## Abstract

Teacher education is central to the development of the professional knowledge of pre-service teachers. The main goal of this paper is to reflect on the development that the analysis (done by a group of pre-service secondary teachers) of a set of tasks, based on elements related to domains of KTMT—*Knowledge for Teaching Mathematics with Technology*—can bring to the knowledge of pre-service teachers of mathematics. Specifically, the goal was to investigate the following questions: (1) What are the factors that guide the pre-service teachers’ task discussion? (2) Which KTMT domains are emphasized by pre-service teachers during task discussion? The elements taken into account are the characteristics of the tasks (focus on cognitive level, structuring level and technology role), the use of representations (focus on balance and articulation of representations), and the equilibrium between experimentation (focus on digital technology affordances) and justification (focus on argumentation and proof). The methodology of this case study involves a qualitative approach. The main conclusions suggest that influences in the pre-service teachers’ discussion of tasks fell into the following categories: the potentialities of technology, the type of tasks, and the prospective teachers’ experience with a set of tasks, and analysis of some real students’ reports. With regard to KTMT, although it was possible to identify some global development, *Teaching and Learning and Technology Knowledge* was the domain in which stronger development took place.

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Rocha, H. Using tasks to develop pre-service teachers’ knowledge for teaching mathematics with digital technology.
*ZDM Mathematics Education* **52, **1381–1396 (2020). https://doi.org/10.1007/s11858-020-01195-1

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### Keywords

- Teacher’s knowledge
- KTMT
- Technology
- Mathematics
- Functions