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Concept substitution: A teaching strategy for helping students disentangle
related physics concepts
Diane J. Grayson
a)
Centre for the Improvement of Mathematics, Science and Technology Education, University of South Africa,
P.O. Box 392, Unisa 0003, South Africa
共Received 11 February 2002; accepted 30 April 2004兲
To be effective, physics teachers need both content knowledge and pedagogical content knowledge,
which includes knowledge of student conceptions and effective teaching strategies. Although much
information is available on student conceptual and reasoning difficulties in physics, much less
information is available on how to remedy such difficulties. In this paper I describe a teaching
strategy, concept substitution, which is useful when student difficulties arise from a failure to
distinguish distinct but related physics concepts. By using the topic of electric circuits as the context,
I show how this strategy enables the teacher to identify and build on students’ correct intuition,
while enabling students to distinguish among related concepts. I also illustrate the complexity of the
conceptual change process, including the presence of intermediate conceptions while the process is
taking place. ©
2004 American Association of Physics Teachers.
关DOI: 10.1119/1.1764564兴
I. INTRODUCTION
Over the past three decades much effort has been devoted
to identifying students’ alternative conceptions in physics.
1
A
number of alternative student conceptions appear across a
wide variety of cultures, countries, and ages.
It is important for physics teachers to be aware of these
student conceptions. However, a knowledge of alternative
conceptions is not enough to ensure improved student learn-
ing. Physics teachers also need access to a range of effective
instructional strategies to help students undergo a process of
conceptual change from the unscientific conceptions they
might hold to acceptable scientific concepts.
2
Such strategies
form part of what Shulman
3
calls ‘‘pedagogical content
knowledge.’’ An important feature of pedagogical content
knowledge is that it is topic-specific. It includes knowledge
of the most useful ways of representing the central ideas in a
topic, powerful analogies and examples, common alternative
conceptions, and teaching strategies that are effective in
helping students reorganize their understanding. According
to Shulman, pedagogical content knowledge extends beyond
subject matter per se to include ‘‘subject matter knowledge
for teaching.’’ It is ‘‘the particular form of content knowl-
edge that embodies the aspects of content most germane to
its teachability.’’ Although secondary and college teachers
are expected to achieve a high level of subject matter knowl-
edge, usually by means of formal courses, and secondary
teachers are expected to learn about pedagogy, neither sec-
ondary nor college teachers usually have a chance to acquire
pedagogical content knowledge in a systematic way.
The fact that much physics instruction is not as effective
as it should be, as evidenced by research which shows that
students often have misconceptions after instruction,
4
indi-
cates that physics instructors need more pedagogical content
knowledge. In particular, we need to know both what unsci-
entific conceptions our students hold and what to do about
them. To know what alternative student conceptions we
should anticipate, research results need to be synthesized and
made accessible to teachers. Grayson et al.
5
have developed
a framework for identifying and categorizing students’ con-
ceptual and reasoning difficulties that can help with this syn-
thesis. Other researchers have summarized students’ thinking
in particular domains. Minstrell
6
has compiled a very useful,
comprehensive list of student thinking that differs from sci-
entific explanations in a number of domains.
To know what to do about students’ unscientific concep-
tions, we need to understand how they arise. Various authors
have argued that certain alternative conceptions parallel the
historical development of scientific concepts.
7
Alternative
conceptions also may arise as a result of what diSessa
8
calls
‘‘phenomenological primitives,’’ or p-prims, which are,
‘‘relatively minimal abstractions of simple common phenom-
ena’’ and ‘‘self-contained explanations for what they
关physics-naive students兴 see.’’ In some cases, the teaching
approach may reinforce students’ p-prims. For example,
many students think that if an image of an object is formed
on a screen by a converging lens and half the lens is covered,
then half of the image will disappear.
9
This misconception
may arise from a p-prim like, ‘‘if there is less lens available
for light to pass through, then there will be less appearing on
the screen.’’ The ‘‘less’’ may be interpreted by students to
mean less of the image, rather than less light 共lower inten-
sity兲. This idea may be reinforced by the standard way in
which students are taught to locate the image, namely by
drawing two 共or three兲 special rays. When students are re-
quired to draw ray diagrams in which rays pass through all
parts of the lens, this misconception may largely disappear.
10
Alternative conceptions also may arise because students
PHYSICS EDUCATION RESEARCH SECTION
All submissions to PERS should be sent 共preferably electronically兲 to the Editorial Office of AJP, and
then they will be forwarded to the PERS editor for consideration.
1126 1126Am. J. Phys. 72 共8兲, August 2004 http://aapt.org/ajp © 2004 American Association of Physics Teachers
confuse related but distinct physics concepts. Brown and
Clement give examples of such concept differentiation prob-
lems in mechanics.
11
In some cases, students hold cluster
concepts
12
that are general and vague. For example, students
may talk about ‘‘electricity,’’ a word that for them has ele-
ments of current, voltage, energy, and power all muddled
together. In such cases, an effective teaching strategy needs
to help students disentangle the related concepts and ascribe
scientifically correct meanings to each concept. In the pro-
cess, the strategy should build on correct student intuitions
while remediating incorrect reasoning or conceptual difficul-
ties. In this paper I shall describe one such teaching strategy
which I call ‘‘concept substitution.’’
II. METHOD
The research described in this paper was conducted with
students in the Science Foundation Programme at the Uni-
versity of Natal. This program was designed to help aca-
demically talented but disadvantaged black students acquire
sufficient skills and knowledge to succeed in science or
science-related degrees.
13
It is a one year predegree program
for students who have completed high school, but who are
not yet ready to begin normal degree studies. The student
responses to pretests, assignments, and tests presented in this
paper were all part of the normal teaching sequence in the
physics component of the program.
14
The exercises and test
questions were taken from Physics by Inquiry.
15
When read-
ing the students’ responses, it is useful to bear in mind that
English is their second or third language.
In Sec. III I shall illustrate how the instructional strategy
of concept substitution was used to address two of the most
prevalent conceptual difficulties in electric circuits, namely,
the belief that current is used up in a circuit and that a battery
supplies a fixed amount of current, regardless of what is in
the circuit.
16
Only the aspects of the teaching sequence and
test questions relevant to these two ideas will be presented.
III. RESULTS
A. Initial identification of student conceptions
At the beginning of the first lecture on electricity, the stu-
dents were asked to write their predictions about the situa-
tions shown in Fig. 1. The purpose of this pretest was to see
whether students thought that current is used up in a circuit
and that a battery is a source of constant current. 共In all the
pretests the students were told to assume that the bulbs and
batteries were identical.兲 About 30% 共11 of 35兲 of the stu-
dents thought that bulb No. 1 would be brighter than bulb
No. 2, because current is used in bulb No. 1 so less current is
available to light bulb No. 2. The other students thought that
the two bulbs would be the same brightness, but not neces-
sarily for the right reason. As discussed in Sec. IIIB, students
may have correct ideas, but do not necessarily know which
physics concepts to associate with their ideas. The following
quotes illustrate this problem. ‘‘The brightness of bulb No. 1
will be the same as that of bulb No. 2 because these bulbs are
connected in a series arrangement and the voltage passed
through each bulb is the same because it’s coming from one
source for both bulbs.’’ ‘‘Bulb No. 1 will have the same
brightness as bulb No. 2. This is because both bulbs are
supplied by one battery, and they both 共bulb兲 share the same
charges.’’
In response to Question 1共b兲, 20% of the class thought
bulb A would have the same brightness as either bulb No. 1
共if they thought bulbs Nos. 1 and 2 would be different兲 or the
same brightness as bulbs Nos. 1 and 2 共if they thought they
would be the same兲, because these students believed that the
battery supplies a fixed amount of current, regardless of what
is in the circuit.
The other 28 students correctly stated that bulb A will be
brighter than bulbs Nos. 1 and 2, but not necessarily for the
right reason. In particular, 16 of 35 students indicated in their
answers that the battery supplied the same amount of current
to both circuits, as illustrated by the typical response: ‘‘The
brightness of bulbs in the circuit above will differ from that
of bulb A. Bulb A will be brighter than the two bulbs above.
This will be because all the current present lights only one
bulb, while above the same current has to be divided into
two bulbs.’’
The responses to the pretest indicate that a significant frac-
tion of the class held the incorrect ideas identified in the
literature that current is used up in a circuit and that the
battery supplies a fixed amount of current. However, the re-
sponses to the pretest also showed that in some of the
‘‘wrong’’ answers, there were some right ideas, as illustrated
by the following response to Question 1共a兲: ‘‘Bulb one will
be brighter than bulb two, because they are connected in
series and the direction of current flow is from positive to
negative. When energy reach关es兴 bulb one it will be used and
not as much energy will reach bulb two, so bulb two will be
dimmer.’’
This student correctly writes that some energy is ‘‘used’’
共converted, strictly speaking兲, but is incorrect in thinking that
this use will affect the brightness of the other bulb. As I will
discuss, such correct intuitions can be turned into useful
building blocks to construct students’ scientifically accept-
able concepts. The seed of a correct idea could also be iden-
tified in the responses to Question 1共b兲, as evidenced by the
fact that even though a fifth of the class thought the bulbs in
series would be equal in brightness to the single bulb, several
of these students had a sense that something must be differ-
Fig. 1. Pretest given to test for the presence of the ideas that current is used
up and a battery is a constant current source.
1127 1127Am. J. Phys., Vol. 72, No. 8, August 2004 Diane J. Grayson
ent. This sense is suggested by the following response: ‘‘The
two bulbs will be bright as equal to A because the two are
connected in series. They were to be a bit dimmer than bulb
A if they were connected in parallel. The only problem is that
the battery for the two bulbs connected in series will only
last a shorter time than A’s.’’
Although this response is not correct, the correct idea that
putting more bulbs in the circuit must somehow make a dif-
ference is evident. This response is an example of how stu-
dents can give the wrong answer but have some right ideas.
Conversely, students can give the right answer for the wrong
reason 共which is a reason why multiple choice questions can
be problematic兲.
B. First remediation sequence
After the students completed their written predictions, a
circuit was shown consisting of a battery in series with three
bulbs, with the switch left open. Students were asked to pre-
dict orally how the brightnesses of the bulbs would compare
with each other when the switch was closed and to justify
their predictions. A very lively debate ensued. As expected, a
significant fraction of the class argued that the bulb closest to
the end of the battery from which they thought the current
flowed would be brightest, and the other bulbs would be less
and less bright because current would be used up as it passed
through successive bulbs. The circuit was then closed and the
students saw that the bulbs were equally bright.
The instructional strategy up to this point resembles what
Champagne et al.
17
call ‘‘ideational confrontation.’’ Students
predicted what they thought would happen and then ob-
served a discrepant event. However, if instruction were to
stop here, there is a risk that students would not actually
undergo conceptual change because they would not know
why their predictions were wrong. After all, batteries go flat
after a while, so surely current must be used up! Under such
conditions it is possible for students to appear to accept the
new idea for a time but then revert back to their previous
idea some time later.
18
To avoid this possibility it is impor-
tant to help students understand why there is a difference
between their intuitive ideas and what they observed.
At this point I told the students that they were correct to
say that something is ‘‘used up,’’ but that ‘‘something’’ is
chemical energy, which gets converted to other forms of en-
ergy. That is why batteries go flat. By contrast, current just
goes round and round the circuit.
19
This teaching strategy of
building on correct student intuitions, but substituting the
name of the appropriate physics concept for an inappropriate
one is what I call concept substitution.
20
Concept substitution
involves creating a situation in which it is likely that students
will associate a correct intuitive idea with an inappropriate
physics concept. When this happens, the instructor reinforces
the students’ correct idea, but assigns it another label. In
other words, the instructor substitutes the name of the con-
cept with which the students’ idea can be correctly associated
for the one used by the students. Some physicists may take
exception to introducing a new concept without a careful
lead-in. However, the research described in this paper sug-
gests that this disadvantage may be outweighed by the ad-
vantage of providing students with a concept early on in the
teaching sequence with which they can associate their intui-
tive ideas, in contrast to expecting them to relinquish their
intuitions. In the process, the concept for which it was sub-
stituted 共current in this case兲 can be freed of some of the
conceptual baggage that students load onto it. Furthermore,
when the newly substituted concept is formally developed at
a later stage, students already have some feeling for it.
To confront the other incorrect idea, namely that the bat-
tery supplies a constant amount of current regardless of what
is in the circuit, three circuits were set up in the front of the
room: one with a battery and one bulb, one with two bulbs in
series, and one with three bulbs in series. The switches were
left open. Students were asked to make verbal predictions of
the brightnesses of the bulbs in the different circuits, assum-
ing that the brightness of the bulb indicates the amount of
current flowing through it.
21
After some debate and discus-
sion, the switches were closed, and students observed that
the more bulbs there are in the circuit, the dimmer they are,
implying that the battery supplies different amounts of cur-
rent depending upon what is in the circuit. There was not
enough time in the period, however, to use concept substitu-
tion again to help students begin to distinguish between the
current supplied by the battery, which is not constant in ev-
ery circuit, and the quantity that is constant 共voltage兲. Before
the next lecture students did a two and half hour laboratory
session on series and parallel combinations of bulbs using
ammeters to measure currents and nichrome wires of differ-
ent lengths instead of bulbs. The concept of resistance was
introduced, and students determined experimentally that cur-
rent is inversely related to resistance.
C. Second identification of student conceptions
At the beginning of the next lecture, students wrote re-
sponses to questions in Fig. 2. All but five of the students
realized that both bulbs in Fig. 2共a兲 would be the same
brightness. In response to Question 2共b兲, 25 of the 35 stu-
dents incorrectly said that bulb A would be brighter than
bulbs Nos. 1 or 2. Once again, the notion that a battery
supplies a fixed amount of current was evident in the stu-
dents’ responses.
Fig. 2. Pretest to further test for the presence of the idea that a battery is a
constant current source.
1128 1128Am. J. Phys., Vol. 72, No. 8, August 2004 Diane J. Grayson
In response to Question 2共c兲, 26 of the 35 students said the
current flowing through the two batteries would be the same,
regardless of the number of bulbs in the circuit. Although at
the end of the previous lecture students had seen that the
brightness of bulbs in series differs when there are differing
numbers of bulbs in the circuit 共we used brightness as an
indication of the current兲, this demonstration and the discus-
sion of the results was not enough to shake students’ belief
that the battery is a constant current source. This belief
seems to be based on the students’ understanding of the
‘‘sameness’’ of the batteries, as illustrated by the following
quote: ‘‘The current through battery No. 1 and A will be the
same because it’s the same battery therefore they are giving
the same amount of current.’’
However, as in the previous lecture, several students felt
that something must be different about the two circuits. In
the following response, the student uses the only other elec-
trical concept she has encountered in the course so far, en-
ergy, to explain the difference: ‘‘The amount of current is the
same because there is one battery in each circuit therefore it
is the energy that will differ but not the electric current.’’
As with the first pretest, correct ideas could be identified
in incorrect responses. In the following quotes students dem-
onstrated correct thinking when they said that the battery that
supplies two bulbs will go flat first, even though they were
not correct in saying that the amount of current supplied by
both batteries was the same. ‘‘Current through battery No. 1
is the same as the current through battery A. The only dif-
ference is that battery No. 1 will go flat quicker than battery
A because it supplies current to two bulbs.’’ ‘‘The amount of
current in battery No. 1 and battery A is the same, the chemi-
cal energy of battery A will last longer than that of battery
No. 1 because battery No. 1 is supplying current to two
bulbs, whereas battery A to a single bulb.’’
Although many students still believed that the batteries
supplied the same amount of current, these quotes show that
students were beginning to distinguish current and energy as
two different concepts. There also was evidence in some of
the responses that the concept substitution employed in the
last lecture helped students accept the idea that the ‘‘some-
thing’’ that gets ‘‘used up’’ in a circuit is not current but
energy 共even if the overall responses were not correct兲: ‘‘The
amount of current through battery No. 1 is the same as the
amount of current through battery No. 2 because there is no
current used up by bulbs. So the current send关t兴 will be equal
to the current received.’’ ‘‘The brightness also will be the
same because above bulbs 关Nos. 1 and 2兴 were parallel to
each other and to the battery. Current will never be used up.
Current will be the same. The difference might be time of
light of bulbs Nos. 1, 2, and A. Bulb A would light long time
because there is 1 bulb to 1 battery.’’
An interesting aspect of these quotes is that it seems as if
the students are using their new knowledge that current is not
used up as a justification for their belief that the current in
the two batteries must be the same. If teaching had ended at
this point this misconception might have been reinforced
rather than remediated by the teaching strategy.
Sometimes students seem to be in a transition state be-
tween their old conception and the new scientific concept.
The two following quotes give an illustration. The first quote
is a student’s response to Fig. 2共b兲 on the second pretest,
while the second quote is his response to Fig. 1共b兲 on the first
pretest. ‘‘Bulb A will have more brightness than Nos. 1 and 2
because all the energy that the battery sends out is used all by
bulb A whereas the energy from the battery No. 1 in diagram
above is shared by both bulbs, Nos. 1 and 2.’’ ‘‘Bulb A will
be more brighter than bulbs Nos. 1 and 2, because all of the
current goes to one bulb, A whereas in the above 关series
circuit兴 the current is shared amongst two bulbs, Nos. 1 and
2.’’
In the second pretest the student has replaced ‘‘current’’
with ‘‘energy’’ as the quantity that is used, but has not yet
clearly separated out the concepts of energy and current. Al-
though he uses the word ‘‘energy,’’ he still associated certain
aspects of current with the word. This association is an ex-
ample of an intermediate conception.
22
The student has
moved away from his original conception, but has not yet
moved all the way to the scientific concept. As shown in Ref.
23 while moving from an alternative conception to scientific
concept, students do not necessarily undergo a discrete
change from one concept to another. Students’ conceptions
are not like two-state systems, which are either right or
wrong. There are all sorts of intermediate conceptions along
the path to conceptual change. Moreover, students may move
back and forth between the ‘‘old’’ and ‘‘new’’ conceptions
depending on the context, remaining for some time in a kind
of metastable conceptual state. It may take multiple passes at
confronting and resolving an alternative conception before a
student finally relinquishes the conception and can be
thought of as being in a stable conceptual state. For this
reason, one-shot efforts at conceptual change may not be
effective.
D. Second remediation strategy
As in the previous lecture, students handed in their predic-
tions and then looked at two circuits with the switches open.
One circuit had two bulbs in parallel with a battery and the
other consisted of a single bulb and a battery. Students de-
bated their predictions in class. When the switches were
closed, students saw that the bulbs were all the same bright-
ness, demonstrating that branches of a parallel circuit are
essentially independent 共when internal resistance can be ig-
nored兲. Thus each bulb in each branch glows with the same
brightness as the bulb in a single bulb circuit. It can then be
deduced that the current through the battery in the circuit
with two bulbs in parallel must be twice that in a single
branch circuit.
At this point concept substitution again was used. The
students were told that they were right to say that something
about the batteries is the same, but the ‘‘something’’ is called
voltage. The same kind of batteries provide the same voltage.
The battery is not a source of constant current. Current de-
pends on what is in a circuit. Adding bulbs in series provides
more of an obstacle to flow, so there will be less current;
adding bulbs in parallel provides more paths so more current
can flow.
Students were shown two more demonstrations to rein-
force this concept. In the first demonstration, they saw a
parallel circuit in which one branch had one bulb and the
other branch had two bulbs. Students made oral predictions
of the brightness of the bulbs and the current through the
batteries. In the second demonstration they saw a parallel
circuit consisting of one branch with 30 cm of nichrome wire
and one branch with 15 cm of nichrome wire. An ammeter
was inserted in each branch and the current was measured.
The current through the battery was also measured. From
these demonstrations it was concluded that current depends
on the resistance in a branch 共or path兲 and the number of
1129 1129Am. J. Phys., Vol. 72, No. 8, August 2004 Diane J. Grayson
paths. A summary of the teaching sequence for the rest of the
section on electricity is given in the Appendix.
E. Time-delayed effects of the instructional strategies
Six days after the class period described in Sec. III D,
students handed in their answers to the homework questions
in Fig. 3. In response to Question 3共a兲, only 9% of the stu-
dents 共3/34兲 incorrectly said the current was the same in all
three circuits. In response to Question 3共b兲, these three stu-
dents and one other student, 4/34 in all, agreed with student
No. 1’s incorrect reasoning.
Twenty days after instruction students handed in responses
to the questions in Figs. 4 and 5. A student who thought that
the battery supplied a fixed amount of current should agree
with student No. 1 in Fig. 4. Only 4/34 incorrectly said stu-
dent No. 1 is right; the rest gave the correct answer. 关It is
interesting that three of these four students were different
from those who gave the incorrect answer in Question 3共b兲.兴
An indication of the degree of understanding most students
seemed to have acquired by this stage is given by the follow-
ing responses: ‘‘Student No. 1 is not correct as the bulbs A, B
and C will be equally bright since the current through the
battery depends on what is in the circuit thus the circuit with
bulb B and C will 关have兴 twice current as circuit with bulb A
and thus bulb B and C share the current which then each get
current equal to current through bulb A thus they light with
the same brightness.’’ ‘‘Student No. 1 is incorrect because we
can’t say something in the circuit gets all the current because
there is no fixed amount of current in the first place. To
correct No. 1 I would say that A⫽B⫽C because since A and
B and C have the same resistance and B and C are connected
directly to the battery, they demand more current from the
battery to keep them burning like bulb A 共depending on their
resistance兲.’’
Any student who still thought that current gets used up in
a circuit should agree with student No. 3 in Fig. 5. Only 18%
of the class 共6/34兲 agreed with student No. 3 and thought that
current gets used up; the rest disagreed 共correct兲. Of those
who disagreed, 70% used the words ‘‘current is never used
up’’ in their responses. The extent to which students seemed
to have incorporated the notion that current does not get used
up into their understanding is suggested by the following
responses in which students were able to modify and elabo-
rate the answers of the ‘‘student’’ in the question. The first
quote suggests that the use of concept substitution helped
him to distinguish between current and energy. The quality
of these explanations is particularly impressive considering
the fact that for these students English is their second or third
language. ‘‘Student No. 3 is incorrect because current isn’t
used up, energy is. The current through A will be the same as
that in B and C except that before B and C current divides.
Some of it goes to C whilst some of it goes to B.’’ ‘‘Student
Fig. 3. Assignment given six days after instruction designed to test for the
presence of the idea that a battery is a constant current source.
Fig. 4. Assignment given 20 days after instruction designed to test whether
students think the battery is a constant current source.
Fig. 6. Test question given 25 days after instruction designed to test for the
presence of the idea that a battery is a constant current source.
Fig. 5. Assignment given 20 days after instruction designed to test for the
presence of the idea that current is used up in a circuit.
1130 1130Am. J. Phys., Vol. 72, No. 8, August 2004 Diane J. Grayson
3 is incorrect because current is never used up but the current
which was gotten by A is now divided between B and C thus
they will have less brightness than A.’’
Twenty-five days after instruction students were given a
test that included the question in Fig. 6. 26% of the students
共9/35兲 thought that the current through batteries s and t
would be the same, of whom only two had given answers to
the questions in Figs. 3, 4, or 5 that indicated that they
thought that batteries supplied a fixed amount of current.
Whether it was the format of the question, the stress of a test
situation, or both that led these students to revert to constant
current notions 关revealed in Question 2共c兲兴 is not known.
However, these results show that conceptual change may be
less stable than instructors may think.
At the end of the semester 共111 days after instruction兲
students wrote the final physics examination, which included
the question in Fig. 7. Only two students thought that the
current would be the same in all cases where the number of
batteries was the same.
IV. DISCUSSION
Many researchers have drawn attention to the need to
identify and address students’ incorrect conceptions.
24
How-
ever, it also is important to identify and exploit students’
correct conceptions and intuitions.
25
I have given several il-
lustrations of student responses that contained correct ideas,
even though the overall response may not have been correct.
There are a number of ways of characterizing these ideas.
For example, they may be thought of as naive conceptions or
intuitions. Some of the students’ responses can be explained
in terms of diSessa’s p-prims.
26
For example, the misconcep-
tion that batteries of the same type always supply the same
amount of current may stem from a p-prim that might be
stated as ‘‘the same kind of objects behave in the same way.’’
In the case of batteries, an implication of such a p-prim is
that ‘‘the same kind of batteries supply the same amount of
electricity.’’ For the novice physics student the problem is
not with the p-prim, because this assertion is reasonable. The
problem lies in deciding how to map the everyday term
‘‘electricity’’ onto the appropriate physics term. For students
who have not yet learned basic electrical concepts, electricity
could mean current, voltage, energy, power, or even some
combination of these concepts. The challenge to instructors
is to use students’ correct ideas, whether they are conceived
of as p-prims or intuitions, as a resource
27
to help students
develop a sound understanding of the physics concepts.
Concept substitution is one teaching strategy for exploit-
ing students’ correct ideas in a particular context. It involves
identifying a correct student intuition that has been linked to
an inappropriate physics concept and helping students asso-
ciate their intuitive idea with the appropriate concept. There
are several possible advantages to using this strategy. First,
students may find it encouraging to hear that they have some
correct ideas. Second, because students are not asked to give
up their intuitive ideas, they may feel that physics makes
more sense to them than often happens when traditional
teaching approaches are used. Third, when the concept that
has been substituted by the instructor is encountered later on
in the course, students already have some intuition about that
concept. Fourth, the approach encourages students to distin-
guish among related concepts that may otherwise remain un-
differentiated in their minds. As a result, certain apparent
misconceptions may be remediated.
I have shown that the percentage of students in a Founda-
tion Physics course who held two prevalent misconceptions,
namely the notion that current is used up in a circuit and the
notion that a battery supplies a fixed amount of current re-
gardless of what is in the circuit, was substantially reduced
during the course. I suggest that this reduction was, at least
in part, a result of using concept substitution to help students
distinguish between current and energy and between current
and voltage. By distinguishing between current and energy,
students were able to hold onto their correct intuition that
something gets used up because batteries go flat, but separate
it from the concept of current. By distinguishing between
current and voltage, students were able to hold onto their
correct intuition that the batteries are the same in some way,
but do not supply the same amount of current. It is likely that
both applications of concept substitution also helped students
develop an understanding of current as something that flows
unattenuated through a circuit and that depends on the com-
ponents and configuration of the circuit.
The sound understanding of the targeted physics concepts
that most of the students were able to demonstrate strongly
suggests that the new ideas made sense to them. The process
of sense-making was almost certainly aided by allowing stu-
dents to retain their correct intuitions and build on them
rather than insisting that these ideas be cast aside. There also
is an affective dimension to the process—when students are
told that their ideas are right, it probably boosts their confi-
dence. Given the widespread perception that physics is diffi-
cult, this point is not trivial.
There are indications that concept substitution also has
been a useful teaching approach in other areas of physics. In
mechanics many students think that if an object is thrown
into the air, it will have a ‘‘force of the thrower’’ acting on it
even when it is in mid air.
28
Concept substitution has been
used to help students associate their correct intuitive idea that
the thrower imparts something that travels with the object
with the concept of momentum rather than force. In the pro-
cess the apparent misconception that a ‘‘force of the
thrower’’ acts on a moving object may largely disappear.
29
In
the area of heat and temperature, students know that objects
made of different materials feel different, even though they
may have been in the same environment for a long time.
Introducing the concept of rate of heat transfer allows stu-
dents to relate the sensation of feeling different to this new
concept, and separate out the concept of temperature. As a
result, most students can make sense of the fact that objects
can be at the same temperature and yet feel different to the
touch. They also learn that temperature cannot be reliably
determined by feel.
30
Fig. 7. Final examination question given 111 days after instruction designed
to test for the idea that a battery is a constant current source.
1131 1131Am. J. Phys., Vol. 72, No. 8, August 2004 Diane J. Grayson
Concept substitution, however, is no magic pill. As I have
shown, conceptual change is not a quick or simple process.
Students may spend some time in an unstable conceptual
state, oscillating between their original conception and the
target scientific concept. For example, in response to Ques-
tion 3共b兲, one student wrote: ‘‘I agree with student No. 2
because when bulbs are connected in parallel they each re-
ceive current from the battery as if the others are not present,
therefore the two bulbs in circuit 共b兲 draw more current than
the bulb in circuit 共a兲.’’ However, in her response to Question
4 2 weeks later, she incorrectly said that student No. 1 was
correct. Students also may combine elements of both con-
cepts into a sort of intermediate conception.
31
As a result,
students may need to confront their old conception and apply
the new concept several times and in a variety of contexts
before an instructor can be reasonably confident that the stu-
dents have really embraced the scientific concept and
reached a stable conceptual state. Nonetheless, concept sub-
stitution seems to provide the conditions proposed in Ref. 32
that are required for conceptual change to occur, namely that
the new concept should be intelligible, fruitful, and plausible
and should not be a source of dissatisfaction. Concept sub-
stitution may be particularly helpful in meeting the fourth
requirement, because allowing students to hold onto their
intuitive ideas means that there is less likelihood that the
target scientific concept will be a source of dissatisfaction to
them.
V. IMPLICATIONS
I suggested in Sec. I that physics teachers need more than
just content knowledge—they also need pedagogical content
knowledge. One component of pedagogical content knowl-
edge is knowledge of likely student difficulties. However,
another, perhaps even more important component, is knowl-
edge of how to help students overcome these difficulties. In
the physics education research community, much more atten-
tion has been devoted to the first kind of pedagogical content
knowledge than to the second. There are notable exceptions.
Arons made an enormous contribution to our knowledge of
how to teach physics effectively,
24
and the curriculum mate-
rials developed by the Physics Education Group at the Uni-
versity of Washington
15
have applied and further developed
the teaching approaches he advocated. Minstrell
33
also has
made significant contributions to our knowledge of effective
teaching strategies. A number of curriculum innovations,
such as Real-Time Physics,
34
center around effective teach-
ing strategies. However, although these contributions are
very valuable, much more effort still needs to go into iden-
tifying specific teaching strategies that are shown to be ef-
fective in helping students develop the desired conceptual
understanding and scientific reasoning skills.
ACKNOWLEDGMENTS
I am grateful to David Schuster and Saalih Allie for dis-
cussions on an earlier draft of this paper, and to Erie Reyn-
hardt for critically reading the final draft. I also appreciate
the useful comments of the referees and valuable discussions
with Joe Redish that helped me clarify my own thinking.
APPENDIX: SUMMARY OF THE TEACHING
SEQUENCE AFTER THE SECOND USE
OF CONCEPT SUBSTITUTION
The day number refers to the number of days after the
second use of concept substitution.
Day 1: Pretest on how students think current varies in
different parts of a series-parallel circuit. Discussion of ex-
periments students conducted in the laboratory related to
how current changes according to the resistance in a circuit
and the configuration of circuit elements. Introduction to Kir-
choff’s First Law.
Day 4: Pretest on how students think voltages will com-
pare across bulbs and across batteries in series and parallel
circuits. Examples of Kirchoff’s first law problems.
Day 6: Laboratory session on measuring voltage across
different parts of a circuit, relating voltage and current, volt-
ages in series and parallel.
Day 7: Lecture on voltage, using gravitational analogy.
Voltages are the same between any points that are electrically
the same. Total voltage determined by the battery. Voltage
divides in proportion to resistance.
Day 8: Demonstrations and discussion of effect of un-
screwing a bulb in a parallel circuit and in a series-parallel
circuit in terms of voltage and resistance. Examples of cal-
culating voltages in series-parallel circuits given resistances
using proportional reasoning 共no current calculations兲. Com-
parison of voltage and current.
Day 11: Introduction of Ohm’s law for a linear resistor.
Introduction and examples of Kirchoff’s second law.
Day 13: Laboratory session on Kirchoff’s second law,
Ohm’s Law and real batteries 共effect of internal resistance兲.
Day 14: Derivation of equivalent resistance for parallel
circuits. Discussion of internal resistance. Problems on inter-
nal resistance and equivalent resistance.
Day 15: Students work on problems involving Kirchoff’s
laws, equivalent resistance, internal resistance.
Day 18: Definition of current as rate of flow of charge,
voltage as difference in electrical potential energy per unit
charge. Introduction to power, power ratings of household
appliances, circuit breakers.
Day 20: Students work on more complex problems on
equivalent resistance, Kirchoff’s laws, power, conversion
from electrical to thermal energy.
a兲
Electronic mail: graysdj@unisa.ac.za
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The strategy of separating out the notions of energy and current also has
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22
I use the term ‘‘intermediate conception’’ to indicate a conception that may
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define as, ‘‘stepping stones to the physicist’s more abstract and general
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See, for example, A. Arons, A Guide to Introductory Physics Teaching
共Wiley, New York, 1990兲, and Ref. 4.
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27
D. Hammer, in Ref. 25.
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In Ref. 20, pp. 152–161.
31
For a much more detailed treatment illustrating the complexities of the
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34
D. R. Sokoloff, R. Thornton, and P. Laws, RealTime Physics 共Wiley, New
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1133 1133Am. J. Phys., Vol. 72, No. 8, August 2004 Diane J. Grayson
