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ABSTRACT: John Mallinckrodt (2008), in a recent PhysLrnR post called
attention to his 2002 Phys-L post "Re: Kinematics First," in which
he wrote ". . . . Newton himself didn't understand acceleration." In
addition: (a) Steinberg, Brown, & Clement (1990) have shown that
Newton encountered conceptual difficulties which were difficult for
him to overcome before he wrote the "Principia," (b) Reif (1995)
reported that some Berkeley physics professors have had trouble with
the concept of acceleration.
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John "Slo" Mallinckrodt (2008) in his PhysLrnR post of 10 Oct 2008
titled "'Acceleration' (was Re: Outrageous error in IPC text - may I
be the poor devils' advocate?)" wrote: [my inserts at ". . . .
[insert]. . . . "]
"I agree with George Nickas. . . .[(2008)]. . . about the likely
pedagogical advantage of avoiding the word "acceleration" and any
discussion whatsoever of 'rates of change of velocity' as long as
possible. I would point interested readers to a number of posts I
have made to the Phys-L and PHYSHARE lists on this point over the
years. . . . .[ Mallinckrodt (2002a,b,c; 2003)]. . . . . . . . . . .
. . . . . . . . . . . . . . . . . . We often say that Newton
expressed his second law as F = dp/dt, but this is simply not the
case. According to Cajori . . . [(1934)]. . . .. . . he [Newton]
wrote 'The change of motion is proportional to the motive force
impressed; and is made in the direction of the right line in which
that force is impressed'--i.e., 'delta p = integral of F dt.' "
In "Re: Kinematics First" [Mallinckrodt (2002c)], John wrote [My CAPS]:
"In recent years I've been going around spouting off my own perhaps
marginally hyperbolic observation that NEWTON HIMSELF DIDN'T
UNDERSTAND ACCELERATION. I believe that a careful reading of the
Principia will reveal that Newton never got very far beyond the idea
of impulse and momentum. Newton's second and third laws are
explicitly about impulses ("action" to Newton) and changES in
momentum ("motion" to Newton), NOT forces and changING velocity--a
subtle but critically important distinction IMO."
And Steinberg, Brown, & J.J. Clement (1990)] in their abstract for
"Genius is not immune to persistent misconceptions: conceptual
difficulties impeding Isaac Newton and contemporary physics
students," document Newton's PRE-Principia conceptual difficulties:
Their abstract reads [bracketed by lines "SBC-SBC-SBC-. . . ."]:
SBC-SBC-SBC-SBC-SBC-SBC-SBC-SBC-SBC-SBC-SBC
Recent research has shown that serious misconceptions frequently
survive high-school and university instruction in mechanics. It is
interesting to inquire whether Newton himself encountered conceptual
difficulties before he wrote the "Principia." Did he have serious
difficulties? (b) If so, were they difficult to overcome? We shall
present evidence from Newton's writings of affirmative answers to
both questions.
Newton's development of his system of mechanics was hampered by a
persistent belief in 'the force of a [moving] body' from 1664 to
1685. His belief in centrifugal force was an additional restraining
factor that remained intact until Hooke's intervention in 1679 and
weakened only gradually over the next two years. Three additional
years passed before the resulting successes weakened his commitment
to impetus sufficiently to permit conceptualization of mass as an
inert surrogate.
This paper will compare Newton's pre-"Principia" beliefs with those
of contemporary students in the areas of impetus force and
centrifugal force. We shall emphasize the retarding effect on
Newton's development of inappropriate but deep-seated models at a
*qualitative level*, and the extent to which his experience suggests
THE NECESSITY FOR STUDENTS TO *STRUGGLE* CONCEPTUALLY IN ORDER TO
CONSTRUCT THE MODELS EMPLOYED BY PHYSICISTS. [My CAPS.]
SBC-SBC-SBC-SBC-SBC-SBC-SBC-SBC-SBC-SBC-SBC
One may not be too surprised by Newton's 17th century problems with
motion - see the Butterfield signature quote. But even some
modern-day Berkeley physics professors. . . (but surely not Indiana
University physics professors ;-) ) have had difficulty with the
concept of acceleration. Fred Reif (1995) in his 1994 Millikan
Lecture "Understanding and teaching important scientific thought
processes" wrote [my inserts at ". . . .[insert]. . . .". ]:
RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR
. . . .[Acceleration]. . . . is a very basic concept, of fundamental
importance in Newtonian mechanics and commonly taught at the
beginning of any introductory physics course. The concept is
specified by its familiar definition that "acceleration is the rate
of change of the velocity with time," a statement which can be
summarized by the equation a = dv/dt . . . .[where a and v are
*vectors*] . . . . .
Someone able to interpret the concept of acceleration should be able
to identify the acceleration of a particle in various specific cases,
such as . . . . . . an oscillating pendulum bob which is momentarily
at rest at the extreme point A of its circular arc, passes the point
B with increasing speed, reaches its maximum speed at its lowest
point C where the string is vertical, continues past the point C, and
is again momentarily at rest at the point E.
In a study carried out by me and some co-workers, we presented 15
specific situations. . . [such as the pendulum bob] . . . to
various persons and observed their responses in detail. The person
was asked to specify whether the acceleration is zero at the
indicated points, or to specify it direction if it is non-zero.
The observed individuals were either students or professors at the
University of California at Berkeley. The students, enrolled in an
introductory college physics course for prospective scientists or
engineers, had been working with acceleration for at least two
months. The professors had all taught an introductory physics course
in the recent past.
The main result of this study (discussed at length by Reif and Allen
(1992) were the following. The students could answer correctly at
most only 35% of such questions. THE PROFESSORS WERE VERY MUCH
BETTER, BUT NOT PERFECT. (For example, one of them answered
correctly only 10 of the 15 questions. [My CAPS.]
RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR
For a Socratic Dialogue Inducing (SDI) experiment on the oscillating
pendulum bob that; consistent with the advice of Steinberg, Brown, &
Clement; requires "students to *struggle* conceptually in order to
construct the models employed by physicists," see Section VIII
"Motion of a Pendulum Bob" on pages 25-31 of SDI Lab #2 "Newton's
Second Law" [Hake (1998)].
B. Clement has recently published two books that may be of interest
to scientists and educators:
1. "Creative Model Construction in Scientists and Students: The Role
of Imagery, Analogy, and Mental Simulation" [Clement (2008)]: a
monograph developing a theory of creativity and imagery-based
conceptual learning in science, developed through his research using
think-aloud protocols from experts and students.
2. "Model Based Learning and Instruction in Science" [Clement &
Ramirez (2008)]: a collection of chapters by Clement's research team
describing new, model-based teaching methods for science instruction.
"Of all the intellectual hurdles which the human mind has confronted
and has overcome in the last fifteen hundred years the one which
seems to me to have been the most amazing in character and the most
stupendous in the scope of its consequences is the one relating to
the problem of motion."
Herbert Butterfield (1949)
REFERENCES
Butterfield, H. 1949. "The Origins of Modern Science." Available in a
1997 Free Press edition. Amazon.com information at
<http://tinyurl.com/4qk3kc>. Note the "Search Inside" feature.
Cajori. F. 1934. "Sir Issac Newton's Mathematical Principles of
Natural Philosophy and His System of the World," revision of Motte's
1729 English translation Univ. of California Press. [This according
to Chirnside (1996).] Incidentally, I was directed by
<http://en.wikipedia.org/wiki/Philosophiae_Naturalis_Principia_Mathematica>
to an ONLINE 75 MB pdf <http://tinyurl.com/4jdsra>: the first
American edition of the Principia (to which is added "Newton's System
of the World") translated by Andrew Moote and published by Daniel
Adee in 1845.
Clement, J.J. 1982. "Students' preconceptions in introductory
mechanics," Am. J. Phys. 50(1), 66-71; online at
<http://tinyurl.com/45k2su> (420kB).
Clement, J.J. 2008. "Creative Model Construction in Scientists and
Students: The Role of Imagery, Analogy, and Mental Simulation."
Springer. Publisher's information at <http://tinyurl.com/5xsgr9>.
Amazon.com information at <http://tinyurl.com/479q9u>. Note the "Look
Inside" feature.
Clement, J.J, & M.A. Rea-Ramirez, eds. 2008. "Model Based Learning
and Instruction in Science." Springer. Publisher's information at
<http://tinyurl.com/53v239>.
Amazon.com information at <http://tinyurl.com/3kbuc9> Note the "Look
Inside" feature.
Hake, R.R. 1992. "Socratic Pedagogy in the Introductory Physics
Laboratory," Phys. Teach 30: 546-552; updated version (4/27/98) at
<http://www.physics.indiana.edu/~sdi/SocPed1.pdf> (88 kB).
Mallinckrodt, J. 2002b. "Third Law or Conservation of Momentum? (was
Re: Hand, brick, which breaks <g>?" Physhare post of 27 Jul 2002
10:50:46-070; online at <http://tinyurl.com/3jucdo>.
Mallinckrodt, J. 2008. "'Acceleration' (was Re: Outrageous error in
IPC text - may I be the poor devils' advocate?)" PhysLrnR post of 10
Oct 2008 10:48:21-0700; online at <http://tinyurl.com/3ml3f5>.
Nicas, G. 2008. "Re: Outrageous error in IPC text - may I be the poor
devils'advocate?" PhysLrnR post of 10 Oct 2008 12:23:14-0400; online
at <http://tinyurl.com/4acdwu>.
Steinberg, M.S., D.E. Brown, and John J. Clement (of Massachusetts,
not the physics discussion list John M. Clement of Texas). 1990.
"Genius is not immune to persistent misconceptions: conceptual
difficulties impeding Isaac Newton and contemporary physics
students," Int. J. Sci. Ed. 12(3): 265-273; online at
<http://www-unix.oit.umass.edu/%7Eclement/pdf/genius.pdf> (588 kB),