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<p>Transitioning from material to theoretical geometry is often considered a significant challenge in compulsory education. Over the last twenty years, research rooted in the Theory of Didactical Situations (TDS) has explored how material geometry can support the teaching and learning of theoretical geometry, promoting continuity in teaching. These studies have defined didactically focused material geometry practices, referred to as “the geometry of tracing,” where figure reproduction is considered a fundamental situation within this geometric practice. In this text, we explore the potential of transposing this fundamental situation into a didactic one within a classroom setting. Based on the analysis of a case study, we examine the relationship between the effective situation and the learning process. We pay attention to the roles and interactions of adaptation and acculturation processes in the observed didactic phenomena. The TDS framework helps us analyze how the combination of the a-didactical potential of the situation and the teacher’s didactic interventions promotes a shift towards theoretical geometry.</p>

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Figure reproduction as a step towards theoretical geometry: analysis of the didactical and a-didactical processes in a classroom setting

  • 期刊论文

  • 发表日期：

    2025年1月7日

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  • Anne-Cécile Mathé,
  • Joris Mithalal

摘要

Transitioning from material to theoretical geometry is often considered a significant challenge in compulsory education. Over the last twenty years, research rooted in the Theory of Didactical Situations (TDS) has explored how material geometry can support the teaching and learning of theoretical geometry, promoting continuity in teaching. These studies have defined didactically focused material geometry practices, referred to as “the geometry of tracing,” where figure reproduction is considered a fundamental situation within this geometric practice. In this text, we explore the potential of transposing this fundamental situation into a didactic one within a classroom setting. Based on the analysis of a case study, we examine the relationship between the effective situation and the learning process. We pay attention to the roles and interactions of adaptation and acculturation processes in the observed didactic phenomena. The TDS framework helps us analyze how the combination of the a-didactical potential of the situation and the teacher’s didactic interventions promotes a shift towards theoretical geometry.