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.

Mathematics Learning in Early Childhood

Some blog followers may be interested in a recent discussion-list post of the above title [Hake (2009). The abstract reads:

ABSTRACT: “Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity" [Cross et al. (2009)] may be of interest to math/science educators. Since, during July 2009, there had been over 70 Math-Teach posts on the thread "Kamii's Articles on Algorithms in Arithmetic,” I searched for “Kamii” on the online version of Cross et al. (2009)] to find references to: (a) “Young Children Reinvent Arithmetic: Implications of Piaget's Theory” [Kamii & Housman (2000)], (b) “Measurement of length: The need for a better approach to teaching” [Kamii & Clark (1997], and (c) “The development of logico-mathematical knowledge in block building activity at ages 1-4” [Kamii, Miyakawa, & Kato (2004)].

According to her website, Constance Kamii studied under Jean Piaget, on and off for 15 years. Wikipedia http://en.wikipedia.org/wiki/Constance_Kamii states that Kamii's ideas influenced the NCTM standards.

Incidentally, judging from the end-of-chapter references in Cross et al., early childhood mathematics is currently more the province of psychologists, cognitive scientists, and education specialists than mathematicians. However, mathematicians might have much to offer, witness the contributions of physicist Robert Karplus to early childhood science instruction.

To access the complete 25 kB post please click on http://tinyurl.com/luayng .

REFERENCES

Cross, C.T., T.A. Woods, & H. Schweingruber, eds. 2009. MathematicsLearning in Early Childhood: Paths Toward Excellence and Equity, Committee on Early Childhood Mathematics; National Academies Press; online at http://www.nap.edu/catalog.php record_id=12519#toc.

Hake, R.R. 2009. “Mathematics Learning in Early Childhood,” online on the OPEN! AERA-L archives at http://tinyurl.com/luayng and also on the Math-Teach archives at http://mathforum.org/kb/thread.jspa?threadID=1969919&tstart=0 . Post of 27 Jul 2009 16:02:41-0700 to AERA-L, Math-Teach, Net Gold, & PhysLnrR. In addition the abstract was transmitted to various discussion lists.