Progress through Calculus

美国数学协会的这个项目将建立在以前资助的项目“大学微积分成功课程的特征”的见解的基础上，以继续探索影响学生成功的因素，这些因素从微积分前开始，并持续到全年的单变量微积分。这个数学序列是大多数STEM专业的要求。 该项目将使用三种不同的方法研究两个重点领域。 首先，全国普查调查大学提供高等数学学位，第二，个案研究访问选定的大学，最后，全国范围内的努力，数学界收集的纵向数据。 重点领域1）目前实现的微积分前到微积分序列的程序和结构是什么？各种方案和结构有多普遍？它们在实践中有多大差异？最近发生或正在发生哪些变化？ 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？成功将评估各种措施，包括持久性和保留的纵向措施，在后续课程的表现，微积分前和微积分主题的知识，和学生的态度。 这些问题的答案将被用来开发一个理论模型，可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和坚持干的成功。 虽然现在已经知道很多关于为什么学生离开STEM领域，但这种理论知识与微积分前到微积分序列的实际结构和程序之间几乎没有联系。该项目将提供这种联系，帮助各部门更合理地决定如何投资其有限的资源。对提供数学研究生课程的机构进行的全国人口普查调查将全面了解微积分序列在全国范围内的结构和实施方式。详细的案例研究将调查前微积分的结构和学生的成功方面之间的联系。将使用各种衡量标准来评估成功，这些标准将从沿着多个维度来表征成功，包括保留和学生学习。传统的传播工作将积极利用MAA的资源和影响力，向整个数学界广泛传播研究结果。

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.