Collaborative Research: Project CLEAR Calculus: Coherent Labs to Enhance Accessible and Rigorous Calculus Instruction

这个合作项目是一项基于研究的努力，旨在让更多的学生在概念上接触微积分，同时提高学生所学内容的连贯性、严谨性和适用性。它的智力优势在于一个正在进行的研究项目，主要研究人员从这个项目中概念化了学习和教授微积分的框架，该框架建立在学生对近似和误差分析的直觉推理的基础上。将这一框架与建构主义方法相结合，项目团队正在完善和传播实验活动，这些活动涉及微积分、积分学和多元微积分标准课程序列的内容，并为学生提供辅助材料和互动技术。该项目正在发挥更广泛的影响，通过一系列努力，帮助围绕这些想法建立实践社区，其中包括：举办暑期研讨会，每周举行视频会议，提供课堂视频和讲师笔记，以支持实施实验室的教师专业发展。最后，一个研究和评估部分是通过使用两个量化指标来评估实验活动对学生微积分中心概念发展的影响：i)微积分概念评估(CCA)衡量学生对微积分核心概念理解的转变；ii)极限模型评估(LMA)衡量学生在用这些微积分概念进行推理时所使用的认知模型的转变。该项目正在进一步增加STEM教育的知识库，通过使用考试特征框架(ECF)对试点教师考试进行分析，研究其教师发展努力的有效性，并不断收集关于项目所有组成部分的详细反馈。

This collaborative project is a research-based effort to make calculus conceptually accessible to more students while simultaneously increasing the coherence, rigor, and applicability of the content students are learning. Its intellectual merit rests on an ongoing program of research from which the principal investigators have conceptualized a framework for learning and teaching calculus that builds on students' intuitive reasoning about approximations and error analyses. Combining this framework with a constructivist approach, the project team is refining and disseminating lab activities that address the content of a standard course sequence in differential, integral, and multivariable calculus with supporting materials and interactive technology for students. The project is exercising broader impact through its efforts to help develop a community of practice around these ideas through a set of efforts that includes: conducting summer workshops, holding weekly video-conferences, and making available classroom video and instructor notes to support faculty professional development for implementation of the labs. Finally, a research and evaluation component is assessing the impact of the lab activities on student conceptual development of the central ideas in calculus through the use of two quantitative measures: i) a Calculus Concept Assessment (CCA) to measure shifts in students' understanding of the central concepts of calculus and ii) a Limit Models Assessment (LMA) to measure shifts in the cognitive models employed by students while reasoning with these calculus concepts. The project is further adding to the knowledge base of STEM education by studying the effectiveness of its faculty development efforts through an analysis of pilot instructors' exams using an Exam Characterization Framework (ECF) and the continuous collection of detailed feedback on all components of the project.