In this paper, we draw on recent research on so-called Fermi problems and situate the fundamental principles underlying this type of tasks and their use from a task design perspective. We use the models and modelling perspective on teaching and learning to elaborate on aspects related to the design of single-use, as well as sequences of, Fermi problems. In addition, we discuss a framework (called the Fermi problem activity template [FPAT] framework) for supporting the design and use of Fermi problems to facilitate students learning within particular mathematics content areas and/or aimed at particular concepts or higher-order thinking skills. We also illustrate how the FPAT framework can be used to (i) facilitate interdisciplinary collaborations with other subjects such as the social sciences, but in particular with the other STEM subjects; and (ii) support teachers in adapting and implementing Fermi problems in their classrooms.

This theoretical paper outlines and discusses our first attempt to formulate the foundation and selected components of an emerging framework for using novel modelling problems (Fermi problem) as a tool in the teaching and learning of mathematics to make different cultural aspects of the world visible and accessible for students. We present (i) an argument relating mathematical modelling, aspects of culture and intercultural awareness; and (ii) an analysis investigating to what extent the six design principles of models eliciting activates aligns with, or need to be developed and modified in order to align with, the three levels of intercultural awareness discussed by Will Baker in a paper from 2011. The focus of the analysis is to evaluate the potential of the (potentially modified) six design principles of model eliciting activities to effectively also be applicable for designing Fermi problems that make different cultural aspects of the world visible and accessible for students.

In this paper 58 Fermi problems posed by grade 4–6 pre-service primary teachers are analysed with respect to (i) what extent the posed Fermi problems are clearly formulated and authentic for grade 4–6 students; (ii) if the Fermi problemsare inviting to, or setting up an introduction to, a relevant mathematical concept or content from the curriculum, or some relevant aspect of the real world; and (iii) what situations and contexts was used in the posed Fermi problems. Both pre-defined coding categories as well as open coding is used to analyse the 58 Fermi problems. The results provide a snapshot of the competence of pre-service primary teachers to pose problems that promote mathematical learning and learning about the proposed and diverse contexts in the problems.

Approaches to integrated STEM education offers opportunities as well as challenges for both teachers and students. Working on problems or projects involving more than one of the STEM disciplines gives access to interesting, motivating and relevant real-world contexts and problem situations, but at the same time increases the complexity of the problems and problem solving process. One contributing factor to this increasing complexity is the need to appreciate, negotiate and coordinate the different perspectives on the nature of knowledge and the characteristics of inquiry in the different STEM disciplines. This paper outlines and discusses a proposal for how so-called Fermi Problems and Fermi Problem Activity Templates (FPATs) can be used as a tool for teachers and students to start navigating and tackling this complexity.

This survey on interdisciplinary aspects of the teaching and learning of mathematical modelling focuses on the period 2012–2021. Based on our review of research literature published during this time, following the brief we were given to conduct the survey, we identified four major threads of contributions as these relate to schooling. These threads were: the importance of a well-understood relation between mathematics and the real world supporting interdisciplinary work in mathematics education; the contribution to knowledge about modelling of interdisciplinary research and teaching teams; issues and challenges in the relationships among mathematical modelling, mathematics, the real world and interdisciplinarity; and, mathematical modelling providing critical high leverage to ensure mathematical depth in STEM integration. Each thread is exemplified with relevant research. Future directions are offered in our final reflections.

This chapter presents arguments and examples highlighting the similarities and differences between statistics, statistical modelling and mathematical modelling. Based on educational research that focuses on statistical modelling and mathematical modelling, we elaborate on the potentially productive connections for the development of, and research on, the teaching and learning of statistics, statistical modelling and mathematical modelling. We outline the development of an ongoing research agenda that pursues a framework for how to conceptualise the connection between statistics and statistical modelling on the one hand, and mathematical modelling on the other, as well as suggest how to further develop this emerging framework in order to provide a richer, more nuanced and useful picture of the relationship between statistics, statistical modelling and mathematical modelling.

This study developed and discussed a framework for characterising rationales for using statistical modelling from a mathematical modelling perspective based on a systematic literature review. We used this framework to provide an overview of the distributions of these rationales in the analysed studies, focusing on statistical modelling. The results identified three categories of rationales for using statistical modelling, namely, competency, content, and socially oriented types. This work discussed how the conceptualised rationales for using statistical modelling in the teaching and learning of statistics can guide the initial step in task design and curriculum development related to statistical modelling. These rationales may also serve as a common point of departure for discussions and collaboration between the mathematics and statistics education communities on the use of models and modelling.

In this methodological paper we discuss the development and testing of a framework for analysing and visualizing the overall structure of the content and tasks in mathe-matics textbooks. The aim of the framework is to provide a lens on mathematics textbooks at the secondary level that is mathematics topic- and content-area-unbiased to facilitate an as objective as possible comparisons between both (a) different contents, topics, and tasks within a textbook; and (b) contents, topics, and tasks across different series of textbooks or within a textbook series. The paper explores the results of the framework applied to four mathematical textbook chapters visualized in terms of so-called hierarchy charts. Inter-rater coding reliability with respect to a developed coding manual, and future development and applications of the framework is also discussed.

This study investigates the potential of engaging secondary pre-service teachers in a team-teaching approach called Socratic lectures to develop their communicational skills. An intervention was designed centered around a workshop sandwiched between a pre- and a post-presentation on natural logarithmic and derivatives to an audience of undergraduate students. A quantitative and qualitative analysis of 155 pre- and 92 documented post-experiences of the undergraduate students’ shows that the pre-service teachers’ presentations and communicating skills developed positively over the course of the intervention. The accompanying statistical analysis of Likert evaluation items shows asignificant increase of multiple communicational aspects of the pre-service teachers, and the line-by-line analysis of written evaluations support this claim regarding the pre-service teachers’interactivity. Issues about generalizability and future research is also discussed.