Revised Calculus Concept Inventory: Measuring the Learning Gains of First Year Calculus Students

在NSF改善本科生STEM教育计划：教育和人力资源(IUSE：EHR)的支持下，该项目旨在通过开发一套改进的问题集来衡量学生对微积分概念的知识，以服务于国家利益。随着STEM学科成为越来越关键的学习领域，将鼓励更多的学生完成大学水平的微积分课程。微积分教师需要对学生的微积分概念知识进行准确的测量，以了解学生的知识是如何随教学而变化的。然后，他们可以使用这些信息来改进和改进他们的课程。这个项目借鉴了以前的相关工作，旨在根据微积分课程教师的反馈，制作一份最新的、内容丰富的微积分概念评估。负责对学生进行评估的微积分教师将获得评估结果，他们可以利用这些结果来改进他们的教学方法。该项目还将通过在本科生微积分I课堂上进行试验来收集该工具的有效性证据。项目目标包括：i)更新、重新设计两个现有的微积分概念清单，并将其合并为一个工具，该工具捕获学生从学生进入微积分课程到第一个微积分课程结束时的概念知识和理解；以及ii)检查和建立结果工具的心理测量学属性。这些目标将使用系统的、形成性的研究方法来实现，这将从对全国各地的高中和大学微积分教师进行的调查开始。来自这项调查的信息将为为期三天的微积分教育专家会议提供信息，他们将提出对先前工具的修订建议。有声思考协议将被用来建立学生对合成仪器的理解能力，然后在全国各地的微积分课程中对该仪器进行试点测试。仪器的心理测量学特性将在整个仪器开发过程中被跟踪和形式化地使用，以改进这些努力和支持最终工具的有效性证据。该项目的主要智力价值在于创建了一个带有支持有效性证据的微积分概念量表，可以用来衡量微积分教学干预的归一化收益，并比较不同教学方法的有效性。这项研究的评估工具和结果将通过与全国数学教师理事会、美国数学协会和美国数学学会的合作广泛传播。采用改进的微积分评估和由此产生的教学干预措施，有可能使学生更深入地理解数学概念，这些概念对于STEM学科中的一系列其他课程的进步至关重要，包括工程、物理、生物和化学。NSF IUSE：EHR计划支持研究和开发项目，以提高所有学生的STEM教育的有效性。这个项目是在IUSE：EHR参与式学生学习轨道上进行的，资助计划通过该轨道支持有前途的实践和工具的创建、探索和实施。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

With support from the NSF Improving Undergraduate STEM Education Program: Education and Human Resources (IUSE: EHR), this project aims to serve the national interest by developing an improved set of questions for measuring student knowledge of calculus concepts. As STEM disciplines become increasingly critical areas of study, more students will be encouraged to complete a college-level calculus course. Calculus instructors need an accurate measurement of students' knowledge of calculus concepts to understand how student knowledge changes in response to instruction. They can then use this information to refine and improve their courses. This project, informed by prior related efforts, aims to produce a current and informative calculus concept assessment based on feedback from calculus course instructors. Calculus instructors who administer the assessment to their students will have access to the results, which they can use to improve their instructional approaches. The project will also collect validity evidence for this instrument by piloting it in a subset of undergraduate Calculus I classrooms. The resulting assessment will be accessible to both high school and college instructors, thus helping to inform and improve calculus instruction nationwide.Project goals include to: i) update, redesign, and merge two existing calculus concept inventories into a single instrument that captures students' conceptual knowledge and understanding of calculus concepts from when students enter to when they exit their first calculus course; and ii) examine and establish psychometric properties of the resultant instrument. These goals will be reached using a systematic, formative research approach, which will begin with a survey administered to high school and college calculus instructors throughout the nation. Information from this survey will inform a three-day meeting of experts in calculus education, who will propose revisions of the prior instruments. Think-aloud protocols will be used to establish the understandability of the resultant instrument by students, followed by pilot testing of the instrument in calculus courses throughout the nation. The psychometric properties of the instrument will be tracked and used formatively throughout instrument development to improve these efforts and the validity evidence supporting the final instrument. The major intellectual merit of the project lies in the creation of a calculus concept inventory with supporting validity evidence that can be used to measure the normalized gains of calculus teaching interventions and to compare effectiveness of different teaching methods. The assessment instrument and results of this research effort will be broadly disseminated through collaboration with the National Council of Teachers of Mathematics, the Mathematical Association of American, and the American Mathematics Society. The adoption of improved calculus assessment and resultant teaching interventions has potential to lead to a deeper student understanding of mathematical concepts that are critical to progress across a range of other courses in STEM disciplines, including engineering, physics, biology, and chemistry. The NSF IUSE: EHR Program supports research and development projects to improve the effectiveness of STEM education for all students. This project is in the IUSE: EHR Engaged Student Learning track, through which the funding program supports the creation, exploration, and implementation of promising practices and tools.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.