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[Phys-l] Understanding Motion: Even Newton and Berkeley Physics Professors Have Had Trouble (was "Acceleration . . . . ."

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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.

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-. . . ."]:

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.]

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]. . . .". ]:

. . . .[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.]

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)].

Incidentally according to information at John J. Clement's homepage <>:

A. Many of Clement's articles, including the classic "Students' preconceptions in introductory mechanics" [Clement (1982)] are now online at <>.

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.

Richard Hake, Emeritus Professor of Physics, Indiana University
24245 Hatteras Street, Woodland Hills, CA 91367
Honorary Member, Curmudgeon Lodge of Deventer, The Netherlands.

"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)

Butterfield, H. 1949. "The Origins of Modern Science." Available in a 1997 Free Press edition. information at <>. 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 <> to an ONLINE 75 MB pdf <>: 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.

Chirnside, D. 1996. "Principia." Phys-L post of 4 Oct 1996 20:51:54 +1200; online at <>.

Clement, J.J. 1982. "Students' preconceptions in introductory mechanics," Am. J. Phys. 50(1), 66-71; online at <> (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 <>. information at <>. 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 <>. information at <> 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 <> (88 kB).

Hake, R.R. 1998. "SDI LAB #2. Newton's Second Law," online at <> (233 kB). See also Hake (1992).

Mallinckrodt, J. 2002a. "Re: Newton's Second Law of Motion," Phys-L post of 9 Apr 2002 06:17:18-0800; online at

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 <>.

Mallinckrodt, J. 2002c. "Re: Kinematics First," Phys-L post of 17 Sep 2002 06:56:25-0700; online at <>.

Mallinckrodt, J. 2003. "Re: transfer of momentum," Phys-L post of 19 Nov 2003 08:28:59-0800; online at <>.

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 <>.

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 <>.

Reif, F. & S. Allen. 1992. "Cognitions for interpreting scientific concepts: A study of acceleration," Cogn. Instruct. 9: 1-44; an abstract is online at <>.

Reif, F. 1995. "Millikan Lecture 1994: Understanding and teaching important scientific thought processes," Am. J. Phys. 63(1): 17-32; online to subscribers at

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
<> (588 kB),