Proposal of a training sequence for future high school mathematics teachers on geometry

In this project we intend to study the mathematical and didactic knowledge that future high school teachers mobilize when they design class sessions on geometry topics, to contribute to the improvement of teacher training. We take as a theoretical approach the Model of Specialized Knowledge of the Mathematics Teacher proposed by Carrillo et al. (2018), which will allow us to generate a reflection script, which implicitly invites future teachers to mobilize elements of specialized knowledge contemplated in the model, and leads to making informed decisions about the design of their class session. Subsequently, we implemented the training task with future high school mathematics teachers from two universities in Peru, through the script generated and validated by expert researchers. Finally, we analyze the specialized knowledge that future teachers mobilize when designing class sessions on geometry topics. We follow a qualitative methodology based on design research, following the proposal of Montes, Pascual and Climent (2021).

In Peru there is no uniformity in the training plans of the universities given their autonomy and therefore in the year 2020 a training plan is proposed for public institutions, but this reform is still insufficient to achieve the necessary basic skills that every teacher requires. (MINEDU, 2020). There is also an absence of standardized references for the training of future teachers that come from research in mathematics education, which allow structuring said training since universities with careers in education have training proposals with different theoretical approaches. Likewise, teacher training in the pedagogical institutes of Peru is based on the National Basic Curriculum Design of the Mathematics Specialty Secondary Education Study Program (MINEDU, 2020), which includes ministerial plans designed by expert committees that often include references not so important. clear or only mathematical questions, without content linked to the didactics of mathematics. What generates that there are different interpretations in each institution. In relation to geometry, Barrantes and Blanco (2004) point out that its teaching faces a stage of crisis both because of the quality and the quantity of the contents that are taught at all educational levels and that are transmitted from generation to generation of the same shape. This problem leads us to investigate the initial training of mathematics teachers, to contribute to the improvement of their mathematical and didactic knowledge, allowing us to understand the complex process of teaching and learning mathematics.