Progress through Calculus

通过微积分取得进展

• 批准号: 1430540
• 负责人: David Bressoud
• 金额: $ 225万
• 依托单位: Mathematical Association of America
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-01-01 至 2021-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1430540&HistoricalAwards=false
• 关键词: Progress; through; Calculus

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.

美国数学协会的这个项目将以先前资助的项目“大学微积分成功课程的特征”的见解为基础，继续探索影响学生在从微积分预科开始到单变量微积分全年的入门数学课程进展中的因素。这个数学序列是大多数STEM专业的必修课程。有两个重点领域的研究项目将调查使用三种不同的方法。首先是对提供高等数学学位的大学进行全国人口普查，其次是对选定的大学进行个案研究访问，最后是在全国范围内由数学界努力收集纵向数据。焦点区域1)目前实施的微积分前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普遍？它们在实践中有多不同？最近进行了哪些变化，或者目前正在进行哪些变化？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课程中的成功有什么影响？课程的成功与否将通过多种方法进行评估，包括持续和保留的纵向测量、后续课程的表现、微积分预科和微积分主题的知识以及学生的态度。这些问题的答案将被用来开发一个理论模型，该模型可用于指导数学系决定如何分配资源，从而最有效地提高学生在微积分方面的成功和在STEM方面的坚持。虽然现在对学生离开STEM领域的原因已经有了很多了解，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的联系很少。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调查将产生一幅全面的图景，说明微积分前到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微积分前到微积分结构和学生成功之间的联系。成功与否的评估将使用多种衡量标准，这些标准将从多个维度来描述它，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成果。