An analysis of mathematical modelling in Swedish textbooks in upper secondary school

A new national curriculum has recently been implemented in the Swedish upper sec-ondary school where one of the goals to be taught is modelling ability. This paper presents a content analysis of 14 ”new” mathematical textbooks with the aim to investigate how the notion of mathematical modelling is presented. An analytic scheme is developed to identify mathematical modelling in the textbooks and to analyse modelling tasks and instructions. Results of the analysis show that there exist a variety of both explicit and implicit descriptions, which imply for teachers to be attentive to complement the textbooks with other material

What is the role and place of mathematics education in (swedish) vocational education?

This paper presents a discussion of some characteristic features regarding the role and place of mathematics education in vocational education. Based on examples from the Swedish vocational educational system, research studies and curricula, it is concluded that central roles of vocational mathematics education include the connection of informal and formal mathematics as well as facilitation of the use of technology such as artefacts, ICT, and pen and paper. To smoothen the transition from school to workplace, the place of vocational mathematics education relates to different learning environments and activities that connect the classroom and workplaces. For creating a starting point for discussions about how vocational mathematics education might be organized analogies are used. They act as tools to visualize and pin point characteristic features that make impact on teaching to prepare individuals for future work and life

Grade 8 students appropriating Sankey diagrams: The first cycle in an educational design research

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The spirit of mathematical modeling – a philosophical study on the occasion of 50 years of mathematical modeling education

We mark the 50th anniversary of mathematical modeling education by reviving the term the spirit of mathematical modeling (SoMM), which idealistically reflects core aspects of mathematical modeling. The basis of our analysis is the notion of bildung, which is an educational philosophy that strives for harmonizing heart, mind, social life and culture. We built SoMM on five descriptions of mathematical modeling: two research studies from the 1970s, two studies about the work of professional modelers, and one about an environmental school project. We captured SoMM as a collection of aspects at the micro, meso and macro level: at the micro level, we found aspects such as agency, anticipating, scrutiny and critique as part of SoMM; at the meso level, we found collaborating, consulting and navigating social norms; and at the macro level, interdisciplinarity, relevance and social justice. Through the lens of bildung-based educational philosophies, we see that instruction and assessment traditions have transposed mathematical modeling into ‘teachable’ practices that drift away from SoMM. We recommend focusing more on fostering mathematical modeling and to assess students through alternative formats (e.g., group projects)

Fostering student’s mathematical literacy through mathematical modelling tasks

This is an Author's Accepted Manuscript version of a chapter published by Brill in International Perspectives on Teaching and Learning for Mathematical Literacy. The Version of Record is available from https://doi.org/10.1163/9789004710962_008In this chapter, we compare mathematical modelling and mathematical literacy, and explore mathematical modelling tasks as a means for fostering students’ mathematical literacy. We draw on our own research on three different classroom-based mathematical modelling tasks in different contexts that yielded rich and varied student activities. We analyse the tasks in light of five components of mathematical literacy: developing human capital, maintaining cultural identity, pursuing social change, creating environmental awareness, and evaluating mathematical applications. These five components can be used to enact or evaluate teaching that fosters studentś mathematical abilities to participate effectively and democratically in society in a productive and critical manner. We use these five components to evaluate how the three modelling tasks can foster mathematical literacy. The results show that all components came to the fore in at least one of the three analysed modelling tasks. More generally, our approach to evaluating mathematical modelling tasks serves as an illustration for teacher educators and teachers concerning how they can analyse modelling tasks to foster mathematical literacy.acceptedVersio

Ämnesintegrering i yrkesautentisk miljö med par-undervisning som didaktisk metod

Effektiva undervisningsmodeller som förbreder yrkeselever att hantera matematik i sitt komande yrkesliv efterfrågas i forskningslitteraturen. Denna artikel analyserar användningen av team-undervisning som metod för ämnesintegrering inom yrkesutbildningar på ett yrkesgymnasium i Sverige. Baserat på en tematisk analys av intervjuer med matematiklärare, yrkeslärare och elever på fem yrkesprogram, visar resultaten att undervisningsmetoden bidrar till ökad motivation och yrkesrelevans för eleverna, samtidigt som den stärker ett produktivt samarbetet mellan matematiklärare och yrkeslärare som gynnar elevers kunskapsutveckling i matematik och i yrkesämnet. Eleverna upplever att undervisningsmetoden förbereder dem för arbetslivet. Olika organisatoriska förutsättningar och ledningens stöd är avgörande för att implementera team-undervisning framgångsrikt. Studien visar även att eleverna har en positiv syn till team-undervisningen och önskar mer sådan undervisning. Studien bidrar med nya insikter om hur team-undervisning kan användas för att främja elevers lärande och förberedelse inför arbetslivet. Fortsatta forskningsprojekt handlar om att undersöka implementeringen av denna undervisningsmetod på fler skolor för att se om resultaten kan upprepas och för att undersöka eventuella skillnader mellan olika skolmiljöer

Thematic issue of Nomad 2025 – call for papers

The teaching and learning of mathematical modelling in the Nordic and Baltic context

Modes of modelling assessment—a literature review

This paper presents a critical review of literature investigating assessment of mathematical modelling. Written tests, projects, hands-on tests, portfolio and contests are modes of modelling assessment identified in this study. The written tests found in the reviewed papers draw on an atomistic view on modelling competencies, whereas projects are described to assess a more holistic modelling competence but obstacles regarding reliability of assessing projects are identified. The outcome of this investigation also indicates that the criteria used in frameworks or modes of assessment seldom are derived from a theoretical analysis, but more often based on ad hoc constructions, experience from assessment situations or empirical studies of students work. Finally, this study suggests that an elaborated view on the meaning of quality of mathematical models is needed in order to assess the quality of students work with mathematical models.</p

Modes of Mathematical Modelling : An analysis of how modelling is used and interpreted in and out of school settings

The relevance of using mathematics in and for out-of-school activities is one main argument for teaching mathematics in education. Mathematical modelling is considered as a bridge between the mathematics learned and taught in schools and the mathematics used at the workplace and in society and it is also a central notion in the present Swedish mathematical syllabus for upper secondary school. This doctoral thesis reports on students’, teachers’ and modelling experts’ experiences of, learning, teaching and working with mathematical modelling in and out of school settings and their interpretations of the notion of mathematical modelling. The thesis includes five papers and a preamble, where the papers are summarised, analysed, and discussed. Different methods are being used in the thesis such as video analysis of students’ collaboration working with modelling problem, interview investigations with teachers and expert modellers, content analysis of textbooks and literature review of modelling assessment. Theoretical aspects concerning mathematical modelling and the didactic transposition of modelling are examined. The results presented in this thesis provide a fragmented picture of the didactic transposition of mathematical modelling in school mathematics in Sweden. There are significant differences in how modellers, teachers and students work with modelling in different practices in terms of the goal with the modelling activity, the risks involved in using the models, the use of technology, division of labour and the construction of mathematical models. However, there are also similarities identified described as important aspects of modelling work in the different practices, such as communication, collaboration, projects, and the use of applying and adapting pre-defined models. Students, teachers and modellers expressed a variety of descriptions of what modelling means. The variety of descriptions in the workplace is not surprising, since their working approaches are quite different, but it makes the notion difficult to transpose into school practise. Questions raised are if it is unrealistic to search for a general definition and if it is really necessary to have a general definition. The consequence, for anyone how uses the notion, is to always be explicit with the meaning. An implication for teaching is that modelling as it shows in the workplace can never be fully ‘mapped’ in the mathematical classroom. However, it may be possible to ‘simulate’ such activity. Working with mathematical modelling in projects is suggested to simulate workplace activities, which include collaboration and communication between different participants. The modelling problems may for example involve economic and environmental decisions, to prepare students to be critically aware of the use of mathematics in private life and in society, where many decisions are based on mathematical models