Abstract Despite mathematics educators’ research into more effective modes of teaching, lecture is still the dominant mode of instruction in undergraduate mathematics courses. Surveys suggest this is because most mathematicians believe this is the best way to teach. This paper answers a call by mathematics education researchers to explore mathematicians’ needs and goals concerning teaching. We interviewed eight mathematicians about findings in the mathematics education research literature concerning common pedagogical practices of instructors of advanced mathematics classes: “chalk talk,” the presentation of formal and informal content, and teacher questioning. We then analyzed the responses for resources, orientations, and goals that might influence the participants to engage in these practices. We describe how participants believed common lecturing practices allowed them to achieve their goals and aligned with their orientations. We discuss these findings in depth and consider what implications they may have for researchers that aim to change mathematicians’ teaching practices.

中文翻译：

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高等数学中数学家教学目标、方向和常见教学实践之间的关系

摘要 尽管数学教育者正在研究更有效的教学模式，但讲座仍然是本科数学课程的主导教学模式。调查表明这是因为大多数数学家认为这是最好的教学方式。本文响应数学教育研究人员的号召，探讨数学家在教学方面的需求和目标。我们采访了八位数学家，了解数学教育研究文献中有关高等数学课程教师常见教学实践的发现：“粉笔谈”、正式和非正式内容的呈现以及教师提问。然后我们分析了可能影响参与者参与这些实践的资源、方向和目标的反应。我们描述了参与者如何相信常见的演讲实践使他们能够实现目标并与他们的方向保持一致。我们深入讨论这些发现，并考虑它们可能对旨在改变数学家教学实践的研究人员产生什么影响。