In this chapter we describe an empirical investigation aimed at generating and testing a research tool that enable eliciting intercultural awareness through solving Fermi problems as mathematical modelling activities. Using aspects of ethnomathematics 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 assumptions 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 paper presents and gives an overview of the papers and posters discussed in the Thematic Working Group 6 (TWG6) at the CERME14 conference taking place in Bolzano, February 4–8, 2025.

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 process as well as didactical aspects and meta-perspective of teaching mathematics.

This study explored secondary school students’ multifaceted perceptions of the role of data from the perspectives of models, modelling, and information, following two or three lessons focused on a data-informed modelling activity with mathematics and statistics at its core. The results showed that half of the students perceived data not only as a well-organised basis to directly achieve the real goals set in the modelling activity, but also as an unorganised basis to be manipulated or mathematised to generate information and knowledge or wisdom from the data. The students’ perceptions were also supported by the real-world contexts of the activity used in the lessons. However, the role of data as an aspect of reality was not found to be naturally recognised and emphasised by the students in the context of the lesson. We argue that students need to experience a range of data-informed modelling activities with a variety of tasks in order to recognise the multifaceted role of data.

This chapter discusses the relationships between mathematical modelling education and two other approaches in mathematics education: mathematical problem solving and problem posing and creativity. By highlighting the similarities and differences between the three, the chapter aims to explore how these approaches can inform and support each other for further progress. Various aspects are highlighted, such as the characterisation of tasks, the emphasis on nonroutine and open-ended solution strategies and processes, nuanced differences in their orientation and focus (especially in relation to the real world), the role of teacher mentoring and scaffolding, and theoretical frameworks. Suggestions for future research developments related to mathematical problem solving and problem posing, creativity, and mathematical modelling are also presented.

In this theoretical paper we present an initial conceptualisation of a new perspective on mathematical modelling. Drawing on seven phases of a creative problem-solving process and making parallels to the purposeful and creative writing process, we first elaborate on the similarities between the modelling process and the writing process. We then reconceptualise the so-called ‘Wheel of Writing’ in the context of mathematical modelling as a ‘Wheel of Modelling’ and articulate the acts and purposes of mathematical models and modelling within this perspective.

The dim²ension project aims to integrate digital tools into mathematical modelling to address real-world problems, particularly those related to the United Nations' Sustainable Development Goals (SDGs). The project’s overarching objective is twofold: firstly, to enhance students' mathematical modelling competencies, and secondly, to foster awareness of global sustainability issues in schools. The present introductory chapter offers a comprehensive overview of the project, while also delineating the structure of the theoretical white paper.

En este artículo compartiremos ideas que podrían ser consideradas al diseñar tareas que fomenten la competencia en modelización matemática en estudiantes de educación infantil y primaria. Proponemos tres tipos de variables didácticas: a) de modelización, que contienen los elementos conceptuales y procedimentales que deberían ser considerados al diseñar la tarea; b) sobre la gestión de la enseñanza, referido a los elementos sobre la implementación de la tarea en el aula; y c) sobre el formato, que tiene relación con el uso de esquemas para representar el proceso de resolución de los alumnos.

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.