In a recent Math-Learn post Paul Tanner (2003) wrote:
"I would love to see research on the question of to what degree
pedagogies discriminate on the basis of natural ability, given fixed
content standards of different levels. One point of interest would be
comparisons of intelligence distributions with achievement distributions."
Research similar to that which Tanner would love to see for math
education has been carried out for physics education. In Hake (2003a)
I wrote [bracketed by lines "HHHHHHHHHHHH. . . ."]:
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. . . . as explained in Hake (2002b,c) some teachers may be
interested in single student g's [normalized gains on standardized
tests] in order to examine possible correlation of g with e.g.,
gender, math proficiency, spatial visualization ability, scientific
reasoning skills, physics aptitude, personality type, motivation,
socio-economic level, ethnicity, completion of other courses, IQ, &
GPA. Work of this sort has been reported by Hake et al. (1994), Hake
(2002c), and Meltzer (2002a,b). One of the goals of such effort is to
discover student-profile characteristics or diagnostic tests that
might alert teachers to potential low-g students. If such were known
then corrective actions might be taken early in the course so as to
improve the overall effectiveness of the course.
HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH
BUT MATHEMATICIANS HAVE FAILED TO PRODUCE STANDARDIZED TESTS THAT ARE
WIDELY REGARDED AS VALID AND CONSISTENTLY RELIABLE and hence usable
in a pre/post test mode to measure single student learning gains in
terms of normalized gains "g." Therefore, as far as I know, the
research of the type indicated above for physics is not easily
accomplished in math [the same can be said for most other disciplines
- thanks in part to the baleful influence of the NRC's education
committees as detailed in Hake (2003b)]. Again, quoting from Hake
(2003a) and with apologies for the repetition:
HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH
As indicated in an earlier post (Hake 2003b), Chris [a math teacher]
is handicapped by the failure of mathematicians to develop valid and
consistently reliable tests of mathematical understanding and to
employ pre/post testing with such tests to gauge the need for and
effects of reform teaching methods. Instead, most mathematicians are
content to engage in math-wars rhetoric that seems to reflect
primarily different value systems (Sowder 1998). In the meantime
under the "direct instruction" mantra [see e.g., Carnine (2000)]
student understanding (as opposed to rote memorization) of math [and
science - see e,g, CCCSC (2003)] in California (and most other
states) continues to deteriorate.
HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH
"...a new scientific truth does not triumph by convincing its opponents and
making them see the light, but rather because its opponents eventually die,
and a new generation grows up that is familiar with it."
- Max Planck
REFERENCES
Carnine, D. 2000. "Why Education Experts Resist Effective Practices
(And What It Would Take to Make Education More Like Medicine),"
online as a 52kB pdf at
<http://www.edexcellence.net/foundation/global/found.cfm?author=72&keyword=&submit=Search>.
The Fordham Foundation's Chester Finn introduces Carnine's paper by
stating that: "After describing assorted hijinks in math and reading
instruction, Doug devotes considerable space to examining what
educators did with the results of "Project Follow Through," one of
the largest education experiments ever undertaken. This study
compared constructivist education models with those based on direct
instruction. One might have expected that, when the results showed
that direct instruction models produced better outcomes, these models
would have been embraced by the profession. Instead, many education
experts discouraged their use."
CCCSC. 2003. "Criteria For Evaluating K-8 Science Instructional
Materials In Preparation for the 2006 Adoption," California
Curriculum Commission Science Committee (CCCSC). Outlined from
CCCSC's serial listing by R.R. Hake on 10 November 2003; online as
ref. 33 at <http://www.physics.indiana.edu/~hake>.
Hake, R.R., R. Wakeland, A. Bhattacharyya, and R. Sirochman. 1994.
"Assessment of individual student performance in an introductory
mechanics course," AAPT Announcer 24(4): 76.
Hake, R.R. 2002a. "Lessons from the physics education reform effort,"
Conservation Ecology 5(2): 28; online at
<http://www.consecol.org/vol5/iss2/art28>. Conservation Ecology is a
free "peer-reviewed journal of integrative science and fundamental
policy research" with about 11,000 subscribers in about 108 countries.
Hake, R.R. 2002b. "Assessment of Physics Teaching Methods,
Proceedings of the UNESCO-ASPEN Workshop on Active Learning in
Physics, Univ. of Peradeniya, Sri Lanka, 2-4 Dec. 2002; also online
as ref. 29 at
<http://www.physics.indiana.edu/~hake/>.
Hake, R.R. 2002c. "Relationship of Individual Student Normalized
Learning Gains in Mechanics with Gender, High-School Physics, and
Pretest Scores on Mathematics and Spatial Visualization," submitted
to the Physics Education Research Conference; Boise, Idaho; August
2002; online as ref. 22 at <http://www.physics.indiana.edu/~hake>.
Meltzer, D.E. 2002a. "The relationship between mathematics
preparation and conceptual learning gains in physics: A possible
'hidden variable' in diagnostic pretest scores," Am. J. Phys. 70(12):
1259-1268; also online as article #7 at
<http://www.physics.iastate.edu/per/articles/index.html>.
Sowder, J.T. 1998. "What are the 'Math Wars' in California All About?
Reasons and Perspectives" Phi Beta Kappa Invited Lecture; online at
<http://mathematicallysane.com/analysis/mathwars.asp>: "I will
discuss today the ways that I see these two sides differing: They
hold different beliefs about what mathematics is, different beliefs
about how mathematics is learned, different understandings of what it
means to know mathematics, and different ways of interpreting what
research has to tell us on these issues. In a nutshell, THEY
REPRESENT DIFFERENT VALUE SYSTEMS. I believe that rational,
reflective discussion and exploration of these issues can bring the
two sides closer together. Thus, although the two sides may not reach
total agreement, they can come to understand the issues better and
find ways to compromise. I am told that California schools educate
one-seventh of the students in this country. THERE IS TOO MUCH AT
STAKE TO CONTINUE THE FIGHTING, to take a chance on sacrificing the
mathematical education of our children by not reaching some agreement
on what that education should be." (My CAPS.)
Tanner, P. 2003. "Pedagogy and Natural Ability (was Inquiry Method
and Motivation)," Math-Learn post of Wed Nov 26, 2003 10:46pm (no
time zone indicated!); online at
<http://groups.yahoo.com/group/math-learn/message/5010>.