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Re: [Phys-L] Can the Cognitive Impact of Calculus Courses be Enhanced? Updated on Aug 2014

This is a remarkable note, given in Hake's usual style with abstract and references, in that it points to a truly remarkable essay: remarkable because the abstract, epilogue and fourteen pages of exposition and epilogue are followed by an encyclopedic twenty one pages of references and then forty seven more pages in a second appendix.

At the risk of trivializing this splendid work, I note that page ten mentions that mathematician Tim Pennings (2003) claims that his dog Elvis is capable of solving the equation
T = (z-y)/r + ((x^2 + y^2)^0.5) / s so as to minimize T in terms of a distance y
- described as pitching a ball diagonally into the sea from the margin of the shore where
z = along shore distance, x = offshore distance, r is running speed, s = swimming speed,
y = distance before the normal at the water's edge to the ball at which the dog enters the water. r>s.

This evidently is intended as a goad to students and their teachers who experience the usual amount of difficulty in solving it. I say only that a single line into a solver such as
provides an expression to zeroize at the point of interest, valid for a range of values of running and swimming speeds, while Pennings' dog has the means to optimize his path only for a known run speed and a known swim speed, a more circumscribed, but still notable achievement, leading to thoughts about the reason for dogs evolving such skills as computing trajectories and interception paths in space - a skill often demonstrated by dogs who catch frisbees, but less so by rocket scientists.

Brian Whatcott Altus OK

On 8/11/2014 5:07 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 <> (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 <>.

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

REFERENCES [URLs shortened by <> 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 <>.The abstract and link to the complete post are being transmitted to several discussion lists and are also on my blog "Hake'sEdStuff" at <>.

"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) <>

"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" <>

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