Abstract Although approximately 6% of students have a mathematics learning disability (MLD) also known as dyscalculia, little is known about how MLD impacts students beyond basic arithmetic. In this study we focused on one mathematical topic foundational to algebra – integer operations – and conducted a videotaped design experiment with one student with MLD. Through 14 teaching episodes we explored the ways in which standard mathematical tools (e.g., symbols, representations) were inaccessible and evaluated the design of alternative tools. Our detailed retrospective analysis revealed that the student had an unconventional understanding of integer quantities and symbolic notation, which resulted in issues of accessibility and persistent difficulties. Deliberate attempts to address inaccessibility revealed nuances in the student’s understanding, and suggests that both number sense and notational issues needed to be addressed in tandem. Implications for instruction are discussed.

中文翻译：

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整数感和符号：一个数学学习障碍学生的案例研究

摘要 虽然大约 6% 的学生有数学学习障碍 (MLD)，也称为计算障碍，但人们对 MLD 如何影响基本算术以外的学生知之甚少。在这项研究中，我们专注于代数基础的一个数学主题——整数运算——并与一名患有 MLD 的学生进行了录像设计实验。通过 14 个教学片段，我们探索了标准数学工具（例如，符号、表示）无法使用的方式，并评估了替代工具的设计。我们详细的回顾性分析表明，该学生对整数数量和符号表示法有非常规的理解，这导致了可访问性和持续困难的问题。为解决交通不便问题的刻意尝试揭示了学生理解中的细微差别，并建议需要同时解决数感和符号问题。讨论了对教学的影响。