Mathematization is critical in providing students with challenges for solving modelling tasks. Inadequate assumptions in a modelling task lead to an inadequate situational model, and to an inadequate mathematical model for the problem situation. However, the role of assumptions in solving modelling problems has been investigated only rarely. In…

An important use of statistical models and modeling in education stems from the potential to involve students more deeply with conceptions of distribution, variation and center. As models are key to statistical thinking, introducing students to modeling early in their schooling will likely support the statistical thinking that underpins later,…

The notion of mathematical modelling has multiple interpretations in research literature and has been included in curriculum documents in various ways. This study presents a thematic analysis of nine professional modellers' conceptions of the notion of mathematical modelling, representing scholarly knowledge. The result is organised according to…

This paper presents the results of a literature review focusing on the use and potential of Fermi problems (FPs) in the STEM disciplines. We identify different usages and roles given to FPs in each of the STEM disciplines and highlight their potential to promote modeling of real phenomena and situations as well as learning about the estimation of…

This paper presents an international research study of long-term professional development courses on modelling. It addresses the question of scaling-up professional development. So far, there has been much research on small-scale professional development courses, but we know very little about what it means to scale up such a course and to reach…

Children have limited exposure to statistical concepts and processes, yet researchers have highlighted multiple benefits of experiences in which they design and/or engage informally with statistical modelling. A study was conducted with a classroom in which students developed and utilised data-based models to respond to the inquiry question,…

The "cardinality principle" (CP) is a conceptual basis of counting collections meaningfully and provides a foundation for understanding other key aspects of numeracy, such as the successor principle or counting-on to determine sums. Unfortunately, little research has focused on how best to teach the CP. One suggestion is that modeling…

Word problems are among the most difficult kinds of problems that mathematics learners encounter. Perhaps as a result, they have been the object of a tremendous amount research over the past 50 years. This opening article gives an overview of the research literature on word problem solving, by pointing to a number of major topics, questions, and…

Comprehending a mathematical modelling task is a central prerequisite for the following modelling process. In this study, we investigated the roles that the language proficiency of the students and the linguistic wording of the task play for the comprehension and the successful solving of mathematical modelling tasks. Five mathematical tasks with…

Despite the incorporation of mathematical modelling in the Singapore mathematics curriculum framework since 2007, Singapore teachers still face readiness issues concerning the use of open-ended real-world problems. This paper presents some preliminary findings from an exploratory study undertaken within a professional development programme on…

In times of rapid technological innovation and global challenges, the development of science, technology, engineering and mathematics (STEM) competencies becomes important. They improve the personal scientific literacy of citizens, enhance international economic competitiveness and are an essential foundation for responsible citizenship, including…

Metacognitive competencies are of great importance for developing modelling competencies. However, there are assumptions about useful metacognitive knowledge and strategies for individuals working on modelling problems as well as for whole groups, but their coherence as well as their influence on modelling processes is not evaluated…

Statistical modeling is emerging as a fertile research environment in which to promote and learn about student statistical reasoning processes. We outline a paradigm shift toward a modeling perspective that is occurring in statistics education research and how statistical modeling processes involve connecting data, chance and context. The…

The goal of this study is to explore the role of model comparison, which is a key activity of young learners' informal reasoning, with statistical models and modeling in the context of informal statistical inference. We suggest a framework to describe this reasoning (the RISM framework), and offer an illustrative case study of two-sixth graders…

Recognizing the roles of mathematics in society is an important goal for the teaching and learning of mathematical modelling. The Likert-scales method is a simple and effective tool to assess student appreciation about the utility of mathematics; however, it does not reveal the detailed aspects of student perceptions of the roles of mathematics in…