In this chapter we describe an empirical investigation aimed at gener-

ating and testing a research tool that enable eliciting intercultural awareness through

solving Fermi problems as mathematical modelling activities. Using aspects of ethno-

mathematics and mathematical modelling as theoretical points of departure, we

designed a Fermi problem to be solved by prospective mathematics teachers from

three different countries. The solutions were analysed to establish the mathematical

structure so that it is possible to identify the predominant cultural elements surfacing

in the solutions in each country. The data analysis process led us to construct local

representative solutions, as a synthetic solution that includes the majority’s assump-

tions in each cultural context. These local representative solutions led us not only to

identify the mathematical aspects of the solutions and the cultural elements embedded

within them but also compare surfacing cultural aspects, hence serving as a tool for

gaining deeper insights into the role of culture in problem-solving.

This paper presents an empirical exploratory study involving 158 Swedish secondary school students (Years 7-11) asked to develop fair prescriptive mathematical models to rank real-life, multi-faceted heptathlon outcomes. A developed framework for identifying Characteristics of Fairness is used to investigate What types of models do the students develop? and What aspects of fairness in the context of heptathlon come to the fore in the students' models? Discussed and situated in relation to previous research, the result highlight and elaborate four identified types of models focusing on Event placement, Individual performance, Comparative performance and Baseline comparison. In particular the results show that students emphasised outcome fairness at the expense of process fairness. Based on the findings, implications and possible future lines of research and theoretical development are suggested.

 This chapter uses a phenomenographic research approach and analyses

84 pre-service secondary teachers’ written responses to the questions: (1) What

is a model?; (2) What is a mathematical model?; and (3) What does it mean to

engage in mathematical modelling? Through the use of open-, axial- and selective

coding, the emerging categories capture the variation of the pre-service teachers’

pre-conceived views of the notions of models and modelling. The results show that

mathematical models were elaborated on in terms of descriptions, representations

and explicit examples of models, models being tools, didactical aspects of models

and encapsulating the structure of mathematics itself . Modelling was found to be

expressed as the use of mathematics and/or models, to create general mathematical

models, in term of the whole/part of the modelling pro

In this symposium, three research and development projects from different Swedish

universities will serve as a starting point for a discussion of different ways in which

mathematicians and mathematics educators can work together to improve the prepa-

ration of prospective secondary mathematics teachers for teaching mathematics.

In this chapter, we outline a theoretical scaffold comprising intercultural awareness and modelling perspective components. Additionally, we report on the outcomes of two exploratory studies that employ Fermi problems to elicit intercultural awareness in pre-service teachers and students. In the first study, the Bikes Problem was successful in promoting 7th graders’ cultural and a-cultural elements in the Fermi problem setting. In the second study, the Teapot Problem enabled pre-service teachers to consider contextual and cultural assumptions in their solutions to the Fermi problem. Consequently, the Fermi problems possess the potential to encourage problem solvers to identify cultural facets of the problem situations, while functioning as a mathematical modelling exercise in enhancing cultural and intercultural awareness.

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 paper presents a discussion and analysis of recent developments and investigations into the multifaceted role of Fermi Problems as content, connectors, and integrators in mathematics and across the STEAM disciplines. In particular, the role of Fermi problems as interdisciplinary activities in the context of mathematical modelling and problem posing is discussed, as well as the utility of the framework known as the Fermi Problem Activity Template (FPAT) as a tool for supporting the design and implementation of Fermi problems at different levels. The paper then proceeds to present a number of illustrative examples and recommendations for facilitating the integration of Fermi problems into curriculum materials and classroom practice. Furthermore, it outlines potential avenues for future research in this field.

This chapter aims to demonstrate how adopting a mathematics education

research perspective on Fermi problems can contribute to and enhance the practice

and understanding of STEM education. To achieve this, we first discuss mathemat-

ical modelling from a mathematics education perspective and then briefly elabo-

rate on modelling as discussed in STEM education. Our attention is then directed

towards the inherent coupling of Fermi problems to mathematical activities and

contents of the mathematical curriculum, in particular, estimates, estimation and

mathematical modelling in mathematics education research. We present a framework

for connecting recent advances in the research on Fermi problems to teaching and

learning in STEM education and discuss the example of The tin foil boat challenge.

This chapter discusses mathematical literacy in the context of the teaching and learning of statistics at the secondary level (Grades 7–9). This includes exemplifying how tasks and activities in statistics can be designed and implemented to support students in developing mathematical literacy using the models and modelling theoretical perspective and model development sequences. The chapter discusses literature on statistical literacy and related notions in the field of statistics education and links these to mathematical literacy more generally. Connections are made and highlighted between mathematical literacy and tenets of the models and modelling perspective as well as model development sequences. These connections are then illustrated as they come to the fore in an example of an activity from a research project focusing on the teaching and learning of statistics, which sheds light on the students’ opportunities to develop their mathematical literacy.