers
This SI focuses on mathematical modelling competencies related to the modelling cycle, a topic frequently addressed in research on mathematical modelling education, as observed by both Stillman (2019) and Geiger and Frejd (2015)
Summary
This is a commentary on the ESM Special Issue (SI) on Innovations in Measuring and Fostering Mathematical Modelling Competencies. Researchers began to incorporate interpretive and reflective methods (e.g., ethnographic, semiotic, or discourse analysis) and socio-cultural theories (e.g., Bernstein, Bourdieu, Brousseau, Freire, Vygotsky, etc.) This social turn created a shift in journals such as ESM and JRME, as evidenced by decreasing numbers of papers based on psychometric methods and psychological theories (Inglis & Foster, 2018). Given the weaker social turn in research on mathematical modelling education, a considerable part of research in this area has retained a more psychological or cognitivist focus on the attributes of individuals This focus cannot include socio-cultural aspects of modelling, such as collaboration between students, this is considered a vital aspect of mathematical modelling (Blum, 2002).
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