(Objective)

The objective of this study was to analyze the practical arguments of a group of mathematics teacher educators during the assessment of the design of a didactic unit on functions for secondary education students (ages 15-16).

(Methodology)

A qualitative methodology was employed, consisting of an intrinsic case study that involved eight mathematics teacher educators with knowledge of the Didactic Suitability Criteria construct, who participated in a Lesson Study cycle. In the reflection stage of this cycle, participants used this construct to assess the design of the didactic unit (which included the teacher's planning and the students' dossier). The emerging practical arguments were structured using Toulmin's model.

(Results)

Three results are highlighted. First, the assessment of the didactic unit using the components of the Didactic Suitability Criteria made it possible to identify strengths and areas for improvement within the teaching and learning process of functions. Second, the participants utilized these components as data, backups, and validation in their practical arguments, leveraging their knowledge of this construct. Third, the participants employed all these components to assess the didactic unit and supported their proposals for change based on these components.

(Conclusion)

The Didactic Suitability Criteria played a role as a generator of practical argumentation for the participants and as a central element in structuring these arguments. Finally, some recommendations are proposed for the implementation of future Lesson Study cycles.

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