Calculus Concept Inventory (CCI)

Developed by Jerome Epstein

Purpose To assess student understanding of the most basic principles of calculus.
Format Pre/post, Multiple-choice
Duration 30 min
Focus Mathematics Content knowledge (functions, derivatives, limits, ratios, the continuum)
Level Intro college, High school
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CCI Implementation and Troubleshooting Guide

Everything you need to know about implementing the CCI in your class.

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J. Epstein, Development and Validation of the Calculus Concept Inventory, presented at the Ninth International Conference on Mathematics Education in a Global Community, Charlotte, NC, 2007.
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Gold Star Validation
This is the highest level of research validation, corresponding to all seven of the validation categories below.

Research Validation Summary

Based on Research Into:

  • Student thinking

Studied Using:

  • Student interviews
  • Expert review
  • Appropriate statistical analysis

Research Conducted:

  • At multiple institutions
  • By multiple research groups
  • Peer-reviewed publication

The multiple-choice questions on the CCI were first developed by a panel of experts who defined the content to be tested and wrote the questions. The questions were tested with about 250 students, and there was no gain in scores between the pre and post-test. The test was revised so that the questions were at a level that faculty would believe was utterly trivial. The revised version was tested with 1100 students at 15 institutions. Statistical analyses of reliability, difficulty and discrimination were conducted, and reasonable values found. Students participated in think aloud interviews while answering test questions, and it was found they were interpreting questions as intended. The CCI has been given to over 5000 in the US and 15 other countries and results published in three papers.


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Language Translator(s)  
Czech Karel Kolář

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Typical Results

In Calculus I at the University of Michigan, 1,342 students in 51 sections were taught using the Harvard Project Calculus text (Hughes-Hallett et al., 1998), as reported in Epstein 2013.

  • Average normalized gain for all sections: 0.35
  • 10 sections had a gain of 0.40 to 0.44
  • The range of the gain scores was 0.21 to 0.44

The latest version of the CCI, released in 2006, is version 5. A preliminary version tested in 2005 was found to be so difficult that scores were equivalent to random guessing, and was modified to make it easier. After testing the easier version, 2 questions were removed, resulting in the "final" version with 22 questions, released in 2006.