A crucial question in science/math education in K-16 is: "What's
'Developmentally Appropriate'?" This seems to be an interdisciplinary
problem cutting across cognitive science (including developmental
psychology), education, math, and scientific disciplines. Many of the
posts on the PhysLrnR
<http://listserv.boisestate.edu/archives/physlrnr.html> threads
"Active learning in theory, active learning in practice, or both?"
and "Children learning science" concern this issue.
[Paradoxically for a list that seeks to promote physics-education
research and disseminate its results, one must subscribe to PhysLnrR
to access its archives, but that can be done in a minute or so by
going to the archives, clicking on "Join the list or change settings"
and then subscribing. Busy people may wish to subscribe in the NOMAIL
option under "Miscellaneous" since then, as subscribers they may
access the archives or post at any time, while receiving NO MAIL from
the list.]
The internet offers a means of communicating across the barriers
which now separate disciplinary areas [Hake (1999)]. As an example, I
recently heard privately from computers-in-education pioneer Alan Kay
(1991) [see <http://www.viewpointsresearch.org/alan.html> and VRI
(2003)], a member of the NRC's Committee on Undergraduate Science
Education (CUSE) responsible for the McCray et al. (2003) report.
Kay wrote (quoted by permission; bracketed by lines "KKKKKKKKK. . . ."):
KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK
My experience with children over the last 30 years or so seems to
show that Piaget was in the ballpark in several important areas, but
that much more is known now about what very young children can do.
An important 2nd order to Piaget is Jerome Bruner's
<http://www.law.nyu.edu/faculty/profiles/bios/brunerj_bio.html>
recharacterization of the "stages" as "multiple (and parallel) ways
of knowing" [c.f. various Bruner books, including "Toward A Theory of
Instruction" [Bruner (1974)], see also Bruner 1977, 1979, 1990,
1996)]. I have found Bruner's ideas to be extremely helpful over the
years, and much more so than Piaget's. Also, Vygotsky [1978] has been
very helpful, especially his careful study of how children form
concepts.
Also, though the progression of Bruner's (1974)
"enactive-iconic-symbolic" progression of learning representations
[for a discussion see e.g., Gardner (1991)] seems to hold up pretty
well, the transition ages from one way of knowing to another can vary
tremendously, especially in rich environments with special care in
how concepts are represented. For example, I have observed a very
talented 1st grade teacher - Julia Nishijima - teach the deep ideas
of the differential and integral calculus to her 6 year olds with
100% success. She was able to do this because she chose
representations that the children could deal with [such
as >progressions of addition rather than multiplications -- what
computer folks call DDA's ("Digital Differential Analysers").
We have been able to consistently help 5th graders observe falling
objects, take videos of the phenomena, bring the videos into our
Squeak system [see at <http://www.squeakland.org> (for children), and
<http://squeak.org/> (for experts)], extract every 5th frame, line
them up, measure the differential velocities, and build a "constant
acceleration" script that matches a simulated falling object
"exactly" to the video. This project has a well-known and high
failure rate in college students. We found some interesting "Piaget
artifacts" in many of the children, but also found ways to bypass the
important perception problems and help the children "see more
clearly" what was actually going on.
One of the big differences in our success is that we use a
representation for dynamics that matches up well with how the
5th >graders are able to think. It's not the same as older children
and adults, but there are different ways of approaching abstractions
than just the classical ways. It is very likely that most college
students also need a different way to represent mathematical ideas --
especially for dynamics -- before being drowned in the
classical/historical forms.
KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK
"The best way to predict the future is to invent it."
Alan Kay
REFERENCES
Bruner, J.S. 1974. "Toward A Theory of Instruction." Norton.>
Bruner, J.S. 1977. "The Process of Education," Harvard University Press.
Bruner, J.S. 1979. "On Knowing: Essays for the Left Hand," Harvard
University Press.
Bruner, J.S. 1990. "Acts of Meaning," Harvard University Press.
Bruner, J.S. 1996. "The Culture of Education," Harvard University Press.
Gardner, H. "The Unschooled Mind: How Children Think & How Schools
Should Teach." Basic Books, esp. p. 77: "the discovery of the waves
of symbolization. . . shows encouraging correspondence with other
reported pictures of symbolization put forth by major theorists. For
instance, it is reminiscent of Jerome Bruner's suggestive sequence of
enactive (read "sensorimotor", iconic (read "topological"), and
symbolic (read "arbitrary" or "conventional") forms of
representation."
Hake, R.R. 1999. "What Can We Learn from the Biologists About
Research, Development, and Change in Undergraduate Education?" AAPT
Announcer 29(4): 99; online as ref. 7 at
<http://www.physics.indiana.edu/~hake>. The potential of the web for
promoting interdisciplinary synergy in education reform is
emphasized and schematically pictured on page 3.
Kay, A. 1991. "Computers, Networks, and Education," Scientific
American. September, pp: 138-148.
McCray, R.A., R.L. DeHaan, J.A. Schuck, eds. 2003. "Improving
Undergraduate Instruction in Science, Technology, Engineering, and
Mathematics: Report of a Workshop" Committee on Undergraduate STEM
Instruction," National Research Council, National Academy Press;
online at <http://www.nap.edu/catalog/10711.html>. Physicists
attending the workshop were Paula Herron, Priscilla Laws, John
Lehman, Ramon Lopez, Richard McCray, Lillian McDermott, Carl Wieman,
and Jack Wilson.
VRI. 2003. Viewpoints Research Institute; online at
<http://www.viewpointsresearch.org/about.html>: "Many who believe in
'progressive education' do not understand the need for thresholds of
achievement (below which nothing much of importance has happened
within the child). The other main faction -- Back to Basics -- wants
thresholds, but misunderstand mathematics and science to the point
that neither of these subjects is even presented in school."
Vygotsky, L.S. 1978. "Mind in society: the development of higher
psychological processes," ed. by M. Cole, V. John-Steiner,
S. Scribner, & E. Souberman. Harvard Univ. Press.