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Exploring student teachers’ instrumental genesis of programming
Other conference contribution, 2021

To theoretically frame the study, we use the instrumental approach, in order to study students’ instrumental genesis, i.e., the process where an instrument is formed from an artefact, when using programming as a tool in mathematics (Trouche, 2004). The instrumental genesis consists of two important processes: the instrumentalization, which is the process where the user gets to know the tool, and the instrumentation, which is the process that allows the user to develop an activity within some boundaries.

Most students enrolled at the secondary teacher education program at the University of Gothenburg do not have any, or have very little, prior experience in programming. In the calculus course the students take part in a computer lab where they – with the help of Python – are asked to explore Riemann-sums of continuous functions. Through observations during the students’ work with exercises, and through a follow-up questionnaire, we explore the potentials for learning mathematics through programming. In particular, we investigate what difficulties regarding programming and mathematical content the students encounter during the beginning of their instrumental genesis. A majority of the students answering the questionnaire argued that the programming part of the lab was difficult, but that it helped them to gain a deeper understanding of Riemann-sums. Some students argued that, to be able to construct a correct program, they had to decompose the concept of Riemann-sums in order to understand how they are structured.

Reference

Trouche, L. (2004). Managing the complexity of human/machine interactions in computerized learning environments: Guiding students’ command process through instrumental orchestrations. International Journal of Computers for Mathematical Learning, 9(3), 281–307.

Mathematics education

Programming

Teacher education

## Author

### Johanna Pejlare

Chalmers, Mathematical Sciences, Algebra and geometry

### Laura Fainsilber

Chalmers, Mathematical Sciences, Algebra and geometry

Oslo, Norway,

### Subject Categories

Didactics

Other Mathematics

### Learning and teaching

Pedagogical work