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
Showing posts with label Calculus. Show all posts
Showing posts with label Calculus. Show all posts
Monday, August 11, 2014
Wednesday, January 15, 2014
Math Education Bibliography
Some blog followers might be interested in a “Math Education Bibliography” that was included on pages 42-83 of a recent essay "Can the Cognitive Impact of Calculus Courses be Enhanced?" [Hake (2013)] at http://bit.ly/1loHgC4 (2.7 MB)
The bibliography contains over 400 hot-linked URLs and references, including:
(a) 3 articles due (or due in part) to Joan Ferrini-Mundy http://1.usa.gov/1iQzxNR, NSF Assistant Director for Education and Human Resources;
(b) a YouTube talk “Joan FERRINI-MUNDY on STEM Education Research Areas”; and
(c) 3 articles by MSU Distinguished Professor William Schmidt http://bit.ly/tMA3oL, among them “U.S. students need new way of learning science” [Schmidt (2012a)]. The latter discusses the PROM/SE project “Promoting Rigorous Outcomes in Mathematics and Science Education” at http://bit.ly/1eCnHUw.
References in categories a, b, and c are in the REFERENCE list below preceded by double asterisks**.
An ERRATUM is in order: One of the references in the “Math Education Bibliography” section of my essay is “Berkeley Websites. . . .” [Schoenfeld (2013a)]. Therein I wrote: “A former Berkeley website, containing links to many of Schoenfeld’s articles, seems to have vanished from the web : - ( .” CORRECTION: Over 15 links to Schoenfeld’s articles have recently been made available at http://bit.ly/1ap7pM9, as indicated in the revised reference below to Schoenfeld (2013a).
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 [All URLs shortened by http://bit.ly/ and accessed on 15 Jan 2014.]
**Ball, D.L., J. FERRINI-MUNDY, J. Kilpatrick, R.J. Milgram, Wilfred Schmid, & R. Schaar, “Reaching for Common Ground in K-12 Mathematics Education,” in Notices of the AMS 52: 1055-1058; online as a 49 kB pdf at http://bit.ly/10Z0msf.
** FERRINI-MUNDY, J. & K.G. Graham. 1991. “An Overview of the Calculus Curriculum Reform Effort: Issues for Learning, Teaching, and Curriculum Development,” American Mathematical Monthly 98(7): 627-635; the first paragraph is online at http://bit.ly/1erhawp. An ERIC abstract is online at http://1.usa.gov/196ebpe.
**FERRINI-MUNDY, J. YouTube video “Joan FERRINI-MUNDY on STEM Education Research Areas,” online at http://bit.ly/IOcTca, 332 views as of 15 Jan 2014 13:24-0800.
**Graham, K. G., and J. FERRINI-MUNDY. 1989. “An Exploration of Student Understanding of Central Concepts in Calculus,” paper presented at the Annual Meeting of the American Educational Research Association. I’ve not found an online version.
Hake, R.R. 2013. “Can the Cognitive Impact of Calculus Courses be Enhanced?” An update of 26 Dec 2013 of an invited talk of 24 April 2012, Department of Mathematics, University of Southern California, online as a 2.7 MB pdf at http://bit.ly/1loHgC4 and as ref. 70 at http://bit.ly/a6M5y0. The abstract and link are being transmitted to various discussion lists and are also on my blog “Hake'sEdStuff” at http://bit.ly/1jXolD6 with a provision for comments.
**Lauten, D., K. Graham, and J. FERRINI-MUNDY. 1999. “Increasing the Dialogue About Calculus with a Questionnaire” in Assessment Practices in Undergraduate Mathematics [Gold et al. (1999, pp. 237-240)] at http://bit.ly/1e6ShtL.
**SCHMIDT, W. 2011. “Want better math teachers? Train them better, scholar argues?” 09 June; online at http://bit.ly/1bP1V2r.
** SCHMIDT, W. 2012a. “U.S. students need new way of learning science,” 05 April; online at http://bit.ly/1csHB5o.
** SCHMIDT, W. 2012b. “Study supports move toward common math standards,” 05 Nov; online at http://bit.ly/J09KXl.
Schoenfeld, A.H. 2013a. Berkeley Websites: (a) Functions Research Group http://bit.ly/18Aod7R; (b) Algebra Teaching Study http://bit.ly/IJD7g8; (c) Mathematics Assessment Project http://bit.ly/1bNlL8e; (d) Formative Assessment with Computational Technologies (FACT) http://bit.ly/187WA5r; (e) Alan Schoenfeld’s Downloadable Publications http://bit.ly/1ap7pM9.
The bibliography contains over 400 hot-linked URLs and references, including:
(a) 3 articles due (or due in part) to Joan Ferrini-Mundy http://1.usa.gov/1iQzxNR, NSF Assistant Director for Education and Human Resources;
(b) a YouTube talk “Joan FERRINI-MUNDY on STEM Education Research Areas”; and
(c) 3 articles by MSU Distinguished Professor William Schmidt http://bit.ly/tMA3oL, among them “U.S. students need new way of learning science” [Schmidt (2012a)]. The latter discusses the PROM/SE project “Promoting Rigorous Outcomes in Mathematics and Science Education” at http://bit.ly/1eCnHUw.
References in categories a, b, and c are in the REFERENCE list below preceded by double asterisks**.
An ERRATUM is in order: One of the references in the “Math Education Bibliography” section of my essay is “Berkeley Websites. . . .” [Schoenfeld (2013a)]. Therein I wrote: “A former Berkeley website, containing links to many of Schoenfeld’s articles, seems to have vanished from the web : - ( .” CORRECTION: Over 15 links to Schoenfeld’s articles have recently been made available at http://bit.ly/1ap7pM9, as indicated in the revised reference below to Schoenfeld (2013a).
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 [All URLs shortened by http://bit.ly/ and accessed on 15 Jan 2014.]
**Ball, D.L., J. FERRINI-MUNDY, J. Kilpatrick, R.J. Milgram, Wilfred Schmid, & R. Schaar, “Reaching for Common Ground in K-12 Mathematics Education,” in Notices of the AMS 52: 1055-1058; online as a 49 kB pdf at http://bit.ly/10Z0msf.
** FERRINI-MUNDY, J. & K.G. Graham. 1991. “An Overview of the Calculus Curriculum Reform Effort: Issues for Learning, Teaching, and Curriculum Development,” American Mathematical Monthly 98(7): 627-635; the first paragraph is online at http://bit.ly/1erhawp. An ERIC abstract is online at http://1.usa.gov/196ebpe.
**FERRINI-MUNDY, J. YouTube video “Joan FERRINI-MUNDY on STEM Education Research Areas,” online at http://bit.ly/IOcTca, 332 views as of 15 Jan 2014 13:24-0800.
**Graham, K. G., and J. FERRINI-MUNDY. 1989. “An Exploration of Student Understanding of Central Concepts in Calculus,” paper presented at the Annual Meeting of the American Educational Research Association. I’ve not found an online version.
Hake, R.R. 2013. “Can the Cognitive Impact of Calculus Courses be Enhanced?” An update of 26 Dec 2013 of an invited talk of 24 April 2012, Department of Mathematics, University of Southern California, online as a 2.7 MB pdf at http://bit.ly/1loHgC4 and as ref. 70 at http://bit.ly/a6M5y0. The abstract and link are being transmitted to various discussion lists and are also on my blog “Hake'sEdStuff” at http://bit.ly/1jXolD6 with a provision for comments.
**Lauten, D., K. Graham, and J. FERRINI-MUNDY. 1999. “Increasing the Dialogue About Calculus with a Questionnaire” in Assessment Practices in Undergraduate Mathematics [Gold et al. (1999, pp. 237-240)] at http://bit.ly/1e6ShtL.
**SCHMIDT, W. 2011. “Want better math teachers? Train them better, scholar argues?” 09 June; online at http://bit.ly/1bP1V2r.
** SCHMIDT, W. 2012a. “U.S. students need new way of learning science,” 05 April; online at http://bit.ly/1csHB5o.
** SCHMIDT, W. 2012b. “Study supports move toward common math standards,” 05 Nov; online at http://bit.ly/J09KXl.
Schoenfeld, A.H. 2013a. Berkeley Websites: (a) Functions Research Group http://bit.ly/18Aod7R; (b) Algebra Teaching Study http://bit.ly/IJD7g8; (c) Mathematics Assessment Project http://bit.ly/1bNlL8e; (d) Formative Assessment with Computational Technologies (FACT) http://bit.ly/187WA5r; (e) Alan Schoenfeld’s Downloadable Publications http://bit.ly/1ap7pM9.
Sunday, January 13, 2013
Do We Learn All the Math We Need For Ordinary Life Before 5th Grade?
Some blog followers might be interested in a recent post “Do We Learn All the Math We Need For Ordinary Life Before 5th Grade?” [Hake (2013)]. The abstract reads:
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ABSTRACT: In response to my post “Einstein on Testing” [Hake (2013)] at http://bit.ly/UHjqET the following lively exchange was recorded on the archives http://yhoo.it/iNTxrH of EDDRA2 [non-subscribers may have to set up a “Yahoo account” as instructed at http://yhoo.it/iNTxrH]:
a. Literature major and Standardista-basher Susan Ohanian http://www.susanohanian.org/ stated that she (paraphrasing) “never seemed to gain any insight from solving the calculus problems in Courant’s text, which struck her then as plodding and now as without meaning.”
b. Susan Harman then opined (my CAPS) “WE LEARN ALL THE MATH WE NEED FOR ORDINARY LIFE BEFORE 5TH GRADE.”
c. Guy Brandenberg countered by calling attention to David Berlinski’s Tour of the Calculus http://amzn.to/11sZIUv whose publisher states: “Were it not for the calculus, mathematicians would have no way to describe the acceleration of a motorcycle or the effect of gravity on thrown balls and distant planets, or to prove that a man could cross a room and eventually touch the opposite wall.”
d. Then Susan Ramlo pointed that students in her algebra-based physics class “almost always make a comment about how suddenly . . .[[after exposure to the real-world of physics]]. . . much more of calculus makes sense.”
With regard to Harman's opinion that “We Learn All the Math We Need For Ordinary Life Before 5th Grade,” basic to “ordinary life” is motion and change, requiring the rudiments of calculus for proper understanding (see the Bartlett signature quote).
And I agree with Ramlo’s point about students’ better understanding calculus after exposure to the real world of physics. In “Interactive-engagement methods in introductory mechanics courses” at http://bit.ly/aH2JQN I wrote: “the term substantive non-calculus-based mechanics course is an oxymoron.”
***************************************************
To access the complete 13 kB post please click on http://bit.ly/10sYmKl.
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
Twitter: http://bit.ly/juvd52
“The greatest shortcoming of the human race is our inability to understand exponential change.”
- Albert Bartlett http://bit.ly/VpN2pm [I have taken the liberty of substituting “exponential change” for Bartlett's more esoteric “the exponential function.”]
REFERENCES [URL shortened by http://bit.ly/ and accessed on 13 Jan 2013.]
Hake, R.R. 2013. “Do We Learn All the Math We Need For Ordinary Life Before 5th Grade?” online on the OPEN! AERA-L archives at http://bit.ly/10sYmKl. Post of 13 Jan 2013 16:52:01-0800 to AERA-L and Net-Gold. The abstract and link to the complete post are being transmitted to several discussion lists.
*******************************************
ABSTRACT: In response to my post “Einstein on Testing” [Hake (2013)] at http://bit.ly/UHjqET the following lively exchange was recorded on the archives http://yhoo.it/iNTxrH of EDDRA2 [non-subscribers may have to set up a “Yahoo account” as instructed at http://yhoo.it/iNTxrH]:
a. Literature major and Standardista-basher Susan Ohanian http://www.susanohanian.org/ stated that she (paraphrasing) “never seemed to gain any insight from solving the calculus problems in Courant’s text, which struck her then as plodding and now as without meaning.”
b. Susan Harman then opined (my CAPS) “WE LEARN ALL THE MATH WE NEED FOR ORDINARY LIFE BEFORE 5TH GRADE.”
c. Guy Brandenberg countered by calling attention to David Berlinski’s Tour of the Calculus http://amzn.to/11sZIUv whose publisher states: “Were it not for the calculus, mathematicians would have no way to describe the acceleration of a motorcycle or the effect of gravity on thrown balls and distant planets, or to prove that a man could cross a room and eventually touch the opposite wall.”
d. Then Susan Ramlo pointed that students in her algebra-based physics class “almost always make a comment about how suddenly . . .[[after exposure to the real-world of physics]]. . . much more of calculus makes sense.”
With regard to Harman's opinion that “We Learn All the Math We Need For Ordinary Life Before 5th Grade,” basic to “ordinary life” is motion and change, requiring the rudiments of calculus for proper understanding (see the Bartlett signature quote).
And I agree with Ramlo’s point about students’ better understanding calculus after exposure to the real world of physics. In “Interactive-engagement methods in introductory mechanics courses” at http://bit.ly/aH2JQN I wrote: “the term substantive non-calculus-based mechanics course is an oxymoron.”
***************************************************
To access the complete 13 kB post please click on http://bit.ly/10sYmKl.
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
Twitter: http://bit.ly/juvd52
“The greatest shortcoming of the human race is our inability to understand exponential change.”
- Albert Bartlett http://bit.ly/VpN2pm [I have taken the liberty of substituting “exponential change” for Bartlett's more esoteric “the exponential function.”]
REFERENCES [URL shortened by http://bit.ly/ and accessed on 13 Jan 2013.]
Hake, R.R. 2013. “Do We Learn All the Math We Need For Ordinary Life Before 5th Grade?” online on the OPEN! AERA-L archives at http://bit.ly/10sYmKl. Post of 13 Jan 2013 16:52:01-0800 to AERA-L and Net-Gold. The abstract and link to the complete post are being transmitted to several discussion lists.
Friday, December 10, 2010
Seventeen very well-spent minutes with Conrad Wolfram
Some blog followers might be interested in a recent post “Re: Do not pass this by: Seventeen very well-spent minutes with Conrad W” [Hake (2010)]. The abstract reads:
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ABSTRACT: Michael Paul Goldenberg called attention to a video by Conrad Wolfram titled: “Teaching kids real math with computers” http://bit.ly/dUWJuB. Jonathan Groves responded:
“. . . .Conrad Wolfram. . . . gets to one root of the problem with mathematics education: We spend far too much time teaching hand computation and too little time on other aspects of problem solving: interpreting the problem, setting up a mathematical model for the problem, and interpreting the results of the mathematics in light of the problem we are trying to solve.”
Well said, Jonathan Groves!
Wolfram made two points worth elaborating:
(1) teaching hand calculation is still useful as a basis for mental estimation - see e.g., Mahajan's (2010) Street-Fighting Mathematics http://bit.ly/ghF5XY.
(2) Because of its computational complexity, calculus has traditionally been taught very late; but by using computers, calculus concepts are “amenable to a much younger age group.”
In my opinion, programs such as Wolfram’s “Computer-based Math” http://bit.ly/h7V2jX and the Kaput Center’s (2010) “Math In Motion” http://bit.ly/f9jeT5 , if used in K-8, can pave the way for the education of ninth graders in the basic ideas of Newtonian mechanics - thus facilitating Leon Lederman's (2001) “Physics First” http://bit.ly/anddW1.
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To access the complete 13 kB post please click on http://bit.ly/g01zyU .
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 10 Dec 2010.]
Hake, R.R. 2010. “Re: Do not pass this by: Seventeen very well-spent minutes with Conrad W,” online on the OPEN! AERA-L archives at http://bit.ly/g01zyU. Post of 10 Dec 2010 14:02:20-0800 to AERA-L and Net-Gold. The abstract and link to the complete post are also being transmitted to various discussion lists.
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