Relationships between domain changes and connections: An analysis from the perspective of mathematical work and teacher knowledge

Introduction: This study addresses the teaching task contextualized in the teaching of different topics of mathematic (functions, sequences, and Thales’ theorem). To do so, the characteristics of the mathematical work and specialized knowledge that the teacher shows during teaching are analyzed, considering as a frame of reference the complementarity between two theoretical perspectives (MWS and MTSK). Methodology: The study is framed in the qualitative approach, based on an integrated multiple case study design, which allows analysis of the proposed mathematical performance (oral and/or written) of three teachers. Results: The analyses allow a deep examination of the development of mathematical work and demonstration of the relationships between the inter-conceptual connections as well as the domain changes that are expressed in teachers’ work. In general, the results reveal the privileging of algebraic treatments and emphasis on the procedural. Conclusion: Contributions are identified in the perspective of the connection between theories in the context of the models involved.