(Objective)

This paper discusses the design, implementation, and analysis of an educational experience focused on linear variation, aimed at prospective secondary school mathematics teachers. The objective of this experience is to improve the prospective teachers' didactic-mathematical knowledge and to contribute to the development of their onto-semiotic analytical skills. Linear variation is an important topic because it is present in different educational moments through multiple approaches and meanings - arithmetic, algebraic, and functional. As a complex mathematical object, it can generate teaching and learning conflicts, which can be studied to provide useful information about improvement of educational activities.

(Methodology)

This is a qualitative investigation, based on the preliminary study, design, implementation, and analysis of 5 didactic activities according to the theoretical principles of the Onto-semiotic Approach. The data gathered for the investigation included video recordings of classes, field notes and written answers provided by nine prospective teachers in the eighth semester of a Licentiate's Degree in Secondary Education program, specializing in Mathematics.

(Results)

The results indicate that linear variation is indeed a complex issue, and deficiencies were found in the didactic-mathematical knowledge of prospective teachers. Likewise, difficulties in terms of knowledge and skills were found when participants were asked to analyze hypothetical responses to tasks related to the concept of linear variation.

(Conclusions)

The results of this investigation indicate that experiences such as these can be a valuable resource in educational programs for teachers to acquire knowledge and skills for the appropriate treatment of mathematical content.

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