Saturday, December 28, 2013

Can the Cognitive Impact of Calculus Courses Be Enhanced

Some blog followers might be interested in a talk "Can the Cognitive Impact of Calculus Courses Be Enhanced" [Hake (2013)]. The abstract reads:

I discuss the cognitive impact of introductory calculus courses after the initiation of the NSF’s calculus reform program in 1987. Topics discussed are:
a. What’s calculus?
b. Calculus, language of nature and gateway to science, technology, engineering, and

c. A typical calculus-course problem (even dogs can solve it).
d. NSF’s calculus reform effort, initiated in 1987.

e. Assessments bemoan the lack of evidence of improved student learning.

f. A glimmer of hope – the Calculus Concept Inventory (CCI).

g. Typical question of the CCI type (dogs score at the random guessing level).
h. Impact of the CCI on calculus education – early trials.

i. Conclusion.

j. Appendix #1: The Lagrange Approach to Calculus.

k. Appendix #2: Math Education Bibliography.

I conclude that Epstein’s CCI may stimulate reform in calculus education, but, judging from 
the physics education reform effort, it may take several decades before widespread improvement occurs - see the review "The Impact of Concept Inventories On Physics Education and Its Relevance For Engineering Education" Hake (2011) at (8.7 MB).

To access the complete 2.7 MB talk please click on

Richard Hake, Emeritus Professor of Physics, Indiana University
Links to Articles:
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"Mathematics is the gate and key of the sciences. . . .Neglect of mathematics works injury to all knowledge, since he who is ignorant of it cannot know the other sciences or the things of this world. And what is worse, men who are thus ignorant are unable to perceive their own ignorance and so do not seek a remedy."
- Roger Bacon (Opus Majus, bk. 1, ch. 4)

Hake, R.R. 2011. "The Impact of Concept Inventories On Physics Education and It's Relevance For Engineering Education," invited talk, 8 August, second annual NSF-sponsored "National Meeting on STEM Concept Inventories," Washington, D.C., online as an 8.7 MB pdf at or as ref. 64 at The abstract and link are being transmitted to various discussion lists and are also on my blog "Hake'sEdStuff" at with a provision for comments.

Hake, R.R. 2013. "Can the Cognitive Impact of Calculus Courses be Enhanced?" An update of 26 Dec 2013 of an invited talk of 24 April 2012, Department of Mathematics, University of Southern California, online as a 2.7 MB pdf at and as ref. 70 at

Labels: What’s calculus? language of nature, gateway to science, NSF’s calculus reform effort, Calculus Concept Inventory (CCI), Math Education Bibliography

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