Abstract
Modelling competencies are currently included in numerous curricula worldwide and are generally accepted as a complex, process-oriented construct. Therefore, effective measurement should include multiple dimensions, like the sub-competencies required throughout the modelling process. Departing from the characteristics of modelling problems as open and often underdetermined real-world problems, we propose to enrich the current conceptualisation of mathematical modelling competencies by including creativity, which plays an important role in numerous phases of the mathematical modelling process but has scarcely been considered in modelling discourse. In the study described in this paper, a new instrument for the evaluation of this enriched construct has been developed and implemented. The modelling competencies incorporating creativity of the students were evaluated based on the adequacy of the models and the modelling processes proposed, and the appropriateness and completeness of the approaches were evaluated in detail. Adapting measurement approaches for creativity that have been developed in the problem-solving discourse, certain criteria of creativity were selected to evaluate the creativity of the students’ approaches in tackling modelling problems—namely, usefulness, fluency, and originality. The empirical study was conducted among 107 Chinese students at the upper secondary school level, who attended a modelling camp and independently solved three complex modelling problems. The results reveal significant correlations between fluency and originality in students’ performances across all tasks; however, the relationships between usefulness and the other two creativity aspects were not consistent. Overall, the results of the study support the importance of the inclusion of creativity in the construct of modelling competencies.
Highlights
With the aim of promoting responsible citizenship, mathematical modelling and related competencies have been recognised as important in numerous national curricula, in order to enhance quality-oriented teaching (Blum, 2015)
Several descriptions of modelling cycles exist in the current discussion on mathematical modelling and in the curricula prescribed in several countries, which have the potential to influence the promotion of mathematical modelling in these countries, as curricula provide a basis for the development of textbooks and are important guidelines for teachers to implement mathematical modelling in their teaching (Borromeo Ferri, 2018; Niss & Blum, 2020)
Mathematical modelling does not entail the solution of real-world problems using standard methods; rather, the development of new methods of finding solutions or new ways of addressing real-world problems based on sound mathematical knowledge is required (Niss & Blum, 2020), which calls for the incorporation of certain aspects of creativity into the discourse on the teaching and learning of mathematical modelling
Summary
With the aim of promoting responsible citizenship, mathematical modelling and related competencies have been recognised as important in numerous national curricula, in order to enhance quality-oriented teaching (Blum, 2015). In the newly released national curricular standards for upper secondary school mathematics in China (Ministry of Education of China [MOE], 2018), mathematical modelling competencies are considered one of the six core competencies of mathematics education They are, on the one hand, “relatively independent” and, on the other hand, “intertwined with one another” to promote the “right values, necessary characters and key abilities” that students should develop in mathematics learning According to these standards, among the biggest challenges to the promotion and implementation of modelling competencies in mathematics teaching and learning are the development and implementation of valid assessments accompanied by the problems students and teachers have with mathematical modelling (Blum, 2015). Mathematical modelling does not entail the solution of real-world problems using standard methods; rather, the development of new methods of finding solutions or new ways of addressing real-world problems based on sound mathematical knowledge is required (Niss & Blum, 2020), which calls for the incorporation of certain aspects of creativity into the discourse on the teaching and learning of mathematical modelling
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