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

Texas Tech University, Lubbock TX

Investigators

Abstract

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.