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:

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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.
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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

Re: Are Tenure Track Professors Better Teachers?

Some blog followers might be interested in a recent post “Re: Are Tenure Track Professors Better Teachers?” [Hake (2013)]. The abstract reads:

ABSTRACT: Scott Jaschik (2013) in his Inside Higher Ed report “The Adjunct Advantage” at http://bit.ly/19PGOZn has pointed to “Are Tenure Track Professors Better Teachers?” [Figlio et al. (2013) at http://bit.ly/1erGvKp. In my opinion, the latter's attempt to indirectly measure students’ learning in introductory courses by means of their next-class-taken performance is problematic at best.

Unfortunately, most of academia is either unaware or dismissive of the direct gauging of students’ higher-order learning by means of pre/post testing with Concept Inventories http://bit.ly/dARkDY, pioneered independently by economist Rendigs Fels (1967) at http://bit.ly/162KSBv and physicists Halloun & Hestenes (1985a) at http://bit.ly/fDdJHm.

For a discussion of pre/post testing with Concept Inventories, see e.g., “Should We Measure Change? YES!” [Hake (2013)] at http://bit.ly/d6WVKO. For recent use of this method see “The Calculus Concept Inventory - Measurement of the Effect of Teaching Methodology in Mathematics” [Epstein (2013) at http://bit.ly/17a8XJd.
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To access the complete 12 kB post please click on http://bit.ly/1829UU4 .

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

“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 [URLs shortened by http://bit.ly/ and accessed on 13 Sept. 2013.]
Hake, R.R. 2013. “Re: Are Tenure Track Professors Better Teachers?” online on the OPEN! AERA-L archives at http://bit.ly/1829UU4. 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.

Wood, W.B., & J.M. Gentile. 2003. “Teaching in a research context,” Science 302: 1510; 28 November; online as a 213 kB pdf http://bit.ly/SyhOvL.

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:

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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)].
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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 #2

Some blog followers might be interested in a recent discussion-list post “Remediation for Remedial Math #2” [Hake (2012)]. The abstract reads:

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ABSTRACT: In a previous post “Remediation for Remedial Math” I wrote: “In my opinion, the major problem may 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' http://bit.ly/bqKSWJ 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 which LrnAsst-L’s Jered Wasburn-Moses responded at http://bit.ly/KKRm0z (paraphrasing; my CAPS): “I think Hake misses a key difference between physics (his own field) and mathematics: EDUCATIONAL INERTIA. By the time they reach college developmental education courses, students have strongly-entrenched beliefs about mathematical content, mathematical classrooms, and themselves as mathematical learners.”

But my experience has been that the same is true for K-16 physics and other sciences, in that not only students but also teachers and professors have strongly-entrenched beliefs about education. So central is the problem of “educational inertia” that I was moved to post:

(a) Lesson #13 of “Lessons from the Physics Education Reform Effort” (Hake, 2002) at http://bit.ly/aL87VT: “The monumental inertia of the educational system may thwart long-term national reform”;

(b) “Eleven Quotes in Honor of Inertia” [Hake (2006)] at http://bit.ly/g7jdeU;

(c) an essay “Can Scientific Research Enhance the Art of Teaching?” [Hake (2007b)] at http://bit.ly/a7xJxR (1.2 MB): “University Leaders Bemoan the Inertia of Higher Education: Why Is It So Slow To Recognize the Value of Interactive Engagement Methods in Promoting Higher-Level Learning?”
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To access the complete 13 kB post please click on http://bit.ly/KZafu5.

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

“If you try to introduce people to a paradigm shift,
they will hear what you have to say and
then interpret your words in terms of their old paradigm.
What does not fit, they will not hear.”
Myron Tribus (2001), former director of the
“Center for Advanced Engineering Study at MIT” -
see http://en.wikipedia.org/wiki/Myron_Tribus


REFERENCES [URL shortened by http://bit.ly/ and accessed on 15 May 2012.]
Hake, R.R. 2012. “Remediation for Remedial Math #2,” online on the OPEN! AERA-L archives at http://bit.ly/KZafu5. Post of 15 May 2012 11:31:16-0700 to AERA-L and Net-Gold. The abstract and link to the complete post are also being transmitted to several discussion lists.

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:

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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.
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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.

Lecture Isn’t Effective: More Evidence #4

Some blog followers might be interested in a discussion-list post “Lecture Isn’t Effective: More Evidence #4” [Hake (2011c)].

The abstract reads:

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ABSTRACT: In response to “Re: Lecture Isn't Effective: More Evidence #2” [Hake (2011b)], EvalTalk’s Jan Hill (2011a) wrote: “Yes, we educators know that lectures are ineffective. . . . .” To which Ricardo Gomez (2011) replied: (a) “What educators know that lectures are ineffective?” and (b) “Different teaching methods serve different learning objectives.”

In answer to “a”: among articles that demonstrate the relative ineffectiveness of traditional passive student introductory lectures in comparison with “interactive-engagement” methods are Hake (1998a); about 25 other physics education research reports consistent with Hake (1998a) as listed in Hake (2008); Epstein (2007); Mazur (2009); Prather, Rudolph, Brissenden, & Schllingman (2009); Prather, Rudolph, & Brissenden (2009); & Deslauriers, Schelew, & Wieman (2011)].

In response to “b”: different teaching methods also serve different audiences - e.g., introductory students vs attendees at professional meetings - see e.g. “Re: Lectures” [Hake (2011f)].

Gomez also wrote: “I can't imagine Stephen Jay Gould, Carl Sagan, or Isaiah Berlin using ‘interactive teaching methods’ . . . . . instead of the great lectures they were famous for. . . . . or maybe they did use one of best interactive teaching methods ever invented: the Socratic method.”

I would agree that the “Socratic Method” of the historical Socrates is “one of the best interactive teaching methods ever invented,” witness “Socratic pedagogy in the introductory physics lab” [Hake (1992)], but the “Socratic Methods” of Plato’s Meno and the law school are, in my opinion, among the worst - see e.g. : “The Socratic Method of the Historical Socrates, Plato's Socrates, and the Law School Socrates” [Hake (2007)].
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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

"…I point to the following unwelcome truth: much as we might dislike the implications, research is showing that didactic exposition of abstract ideas and lines of reasoning (however engaging and lucid we might try to make them) to passive listeners yields pathetically thin results in learning and understanding - except in the very small percentage of students who are specially gifted in the field."
Arnold Arons in Teaching Introductory Physics (1997, p. vii)

REFERENCES [URL’s shortened by http://bit.ly/ and accessed on 22 July 2011.]
Arons, A.B. 1997. Teaching Introductory Physics. Wiley. Amazon.com information at http://amzn.to/bBPfop. Note the searchable “Look Inside” feature.

Hake, R.R. 2011a. “Re: Lecture Isn’t Effective: More Evidence,” online on the OPEN! MathEdCC archives at http://bit.ly/r80W5i along with 10 responses as of 22 July 2011. Post of 15 July, shamelessly cross-posted to Math-Teach, Math-Learn, MathEdCC, and RUME.

Hake, R.R. 2011b. “Re: Lecture Isn't Effective: More Evidence #2,” online on the OPEN! AERA-L archives at http://bit.ly/mXiXoh. Post of 20 Jul 2011 17:13:46-0400 to AERA-L and Net-Gold. The abstract and link to the complete post were transmitted to various discussion lists and are also on my blog “Hake'sEdStuff” at http://bit.ly/rr2BQU with a provision for comments. See also the precursor Hake (2011a).

Hake, R.R. 2011c. “Re: Lecture Isn't Effective: More Evidence #4,” online on the OPEN! AERA-L archives at http://bit.ly/oVqvml. Post of 22 Jul 2011 14:52:44 -0700 to AERA-L and Net-Gold. The abstract and link to the complete post are being transmitted to various discussion lists.

Re: A Question: Where Does Current Reform Come From?

Some blog followers might be interested in a discussion-list post “Re: A Question: Where Does Current Reform Come From?” [Hake (2011)].

The abstract reads:

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ABSTRACT: Joshua Fisher (2011) in his Math-Teach post “A Question: Where Does Current Reform Come From?” wrote (paraphrasing): “How does one enable middle school kids to know the formula for the area of a sphere as required by the standards? . . . .So just give it to ‘em, right? Yet, my supervisor tried to avoid this consequence. My question is . . . . ‘What is the incentive to promote Not Telling over Telling?’ ”

For physics education, Fisher’s last question might be better posed as “What is the incentive to promote ‘Interactive Engagement’ (IE) over ‘Direct Instruction’ (DI).” The answer is that over 40-years worth of physics education research has demonstrated that IE is far more effective in promoting students' conceptual understanding of physics than DI.

I suspect that a similar statement might be made for math education, but except for the work of Jerry Epstein (2007) at http://bit.ly/bqKSWJ, there's been little, if any, pre- to post-course testing of math concepts. Thus math educators have little information on the relative effectiveness of IE and DI courses in promoting conceptual understanding.
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To access the complete 19 kB post please click on http://bit.ly/iHzGwm.

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

“…I point to the following unwelcome truth: much as we might dislike the implications, research is showing that didactic exposition of abstract ideas and lines of reasoning (however engaging and lucid we might try to make them) to passive listeners yields pathetically thin results in learning and understanding - except in the very small percentage of students who are specially gifted in the field.”
Arnold Arons in Teaching Introductory Physics (p. vii, 1997)


REFERENCES [URL’s shortened by http://bit.ly/ and accessed on 26 June 2011.]
Arons, A.B. 1997. Teaching Introductory Physics. Wiley. Amazon.com information at http://amzn.to/bBPfop. Note the searchable “Look Inside” feature.

Hake, R.R. 2011. “Re: A Question: Where Does Current Reform Come From?” AERA-L archives at http://bit.ly/iHzGwm. Post of 26 Jun 2011 15:07:50-0700 to Math-Teach, AERA-L, and NetGold. The abstract and link to the complete 19 kB post are being transmitted to various discussion lists.