[net-gold] Is It Possible For Students Who Can Solve Traditional Problems To Lack Conceptual Understanding?
- From: "David P. Dillard" <jwne@xxxxxxxxxx>
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- Date: Tue, 6 Mar 2012 16:32:26 -0500 (EST)
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Date: Mon, 5 Mar 2012 19:42:03 -0800
From: Richard Hake <rrhake@xxxxxxxxxxxxx>
Reply-To: Net-Gold@xxxxxxxxxxxxxxx
To: AERA-L@xxxxxxxxxxxxxxxxx
Cc: Net-Gold@xxxxxxxxxxxxxxx
Subject: [Net-Gold] Is It Possible For Students Who Can Solve Traditional
Problems To Lack Conceptual Understanding?
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ABSTRACT: Math-Teach's Robert Hansen, in his post "An Interesting
Study" <http://bit.ly/xRJ4Nw> wrote (paraphrasing): "Thomas Judson's
study 'High School Calculus in the United States and in Japan'
<http://bit.ly/z13oSx>] shows what I've been asserting all along -
Hake's hypothesis that good students who can solve problems lack
conceptual understanding is BS."
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That "good students who can solve problems lack conceptual
understanding" is NOT the "Hake Hyopothesis" and is NOT "BS," unless
"BS" means something like "Basic Sense." See, for example Kim & Pak's
"Students do not overcome conceptual difficulties after solving 1000
traditional problems" <http://bit.ly/ApWSju>.
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Math-Teach's Robert Hansen [1], in his Math-Teach post "An
Interesting Study" wrote [bracketed by lines "HHHHHH. . . . .", my
insert at ". . . . .[[insert]]. . . . .":
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HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH
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I came across a study that should be done over and over . . . . .
[["High School Calculus in the United States and in Japan" (Judson
[2]).
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Essentially, high performing students in the US and Japan were given
two calculus exams. One exam was filled with conceptual questions
while the second required much more algebraic manipulation.
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Both sets of students did well on the concept exam, and the Japanese
students hadn't even seen these types of problems before.
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The US students did poorly on the algebraic problems while the
Japanese students did well.
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It has been my assertion all along that the notion (the HAKE
HYPOTHESIS) THAT GOOD STUDENTS WHO CAN SOLVE PROBLEMS LACK CONCEPTUAL
UNDERSTANDING IS BS. . . . . .[[My CAPS.]]. . . You don't achieve a
level of acumen without knowing what the heck you are doing.
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HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH
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That "good students who can solve problems lack conceptual
understanding" is NOT the "Hake Hypothesis " and is NOT "BS," unless
"BS" means something like "Basic Sense."
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For example, the abstract of "Students do not overcome conceptual
difficulties after solving 1000 traditional problems"(Kim & Pak [3])
reads as follows:
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"The relation between traditional physics textbook problem solving
and conceptual understanding was investigated. The number of problems
a student solved, as estimated by students themselves, ranged from
300 to 2900 with an average of about 1500. The students did not have
much difficulty in using physics formulas and mathematics. However,
we found that they still had many of the well-known conceptual
difficulties with basic mechanics, and there was little correlation
between the number of problems solved and conceptual understanding.
This result suggests that traditional problem solving has a limited
effect on conceptual understanding."
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Kim & Pak's first two and last paragraphs are [bracketed by lines
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"K&P-K&P-K&P-K&P. . . . .]:
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K&P-K&P-K&P-K&P-K&P-K&P-K&P-K&P-K&P-K&P-K&P-K&P
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Because a major goal of physics teaching and learning is problem
solving, the solution of exercises and problems is a major component
of most physics classes, both in high schools and universities.
Recent research in physics education has demonstrated that many
students retain fundamental conceptual difficulties, even after
instruction.[4-9]
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One possible explanation for this situation is that students "haven't
done enough problems." In Korea, as a result of the particular
procedures for admission to the university, the students in this
study have solved many exercises and problems, an average of 1500, as
part of their preparation. In this paper we investigate whether this
problem solving eliminates the conceptual difficulties found by
researchers elsewhere. The conceptual understanding of these students
was investigated using qualitative questions about basic mechanics .
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. . . . . . . . . . . . . . . . . . . . .
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The result of this investigation provides evidence for the limits of
traditional problem solving. Although traditional problem solving is
an important part of studying to understand physics concepts, some
aspects of conceptual understanding might require other approaches.
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K&P-K&P-K&P-K&P-K&P-K&P-K&P-K&P-K&P-K&P-K&P-K&P
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Of course it's conceivable that e.g., in math education "Students DO
overcome conceptual difficulties after solving 1000 traditional
problems." But, unfortunately, little *substantive* math education
research has been undertaken in this area (please correct me if I'm
wrong).
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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@xxxxxxxxxxxxx>
Links to Articles: <http://bit.ly/a6M5y0>
Links to SDI Labs: <http://bit.ly/9nGd3M>
Blog: <http://bit.ly/9yGsXh>
Academia: <http://iub.academia.edu/RichardHake>
Twitter <https://twitter.com/#!/rrhake>
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REFERENCES [All URL's shortened by <http://bit.ly/> and accessed on
05 March 2012.]
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1. R. Hansen, "An Interesting Study," online on the Math-Teach
archives at <http://bit.ly/xRJ4Nw>. Post of 4 March, 1:32am (2012).
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2. T.W. Judson, "High School Calculus in the United States and in
Japan," NCTM Dialogues, unpublished (undated); online at
<http://bit.ly/z13oSx>.
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3. E. Kim & S-J Pak, "Students do not overcome conceptual
difficulties after solving 1000 traditional problems," Am. J. Phys.
70(7): 759-765 (2002), online to subscribers at
<http://bit.ly/ApWSju>.
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4. A.B. Champagne, L.E. Klopfer, and J.H. Anderson, "Facts
influencing the learning of classical mechanics,'' Am. J. Phys. 48:
1074-1079 (1980); online at <http://bit.ly/zWdbOo>.
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5. J. Clement, "Students' preconceptions in introductory mechanics,"
Am. J. Phys. 50, 66-71 (1982); online as a 430 kB pdf at
<http://bit.ly/xyJ9ta>.
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6. R.F. Gunstone, "Student understanding in mechanics: A large
population survey," Am. J. Phys. 55: 691-696 (1987); online at
<http://bit.ly/zDz2um>.
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7. L.C. McDermott, P.S. Shaffer, and M.D. Somers, "Research as a
guide for teaching introductory mechanics: An illustration in the
context of the Atwood's machine," Am. J. Phys. 62: 46-55 (1994),
online as a 1.2 MB pdf at <http://bit.ly/wU8u9s>.
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8. L.C. McDermott, "Research on conceptual understanding in
mechanics," Phys. Today 37 (7): 24-32 (1984);online at
<http://dx.doi.org/10.1063/1.2916318>.
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9. D. Twigger et al., "The conception of force and motion of students
aged between 10 and 15 years: An interview study designed to guide
instruction," Int. J. Sci. Educ. 16: 215-229 (1994); the first page
is online at <http://bit.ly/A3yrlv>.
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