Peter Frejd

First Results from a Study Investigating Swedish Upper Secondary Students’ Mathematical Modelling Competencies

This paper reports on the first results from a study investigating Swedish upper secondary students’ (11th – 12th grade) mathematical modelling competency. Using non-parametric statistical methods ...

A reflection on mathematical modelling and applications as a field of research : theoretical orientation and diversity

This chapter explores the nature of theoretical approaches used in research literature focusing on mathematical applications and modelling, in particular, the orientation and diversity of theoretic ...

Modelling from the Perspective of Commognition – An Emerging Framework

This chapter explores an emerging framework on mathematical models and modelling using the theoretical perspective of commognition to analyse and discern discursive objects in a dialogue between two students engaged in a modelling activity. The results, partly presented as realization trees, show a variety of signifiers from different discourses coming into play during the modelling, and examples are given of the activity of negotiation, which plays an important role in any modelling activity. In addition, it is argued that the framework has potential to bridge different research perspectives on mathematical models and modelling.

Mathematical Modellers’ Opinions on Mathematical Modelling in Upper Secondary Education

This chapter examines and discusses how professional mathematical modellers have learned about modelling as well as their opinions on the teaching of mathematical modelling in upper secondary education. An interview study showed that they developed most of their knowledge about mathematical modelling during their PhD studies and through their occupation by working with ‘real modelling’. According to the interviewees mathematical modelling should be a part of mathematics education in upper secondary school, and in particular it should be more emphasized as a part of general education to develop students’ critical awareness about how models are used in society. They also gave suggestions for approaches to teach modelling and examples of modelling problems to work with from their own workplace.

Mathematical Modelling as a Professional Activity: Lessons for the Classroom

This chapter presents a discussion about similarities and differences between working with mathematical modelling in ‘school’ and mathematical modelling as a ‘professional task’ in the workplace based on empirical and theoretical research studies. Issues discussed concern goals; technology; division of labour, communication and collaboration; model construction, including the application and adaption of predefined models; projects; and risks involved in using the models. Based on this discussion and examples from innovative teaching practices, approaches to simulate modelling as a ‘professional activity’ in educational settings are explored and exemplified with a role-play activity.

Initial Results of an Intervention Using a Mobile Game App to Simulate a Pandemic Outbreak

This chapter presents the design and results from the first iteration of a classroom activity using the context and simulation provided by a commercial game app for smartphones and tablets. The aim was to study students’ experiences of an intervention entailing the game app in order to inform a more mature design with the long-term goal of being able to develop principles to design and implement modelling activities using game apps. An analysis focusing on the interplay between the designed intervention environment and students’ work from two upper secondary classes resulted in information in terms of affordances to inform the redesign. In addition, students experienced the activity as interesting and engaging, but with significant gender differences. The results inform a discussion of the role of new technology and simulation within classroom teaching and learning of mathematical modelling.

Exploring the Notion of Mathematical Literacy in Curricula Documents

The notion of mathematical literacy has gained momentum internationally recently through the influence of international assessment regimes such as the Programme of International Student Assessment (PISA) and national concerns about the ability of citizens to use mathematics effectively in personal, civic and work life. Accordingly, it is to be expected that these concerns should be reflected in relevant curriculum documents. This chapter presents a content analysis of a sample of 12 national curriculum documents in relation to mathematical literacy. The analysis shows that there does not appear to be general agreement about the definition of mathematical literacy within the analysed documents and that the idea of mathematical literacy is represented in a limited fashion.

Old algebra textbooks: a resource for modern teaching

This paper is the result of a comparative literature study aimed at identifying relevant historical mathematical contexts that may be applicable to present day mathematics education. Five Swedish textbooks in algebra from the period around the year 1800 are scrutinized. A content analysis and a comparison between seven categories shows that there exist several historical features that may be used in teaching. These have the potential to serve both teachers and learners of mathematics.