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Student teachers' learning and teaching mathematics with
programming
Laura Fainsilber and Johanna Pejlare
Chalmers University of Technology and University of Gothenburg, Gothenburg, Sweden;
laura@chalmers.se; pejlare@chalmers.se
Sweden’s school curriculum was revised to include programming as a mathematical content from
the year 2018. However, teacher education included using IT-tools for teaching, but not specifically
programming. To correct this situation, we have developed a new programming strand in the
training of secondary school mathematics teachers at the university of Gothenburg. The aim of this
study is to observe how student teachers towards the end of the program use their knowledge to
plan uses of programming in their own mathematics teaching. It is part of a larger research and
development project on introducing programming in secondary school mathematics education.
Two theoretical frameworks are relevant here: instrumental genesis, i.e., the process where an
instrument is formed from an artefact, when students use programming as a tool in mathematics
(Trouche 2004), and the theory of didactic transposition, to frame the student teacher's
transformation of their own knowledge into knowledge to be taught (Chevallard 2006).
Each mathematics course in the teacher education program for secondary teachers at the university
of Gothenburg contains a few computer lab sessions. About half of them are focused on using IT-
tools (e.g. Geogebra) to learn mathematics. The other half of the computer labs use programming to
highlight mathematical concepts. There is no course in programming per se. In the first mathematics
course, the students build a first block program in Scratch to draw regular polygons, using loops
and variables. In the second course, in Calculus, they estimate integrals with Riemann sums, using
loops in Python. The strand then continues in Python, with data analysis in Statistics and prime
numbers and cryptography in Number theory. Four school practice periods are spread throughout
the program, and in the third of these, student teachers plan a mathematics lesson with
programming, to use with their school class.
In this study we analyze the student’s lesson plans and discussion in a seminar where the students
discuss their lesson design. Of interest is both the design itself and the students’ attitude, self-
efficacy and reflections regarding their teaching of mathematics through programming. In
particular, we are interested in the students’ argumentation on how their planned lessons may help
the pupils to achieve the learning goals. Preliminary results indicate that students struggle to meet
the double goal of introducing programming and supporting the mathematics in the curriculum.
References:
Chevallard, Y. (2006). Steps towards a new epistemology in mathematics education. In Bosch, M.
Proceedings of the 4th Conference of the European Society for Research in Mathematics
Education (CERME 4) (pp. 21–30).
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.
