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Cognition, 9 (1981) 117-123
@ Hsevier Sequoia S.A., Lausanne - Printed in the Netherlands
in “sophistkated” subjects:
ceptions abo t traject&ies of obj
ALFONSO CARAMAZZA,
MICHAEL McCLOSKEY
BERT GREEN
77~ Johns ~o~kr’ns Univmity
Abstract
University students were asked to solve simple problems about the trajec-
tories of falling objects. A majority of the student? revealed a variety of
misconceptions about motion. However, the few basic patterns of responses
produced by the subjects suggest considerable commonality in the types of
naite physical ‘laws” people develop on the basis of everyday experience
with the world.
The ability to interact successfully with moving objects implies some sort of
knowledge about motion. For example, a baseball player who is able to catch
a fly ball must have abstracted from his perceptual experience some form of
knowledge that enables him to position himself at the location where the
ball will land. It is not obvious, however, what types of knowledge are
the case that normal experience with
n of coherent abstract principles that are
al laws of physics: Alternatively, experi-
on of limited, concrete information about
of several ex~e~ments we have recently con-
from perience the world
on of
at variance with Surprisi , however,
the most fundamental
*Tla ruch Instftlm of
EduMi stion he Structure
sf KacbwWge in Scienos and Mathe Grant SSO7
RR070464 3.
Any opinfons, fin&~, sonc?lusfonar or recommendations expressed herein we thoac of the authors
and ds not neceasariJy reflect the view of the National Science Foundation or the Nationa! Institute
of Education.
Reprint requeets should be wat to: Alfonso Caamazza, Department of Pswhology, The %ohns
Hopkins UniversSty, Baltimon, Maryland 21218.
118 A. Caramazza, M. McCdoskey GE& B. Green
physical laws. Furthermore, the naive principles are espoused not only by
people with no formal instruction in physics, but also by a large proportion
of those who have completed high school or college physics courses.
In this report we describe an experiment concerned with people% beliefs
about projecer’le motion. Fifty undergraduate students at the Johns Hopkins
University served as subjects. Six subjects failed to follow instructions, and
their data were not included in our analyses. Of the remaining 44 subjects,
10 had completed at least one college-level course in physics, 20 had taken
high school physics, and 14 had received no formal physics instruction at the
high school or college level. Each student was asked to solve 13 simple
problems, of which 4 will be discussed in this report. These 4 problems,
shown as problems A through D in Figure 1, required the students to trace
the trajectory of a falling object. The problems were pxsented separately,
one per page, as line drawings of a metal ball suspended by a string.
Subjects were instructed to consider the ball and string depicted in the
line drawings as moving in an arc as a pendulum. They were then asked to
draw the path the ball would follow if the string were cut when the ball was
at the location indicated and moving in the direction indicated in the line
drawing.
The results of the experiment are remarkable in what they reveal about
subjects’
responses
responses
Kgure 1.
knowledge about motion. Only 25% of t e subjects produced
that demonstrated a basic underst:.rding of projectile motion. The
of the remaining 75% revealed a variety of gross misconceptions.
Line drawings for the four problems.
PROBLEM A
/
\ \ \ \ \
f \ \.
‘--Z- &CA
PROBLEM C
PROBLEM 8
PROBLEM D
/ \ \
,I1 ‘\
/I z
\
:
L_ \
\
\
-a-
Naite beliefs in ’ ‘sophisticated ” subjects 119
We have classified subjects’ responses on the four problems into six
different types on the basis of criteria described below.* AP example of each
response type is shown in Figure 2, along with the percentage of subjects
producing each type of response.
Eleven of the 44 subjects produced the pattern of response referred to as
Type 1. As indicated in Figure 2, these 11 subjects drew vertical trajectories
for problem A, and parabolic trajectories for problems B, C and D. The Type
1 subjects understand that in Problem A the ball has a velocity of zero when
the string is cut, so that the ball’s trajectory is determined by the force of grav-
ity alone. Furthermore, the Type 1 subjects are aware that for problems B
through D the initiaLvelocity of the ball as well as the action of gravity must
be considere; rn determining t.Le trajectory. Finally, the subjects appear to
know that the ball will accelerate as it falls, producing a parabolic trajectory.
Figure 2. Exarnpks of the six basic responsti types, with the percentage of subjects who
made each type of response.
‘To ensure that our classification of subjects’ responses was reliable, we gave three undergraduate
research assistants the criteria for Types 1 through 6, and asked them to sort the subjects’ responses
into types. Two of the judges agreed tith our clas&ication for all 44 subjects, while the third judge
agreed with our claaification for 43 of the $4 subjects. (The point of disagreement concerned whether
8 response was a st! qht line or a parabolic arc.)
120 A. Caramazza, M. McCloskey and El. Greers
This is not to say, however, that all of the subjects producing Type II
responses have a full understanding of projectile motion. For example, five
of the 11 subjects do not appreciate that the horizontal displacement of the
ball will be greater in problem C than in problem , because of t
greater horizontal velocity in problem C. Wowever, this error is a minor one
relative to the sorts of misconceptions revealed by subjects producing Type 2-
Type 6 responses.
Fourteen subjects (11 of whom had received formal instruction in physics
at the high school or college level) produced responses designated as Type 2.
These subjects made essentially correct responses to problems B and D,
suggesting that they had some understanding of (1) the importance of the
initial velocity of the ball, and (2) the fact that the ball accelerates as it falls.
However, the Type 2 subjects each made an errs3r on problem A, problem C
or both. The eieven subjects who made an error on problem A drew parabolic
trajectories to the left (shown in Fig. 2) or to the right of the ball’s initial
position. This error seems to represent a failure to understand that in problem
A the ball has a horizontal velocity of zero, and so will fall straight down.
The eight subjects who made an error on problem C (five of whom also erred
on problem A) for some reason believed that the ball would fall straight
down. informal questioning of subjects who made this error suggests that it
does not represent a failure to realire that the ball is moving horizontally. In
fact, most subjects are aware that the velocity of the pendulum is at a maxi-
mum at the position shown in problem C. Thus, it appears that the subjects
who made straight down responses on problem C believe that when an object
is “‘pointing” straight down, it will fall directly to the ground, regardless of
whether or not it is moving.
The responses designated Type 3 were similar to the Type 1 an
responses, with the exception that all Type 3 trajectories were st
The six subjects who produced Type 3 responses evidence s
standing of the fact that the initial velocity of the ball in problems B and D
will result in a horizontal displacement of the ball as it falls, Mowever, the
Type 3 subjects fail to understand that the ball will undergo a vertical
acceleration as it falls and as a result will describe a parabolic trajectory. In
addition, many of the Type 3 subjects made the same sort of errors on pro-
blems A and C as did the subjects producing Type 2 responses. %pecifically,
two of the six subjects believed that the ball would be displaced horizontally
in problem A, and four of the six believed that the ball would fall st
down in problem C. Only one of the Type 3 subjects made correct
ments about the horizontal displacement of the in all four problems.
The subjects producing Type 4, 5 and 6 res es evidenced misconcep-
tions about motion even more serious than those of tlte Type 2 and 3 subjects.
ffaiiie beliefs ipl “sophisticated ‘* subjects 121
responses were des ieved that the
se subjects, all
ion in physics, fail to understand
of the ball plays a role in determinin
We have no indication that these subje ts have any unders
5 responses also ha
subjects drew for a
the line formed b
an attempt to analyze the problems
ball, In other words, the Type 5 subjects
al in one direction while
the ball in the opposite
direction. Thus, when the string was cut, the ball fell in a direction opposite
to that of the force exerted by the string.
Finally, consider the five subjects who produced pe 6 responses. These
subjects (all but one without previous instruction in sits) present perhaps
the most intriguing conception of projectile motion. The Type 6 subjects
believe that vhen the skin is cut, the ball will continue for a short time
nal arc, and t en will fall directly to bh round (see Fig. 2).
s’ ideas about motion seem to be relat to the gre=Galilean
notion that a mov object is kept in motion by an “impetus” that
disspitates2. In g ular, these subjects apparently believe that the
the pendulum imparts to the ball a sort of impetus that eaut~es it to retain
on of the impetue
theory and other e&y eon
s that axperiencti with m
lead to tha con otisn. The first 8 unt of pfajactib motion
was provlclad by SalUao in the early 17th Century, and not until Mawton’s Arlnelpia MarhtmafkrR in
168% was an adequate general description of motion at&able.
122 A. Caramaza, ?It McCloskey and B,) Gwen
motion are not entirely idiosyncratic. In other words, it appears that exper-
ience with the world leads naturally to the development of only a few basic
models of motion. Consistent with this view is the fact that the naive beliefs
of many of our subjects were reminiscent of preGaMean models of motion.
‘The historical persistence of these beliefs suggests that they are a natural
outcome of experience with the world.
In the light of the above comments it is of considerable interest to deter-
mine the source of people’s beliefs about motion. Although the IXG’VC beliefs
would appear to have their origin in experience with moving objects, it is
quite unlikely that these beliefs are produced by direct induction from per-
ceptual experience,. It is difficult to imagine, for example, how the beliefs
reflected in response Type 6 could hay; developed through induction from
real-world experience. It is much mo,e likely that, as Piaget (1971) has
argued, deduction plays a crucial role in the development of models of the
physical world. On this view, subjective models of laws of motion reflect the
conceptual system people use to organize and draw inferences from their
experience with moving objects.
Futclre research needs to address at least three issues. First, there is need
to provide a more detailed description of people’s beliefs about the behavior
of moving objects and, second, an attempt must be made to provide an
account of the origin of these beliefs. Finally, it is important to ask what
effect formal instruction in physics has on people’s conceptions of motion.
Our results clearly indicate that formal instruction does not always lead to
an understanding of the fundamentals of projectile motion: only 33% of the
subjects who had completed a high school and/or a college physics course
produced the basically-correct Type 1 responses. Thus, one important topic
for future research will be to determine why physics courses do not provide
most students with a grasp of even the rather basic principles we have con-
sidered here. One possibility is that instruction is frequently ineffective
because it fails to take into account students’ misconceptions about motion
(such as the misconceptions reflected in Type 5 and 6 responses) but instead
treats students as if they understand basic principles and only need to le
to formalize and quantify these principles.
Although physics courses clearly did not provide our subjects with a full
understanding of the basics of projectile motion., our results su st that
instruction probably has some effect Specifically, 70% of the subjects with
some formal instruction produced Type 1 or Type 2 responses, suggesting
that these subjects have at least some understanding of (a) the importance of
the ball’s horizontal velocity and (b) the fact that the ball will accelerate
vertklly as it falls. In contrast, 71% of the subjects with no formal instruc-
tion produced responses falling into Types 3-6, indicating that these subjects
Naiire beliefs in “sophisticated” sub&ts 123
failed te underst d the effect of the initial horizontal velocity or the vertical
(in the case of Types 5 and 6) had $ome
ptions about projectile .motion. Although
~st~~t~on~ firm conclusions cannot be
e, ~on~e~vab~e that the subjects who have completed
physics courses are somehow different from ose who lack formal tnstruc-
t-ion, such that the former would have respo ed differently from the latter
even before ta ysics courses. Thus, additional research will be necessary
to specify the of instruction.
In research currently in progress we are attemptin to explore the ori
of naive beliefs about motion, as well as the ways in which these beliefs are
altered by instruction in physics. This research should enable us to provide a
more detailed characterization of the nature and development of people’s
conceptions of the physical world.
References
Clagett, M. (1959) The Science of Mechmics in the MVdle Ages. University of Wimmsin Press,
Madison, Wisconsin.
Dijkstethuis, E. J. (1961) like Mechanizutim c/f the World Picture, (7. Dikshootn, trans., C’larendon
Press, Oxford.
Piaget, J. (1971) Psychology and epistemology: Towards 4 theory of knawiedge. Vikin
York.
On a demand6 g des &u&ants d”Unhrersir~ de rhaudrc des probl&nes simptcs SUI la tra,jc+ztoire dos
objets ton&ants, mejorltd de ces %tudients s’eat r&ml&z av& de3 id&~ fausscs SUI Ic mouvcmcnt.
Les qaralques pat s de ime quf rendmt csmpte de3 r6ponMss QU Orent une mmdardisatisn eon-
aid&able des types de ‘lois” phystqum nabs que leg gem dbeloppent aur la baw dc lcur expbricnccs
du nsndc,
