[net-gold] Psychology Readings for Mathematicians (was Important Website for Mathematics Educators)
- From: "David P. Dillard" <jwne@xxxxxxxxxx>
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- Date: Mon, 1 Feb 2010 16:53:10 -0500 (EST)
.
Date: Mon, 1 Feb 2010 11:51:54 -0800
From: Richard Hake <rrhake@xxxxxxxxxxxxx>
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To: math-teach@xxxxxxxxxxxxx
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Subject: [Net-Gold] Psychology Readings for Mathematicians (was Important
Website for Mathematics Educators)
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ABSTRACT: Mathematics educator Wayne Bishop (2010) stated that in
his college years "ed psych and sociology were two of the most
useless, objective-evidence-free, courses that [he] was obligated to
take." Bill Marsh (2010) responded that Bishop owed himself and
others "a little good reading in good psychology," suggesting the
works of Eleanor or J.J. Gibson, George Miller of "Magic Number
Seven" fame, Peter Bryant, Robbie Case, and Catherine Sophian.
In this post I:
(a) list two other suggestions - "Mathematics Learning in Early
Childhood [Cross et al. (2009)] and "Psychology's role in mathematics
and science education" [Newcombe et al. (2009)], and
(b) break with discussion-list protocol by listing some academic
references to works by the authors suggested by Marsh.
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Mathematics educator Wayne Bishop (2010) wrote (my CAPS):
"How it was when I was in school, specifically my college years training
at a teachers' college to become a high school mathematics teacher, was
that ED PSYCH AND SOCIOLOGY WERE TWO OF THE MOST USELESS,
OBJECTIVE-EVIDENCE-FREE, COURSES THAT I WAS OBLIGATED TO TAKE. Any
competitors were in the education department along with the ed psych
course. I took one real course in the psychology department that was a
useful experience but, except for student teaching, the education
department courses were at best a waste of time."
To which Bill Marsh (2010) replied [bracketed by lines "MMMMM. . .
."; my insert at ". . . . [[insert]]. . . ."]:
MMMMMMMMMMMMMMMMMMMMMMMM
Wayne - Given your commitment to math education, you owe yourself,
and maybe the rest of us, a little good reading in good psychology.
Others may have other suggestions to help you get started. Here are
mine.
For older stuff, I suggest anything by Eleanor or J.J. Gibson or by
George Miller. His ? . . . .[No "?" about it!]]. . . . "The Magic
Number Seven, Plus or Minus Two?" is a classic. For more recent work,
more closely connected to math education, I suggest books and
articles by Peter Bryant, Robbie Case, and Catherine Sophian.
For example, a talk by Eleanor Gibson about how children come to
understand about reversible operations led me to think about
semigroups generated by invertibles and idempotents. A student wrote
a great undergraduate thesis on the topic, with a little help from
me, and a lot from a psychology colleague.
MMMMMMMMMMMMMMMMMMMMMMMM
In the REFERENCES below I list some works by each of the authors
recommended by Marsh. Note that several references are to entries in
Wikipedia. For those distrustful of Wikipedia, please see "In
Defense of Wikipedia" [Hake (2009a)].
Two other suggestions for Bishop's (and others') consideration are
"Mathematics Learning in Early Childhood: Paths Toward Excellence and
Equity" [Cross et al. (2009)] - primarily the work of psychologists,
cognitive scientists, and education specialists rather than
mathematicians - and "Psychology's role in mathematics and science
education" [Newcombe et al. (2009)], especially the section "Early
Understanding of Mathematics."
Richard Hake, Emeritus Professor of Physics, Indiana University
24245 Hatteras Street, Woodland Hills, CA 91367
Honorary Member, Curmudgeon Lodge of Deventer, The Netherlands.
<rrhake@xxxxxxxxxxxxx>
<http://www.physics.indiana.edu/~hake/>
<http://www.physics.indiana.edu/~sdi/>
<http://HakesEdStuff.blogspot.com/>
<http://iub.academia.edu/RichardHake>
REFERENCES [With apologies to reference detester Michael Paul
Goldenberg. Tiny URL's courtesy <http://tinyurl.com/create.php>. All
URL's accessed on 1 Feb 2010.]
Bishop, W. 2009. Re: Important Website for Mathematics Educators,"
Math-Teach post of Jan 22, 2010 12:35 AM; online at
<http://mathforum.org/kb/message.jspa?messageID=6955058&tstart=0>
Hake, R.R. 2009a. "In Defense of Wikipedia (was Mathematics Learning
in Early Childhood)," online on the OPEN ! AERA-L archives at
<http://tinyurl.com/m5xpu9>. Post of 31 Aug 2009 16:41:53 -0700 to
AERA-L, Net-Gold, and MathTeach. Abstract only to various discussion
lists. The abstract is also online with a provision for comments at
<http://hakesedstuff.blogspot.com/search/label/Wikipedia>.
Marsh, B. 2010. Re: Important Website for Mathematics Educators,"
Math-Teach post of Jan 23, 2010 5:33 PM, online on the OPEN!
Math-Teach archives at
<http://mathforum.org/kb/thread.jspa?threadID=2031349&tstart=15>
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PETER BRYANT
Nunez, T. & P. Bryant. 1996. "Children Doing Mathematics
(Understanding Children's Worlds)." Wiley-Blackwell. Amazon.com
information at <http://tinyurl.com/yjd2x68>. Note the seachable
"Look Inside" feature.
Bryant, P.E. 1974. "Perception and Understanding in Young Children:
An Experimental Approach" Basic Books. Amazon.com information at
<http://tinyurl.com/y9oqo2r>.
Bryant, P.E. 1982. "The role of conflict and of agreement between
intellectual strategies in children's ideas about measurement,"
British Journal of Psychology 73: 242-251.
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ROBBIE CASE . . . .[[ for a listing of books by Robbie Case, see
<http://openlibrary.org/a/OL768208A/Robbie_Case>]
Case, R. 1985. "Intellectual Development: Birth to Adulthood."
Academic Press. Amazon.com information at
<http://tinyurl.com/yejdzwg>.
Case, R., & S. Griffin. 1990. "Child cognitive development: The role
of central conceptual structures in the development of scientific and
social thought," in E.A. Hauer, ed. "Developmental Psychology:
Cognitive, Perceptuo-Motor, and Neurological Perspectives (pp.
193-230). Elsevier Science.
*********************
Case, R., ed. 1992. "The Mind's Staircase: exploring the conceptual
underpinnings of children's thought and knowledge." Psychology Press.
Amazon.com's information at <http://tinyurl.com/yajrnyx> carries
these comments:
(a) from the "American Journal of Psychology": " 'The Mind's
Staircase' is a remarkable book presenting Case's attempt to take
into account a thoroughly alien set of perspectives and results and
generate a new model that could integrate and account for results
across the entire span of consideration -- in particular, both
domain-general and domain-specific aspects of development. Case ends
up with a model that seems to have just the right integrations and
differentiations to be able to handle both specificity and generality
of development."
(b) from the "Product Description": "The shortcomings of Piaget's
theory of intellectual development are well-known. Less clear is what
sort of theory should be devised to replace it. This volume describes
the current 'main contenders,' including neo-Piagetian,
neo-connectionist, neo-innatist and sociocultural models. Its
contributors conclude that none of these models are adequate because
each one implies a view of the human mind which is either too
general, too particular, or too modular. A collaborative program of
research -- seven years in the making -- is then described, which
gives support to a newly emerging synthesis of these various
positions.
*********************
Case, R., and Y. Okamoto. 1996. "The role of central conceptual
structures in the development of children's thought." Monographs of
the Society for Research in Child Development, 61(Serial No. 246,
Nos. 1-2).
Case, R., S. Griffin, & W.M. Kelly. 1999. "Socieconomic gradients in
mathematical ability and their responsiveness to intervention during
early childhood," in D.P. Keating and C. Hertzman, eds.
"Developmental Health and the Wealth of Nations" (pp. 125-149).
Guilford.
Griffin, S., R. Case, & R.S. Siegler. 1994. "Classroom lessons:
Integrating cognitive theory and classroom practice," in K. McGilly,
ed., "Rightstart: Providing the Central Conceptual Prerequisites for
First Formal Learning of Arithmetic to Students at Risk for School
Failure" (pp. 25-50). Cambridge, MA: MIT Press.
Griffin, S., R. Case, & A. Capodilupo. 1995. "Teaching for
understanding: The importance of the central conceptual structures in
the elementary mathematics curriculum," In A. McKeough, J. Lupart,
and A. Marini, eds. "Teaching for Transfer: Fostering Generalization
in Learning" (pp. 121-151). Erlbaum.\
Griffin, S., & R. Case. 1997. "Re-thinking the primary school math
curriculum: An approach based on cognitive science," Issues in
Education 3: 1-49.
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ELEANOR & J.J. GIBSON
Gibson, E.J., J.J. Gibson, A.D. Pick, and H. Osser, 1962. "A
developmental study of the discrimination of letter-like forms,"
Journal of Comparative and Physiological Psychology 55: 897-906.
Gibson, E.J. 1969. "Principles of Perceptual Learning and
Development." Prentice Hall. Amazon.com information at
<http://tinyurl.com/yapgnhl>. [Erroneously referenced as "Principles
and Perceptions of Learning Development" in Cross et al. (2009).
Gibson, E.J. 1991. "An Odyssey in Learning and Perception (Learning,
Development, and Conceptual Change)." MIT Press; the publisher's
information at
<http://mitpress.mit.edu/catalog/item/default.asp?tid=9043&ttype=2>
carries this endorsement by Ulric Neisser: "Eleanor Gibson is surely
the most distinguished developmental psychologist in the world. Her
work has transformed our conceptions of the origins of mental life."
Amazon.com information at <http://tinyurl.com/yfb7gzd>. See also
the Encyclopedia of Psychology's entry on Gibson by Skinner (2001).
Gibson, E.J. 2001. "Perceiving the Affordances: A Portrait of Two
Psychologists." Routledge; publisher's information at
<http://www.routledge.com/9780805839494>, wherein it is stated: "
'Perceiving the Affordances' is a personal history and intellectual
autobiography of Eleanor Gibson, the groundbreaking research
psychologist who was influential in the founding of the theory of
perceptual development. It is also a biography of her husband, James
J. Gibson, who was a major perceptual theorist and the founder of the
ecologically-oriented theory of perception. This is the story of
their lives together and how each came to make particular
contributions. This book is of interest to people who study
perception, perceptual development, infancy, developmental
psychology, and the history of psychology." Note the "View Inside"
feature. Amazon.com information at <http://tinyurl.com/y9lx3vg>.
Note the searchable "Look inside" feature.
Gibson, E.J. & A.D. Pick. 2003. "An Ecological Approach to Perceptual
Learning and Development." Oxford University Press; publisher's
information at <http://tinyurl.com/yc7acy6>. Amazon.com information
<http://tinyurl.com/yasvezb>. A Google book preview is online at
<http://tinyurl.com/yjefbc9>.
Skinner, P. 2001. "Gibson, Eleanor J. (1910- )" Encyclopedia of
Psychology, 6 April, online at
<http://findarticles.com/p/articles/mi_g2699/is_0004/ai_2699000482>.
Wikipedia. 2010b. "Eleanor J. Gibson," online at
<http://en.wikipedia.org/wiki/Eleanor_J._Gibson>.
Wikipedia. 2010c. "J. J. Gibson," online at
<http://en.wikipedia.org/wiki/J._J._Gibson>.
****************************************************
GEORGE MILLER
Miller, G.A. 1956. "The magical number seven, plus or minus two: Some
limits on our capacity for processing information". Psychological
Review 63 (2): 81-97; online as a 96 kB pdf at
<http://tinyurl.com/3b5rat>. See also Wikipedia (2010).
Wikipedia. 2010a. "The Magical Number Seven, Plus or Minus Two,"
online at
<http://en.wikipedia.org/wiki/The_Magical_Number_Seven,_Plus_or_Minus_Two>.
Wikipedia. 2010b "George Armitage Miller ", online at
<http://en.wikipedia.org/wiki/George_Armitage_Miller>
****************************************************
CATHERINE SOPHIAN
Sophian, C., ed. 1984. "The Origins of Cognitive Skills: The 18th
Annual Carnegie Mellon Symposium on Cognition" Psychology Press.
Amazon.com information at <http://tinyurl.com/ycf94jl>.
Sophian, C. 1988. "Early developments in children's understanding of
number: Inferences about numerosity and one-to-one correspondence,"
Child Development 59: 1397-1414.
Sophian, C., D. Garyantes, & C. Chang. 1997. "When three is less than
two: Early development in children's understanding of fractional
quantities," Developmental Psychology 33: 731-744.
Sophian, C., and C. Kailihiwa 1998. "Units of counting: Developmental
changes," Cognitive Development 13: 561-585.
Sophian, C. 2002. "Learning about what fits: Preschool children's
reasoning about effects of object size," Journal for Research in
Mathematics Education 33: 290-302.
Sophian, C. 2004. "Mathematics for the future: Developing a Head
Start curriculum to support mathematics learning." Early Childhood
Research Quarterly 19(1): 59-81.
Sophian, C. 2007. "Rethinking the starting point for mathematics
learning." in O.N. Saracho and B. Spodek, eds. "Contemporary
Perspectives in Early Childhood Education: Mathematics, Science, and
Technology in Early Childhood Educatio" (pp. 21-44). Information Age.
Sophian, C. 2009. "The Origins of Mathematical Knowledge in
Childhood." Routledge; publisher's information at
<http://tinyurl.com/yftjq5z>. Amazon.com information at
<http://tinyurl.com/ydxnk4k>.
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TWO OTHER SUGGESTIONS
Cross, C.T., T.A. Woods, & H. Schweingruber, eds. 2009. "Mathematics
Learning 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> -
primarily the work of psychologists, cognitive scientists, and
education specialists rather than mathematicians. See also Hake
(2009b).
Hake, R.R. 2009b. "Mathematics Learning in Early Childhood," online
on the OPEN! AERA-L archives at <http://tinyurl.com/yhsnwzq>. Post of
27 Jul 2009 16:02:41-0700 to AERA-L, Math-Teach, & PhysLnrR; abstract
only to various discussion lists. The abstract is also online with a
provision for comments at
<http://hakesedstuff.blogspot.com/2010/01/
science-and-mathematics-learning-in.html>
Newcombe, N.S., N. Ambady, J. Eccles, L. Gomez, , D. Klahr, M. Linn,
K. Miller, & K. Mix . 2009). "Psychology's Role in Mathematics and
Science Education." American Psychologist 64(6): 538-550; online at
<http://www.psy.cmu.edu/faculty/klahr/personal/pubs.htm>.
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