(Objective)

This study seeks to characterize the specialized mathematical knowledge that preservice teachers make use of when solving tasks that involve comparison of areas of flat figures.

(Methodology)

Seventy (70) preservice teachers, in the third year of the Primary Education degree at the Universidad Autónoma de Barcelona during the period 2020-21, participated in the study. Preservice teachers answered a semi-structured open-ended questionnaire, which included eight tasks. A qualitative content analysis was carried out to analyze the procedures and justifications used by preservice teachers when solving two tasks. The analysis focuses on two of the subdomains of the Mathematics Teacher's Specialized Knowledge model, Knowledge of Topics and of the Structure of Mathematics.

(Results)

The use of procedures related to the decomposition and reorganization of surfaces facilitates making use of categories of specialized knowledge, and establishing connections with other types of mathematical content. Furthermore, coordination of different registers of representation makes it possible to establish intra conceptual connections in the solution of the two tasks presented.

(Conclusions)

Representations, in their discursive and non-discursive registers, are presented as key indicators which assist in making explicit the procedures used by preservice teachers, and based on them, the justifications, properties and geometric principles that support the resolution process.

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