Researchers have been interested in students’ transition to calculus since the early 1900s. One line of inquiry highlights students’ understandings of high school mathematics as impeding or supporting their successful transition to university mathematics. This paper addresses an underlying question in this line of inquiry: does school mathematics provide opportunities for students to develop productive meanings for calculus? This article reports on U.S. calculus students’ responses to items that assessed students’ variational reasoning, meanings for average rate of change, and representational use of notation—ideas ostensibly addressed in school mathematics. To make sense of students’ difficulty on these items we sought to understand the opportunities students had to reason with these ideas prior to calculus. We use two data sources to understand the likelihood that students have opportunities to construct productive meanings for function notation, variation, and average rate of change in their secondary mathematics education: meanings for these ideas supported by precalculus textbooks and meanings secondary teachers demonstrated. Our analysis revealed a disconnect between meanings productive for learning calculus and the meanings conveyed by textbooks and held by U.S. high school teachers. We include a comparison of meanings held by U.S. and Korean teachers to highlight that these meanings are culturally embedded in the U.S. educational system.

自1900年代初以来，研究人员一直对学生向微积分的转换感兴趣。一条查询线强调了学生对高中数学的理解，认为这阻碍或支持了他们成功地过渡到大学数学。本文解决了这一研究领域中的一个基本问题：学校数学是否为学生提供了发展微积分的生产意义的机会？本文报道了美国微积分学生对评估学生的变异推理，平均变化率的含义以及表示法的代表性使用的项目的反应，这些在学校数学中显然是解决的。为了弄清学生在这些项目上的困难，我们试图了解学生在进行微积分之前必须对这些想法进行推理的机会。我们使用两个数据源来理解学生在中学数学教育中有机会构建功能性表示法，变异和平均变化率的生产性意义的可能性：这些概念的含义得到了初等数学教科书的支持以及中学教师所展示的含义。我们的分析表明，学习微积分的意义与教科书所传达的意义以及美国高中教师所持有的意义之间没有联系。我们对美国和韩国教师的含义进行了比较，以强调这些含义在文化上已根植于美国的教育体系中。初等数学教科书所支持的这些思想的含义以及中学教师所展示的含义。我们的分析表明，学习微积分的意义与教科书所传达的意义以及美国高中教师所持有的意义之间没有联系。我们对美国和韩国教师的含义进行了比较，以强调这些含义在文化上已根植于美国的教育体系中。初等数学教科书所支持的这些思想的含义以及中学教师所展示的含义。我们的分析表明，学习微积分的意义与教科书所传达的意义以及美国高中教师所持有的意义之间没有联系。我们对美国和韩国教师的含义进行了比较，以强调这些含义在文化上已根植于美国的教育体系中。