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Topic: Epstein's Calculus Concept Inventory: Response to Schremmer
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Richard Hake

Posts: 1,251
From: Woodland Hills, CA 91367
Registered: 12/4/04
Epstein's Calculus Concept Inventory: Response to Schremmer
Posted: Sep 16, 2013 6:17 PM
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My apologies if this message was previously received by some subscribers to Math-Teach, even though it has not shown up on the archives.

In response to my post "Re: Are Tenure Track Professors Better Teachers?" [Hake (2013)], Alain Schremmer (2013) of the MathEdCC list made 3 points:

1. "There are several ways to look at the calculus and several ways to decide what is important and what is secondary. On the other hand, in his article in the Notices Epstein gives the impression that he sees Calculus as one monolithic conglomeration of given concepts. I have tried to find out what 'concepts' he has selected to be tested in his Calculus Concept Inventory but with no success whatsoever. So I cannot be more precise."

If you email a request for his "Calculus Concept Inventory" (CCI) to Jerry Epstein <jerepst@ATT.NET>, I think he will probably send it to you. I realize that you've probably done that before with zero response, but my experience has been that Jerry may not be the world's most efficient email manager.

2. "In any case, Epstein seems completely to ignore Hestenes' 'Course content is taken [by many] as given, so the research problem is how to teach it most effectively. This approach [...] has produced valuable insights and useful results. However, it ignores the possibility of improving pedagogy by reconstructing course content.' For instance, Lagrange thought that the concept of limit could be entirely avoided. He was wrong of course, except that for all functions actually encountered in College Calculus it can. Limits really belong to advanced calculus."

See e.g.:

(a) "A Story Line for Calculus," [Alain Schremmer (1998)];

(b) "The History of the Calculus and Its Conceptual Development" [Carl Boyer (1959)];

(c) "A Historian Looks Back: The Calculus as Algebra and Selected Writings." [Judith Grabiner (2010)].

3. "P.S. By the way, there is no article in Wikipedia about "interactive engagement."

Looks like I'll have to withdraw my defense of Wikipedia [Hake (2009)]! ; - ) In Hake (1998a) I defined "interactive engagement" methods as "those designed at least in part to promote conceptual understanding through active engagement of students in heads-on (always) and hands-on (usually) activities which yield immediate feedback through discussion with peers and/or instructors."

Richard Hake, Emeritus Professor of Physics, Indiana University; Links to: Articles <>; Socratic Dialogue Inducing (SDI) Labs <>; Academia <>; Blog <>;GooglePlus <>; Google Scholar <>;Twitter <>; Facebook <>; Linked In <

REFERENCES [URLs shortened by <> and accessed on 16 Sept. 2013.]
Boyer, C.B. 1959. "The History of the Calculus and Its Conceptual Development." Dover, publisher?s information at <>. information at <>. An expurgated Google book preview is online at <> see especially at <>.

Grabiner, J.V. 2010. "A Historian Looks Back: The Calculus as Algebra and Selected Writings." Mathematical Association of America, publisher?s information at <>. information at <>, note the searchable ?Look Inside? feature. A thoughtful review by mathematician David J. Hand (2012) in online to subscribers at <>.

Hake, R.R. 1998a. "Interactive-engagement vs traditional methods: A six-thousand-student survey of mechanics test data for introductory physics courses," Am. J. Phys. 66: 64-74; online as an 84 kB pdf at <> . See also the crucial but ignored companion paper Hake (1998b).

Hake, R.R. 1998b. ?Interactive-engagement methods in introductory mechanics courses,? online as a 108 kB pdf at <>. A crucial companion paper to Hake (1998a). Submitted on 6/19/98 to the ?Physics Education Research Supplement? (PERS) of the American Journal of Physics, but rejected by its editor on the grounds that the very transparent, well organized, and crystal clear Physical-Review-type data tables were "impenetrable"!

Hake, R.R. 2009. ?In Defense of Wikipedia,? online on the OPEN ! AERA-L archives at <>. Post of 31 Aug 2009 16:41:53-0700 to AERA-L, Net-Gold, and MathTeach.

Hake, R.R. 2013. "Re: Are Tenure Track Professors Better Teachers?" online on the OPEN! AERA-L archives at <>. Post of 13 Sep 2013 16:41:24-0400 to AERA-L and NetGold. The abstract and link to the complete post are being transmitted to various discussion lists and are also on my blog "Hake'sEdStuff" at <> with provision for comments.

Hand, D.J. 2012. "A Historian Looks Back: The Calculus as Algebra and Selected Writings by Judith V. Grabiner." International Statistical Review 80(1):180?181, online to subscribers at <>.

Schremmer, A. 1998. "A Story Line for Calculus," Notes from the Mathematical Underground, AMATYC Review 20(1); online as a 29 kB pdf at <>.

Schremmer, A. 2013. "Re: Are Tenure Track Professors Better Teachers?" online on the OPEN! MathEdCC archives at <>. Post of 15 Sept 2013 12:01 AM to MathEdCC. [The MathForum fails to specify the time zone.]
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