Creativity in students’ modelling competencies: conceptualisation and measurement

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.

Can mathematical modelling work as a creativity-demanding activity? An empirical study in China

“…More importantly, transverse ideas could be used to interpret and validate mathematical results, making sense of the results and linking them with new understandings of real-world situations based on the use of mathematical methods. As such, creativity should be integrated into the further development of the modelling competencies construct (Lu & Kaiser, 2021), with various creativity aspects embedded in the phases of the process, as represented by an enriched diagram (Fig. 1) originally provided by Kaiser and Stender (2013, p. 279).…”

“…The evaluation of originality in mathematical modelling should include not only the originality of the mathematical means used, but also unique perspectives applied in interpreting real-world situations, which might generate multiple solutions to a problem (Lu & Kaiser, 2021). Expert solvers may employ mathematical means and heuristic strategies in modelling that go beyond school mathematics (Stender, 2017), but this does not mean that they can always show a higher level of originality in interpreting real-world situations than inexperienced solvers.…”

“…It appears that flexibility can be evaluated naturally based on the fluency and originality in the modelling, as each process includes several phases that may reveal a set of changes. Therefore, Lu and Kaiser (2021) suggested including only fluency as a creativity component in the evaluation of modelling competencies.…”

“…Usefulness is considered a unique component in the evaluation of creativity in modelling, considering the nature of modelling as applying mathematics in complex real-world problems (Lu & Kaiser, 2021). This approach differs from Sriraman's (2009) conceptualisation of creativity in pure mathematics, whereby creative mathematical work may not always be applicable in other problems.…”

“…This approach differs from Sriraman's (2009) conceptualisation of creativity in pure mathematics, whereby creative mathematical work may not always be applicable in other problems. Creativity in modelling should include usefulness, relevance, and adaptability; the reusability of modelling approaches in other real-world situations is thus included as an indicator of usefulness (Lu & Kaiser, 2021;Wessels, 2014).…”