Can the Cognitive Impact of Calculus Courses be Enhanced? Updated on Aug 2014

Some blog followers 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; Honorary Member, Curmudgeon Lodge of Deventer, The Netherlands; President, PEdants for Definitive Academic References which Recognize the Invention of the Internet (PEDARRII). 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.

“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

Can the Cognitive Impact of Calculus Courses Be Enhanced: Response to Dubinsky

Some blog followers might be interested in a post "Can the Cognitive Impact of Calculus Courses Be Enhanced: Response to Dubinsky." The abstract reads:

**************************************************
ABSTRACT: In response to my post "Can the Cognitive Impact of Calculus Courses be Enhanced?" [Hake (2013)] at http://bit.ly/1loHgC4 (2.7 MB), Ed Dubinsky (2013) at http://bit.ly/JRB9Km of the RUME (Research in Undergraduate Math Education) list made t6 points that I have abbreviated below and to which I respond in this post:

1. "I agree with most of what you wrote."

2. "As far as I know, 'UME Trends' has not been archived. . . . the articles are historically important because they represent a major turning point in the mathematical community towards undergraduate education."

3. "I think more has gone on in MER during the last 20 years than is indicated in your piece. There is a special interest group SIGMAA ON RUME, which stands for Special Interest Group of the MAA on Research in Undergraduate Mathematics Education."

4. "I think we who work in RUME must acknowledge our debt to Physics Education Research."

5. "I am not quite as enthusiastic about CCI as you are. . . . . How are you going to keep the educational community from using CCI to 'teach to the test' and even to cheat?"

6. "I wonder what you have to say about the C4L calculus reform project that we developed at Purdue and was funded by the NSF Calculus Reform movement?"
**************************************************

To access the complete 152 kB post please click on http://bit.ly/1iHGJOL.

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.

What Mathematicians Might Learn From Physicists - Response by Bressoud

In response to “What Mathematicians Might Learn From Physicists” [Hake (2012)], David Bressoud http://bit.ly/RPx5L4 wrote to me (quoted with permission; my bold text; my inserts at “ . . .[[insert]]. . . . . . .”):

“I am very much aware of the Force Concept Inventory and Jerry's Calculus Concept Inventory. I attribute to the FCI much of the reason why the physics community has moved so effectively to rethink their approaches to introductory physics. It is precisely Michigan's notable results on the CCI that are the primary reason that the MAA's Calculus Study . . . . .[[ http://www.maa.org/cspcc ]]. . . . . will be visiting them this fall to conduct a case study.”

I’m delighted to learn that David Bressoud is aware of:

(a) the importance of the FCI in stimulating reform pedagogy in physics, even though Henderson et al. (2012) and many Physics Education Researchers seem NOT to be aware;

(b) the effective utilization of Epstein's CCI at the University of Michigan - see e.g., “How Do We Evaluate Student Understanding?” [Rhea (2009].

Richard Hake, Emeritus Professor of Physics, Indiana University
Links to Articles: http://bit.ly/a6M5y0
Links to SDI Labs: http://bit.ly/9nGd3M
Academia: http://bit.ly/a8ixxm
Blog: http://bit.ly/9yGsXh
Twitter http://bit.ly/juvd52
GooglePlus: http://bit.ly/KwZ6mE

REFERENCES [URL’s shortened by http://bitly.com/ and accessed on 15August 2012.]
Hake, R.R. 2012. “What Mathematicians Might Learn From Physicists,” online on the OPEN AERA-L archives at http://bit.ly/ROjN2T. Post of 13 Aug 2012 16:59:34-0700 to AERA-L and Net-Gold. The abstract and link to the complete post are being transmitted to several discussion lists and are on my blog “Hake'sEdStuff” at http://bit.ly/PSiidP.

Henderson, C., M. Dancy, & M. Niewiadomska-Bugaj. 2012. “The Use of Research-Based Instructional Strategies in Introductory Physics: Where do Faculty Leave the Innovation-Decision Process?” Physical Review Special Topics - Physics Education Research 8(2), online as a 934 kB pdf at http://bit.ly/MWSxIU.

Rhea, K. 2009. “How Do We Evaluate Student Understanding?” online as a 209 kB pdf at http://bit.ly/LE0xBe .

What Mathematicians Might Learn From Physicists

Some blog followers might be interested in a recent discussion-list post “What Mathematicians Might Lean From Physicists” [Hake (2012)]. The abstract reads:

*********************************************'
ABSTRACT: Mary Shepherd of the RUME list has called attention to David Bressoud's recent MAA “Launchings” columns (a) “Learning from the Physicists” [Bressoud (2012a)] at http://bit.ly/MrAuyZ, and (b) “Barriers to Change” [Bressoud (2012b)] at http://bit.ly/NkW9dE.

Unfortunately, Bressoud neglects to point out that the most important lesson mathematicians might learn from physicists is the advantage of discovering what instructional methods do and do not work by means of pre/post testing with Concept Inventories http://en.wikipedia.org/wiki/Concept_inventory - see e.g., “Lessons from the Physics Education Reform Effort” [Hake (2002) at http://bit.ly/aL87VT and “Bioliteracy and Teaching Efficiency: What Biologists Can Learn from Physicists” [Klymkowsky et al. (2003)] at http://bit.ly/9A1Arx. Pre/post testing with Concept Inventories has only recently been brought to math education by Jerry Epstein http://bit.ly/bqKSWJ with his “Calculus Concept Inventory.”

In my opinion, Bressoud is handicapped by the neglect of any mention of pre/post testing in his primary source “The Use of Research-Based Instructional Strategies in Introductory Physics: Where do Faculty Leave the Innovation-Decision Process?” [Henderson, Dancy, & Niewiadomska-Bugaj (2012)] at http://bit.ly/MWSxIU. The second sentence of their abstract reads: “Significant empirical research has shown that student learning can be substantially improved when instructors move from traditional, transmission-style instruction to more student-centered, interactive instruction [Bransford et al. (2000), Handelsman et al. (2004)].”

In referencing Bransford et al. (2000) and Handlesman et al. (2004)], Henderson et al. carry on the PER tradition of mindlessly dismissing the breakthrough research of Halloun & Hestenes (1985a) - see e.g. “The Initial Knowledge State of College Physics Students” http://bit.ly/b1488v (scroll down to “Evaluation Instruments”). As far as I know, that research constituted the first “significant empirical research [showing] that student learning can be substantially improved when instructors move from traditional, transmission-style instruction to more student-centered, interactive instruction.” Instead of emphasizing the preeminent role of PER in education research Henderson et al. erroneously imply that physicists simply followed the lead of cognitive scientists [Bransford et al. (2000)] and biologists [Handlesman et al. (2004)].
*********************************************

To access the complete 22 kB post please click on http://bit.ly/ROjN2T.

Richard Hake, Emeritus Professor of Physics, Indiana University
Links to Articles: http://bit.ly/a6M5y0
Links to SDI Labs: http://bit.ly/9nGd3M
Academia: http://bit.ly/a8ixxm
Blog: http://bit.ly/9yGsXh
Twitter http://bit.ly/juvd52
GooglePlus: http://bit.ly/KwZ6mE

“Physics educators have led the way in developing and using objective tests to compare student learning gains in different types of courses, and chemists, biologists, and others are now developing similar instruments. These tests provide convincing evidence that students assimilate new knowledge more effectively in courses including active, inquiry-based, and collaborative learning, assisted by information technology, than in traditional courses.”
- William Wood & James Gentile (2003).

REFERENCES [URL's shortened by http://bit.ly/ and accessed on 13 August 2012.
Hake, R.R. 2012. “What Mathematicians Might Learn From Physicists” online on the OPEN AERA-L archives at http://bit.ly/ROjN2T. Post of 13 Aug 2012 16:59:34 -0700 to AERA-L and Net-Gold. The abstract and link to the complete post are being transmitted to several discussion lists.

Wood, W.B. & J.M. Gentile. 2003. "Teaching in a research context," Science 302: 1510; 28 November; online to subscribers at . A summary is online to all at http://bit.ly/9qGR6m.

Remediation for Remedial Math

Some blog followers might be interested in a recent discussion-list post “Remediation for Remedial Math” [Hake (2012)]. The abstract reads:

*************************************************
ABSTRACT: Norman Stahl of the LRNASST-L list has pointed to Mitch Smith’s (2012) Inside Higher Ed article “Remediation for Remedial Math” at http://bit.ly/JtnbKp. Smith wrote (paraphrasing; my CAPS):

“Texas appears to be the first state to adopt drastic rethinking of remedial math in all its community colleges. When the new system, dubbed Mathways, is fully in place, remedial students who intend on majoring in a science- or math-based field will still take a traditional, algebra-based developmental course. BUT OTHER STUDENTS MIGHT TAKE CLASSES IN STATISTICS OR QUANTITATIVE REASONING, subsets of math that could prove more relevant to their careers and present less of a barrier to [those] emerging from remedial education.”

In my opinion, the major problem my not be inherent difficulty for many students of the algebra on which remedial courses concentrate, but the fact that such courses are ineffectively taught as passive-student lecture courses. Jerry Epstein’s (2007) “Calculus Concept Inventory” is beginning to show the abysmal ineffectiveness of standard introductory calculus courses. Similarly, an “Algebra Concept Inventory” might show the same thing for current algebra courses.
*************************************************


To access the complete 8 kB post please click on http://bit.ly/IQoSPw.

Richard Hake, Emeritus Professor of Physics, Indiana University
rrhake@earthlink.net
Links to Articles: http://bit.ly/a6M5y0
Links to SDI Labs: http://bit.ly/9nGd3M
Blog: http://bit.ly/9yGsXh
Academia: http://iub.academia.edu/RichardHake
Twitter https://twitter.com/#!/rrhake



REFERENCES [All URL’s shortened by http://bit.ly/ and accessed on 12 May 2012.]
Hake, R.R. 2012. “Remediation for Remedial Math,” online on the OPEN! AERA-L archives at http://bit.ly/IQoSPw. Post of 12 May 2012 10:24:19-0700 to AERA-L and Net-Gold. The abstract and link to the complete post are also being transmitted to several discussion lists.

Re: FCI and CCI in China #2

Some blog followers might be interested in a recent discussion-list post “Re: FCI and CCI in China #2” [Hake (2012)]. The abstract reads:

***********************************************
ABSTRACT: PhysLrnR’s Jerry Epstein wrote (paraphrasing): “The Calculus Concept Inventory (CCI) has been given to about 1000 university students enrolled in a TEACHER-CENTERED calculus course in Shanghai, China. Their average normalized gains g(ave) were about two-standard deviations above those of U.S. university calculus courses, possibly due to student-organized out-of-class interactive group work.”

Craig Ogilvie responded: “Are there FCI (Force Concept Inventory) gains reported for a similar group of students/physics courses in China? It would support your hypothesis if they also showed high gains for non-IE pedagogy.” Here “IE” = “Interactive Engagement,” operationally defined [Hake (1998a)] as “those courses designed at least in part to promote conceptual understanding through the active engagement of students in heads-on (always) and hands-on (usually) activities that yield immediate feedback through discussion with peers and/or instructors.”

David Meltzer then pointed to the research of Bao et al. on FCI pretest scores of Chinese and U.S. freshmen university students enrolled in science/engineering major courses, whose publication in the Science article “Learning and Scientific Reasoning: Comparisons of Chinese and U.S. Students” at http://bit.ly/90sdAG has been widely publicized.

Although Bao et al. measured only pretest scores (not pre-to-posttest gains) for Chinese freshmen university students enrolled in science/engineering major courses, they pointed out that those students had taken “algebra-based courses with emphasis on development of conceptual understanding and skills needed to solve problems” for FIVE YEARS in grades 8-12, whereas the U.S. students had taken at most ONE YEAR of physics.

That suggests that the Chinese K-12 math curriculum might also be more intensive than that in the U.S. IF that’s the case then it might help to explain the relatively high CCI gains for non-IE pedagogy, irrespective of possible student-organized out-of-class interactive group work.
***********************************************


To access the complete 16 kB post please click on http://bit.ly/zz7WXk

Richard Hake, Emeritus Professor of Physics, Indiana University
Honorary Member, Curmudgeon Lodge of Deventer, The Netherlands
President, PEdants for Definitive Academic References which
Recognize the Invention of the Internet (PEDARRII)

rrhake@earthlink.net
http://www.physics.indiana.edu/~hake
http://www.physics.indiana.edu/~sdi
http://HakesEdStuff.blogspot.com
http://iub.academia.edu/RichardHake

REFERENCES [URL shortened by http://bit.ly/ and accessed on 22 Jan 2012.]
Hake, R.R. 2012. “Re: FCI and CCI in China #2 online on the OPEN! AERA-L archives at http://bit.ly/zz7WXk. Post of 22 Jan 2012 16:27:43-0800 to AERA-L and Net-Gold. The abstract and link to the complete post are being transmitted to several discussion lists.