Measurements for Learning and Practice: The Revised Calculus Concept Inventory

Jerry Dwyer
Texas Tech University

Calculus has been a gatekeeping course in many colleges and universities. Students who struggle with their first course in calculus have difficulty progressing through science, technology, engineering, and mathematics (STEM) degrees. Understanding calculus is essential to students’ future STEM learning; understanding what students know is essential for instructors and researchers to support the advancement of student learning. A student assessment instrument which accurately measures students’ knowledge and understanding of the concepts taught in the first calculus course is needed. This presentation will highlight the efforts of the NSF funded Revised Calculus Concept Inventory (RCCI; IUSE 1916751) led by Texas Tech University (TTU) which seeks to develop a validated concept inventory for the first calculus course. Prior instruments have been created for similar purposes. Epstein and Yang developed the Calculus Concept Inventory (CCI) in 2004 (NSF DUE 0404818). Unfortunately, Epstein passed away in 2015 prior to responding to questions concerning the validation of this instrument. Thompson and Ashbrook developed two more inventories, one in Calculus I (C1CI) and the other in Calculus II (C2CI) (DUE 1625678; DUE 1625873). These instruments measure the impact of the Developing and Investigating a Rigorous Approach to Conceptual Calculus (DIRACC; Thompson & Ashbrook, 2016) curriculum. The RCCI is informed by these prior research and concept inventory efforts and is designed to match current needs while establishing a firm evidence base supporting the RCCI’s psychometric properties. Our research questions are:1.How can the CCI and C1CI be merged, revised and/or extended to better capture conceptual changes in students’ pre and post calculus knowledge? 2.What alterations or updates are necessary to the questions that comprise the CCI and C1CI to improve the resultant merged instrument and its psychometric properties? 3.How can calculus-specific notation be minimalized in the RCCI in a manner that supports the valid use of the RCCI as a pre and post assessment instrument?The RCCI was funded in October 2019. In November and December, we administered a national survey to high school and college calculus instructors concerning the concepts that comprise the first calculus course. The results were discussed by a panel, comprised of high school, community college and university calculus instructors, during a three-day workshop. This nine-person panel drafted the RCCI based on prior instruments and feedback from the survey. Think-aloud protocols were completed by four calculus-ready students, or students who had completed and passed all prerequisite courses and had the intention of completing calculus within the next year. The RCCI is currently being pilot tested in the panel members’ courses. A major outcome is the 20-question, draft instrument. Statistical analyses are underway to establish the psychometric properties. The Broader Impacts include the design of this instrument to support successful completion of the first calculus course by diverse student populations. We will examine the consequential validity of the resultant RCCI on diverse populations and adapt as is supported by the evidence. The purpose of this presentation is to share the RCCI progress with the broader community. Epstein, J. (2013). “The calculus concept inventory-Measurement of effect of teaching methodology in mathematics.” Notices of the AMS (60), 8, p. 1018-1026. Available at:, P.T. & Ashbrook, M. (2016). “Developing and Investigating a Rigorous Approach to Conceptual Calculus.” Available at:


Moskal, B., Dwyer, J., Lee, J., Williams, G. & Johnson, L., Texas Tech University