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<p><?tk 2?>Felix Klein pointed out the “double discontinuity” teachers face between school and university mathematics. This paper is focused on the second discontinuity, which speaks to the challenge of having university mathematics meaningfully prepare prospective and practicing teachers for the secondary classroom. Broadly, this line of inquiry can be connected to the notion of pedagogical content knowledge (PCK), albeit specific to the role of university mathematics in supporting the development of PCK. The paper builds on prior work that differentiated three types of mathematical connections (Wasserman, N. (2025). Adding diversity to mathematical connections to counter Klein’s second discontinuity. <i>Recherches en Didactique des Mathématiques</i>, <i>45</i>(1), 5-31. <a href="https://doi.org/10.46298/rdm.13675">https://doi.org/10.46298/rdm.13675</a>). Primarily, the paper presents an analysis of data to explore the relationship between the three different types of mathematical connections and the differing kinds of reflections teachers had about their potential enactment of that disciplinary knowledge in their own classrooms. Results indicate that some types of connections fostered different kinds of reflections about the use of that disciplinary knowledge in teaching. Through these different connections, the paper highlights insights about how to facilitate teachers’ construction of disciplinary knowledge in ways that may promote its enactment in their subsequent instruction. Implications for teacher education and task design are discussed.</p>

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Framing connections between secondary and advanced mathematics in ways that help teachers reflect on the potential utility of disciplinary knowledge

  • 期刊论文

  • 发表日期：

    2026年1月29日

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  • Nicholas H. Wasserman

摘要

Felix Klein pointed out the “double discontinuity” teachers face between school and university mathematics. This paper is focused on the second discontinuity, which speaks to the challenge of having university mathematics meaningfully prepare prospective and practicing teachers for the secondary classroom. Broadly, this line of inquiry can be connected to the notion of pedagogical content knowledge (PCK), albeit specific to the role of university mathematics in supporting the development of PCK. The paper builds on prior work that differentiated three types of mathematical connections (Wasserman, N. (2025). Adding diversity to mathematical connections to counter Klein’s second discontinuity. Recherches en Didactique des Mathématiques, 45(1), 5-31. https://doi.org/10.46298/rdm.13675). Primarily, the paper presents an analysis of data to explore the relationship between the three different types of mathematical connections and the differing kinds of reflections teachers had about their potential enactment of that disciplinary knowledge in their own classrooms. Results indicate that some types of connections fostered different kinds of reflections about the use of that disciplinary knowledge in teaching. Through these different connections, the paper highlights insights about how to facilitate teachers’ construction of disciplinary knowledge in ways that may promote its enactment in their subsequent instruction. Implications for teacher education and task design are discussed.