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Statistics is a discipline that allows implementing novel teaching proposals based on inquiry. Students’ reasoning in the statistical context can be encouraged by implementing project-based learning in statistics courses. Statistical processes often involve other disciplines apart from statistics itself. We present an analysis of the staging of cross-disciplinary characteristics of an inquiry-based project in statistics for the degree in Business Administration. Three moments of cross-disciplinary collaboration are described and analysed from both the viewpoint of teachers and students. Broadening the perspective beyond the domain of statistics provides us with new insights regarding student engagement, challenges related to project organisation and management, and a venue for cross-disciplinary dialogue.

This chapter provides an overview of theoretical frameworks and methodologies used to analyse a range of mathematics curriculum reforms from across the globe. The means for analysis that has been developed includes linking broad theoretical frameworks and the levels within these to the lines of research and research questions; units of analysis and data considered; methodological choices; and results obtained in case studies of mathematics curriculum reform. It is proposed that the approach developed and findings presented could inform more systematic and scientific approaches to the design of reforms as well as their analysis.

Denne antologi udgives af Institut for Naturfagenes Didaktik på Københavns Universitet i forbindelse med den tværinstitutionelle kandidatuddannelse i STEM didaktik. Antologien er baseret på udvalgte artikler fra kurset “De matematisk modellerende videnskaber”, som handler om at omsætte aktuel naturvidenskabelig forskning og samfundsmæssige problematikker til matematiske modeller og modelleringsbaseret undervisning i grundskolen. Deltagerne har skrevet 3 artikler på kurset. Én hvor der udvikles en selvstændig matematisk model, én hvor der udvikles et undervisningsforløb og én hvor matematiske modellers betydning i samfundet diskuteres og belyses.

Mathematical modelling is as most parts of mathematics education affected by the use of digital technologies. In this chapter, we analyse two modelling cases designed with the aim of supporting students’ development of modelling competency and learning content knowledge whilst explicitly drawing on digital tools. One case addresses the notion of vectors at upper secondary level whereas the other case deals with more advanced uses of differential equations at tertiary level. We employ the notion of media-milieu dialectics from the Anthropological Theory of the Didactic, which allows us to study the role played by the digital tool, the modelling problem and other resources available to the students. Based on this analysis, we discuss to what degree the students demonstrate and develop mathematical modelling competency as well as mathematical digital competency, where we refer to the frameworks emerging from Mathematical Competence Theory. Networking these theoretical frameworks allows us to discuss how the merger between mathematical modelling and digital tools can support students learning of mathematical knowledge.

In this paper we address recent years'' attempt to include data science in school mathematics treated from the perspective of mathematical modelling. In our analysis we draw on the notion of scale of levels of co-determinacy from the Anthropological Theory of the Didactic (ATD) to identify the options or limitations for implementing data science in mathematics education as part of mathematical modelling. We analyse trends in educational debate, curriculum documents, textbooks and teaching material developed for Danish upper secondary school and called ‘Data analysis and Cancer’. We identify fruitful conditions and delimiting constraints for merging mathematics and data science in upper secondary mathematics.

This paper presents and gives an overview of the papers and posters discussed in the Thematic Working Group 6 (TWG6) at the CERME 13 conference taking place in Budapest, July 11–14, 2023.

In this paper we present a case study from upper secondary mathematics in Denmark, where students were invited to solve an open problem regarding the design of a facial recognition system. We analyse the activity as a study and research path, where we focus on the media-milieu dialectic. This allows us to identify new potentials regarding resources available to students during mathematics classes but also the need for methodologies on how to design teaching capturing these new resources in order to fully exploit those

Over the last decades digital resources of various kinds have entered mathematics education including mathematical modelling. In this paper we present the a priori analysis of a modelling activity based on Study and Research Path using the notions of media-milieu dialectic and Herbartian schema from the Anthropological Theory of the Didactic. We use these notions to differ between resources: digital tools, textbooks, data and to differ between the pragmatic and epistemic value of the resources. Finally, we discuss how task design can benefit from addressing the potential roles resources can play in modelling processes.

See the planning, observation and reflection from a study lesson completed with grade 11 students at Midtsjællands Gymnasium

Introduktion til undersøgelsesbaseret matematikundervisning på gymnasialt niveau

In this paper, we present a model for upper secondary in-service teacher courses based on the Anthropological Theory of the Didactics and explore how we can teach teachers to design and implement mathematical modelling in their classrooms. The course evolves around Study and Research Path based teaching and strives to create para-didactic infrastructures as a framework for teachers’ development of teaching practice. The novelty in this study is the sequence of shared preparation, observation and evaluation of teaching in the course. We describe the structures and their functioning through an example of a group of teachers’ work. Based on the activity we discuss the potentials of creating such structures and the needs for further research in this field.

In this paper, we discuss how the adoption of a particular theoretical framework affects task design in the research field of modelling and applications. With this purpose, we start by referring to the existence of different reference epistemological models about mathematical modelling to analyse better the consequences they have for decision making concerning designing modelling tasks and their implementation. In particular, we present the analysis of three case studies, which have been selected as representatives of different theoretical perspectives to modelling. We discuss the impact of the chosen reference epistemological model on the task design process of mathematical modelling and the local ecologies suited for their implementation., En este trabajo discutimos cómo la adopción de un marco teórico concreto incide en el diseño de tareas en el ámbito de investigación de modelización y aplicaciones. Con este objetivo, comenzamos refiriéndonos a la existencia de distinto modelos epistemológicos de referencia sobre la modelización matemática para analizar sus consecuencias en la toma de decisiones sobre el diseño e implementación de tareas de modelización. En particular, presentamos el análisis de tres estudios de caso, que han sido seleccionados como representantes de diferentes enfoques teóricos sobre modelización matemática. En base a estos, discutimos el impacto del modelo epistemológico de referencia elegido en el proceso de diseño de tareas sobre modelización y las ecologías locales planeadas para su implementación.

n this paper we present ideas regarding what elements of the anthropological theory of didactics in-service teachers need to design study and research paths and realise them in their classrooms. Based on preliminary experiences from other projects we try to identify crucial notions and how they can be transposed in order to support Danish in-service teachers, who has very diverse didactical knowledge

In this paper we present ideas regarding what elements of the anthropological theory of didactics in-service teachers need to design study and research paths and realise them in their classrooms. Based on preliminary experiences from other projects we try to identify crucial notions and how they can be transposed in order to support Danish in-service teachers, who has very diverse didactical knowledge.

In this paper, we discuss how the adoption of a particular theoretical framework affects task design in the research field of modelling and applications. With this purpose, we start by referring to the existence of different reference epistemological models about mathematical modelling to analyse better the consequences they have for decision making concerning designing modelling tasks and their implementation. In particular, we present the analysis of three case studies, which have been selected as representatives of different theoretical perspectives to modelling. We discuss the impact of the chosen reference epistemological model on the task design process of mathematical modelling and the local ecologies suited for their implementation.

Hvad gik galt ved sommereksamen 2019 på det gymnasiale B-niveau i matematik? Var kravene for høje, eller havde eleverne lært for lidt? Hvad skal der gøres fremadrettet? Vi ser på disse spørgsmål på baggrund af Matematikudredningens og Matematikkommissionens anbefalinger, særlig de som (endnu) ikke er fulgt

Within the anthropological theory of the didactic, it has been suggested that the dominant teaching paradigm should be changed from transmission of knowledge to the paradigm of “questioning the world”. This can be realised through teaching designed as “study and research paths” (SRPs). In recent years, this design tool has been experimented on in Denmark and Japan within the existing constraints and conditions. Though these two educational systems are different, the experiments have been fruitful. Therefore, in this chapter, we analyse the constraints and conditions—the ecology—of the two countries for implementing SRP-based teaching to identify favourable conditions for doing this.

This paper discusses the role of the exam and its impact on the teaching of mathematics using the notion of levels of codetermination from the anthropological theory of the didactics. It is argued that a discussion of exam in relation to study and research paths is crucial in order to succeed in changing the current teaching paradigm from “visiting monuments” to “questioning the world”.

In this paper, we analyse the conditions and constraints that exist when implementing inquiry-based mathematics education defined and framed by school mathematics curricula. Within the theoretical framework of the anthropological theory of the didactic, we organize our analysis using two main tools. On the one hand, we focus on the external didactic transposition of inquiry in mathematics education. That is, we focus on analysing how the “knowledge to be taught” addresses inquiry, how it is selected, adapted and declared to be taught from international studies to local curriculum reforms. With this purpose in mind, we present an analysis of curricula of four European countries (Denmark, France, Portugal and Spain) to explore which kind of conditions (and constraints) each curriculum establishes for inquiry-based mathematics education. We use the levels of didactic codeterminacy to identify where these conditions and constraints for inquiry come from. It will allow us to compare relevant situations between aforementioned countries.