Developing a Calculus Concept Inventory for Assessing Learner’s Conceptual Understanding

Grant program: Teaching and Learning Development Grant (TLDG)

Grant recipient: Jamie Mulholland, Department of Mathematics

Project team: Veselin Jungić, Department of Mathematics and Cindy Xin, Teaching and Learning Centre, and Abhishek Nanjundappa, research assistant

Timeframe: January 2015 to August 2017

Funding: $5,000

Courses addressed:

  • MATH 150 – Calculus I with Review
  • MATH 151 – Calculus I
  • MATH 152 – Calculus II

Interim report: View Jamie Mulholland's interim report (PDF)

Description: Our project aims to develop and test a calculus concept inventory while continuing our effort to implement and investigate the flipped classroom for calculus courses (MATH 150, 151 and 152). Students are not blank slates; instead, students bring with them often deep-seated preconceptions. Identifying the levels and types of the preconceptions of individual students is a critical first step to ensure the effectiveness of subsequent instruction.

A concept inventory (CI) is one of the tools that can be used to assess a learner’s understanding of fundamental concepts of a subject matter. A concept inventory is defined as a criterion-referenced test designed to evaluate whether a student has an accurate working knowledge of a specific set of concepts. Such a test can be used to assess students’ understanding of a subject matter’s fundamental concepts prior to instruction. This knowledge would guide subsequent instruction to address students’ preconceptions and allow measuring of learning gains at the end of instruction. Surprisingly, there is no well-established CI in wide use in calculus despite its foundational importance for many science and applied science disciplines. Additionally, the present best-known Calculus inventory uses the words such as “limit” and “derivative” which are fundamental concepts of calculus. Problematically, it is difficult to test students’ preconception of these concepts when they are explicitly referred to in the questions

We plan to engage in the challenging process of developing a CI for Calculus that does not make explicit reference to Calculus concepts. Such a tool would allow us, as well as others, to assess the students prior understanding of calculus concepts before they are introduced to the concepts through formal instruction.

Questions addressed:

  • What previous work has been done to develop a calculus concept inventory (CCI)?
  • What are the fundamental concepts that need to be assessed in a CCI?
  • What test items need to be developed for each of the identified concepts in a CCI? What would these items and their answer options look like to reflect different levels of understanding? How can these options be best weighted to give partial credit/score?
  • How can we begin to build and improve our CCI’s validity and reliability through pilot testing of the developed items in SFU first-year calculus courses?

Knowledge sharing: Dissemination will be done through discussing and sharing the instrument with the math department, via the Teaching Matters Seminar at SFU, and with colleagues who teach calculus at other institutions nationally and internationally. We also plan to present our initial results at the annual SFU Teaching and Learning Symposium and other local, national, and international conferences. Additionally, the development of the CCI can have wide application at other institutions nationally and internationally. It can contribute significantly to calculus assessment and teaching practices.

Jungic, V., Mulholland, J., & Xin, C. (2016, May). Calculus concept inventory: A tool for assessing learner’s conceptual understanding. Presentation at Simon Fraser University: Changing the Culture, Simon Fraser University, Vancouver, BC.

Keywords: concept inventory; flipped classroom; student understanding of concepts; students' preconceptions; learning gains; working knowledge