In the transition from secondary to tertiary mathematics, students try to participate in tertiary mathematics by replicating familiar school mathematical discourses. The objective of this case study is to investigate the conditions and affordances under which students proceed from familiar school mathematical discourses to new, tertiary discourses with a specific perspective on learning processes. The study was located in an upper secondary transition course in a teaching unit on elementary number theory in which highly proficient students in their penultimate year of schooling participated. The main finding is that there was not a linear progression towards the intended tertiary mathematical discourse of modular multiplication but a coexistence of two discourses developing in parallel: the intended tertiary discourse and a continuation of school mathematical discourses. Students see these two discourses as the same, connected by the same perceived aim of searching for patterns. Further hindering discursive development are utterances, in which elements of the intended tertiary discourse (words and representations) are used superfluously, so that elementary/secondary utterances appear to be tertiary. These findings illustrate the need to explicate and address metanarratives. Metanarratives can connect two discourses developing in parallel in ways that, in this case, hinder discursive development towards the intended tertiary discourse.

中文翻译：

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学生如何以模块化算法重新审视学校数学？着重于学习过程的高等数学过渡的条件和能力

在从中学数学过渡到大学数学的过程中，学生试图通过复制熟悉的学校数学课程来参与大学数学。本案例研究的目的是调查学生从熟悉的学校数学课程发展到新的，第三级课程的条件和能力，并从特定的角度对学习过程进行研究。该研究位于基本数论教学单元的高中过渡课程中，参加倒数第二学年的高水平学生参加了该课程。主要发现是，向预期的模块化乘法第三级数学话语并没有线性进展，而是并行发展的两种话语并存：预期的第三级话语和学校数学话语的延续。学生认为这两种话语是相同的，它们通过相同的感知模式搜索目的联系在一起。进一步阻碍话语发展的是话语，其中多余地使用了预期的第三级话语的元素（单词和表示），因此基本/次要话语似乎是第三级的。这些发现表明，有必要阐明和论述元叙事。元叙事可以将两种平行发展的话语联系起来，在这种情况下，阻碍了话语向预期的第三级话语发展。其中多余地使用了预期的第三级话语的元素（单词和表示），因此基本/第二级话语似乎是第三级的。这些发现表明，有必要阐明和论述元叙事。元叙事可以将两种平行发展的话语联系起来，在这种情况下，阻碍了话语向预期的第三级话语发展。其中多余地使用了预期的第三级话语的元素（单词和表示），因此基本/第二级话语似乎是第三级的。这些发现说明了阐述和叙述元叙事的必要性。元叙事可以将两种平行发展的话语联系起来，在这种情况下，阻碍了话语向预期的第三级话语发展。