I was discussing this with a colleague, who showed some papers on "interactive engagement" in physics education. Another keyword there was "force concept inventory", and the realted (newer) "calculus concept inventory". Any references to good empirical papers?

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    $\begingroup$ Would it be possible to include some information (or pointer to such information) what the terms "interactive engagement" and others mean in that context? This could be convenient for some readers (including this one :-) ). $\endgroup$
    – quid
    Commented Jun 19, 2014 at 11:49
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    $\begingroup$ This paper should answer that: web.mit.edu/rsi/www/2005/misc/minipaper/papers/Hake.pdf $\endgroup$ Commented Jun 19, 2014 at 11:54
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    $\begingroup$ The Hake paper that Kjetil B Halvorsen posted the link to is AFAIK the classic for physics. There's also a summary of physics-related evidence in Mazur, Peer Instruction: A User's Manual. Both of these are 20 years old, though. Force Concept Inventory is the title of an old version of the test; the latest version is called the IBCM. I haven't heard of a calculus concept inventory. Who is the author? In physics, there are a bunch of these "inventory" tests out there, but they vary wildly in quality. The IBCM is very carefully constructed. $\endgroup$
    – user507
    Commented Jun 19, 2014 at 13:25
  • $\begingroup$ @BenCrowell: The Calculus Concept Inventory was discussed last year in the AMS Notices. $\endgroup$ Commented Jun 19, 2014 at 14:00
  • $\begingroup$ @KjetilBHalvorsen: it just occurred to me that the AMS Notices article also may have some stuff or citations that may interest you. $\endgroup$ Commented Jun 19, 2014 at 14:05

1 Answer 1


The following web sites seem to be good starting places:

The "news" link from the Cornell site has a link labeled "Preliminary Project Results (password needed)"


  • Jerome Epstein

  • David O. Lomen

  • Scott Pilzer

  • Maria K. Robinson

  • Maria Terrell


Epstein, "Development and validation of the calculus concept inventory"

Epstein, "The calculus concept inventory -- measurement of the effect of teaching methodology in mathematics," Notices of the AMS 60 (2013) 1018

Pilzer, "Peer instruction in physics and mathematics," Primus XI (2001) 185

Lomen and Robinson, "Using conceptests in single and multivariable calculus"

Thomas and Lozano, "Analyzing calculus concept inventory gains in introductory calculus"

All of these papers can be found online by googling.


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