Progress through Calculus

美国数学协会的这个项目将建立在一个先前资助的项目“大学微积分成功课程的特点”的基础上，以便继续探索影响学生成功的因素，从微积分预科开始，一直持续到单变量微积分的一整年。这一数学顺序是大多数STEM专业的必修课。这项研究有两个重点领域，该项目将使用三种不同的方法进行调查。首先，对提供数学高级学位的大学进行全国人口普查，其次，对选定的大学进行个案研究访问，最后，数学界在全国范围内努力收集纵向数据。重点领域1)目前实施的微积分预科到微积分序列的程序和结构是什么？不同的程序和结构有多常见？它们在实践中有多大的不同？最近或目前正在进行哪些类型的变化？重点领域2)结构、课程和教学决策对学生在微积分预科到微积分的成功有什么影响？成功与否将通过各种衡量标准进行评估，包括坚持和保持的纵向衡量标准、后续课程的表现、对微积分预科和微积分主题的了解，以及学生的态度。这些问题的答案将被用来开发一个理论模型，用于指导数学系决定如何分配资源，以最有效地提高学生在微积分方面的成绩和STEM的坚持性。虽然现在很多人都知道学生为什么离开STEM领域，但这些理论知识与微积分预科到微积分序列的实际结构和程序之间几乎没有联系。该项目将提供这一联系，帮助各部门更理性地决定如何投资有限的资源。一项对提供数学研究生课程的机构进行的全国人口普查将产生一幅关于微积分预科到微积分序列的综合图景，并在全国范围内实施。详细的案例研究将调查微积分基础、微积分结构和学生成功之间的联系。将使用各种衡量标准对成功进行评估，这些衡量标准将从多个方面表征成功，包括留存和学生学习。传统的传播工作将积极利用MAA的资源和影响范围，向整个数学界广泛传播研究成果。

This project of the Mathematical Association of America will build on the insights from a previously funded project "Characteristics of Successful Programs in College Calculus" in order to continue to explore the factors influencing student success over the progression of introductory mathematics courses that begins with pre-calculus and continues through the full year of single variable calculus. This mathematics sequence is required of most STEM majors. There are two focal areas for the research the project will investigate using three distinct methods. First a national census survey of universities offering advanced degrees in Mathematics, second, case study visits to selected universities, and finally, a nationwide effort of the mathematics community for gathering of longitudinal data. Focal Area 1) What are the programs and structures of the pre-calculus to calculus sequence as currently implemented? How common are the various programs and structures? How varied are they in practice? What kinds of changes have recently been undertaken or are currently underway? Focal Area 2) What are the effects of structural, curricular, and pedagogical decisions on student success in pre-calculus to calculus? Success will be assessed on a variety of measures including longitudinal measures of persistence and retention, performance in subsequent courses, knowledge of both pre-calculus and calculus topics, and student attitudes. The answers to these questions will be leveraged to develop a theoretical model that can be used to guide mathematics departments in deciding how to allocate resources so as to most effectively improve student success in Calculus and persistence in STEM. While much is now known about why students leave STEM fields, there is little connection between this theoretical knowledge and the actual structures and programs of the pre-calculus to calculus sequence. The project will provide that link, helping departments to more rationally decide how to invest their limited resources. A national census survey of institutions offering graduate programs in mathematics will produce a comprehensive picture of the ways that pre-calculus to calculus sequences are structured and implemented across the country. Detailed case studies will investigate connections between aspects of pre-calculus to calculus structures and student success. Success will be assessed using a variety of measures that will characterize it along multiple dimensions, including retention and student learning. Traditional dissemination efforts will actively draw upon the resources and reach of the MAA to broadly disseminate findings to the entire mathematics community.