This paper relates to an ongoing project using design-based research as a methodol- ogical approach in which students with no prior experiences of using programming as a mathematical tool are observed trying to solve mathematical problems with the help of programming. The Instrumental Approach is used as conceptual framework in which the concept of instrumental genesis describes the process where the programming environment as an artefact together with student-developed mental schemes forms an instrument in order to solve mathematical problems. The development of schemes is of special interest in this paper where Vergnaud’s components of a scheme provide a framework for analysing transcripts of talk between student pairs and the programming code that they generate.

This study explored Swedish upper secondary school students’ use of programming for mathematical purposes. The aim of the study was to investigate the process through which students learn how to use a programming environment as a technical artefact during mathematical problem solving and how the orchestration of such learning situations could facilitate this process. In order to study the students’ use of the programming environment, design-based research was used as the main methodological approach. The design involved the development of specific mathematical tasks to be tried out with students, as well as the orchestration of the learning situation within the classroom e.g., by preparing scaffolding to be offered to the students. The subsequent implementation of the design was analysed so that, in accordance with the cyclic approach of design-based research, it could be revised ahead of the following design cycle. The study involved two complete design cycles. In the study, the Instrumental Approach was used as the theoretical framework and the instrumental genesis of the students in using a programming environment for mathematical purposes was thus of special interest. In order to analyse this process and the associated mental schemes developed by the students, Vergnaud’s concept of scheme served as an analytical framework. The findings revealed how the students, despite having basic knowledge in programming, experienced several difficulties when trying to use the programming environment as a technical mathematical artefact. These difficulties were related both to the fact that the mathematical affordances offered by the programming environment were unclear to many of the students, as well as to the handling of more specific computational concepts such as nested loops. The findings also revealed that the transformation of mathematical notations and ideas into programming code caused students difficulties. 

This study explored Swedish upper secondary school students’ use of programming for mathematical purposes. The aim of the study was to investigate the process through which students learn how to use a programming environment as a technical artefact during mathematical problem solving and how the orchestration of such learning situations could facilitate this process. In order to study the students’ use of the programming environment, design-based research was used as the main methodological approach and the Instrumental Approach served as the theoretical framework. The design involved the development of mathematical tasks to be tried out with students, as well as the orchestration of the learning situation within the classroom. The findings revealed how the students experienced several difficulties when trying to use the programming environment as a technical mathematical artefact. These difficulties were related to the fact that the mathematical affordances offered by the programming environment initially were unclear to many of the students, as well as to the handling of more specific computational concepts such as nested loops. The findings also revealed that the transformation of mathematical notations and ideas into programming code caused students difficulties.

The use of programming in mathematics education is undergoing a renaissanceand, in this paper, we analyse students’ handling of programming in mathematicsusing the Instrumental approach as a theoretical lens. We are especially interestedin analysing the development of mental schemes using two analytical frameworkswhich are compared and contrasted according the idea of networking theories. Thestudy illustrates that the frameworks’ detail of richness can have both advantagesand disadvantages and that one of the frameworks are more customed to be appliedwhen analysing students’ instrumental genesis concerning the use of a programmingenvironment as a mathematical artefact.

In recent years, programming has gained a more prominent role in mathematics education in various European countries. However, the incorporation of digital tools, such as programming, is not always a straightforward process as it may require, among other things, an adaptation of teachers’ craft knowledge. This paper reports on a case study analysing a Swedish teacher’s incorporation of programming into his mathematics teaching and the rationales behind such design, using the Structuring Features of Classroom Practice framework as a conceptual lens. The results reveal how the teacher’s background shapes the use of programming in his classroom. It also illustrates that the way programming is intended to be incorporated into Swedish school mathematics places high demands on teachers when it comes to teaching students both how to program and how programming can serve as a tool for learning mathematics.

 Through educational reforms, programming has in recent years been integrated into school curricula in many countries, often in conjunction with mathematics education. Using programming in school mathematics presents new mathematical possibilities but also introduces challenges for both students and teachers. In this case study, we employ the Instrumental Approach as a theoretical lens to investigate how students’ perceptions of function limits are affected by their use of programming. The findings reveal how a careful design of lesson activities involving programming can enhance students’ ability to use programming as a mathematical tool. However, the study also demonstrates that using programming to numerically determine limits primarily fosters a dynamic process view of limits. In this view, students focus on the process in which the dependent variable approaches a specific value but struggle to coordinate this with the corresponding process of the independent variable approaching a given value. We contend that it is essential for mathematics teachers to thoughtfully integrate programming into their teaching and to consider how students’ use of programming might influence their perception of mathematical concepts such as limits.