@article{10272/24709,
year = {2024},
month = {11},
url = {https://hdl.handle.net/10272/24709},
abstract = {In this article, we analyse a lesson on Thales’s theorem in a Chilean secondary school classroom through the combination of two theories: Mathematics Teachers’ Specialised Knowledge (ThMTSK) and Mathematical Working Spaces (ThMWS). Both theories, first separately and then in relation to one another, are used to analyse two tasks proposed by the teacher in the classroom following a cross-methodology for networking of theories. Through a single case study research design, a content analysis of the transcript of the video recording of the lesson was conducted. The joint analysis of this lesson allows us to better understand the mathematical work taking place in the classroom. In particular, the results show the scope of each model and their complementarity through the detection of meeting points and blind spots, through the role of proof, representations, and the change between geometrical and numerical work in teaching Thales’s theorem. This allows for a deeper understanding of a teacher’s practice and teaching. Ultimately, relationships between the theoretical elements of both theories are established to show their complementarity. We conclude that networking between theories can contribute to the development of these theories by raising questions that involve examining their foundations and assumptions in greater depth},
organization = {Funding for open access publishing: Universidad de Huelva/CBUA. This work was supported by the Ministerio de Ciencia e Innovación of Spain [Reference PID2021-122180OB-I00] and the Library of the University of Huelva. Gonzalo Espinoza-Vásquez thanks the Agencia Nacional de Investigación y Desarrollo de Chile (ANID), Fondo Nacional de Desarrollo Científico y Tecnológico de Iniciación 2023, Folio 11231088. Carolina Henríquez-Rivas thanks ANID, Fondo Nacional de Desarrollo Científico y Tecnológico de Iniciación 2023, Folio 11230523. Paula Verdugo-Hernández thanks ANID, Fondo Nacional de Desarrollo Científico y Tecnológico de Iniciación 2023, Folio 11230240. },
publisher = {Springer},
title = {Teaching Thales’s theorem: relations between suitable mathematical working spaces and specialised knowledge},
doi = {10.1007/s10649-024-10367-9},
author = {Espinoza Vásquez, Gonzalo and Henríquez Rivas, Carolina and Climent Rodríguez, Nuria and Ponce, Rodrigo and Verdugo Hernández, Paula},
}