Fernández León, AuroraGavilán Izquierdo, José MaríaToscano Barragán, Rocío2025-01-272025-01-272019Fernández León, A., Gavilán Izquierdo, J.M. y Toscano Barragán, R. (2019). A Case Study of the Practices of Conjecturing and Proving of Research Mathematicians. International Journal of Mathematical Education in Science and Technolog, 52 (5), 1-28. https://doi.org/10.1080/0020739X.2020.1717658.0020-739X1464-5211https://hdl.handle.net/11441/167603In this paper we investigate how a research mathematician conjectures and proves when conducting her research. To be precise, the aim of this study is to achieve a comprehensive understanding of the way this research mathematician develops these mathematical practices and thus gain insight to improve the teaching and learning of these two practices in an educational context. For this purpose, we consider Rasmussen, Zandieh, King and Teppo’s [1] theoretical constructs of horizontal and vertical mathematising. In particular, we have adopted a case study methodological approach with a single research mathematician. Analysis of the data lead to the identification of eleven categories of activities. Each category is linked either to the practice of conjecturing or proving and also to the horizontal or vertical dimension of such practice. Finally, we compare and contrast our results with other related studies and give some educational suggestions that may derive from our workapplication/pdf29 p.engAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Advancing mathematical activityMathematisingConjecturingProvingResearch mathematiciansinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.1080/0020739X.2020.1717658