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This essay explores the possibility of achieving two concurrent visions in secondary school mathematics: a civic education in mathematics for all students (Mathematics for All) and specialized preparation for future experts in mathematics, science, and technology. Historically, it has been difficult to achieve both visions at the same time. We investigate in what respect Sweden has managed to do so. The analysis focuses on the evolution of Swedish mathematics curriculum, particularly the distinction between a civic education at lower secondary level and upper secondary advanced courses. The essay is based on existing research on Swedish mathematics education. New facts have been gathered using official statistics. The main result is that Mathematics for All to large degree has been implemented in Sweden at lower secondary level and in certain periods of time it functioned with success and both visions were achieved. But, not without setbacks, even during the successful years. A Mathematic for All curriculum, at the lower secondary level, with a strong focus on basic mathematics and everyday applications seems to have a selective, rather than inclusive, function in relation to advanced mathematics courses at the upper secondary level.

Students’ development of routines is essential to learning, particularly in STEM studies where there is a goal of preparing students for directly applying mathematics for practical ends. We hypothesize that this impacts on how they engage with routines. We report from an empirical study which explores different types of routines that undergraduate students engage in when using an animation tool to model motion in a real-world context. Drawing on commognitive theory, we conducted a fine-grained qualitative analysis of the discursive activity of one group of three engineering students. Rather than aiming for a broad generalization, the study uses this dataset to examine the mechanisms through which students shift between deed-oriented and explorative routines. The analysis shows that these routines do not function as separate forms of engagement, rather they developed as a mutually reinforcing dyad – a dyadic relationship. We argue that recognizing this relationship provides a refined lens for understanding how environments may support possibilities not only for practical learning, but also for discursive learning.

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 preparation of prospective secondary mathematics teachers for teaching mathematics.

Lectures using “chalk talk” are a central means by which students are introduced, often implicitly, to standards of proof in university mathematics. In a case study of one lecturer, video recordings of lectures on algebraic geometry are analysed, with the aim of characterising ways in which statements are communicated as being true. The lecturer uses a range of substantiation routines less rigorous than formal proof, but still playing a key role in becoming convinced of mathematical claims. Although precise communication supports substantiation, low levels of precision are not always associated with low levels of endorsement. This adds new insights into where and how precision is communicated in chalk talk. We argue that decisions about what to omit and when to be imprecise are important features of mathematical discourse.

In this article, an analysis of six fisheries biology assignments involving mathematical models is conducted, focusing on the type of participation that they offer. The purpose of the analysis is to identify the characteristics of the mathematical discourse of the assignments and to expose their relationship with the biological context with the purpose of understanding the role of mathematics discourse in other academic discourses. The theoretical orientation of the study is informed by commognitive theory which views learning of an academic discourse as the process of becoming a participant in that discourse. Data analysis revealed various aspects of mathematics wordings, tools and routines essential in the expected solution trajectories of the assignments and two types of required transitions, intrinsic and extrinsic, between mathematics and biology narratives. The article offers analytical and theoretical explanations for why this is the case as well as directions for future research.

We compare the algebra content in the Swedish upper secondary syllabi for higher educational preparatory (HEP) and vocational educational and training (VET) programmes. The study is theoretically embedded in the Anthropological Theory of the Didactic (ATD), where praxeology is used as an analytical tool. The results reveal that the algebra content in the VET programmes is more focused on praxis (‘know-how’) aspects compared to the HEP programmes, in which the balance between praxis and logos (‘know-why’) aspects is more even. We discuss the results in view of students’ opportunities to develop algebraic knowledge within the framework of the given syllabi. 

We report from the first iteration of a small-scale project introducing elements of inquiry-oriented education in a first-year engineering Calculus course. In four of the exercise sessions we introduced problem solving in groups, using problems designed to provide alternative viewpoints on central topics of the course, for example limits, differentiation and integration, and containing elements of modelling and numerical methods. The theoretical perspective underlying the design was commognitive theory. We discuss some of the problems used in the intervention, focusing particularly on the numerical differentiation and integration problems. We also report some observations made during the first two iterations of the project, and how these have fed into the continued evolution of the project.

In this symposium, we will discuss different ways of analysing mathematics textbooks from a methodological point of view. The discussion will be based on examples from five separate ongoing analyses of Swedish textbooks divided into two methodological approaches; one where analysis is conducted within an established theoretical framework, and one where analytical tools are constructed through combining aspects of different theories. The symposium will be held at the conference MADIF13.

As a first step in an investigation of what is done to prepare prospective upper secondary teachers to teach calculus, an international survey of calculus in upper secondary school, at university and in teacher education was conducted. As a result, 14 national accounts, written by experts in the field, were collected. These were then analyzed, focusing on the institutional context, the role of the content in the institutions and differences in content between institutions. Differences and similarities between the countries, as described in the accounts, are presented, and implications of the results regarding how Klein’s double discontinuity plays out in the different countries are discussed.