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

Abstract

Creativity has been identified as a key characteristic that allows students to adapt smoothly to rapid societal and economic changes in the real world. However, Chinese students appear to perform less well in mathematical problem-solving and problem-posing abilities, which are strongly connected to mathematical creativity. Mathematical modelling has recently been introduced as one of the six core competencies in the Chinese mathematical curriculum and is built on students’ ability to solve real-world problems using mathematical means. As mathematical modelling is characterised by openness regarding the understanding of complex real-world problems and the complex relationship between the real world and mathematics, for the strengthening of creativity, mathematical modelling activities seem to be adequate to accomplish this purpose. In this paper, we describe a study with 71 upper secondary school students, 50 pre-service mathematics teachers, and 66 in-service mathematics teachers, based on an extended didactical framework regarding mathematical modelling as a creativity-demanding activity. The results of the study indicate a significant correlation between modelling competencies and creativity aspects. Especially significant correlations between the adequacy of the modelling approaches and the two creativity aspects of usefulness and fluency could be identified, as well as a significant negative correlation between usefulness and originality. The results of the correlational analysis of relationships among the four criteria were not always consistent in the three participant groups. Overall, the results have implications for the promotion of creativity for various expertise groups and demonstrate the dependency of the modelling activities on the mathematical knowledge of the participants and the mathematical topic with which they are dealing.

Farewell to Virtual Environments and Welcome to Post-pandemic Mathematical Problem Posing and Solving

“…Research has identified that knowledge and experience are the basis for credibility in problem solving with approaches and capabilities to translate mathematical theory into practice [24]. In China, the mathematical model exists as a mathematical competence within the curriculum, which is responsible for providing solutions to real world problems, only using mathematics whose basis for solving these problems is creativity [25], which manages to develop problem-solving skills together with cognitive skills in group tests in which they were forced to create social networks to share information and solve the evaluations [29]. The tasks for students whose approach has creative reasoning overcome the complex versions of learning in the area of mathematics and it is much better if it is programmed because it becomes of great support for the teacher and helps to improve the quality of reasoning in the classroom [39] because there is a change of attitude and surprise in the students where they only exchange glances among them when they start to solve the mathematical problems posed with this methodology of presenting problems with each situation.…”

“…The relevance of seeking the solution of mathematical problem solving in elementary level students has repercussions in finding a mathematical model that can work and provide a solution to this problem of yesteryear, it is for this reason that creativity manages to bear its first fruits in adapting the skills of approaching and solving mathematical problems [25], as well as in the curricula of schools with a degree of difficulty to achieve a modeling process and favor the current concepts of mathematical modeling competence in which creativity is immersed as an important point [26], the models currently have as a basis the technology which supports educational environments whose purpose is to develop creative and technical thoughts with psychodiagnostic type approach (creative thinking) [27].…”

How does mathematical modeling competency affect the creativity of middle school students? The roles of curiosity and guided inquiry teaching

“…This model was applied to high school students, preservice mathematics teachers and in-service mathematics teachers. The results showed that mathematical modeling competency is significantly correlated with creativity (Wessels, 2014;Suh et al, 2017;Lu and Kaiser, 2022b). For high school students, the difficulty of modeling tasks may affect the relationship between mathematical modeling competency and creativity (Lu and Kaiser, 2022a).…”

Assessing authenticity in modelling test items: deriving a theoretical model

“…Mathematical modelling is of great importance in mathematics education (Stillman, 2019). The competence of mathematical modelling, i. e. solving real-world problems by using mathematics, is especially significant with regard to the challenges of the 21st century and the skills required to master these challenges (Lu and Kaiser, 2022;Luczak and Erwin, 2023). In order to ensure that those modelling problems are close to reality and are not artificially created for educational purposes, authenticity is regularly demanded being an indispensable property of modelling tasks in mathematics education (Kaiser, 2017;Greefrath, 2018).…”