Mathematical Thinking and Learning

This research group focuses on students’ mathematical thinking from the primary years through high school and the practices that enhance mathematical learning. The group investigates how learners develop understanding, reasoning, and problem solving competence in a variety of instructional contexts.

In particular, researchers explore students’ mathematical learning through programming, problem solving supported by bar model heuristics, and the use of written communication as a tool for learning mathematics.

Related Publications (listed by year)

- Teledahl, A., Harvey, F., Esbjörner, M. & Von Malortie, S. (2025). Progression i elevers begreppsmässiga kunskap om bråk som delar av helhet. Forskning om undervisning och lärande, 13(2), 70-95

- Hackenberg, A. J., & Sevinc, S. (2024). Students’ units coordinations. In Dawkins, P.C., Hackenberg, A.J., Norton, A. (eds) Piaget’s Genetic Epistemology for Mathematics Education Research (pp. 371-411). Springer, Cham. https://doi.org/10.1007/978-3-031-47386-9_11

- Bergwall, A. (2023a). Students’ arguments about the growth of a two-variable function. In P. Drijvers, C. Csapodi, H. Palmér, K. Gosztonyi, & E. Kónya (Eds.), Proceedings of the Thirteenth Congress of the European Society for Research in Mathematics Education (CERME13, July 10–14, 2023) (pp. 2275–2282). Alfréd Rényi Institute of Mathematics & ERME.   

- Bergwall, A. (2023b). Topic-specific characteristics of proof-related reasoning. International Journal of Mathematical Education in Science and Technology, 1–22. https://doi.org/10.1080/0020739X.2023.2255190             

- Hackenberg, A. J., & Sevinc, S. (2022). A boundary of the second multiplicative concept: the case of Milo. Educational Studies in Mathematics, 109, 177–193. https://doi.org/10.1007/s10649-021-10083-8

- Hackenberg, A. J., & Sevinc, S. (2022). Middle school students’ construction of reciprocal reasoning with unknowns. The Journal of Mathematical Behavior, 65, 100929. https://doi.org/10.1016/j.jmathb.2021.100929

- Baysal, E., & Sevinc, S. (2022). The role of the Singapore bar model in reducing students’ errors on algebra word problems. International Journal of Mathematical Education in Science and Technology, 53(2), 289-310. https://doi.org/10.1080/0020739X.2021.1944683

- Bergwall, A. (2021a). Proof-related reasoning in upper secondary mathematics textbooks: Characteristics, comparisons, and conceptualizations [Doctoral dissertation, Mälardalen University].                    

- Bergwall, A. (2021b). Proof-related reasoning in upper secondary school: characteristics of Swedish and Finnish textbooks. International Journal of Mathematical Education in Science and Technology, 52(5), 731–751. https://doi.org/10.1080/0020739X.2019.1704085                            

- Sevinc, S. & Brady, C.(2019). Kindergarteners’ and first-graders’ development of numbers representing length and area: Stories of measurement. In K. Robinson, H. Osana, & D. Kotsopoulos (Eds), Mathematical learning and cognition in early childhood (pp. 115-137). Springer. https://doi.org/10.1007/978-3-030-12895-1_8

- Bergwall, A. (2017). Conceptualizing reasoning-and-proving opportunities in textbook expositions: cases from secondary calculus. In T. Dooley & G. Gueudet (Eds.), Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education (CERME10, February 1–5, 2017) (pp. 91–98). DCU Institute of Education & ERME.   

- Bergwall, A., & Hemmi, K. (2017). The state of proof in Finnish and Swedish mathematics textbooks—capturing differences in approaches to upper secondary integral calculus. Mathematical Thinking and Learning, 19(1), 1–18. https://doi.org/10.1080/10986065.2017.1258615

- Bergwall, A. (2015). On a generality framework for proving tasks. In K. Krainer & N. Vondrová (Eds.), Proceedings of the Ninth Conference of the European Society for Research in Mathematics Education (CERME9, 4–8 February 2015) (pp. 86–92). Charles University in Prague, Faculty of Education and ERME.