Metacognition in mathematical modeling: the connection between metacognitive individual strategies, metacognitive group strategies and modeling competencies

ABSTRACT

There are several conceptualizations of modeling competencies, including among others on the one hand so-called sub-competencies, which are required to progress from one step of a modeling process to the next, and metacognitive individual and group strategies. However, the relationship between metacognitive strategies and modeling sub-competencies remains unclear, as does the influence of metacognitive strategies on the development of modeling competencies. The current paper presents the results of a study conducted with 170 students in grades nine and ten. This intervention study concerns the relationships between metacognitive strategies and the development of these strategies and modeling sub-competencies over the course of the study. The results illustrate that metacognitive individual strategies are highly correlated with each other, and metacognitive group strategies are highly correlated with each other, but metacognitive individual strategies are not correlated with metacognitive group strategies. Analysis of the development of metacognitive strategies and modeling sub-competencies within the intervention study reveals that not all of these developed as expected. Additionally, the factors of metacognitive strategies that were measured within the study allow for limited conclusions about the development of students’ modeling sub-competencies. These results have implications for further research.

KEYWORDS:

• Mathematical modeling
• modeling competencies
• metacognitive strategies
• metacognition
• social metacognition

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1. Sometimes, working mathematically is not regarded as a sub-competence of mathematical modeling, as it is not considered to be specific to mathematical modeling.

2. The factors reconstructed in the analyses presented in this paper differ from the three factors mentioned by Vorhölter (2018). At a methodological level, the different factors can be attributed to different samples and the claim of measurement invariance. In terms of content, one can assume that, by working on modeling problems several times in small groups, students independently developed a construct of metacognition.

Additional information

Notes on contributors

Katrin Vorhölter

Katrin Vorhölter is a researcher in the Department of Mathematics Didactics at the Faculty of Education, University of Hamburg. She completed her postdoctoral thesis in 2020 on the subject of metacognitive group strategies of students in mathematical modeling.