Collaborative Research: Project DIRACC: Developing and Investigating a Rigorous Approach to Conceptual Calculus

合作研究：DIRACC 项目：开发和研究严格的概念微积分方法

• 批准号: 1625873
• 负责人: Chandra Lewis
• 金额: $ 5.54万
• 依托单位: RMC Research Corporation, OR
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-09-15 至 2019-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1625873&HistoricalAwards=false
• 关键词: Collaborative; Research; Project; DIRACC; Developing

Calculus is an essential tool, and provides a conceptual foundation, in each of the STEM disciplines. Acquiring deep conceptual understandings when first learning calculus poses many difficulties for students and creates many challenges for teachers. As a consequence, many concerted efforts in calculus reform appear to have failed to make educationally significant differences in student understanding that their proponents predicted. Project DIRACC: Developing and Investigating a Rigorous Approach to Conceptual Calculus will build on the documented success at Arizona State University's already-redesigned and already-deployed Calculus I to redesign and implement Calculus II, and will research students' learning in both the redesigned and traditional calculus sequences. In addition, Project DIRACC will develop short-answer assessment tools (also known as concept inventories) for Calculus I and Calculus II that other institutions can use to assess, compare and contrast their students' progress in understanding central ideas of the calculus. Students taking this redesigned calculus sequence will be better prepared for, and will be more likely to apply, their comprehension of rate-of-change functions and accumulation functions in other STEM courses and to learn calculus-dependent material in subsequent mathematics courses. The textbook produced by this project will be made available as an open resource for others to use or build upon. Finally, the results on students' calculus learning, and the calculus concept inventories built to investigate students' learning, will inform future research in these areas. Results from Project DIRACC will be disseminated widely at regional, national and international conferences and published in peer reviewed mathematics education journals and conference proceedings. One possible reason for the lack of effectiveness of calculus reform is that the fundamental structure of the underlying curriculum has remained unchanged in the vast majority of contexts where the subject is taught. Specifically, reform projects have not focused on students' development of richly connected meanings for rate-of-change functions and accumulation functions, which are essential to any introductory calculus. The Project DIRACC courses are highly conceptual because they are based upon students' development of coherent meanings for ideas applicable throughout calculus and that also facilitate the learning of mathematical ideas beyond calculus. The first course addresses this challenge by making the fundamental theorem of calculus central to every aspect of students' experience of calculus in the course. At the same time, the Project DIRACC calculus sequence will be explicitly computational because, as in the existing first course, students will use computers to represent processes that define functions as models of dynamic situations, which then become objects of study themselves. The courses will also acknowledge and address known weaknesses in students' preparation for calculus. The calculus concept inventories will be developed using standard instrument-development techniques, given at the beginning and end of their respective courses, and their psychometric properties will be established with approximately 600 students per course.

微积分是必不可少的工具，并在每个茎学科中提供了一个概念基础。当首次学习演算为学生带来许多困难时，获得深刻的概念理解，并为教师带来了许多挑战。结果，许多在微积分改革方面的一致努力似乎未能使他们的支持者所预测的学生理解在教育上有显着差异。 DIRACC项目：开发和调查一种严格的概念演算方法将建立在亚利桑那州立大学已经重新设计且已经部署的演算I以重新设计和实施演算II的成功的基础上，并将研究学生在重新设计和传统的计算序列中的学习。此外，DiRACC项目还将为微积分I和微积分II开发简短的评估工具（也称为概念清单），其他机构可以用来评估，比较和对比学生在理解计算中心思想方面的进步。接受重新设计的演算序列的学生将得到更好的准备，并且更有可能应用他们对其他STEM课程中的变化率和累积功能的理解，并在随后的数学课程中学习依赖有线的材料。该项目生产的教科书将作为开放资源提供，供其他人使用或建立。最后，关于学生的微积分学习的结果以及用于调查学生学习的微积分概念清单，将为这些领域的未来研究提供信息。 DIRACC项目的结果将在区域，国家和国际会议上广泛传播，并在同行评审的数学教育期刊和会议记录中发表。缺乏微积分改革有效性的一个可能原因是，在教授主题的绝大多数情况下，基础课程的基本结构一直保持不变。具体而言，改革项目并未集中在学生开发有关变化速度功能和积累功能的富裕含义上，这对于任何介绍性的演算都是必不可少的。该项目DirACC课程是高度概念性的，因为它们是基于学生在整个微积分中适用的想法的连贯含义的发展，这也有助于学习微积分以外的数学思想。第一门课程是通过使计算本课程中各个方面的微分方面的基本定理来解决这一挑战。同时，项目Diracc微积分序列将是明确的计算，因为与现有的第一课程一样，学生将使用计算机来表示将函数定义为动态情况模型的过程，然后将其本身成为研究对象。这些课程还将承认并解决学生为微积分准备的已知弱点。微积分概念清单将使用标准的仪器开发技术（在其各自课程的开头和结尾）开发，其心理计量学特性将建立，每个课程约600名学生。