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In the wake of the present inclusion of programming in mathematics education, which is a feature of curricular revisions in many countries, we have analysed newly inserted programming activities in mathematics textbooks. The aim was to investigate how such activities relate to and potentially affect students' opportunities to learn mathematics. Data consist of Swedish textbooks for grades 7-9 (ages 13-15) intended for mathematics classes, where all units labelled as or including programming activities were analysed. Concerning the relation between mathematics and programming, our results show that in the intricate balance between teaching mathematics on the one hand and teaching programming on the other hand, the textbooks seem to lean towards the latter, thus not greatly contributing with mathematical learning opportunities. We see a dominance of mathematics as a context for programming, rather than programming as a tool for learning mathematics. The lack of exploration and rare occurrence of novel mathematics in the programming activities implies a weak relationship between mathematics and programming.

Computational thinking has become part of the mathematics curriculum in several countries. This has led recently available teaching resources to explicitly integrate computational thinking (CT). In this paper, we investigate and compare how curriculum resources developed in Denmark — digital teaching modules — and Sweden — printed mathematics textbooks — have incorporated CT in mathematics for grades 1–6 (age 7–12). Specifically, we identify and compare the CT and mathematical concepts, actions, and combinations in tasks within these resources. Our analysis reveals that Danish tasks are oriented toward CT concepts related to data, actions related to programming, and mathematical concepts within statistics. This is different from Swedish tasks, which are oriented toward CT concepts related to instructions and commands, actions related to following stepwise procedures, and mathematical concepts related to patterns. Moreover, what is most dominant in one country is almost or completely absent in the other. We conclude the paper by contrasting these two approaches with existing knowledge on computational thinking in school mathematics.

Although there have been a huge number of attempts to improve school algebra teaching, several countries are still struggling to improve students algebraic skills. In this study, we focus on the specific case of Sweden where students for several decades have had major problems mastering algebra. In order to get a better understanding of the Swedish situation, we consider what constitutes Swedish school algebra by investigating the development of algebraic content in the Swedish mathematics curriculum documents over the past 40 years. The results reveal that the connection between arithmetic and algebra, the so-called generalized arithmetic, is almost absent in all three curricula although researchers argue that generalized arithmetic is one of the most relevant topics within early algebra. Instead, Sweden has chosen a unique approach as programming, with a specific focus on stepwise instructions and algorithms, recently has been implemented within the core content of algebra.

In this chapter, we consider opportunities and challenges of integrating programming in school mathematics by looking closer at the Swedish case. Especially, we aim to unpack how the integration of programming in mathematics can affect students’ opportunities to develop mathematical competencies. Three examples taken from a Swedish research project are described and discussed in detail. In the first example, we focus on differences regarding syntax and semantics in programming and mathematics, relevant in a learning perspective. In the second and third examples, we highlight the teachers’ views of how programming may enhance the traditional learning of school mathematics, and describes one particular lesson where students solve pattern problems in Python. Each example is discussed in relation to different mathematical competencies.

This chapter deals with the recently re-emerged concept of computational thinking (CT) and its reception in mathematics education research and mathematics curriculum policy. We provide an overview of CT’s claimed potentials for mathematics teaching and learning and outline the most widely used definitions of CT in mathematics education research. Based on three illustrative cases from Denmark, Sweden, and England, we develop three typologies of ways in which CT and mathematics are related to each other in curricular resources. We also describe the opportunities and challenges these typologies are associated with for teachers in relation to connecting CT and mathematics in the mathematics education classrooms. We conclude the paper by discussing the relation between tendencies in how CT is enacted in mathematics curriculum policy and how it is studied in the mathematics education research community. Moreover, we reflect on the implications of this relation for the opportunities of informing CT in mathematics education through state-of-the-art research.

In the last decade, programming and computational thinking (CT) have been introduced on a large scale in school curricula and standards all over the world. In countries such as the UK, a new school subject—computing—was created, whereas in countries such as Sweden, programming was included in existing subjects, notably mathematics and technology education. The introduction of programming and CT in technology education implies a particular relationship between programming and technology. Programming is usually performed with technological artefacts—various types of computers—and it can also be seen as a specific branch of engineering.

This book analyses the background to and current implementation of programming and computational thinking in a Swedish school technology context, in relation to international developments. The various chapters deal with pertinent issues in technology education and its relation to computers and computing, for example, computational thinking and literacy, teachers’ programming competence, and computational thinking, programming, and learning in technology education. The book includes examples from educational research that could also be used as inspiration for school teaching, teacher education and curriculum development

Här redovisas resultat från ett fyraårigt forskningsprojekt om implementeringen av programmering i skolans matematikundervisning. Både lärare och läromedel har studerats och resultaten väcker frågor om satsningen varit så genomtänkt som man hade kunnat önska. 

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. 

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.

In this study, we focused on grade-6 students’ justifications during mathematical problem solving in small group interaction. Video recordings from two classrooms were analyzed, using Harel and Sowder’s (2007) taxonomy of proof schemes as a tool to categorize students’ justifications, which showed that the frequency of various types of justifications corresponded to previous studies of adult students’ demonstrations of proof schemes. Results also showed that both Non-referential Symbolic and Transformational justifications contributed to students’ formulations of general arguments. In addition, agreements between proximately located justifications based on examples and calculations supported students’ improvements of solutions. However, in cases of disagreements, justifications based on calculations often had most influence on the proving process even when the calculation was incorrect. Our results imply that teachers should emphasize the importance of agreement between calculations and empirical examples, as well as the significance of counterexamples, as a support to students’ progression towards mathematical proving.