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*From*: Philip Keller <pkeller@holmdelschools.org>*Date*: Tue, 12 Aug 2014 13:42:04 -0400

Is there a list where math teachers debate the items on the CCI?

I am asking because I would have given the "wrong" answer to the question about which functions are continuous. First, I would have complained about the question...continuous on what interval? But with no other guidance, I'd assume that they meant on the real line. In that case, I'd say the f(x)=1/(x-1) is not continuous. Not because "I have to lift my pencil" but because it is not the case that f(1)= lim x->1 f(x). If the question read: which of these functions is continuous _on its domain_" then I'd change my answer.

They mention that this particular item has sparked debate among mathematicians. Maybe that suggests it needs re-working. I'd be curious to see the rest of the test. Did I miss a link?

On 8/11/2014 6:07 PM, Richard Hake wrote:

Some subscribers to Phys-L might be interested an essay "Can the Cognitive Impact of Calculus Courses be Enhanced? Updated on Aug 2014 from a Talk at USC on 24 April 2012" [Hake (2014)]. The abstract reads:

***************************************************

ABSTRACT: 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 mathematics.

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 (2011c)] at <http://bit.ly/nmPY8F> (8.7 MB).

With over 500 references and over 600 hot links this report can serve as a window into the vast literature relevant to calculus reform.

***************************************************

To access the complete 2.8 MB essay please click on <http://bit.ly/1B9dyvD>.

Richard Hake, Emeritus Professor of Physics, Indiana University. LINKS TO: Academia <http://bit.ly/a8ixxm>; Articles <http://bit.ly/a6M5y0>; Blog <http://bit.ly/9yGsXh>; Facebook <http://on.fb.me/XI7EKm>; GooglePlus <http://bit.ly/KwZ6mE>; Google Scholar <http://bit.ly/Wz2FP3>; Linked In <http://linkd.in/14uycpW>; Research Gate <http://bit.ly/1fJiSwB>; Socratic Dialogue Inducing (SDI) Labs <http://bit.ly/9nGd3M>; Twitter <http://bit.ly/juvd52>.

REFERENCES [URLs shortened by <http://bit.ly/> and accessed on 11 Aug 2014.]

Hake, R.R. 2014. "Can the Cognitive Impact of Calculus Courses be Enhanced? Updated on Aug 2014 from a Talk at USC on 24 April 2012," online at <http://bit.ly/1B9dyvD>.The abstract and link to the complete post are being transmitted to several discussion lists and are also on my blog "Hake'sEdStuff" at <http://bit.ly/1uj8K52>.

"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) <http://bit.ly/dzjbWv>

"To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature ... If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in." - Richard Feynman (1965, 1994) in "The Character of Physical Law" <http://amzn.to/19vE4AO>

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**References**:**[Phys-L] Can the Cognitive Impact of Calculus Courses be Enhanced? Updated on Aug 2014***From:*Richard Hake <rrhake@earthlink.net>

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