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Mental models of electricity

International Journal of Science Education
ISSN: 0950-0693 (Print) 1464-5289 (Online) Journal homepage: https://www.tandfonline.com/loi/tsed20
Mental models of electricity
A. Tarciso Borges & John K. Gilbert
To cite this article: A. Tarciso Borges & John K. Gilbert (1999) Mental models of electricity,
International Journal of Science Education, 21:1, 95-117, DOI: 10.1080/095006999290859
To link to this article: https://doi.org/10.1080/095006999290859
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1999, VOL. 21,
1, 95–117
Mental models of electricity
A. Tarciso Borges, Colegio Tecnico, Universidade Federal de Minas Gerais,
Belo Horizonte, Brazil and John K. Gilbert* Department of Science and
Technology Education, The University of Reading, UK
The mental models people use to think about the nature of electric current were investigated.
Interviews, based on sequences of prediction–observation–explanation, were conducted with
Brazilian secondary students, technical school students, teachers, engineers and practitioners who
deal with electricity as part of their daily activities. Four models are reported, showing a possible pattern
of progression which may be related to individual’s acquisition of conceptual knowledge about electricity.
Over the last two decades the understanding of physical concepts such as force,
energy and motion, have been extensively studied (see Driver et al. 1994).
Comparatively few studies of adults’ ideas about physical notions have taken
place. Most studies involving adults concern the differences between experts
and novices (Chi et al. 1981). Students’ conceptions of electric current have
been extensively studied, ranging from the simple notions treated in primary
school science up to the more sophisticated notions only addressed in introductory
physics courses at university level. The collection edited by Duit et al. (1985)
provides an overview of the research conducted up to 1985. Such research has
revealed the conceptions that students hold and the difficulties they have in understanding the concept of electric current, even in simple situations. Similar studies
have addressed children’ s understandings of the concepts of voltage, energy and
resistance (see Duit et al. 1985). The emphasis on an understanding of electricity is
justified in terms of its importance as a school science subject and for its pervasiveness in adult life. Most of this research is exploratory and descriptive. The
methodologies employed are diverse and are constrained by the age range of the
subjects. For instance, most of the studies involving younger children who have
not yet studied the subject seek to identify their conceptions of electricity and
electric current in simple practical situations. When individuals who have already
had instruction in the subject are involved, different approaches can be used.
Among them are paper and pencil tests involving diagrams of simple circuits,
the solution of problems, and the interviewing and observation of individuals’
actions while completing a task.
*Author for correspondence:
0950–0693/99 $12 ´ 00
1999 Taylor & Francis Ltd.
This paper discusses what is known about mental models of electricity and
presents the findings of an empirical research involving Brazilian students and
Mental models
The processes through which we understand a novel situation have been the subject of endless discussion among philosophers, psychologists and cognitive scientists. There is no simple answer to such an issue, though it is broadly accepted that
our ability to talk about a phenomenon or an object is closely tied to our understanding of it. Mental models are, therefore, internal representations of objects,
state of affairs, of a sequence of events or processes, of how the world is like and of
psychological and social actions. They enable individuals to make predictions and
inferences, to understand phenomena and events, to make decisions and to control
their execution. They are incomplete, despite being structural analogues of the
processes taking place in the world (Johnson-Laird 1983). Johnson-Laird’ s concern is not with the processes by which one constructs mental models but with how
one uses mental models in giving explanations and making predictions. In his
view, our ability to give explanations is intimately tied to understanding: in
order to understand any phenomenon or state of affair we must have a ’ working
model’ of it.
The notion of mental model has been used in research in different areas with
different meanings [see Rouse and Morris (1986) and Borges (1996) for a longer
discussion of this]. As a result, different terminologies are employed, sometimes
leading to confusion. For some researchers a mental model is just a representation
of some aspects of the world, whereas for others it is an analogue of objects in the
world. The first sense of ’ mental models’ is essentially pragmatic, but weak since it
does not suggest any strong epistemological or ontological commitments. We can
speak of the model that someone has about a given issue, without being concerned
with the origins of such a model or about how the possession of such a model
affects thinking about that issue. The concern is mainly with the content of the
mental model. On the other hand, the second sense is stronger and implies that
mental models represent aspects of an external reality. Mental models serve as
means with which to explain the relation between one’ s cognitive activity and
the world. In this view, mental models are unstable, naturally evolving and incomplete (Norman 1983). The views adopted by most researchers may be seen as
delimited by these two extreme positions.
Models and model-based reasoning have mainly been addressed by philosophers. Only recently have educational psychologists and science education
researchers begun to address the use of models in education (Mayer 1992
Gilbert 1993) and the issue of learning via model construction (Clement 1989).
In the task of constructing a mental model of a given system, one simplifies it, that
is one selects only some parts of the situation and the relations between them for
representation (Gilbert and Boulter 1995). This initially produced model describes
the functioning or the behaviour of the target system by referring to the structures
and mechanisms existing or assumed to exist in it. The initial focus of the knower
is likely to depend on the purposes intended for the model and on his/her prior
knowledge of the domain.
Previous research into people’s ideas about electricity
Explaining the functioning of a simple circuit
Most of the studies of this issue use the same basic structure. Children are given a
battery, some wires and a torch bulb and then are asked to light the bulb. While
they are involved in the task, their actions and behaviour are recorded or observed
(Tiberghien 1983, Osborne and Freyberg 1985). They are then interviewed and
asked to explain what they have done and what they were thinking while they were
doing it. From the protocols generated, researchers are able to infer the underlying
ideas about simple circuits.
This type of task has been used with individuals from primary school up to
university level to elicit their understandings of electricity. For instance, Fredette
and Lochhead (1980) have used it to assess North-American university students’
conceptions of simple circuits, and Osborne used it in a number of studies involving secondary school students in New Zealand and in the UK (Osborne 1983,
Osborne and Freyberg 1985). It was found that, independent of their ages, subjects
attempted to connect the bulb to the battery according to one of the diagrams
shown in figure 1 (Osborne and Freyberg 1985). These types of diagrams may
vary slightly, depending on the level of description of the researchers, but can be
found in a number of the studies about children’ s conceptions of electricity. Only
diagrams (g) and (h), where the light will glow, are perfectly equivalent from a
physicist’ s point of view.
Such research has showed that, in children’ s accounts, there is a cause located
in the battery and an effect, that is the lighting of the bulb. A causal agent acts in
between them. This causal agent is named ’ electricity’ , ’ current’ , ’ energy’ , and
these terms are often used interchangeably. This causal agent is endowed with a
Figure 1.
Methods of connecting a bulb to a battery (Osborne and
Freyberg 1985).
number of properties. it is thought to move, normally with great speed, according
to one of the following schemas:
Leaving one terminal of the battery and moving to the bulb;
Leaving both terminals of the battery simultaneously and moving along
both wires into the bulb;
Moving from one terminal through the circuit to the bulb and hence to the
other terminal, in a cycle.
Kärrqvist (1985) found six mental models among secondary students, which
encompass those proposed by both Osborne (1983) and Shipstone (1984, 1985).
These are:
Unipolar model: Named by Osborne (1981), in this model there is a flow of
current from the positive terminal of the battery to the base of a bulb, where
it is all used up. The second wire is seen as unnecessary or just an extra wire
required to light the bulb, but with no active role in the circuit. This is
similar to Fredette and Lochhead’ s (1980) ’ sink model’ . It is usually found
among younger children (Osborne and Freyberg 1985) and tends to disappear with instruction. This model implies that current is not distinguished
from energy and that it is not conserved. Furthermore, the bipolarity of
both the battery and of the bulb is not acknowledged.
Two-component model: ’ Plus’ and ’ minus’ currents travel from the battery
terminals to the bulb where they meet and produce energy, lighting the
bulb up. It is similar to Osborne’ s (1983) ’ clashing currents’ model and to
Shipstone’ s (1984) ’ model 1’ . Such a model is particularly popular among
children from 10 to 13 years old, but it is practically absent by the end of
secondary education (Osborne and Freyberg 1985).
Closed circuit model: According to this model all the circuit elements have
two connections. Current circulates around the circuit in a given direction
and the circuit only functions when the switch is closed. Current flow
through a resistive circuit element liberates energy. There is no equivalent
model in the studies by Osborne and by Shipstone. This model recognizes
the bipolarity of circuit elements but it suggests that current is not conserved, perhaps because of a lack of differentiation between current and
Current consumption model: Current is described by means of a timedependent sequence of events. Current is consumed as it goes through
resistive circuit components, though a fraction of it returns to the other
end of the battery. This model is similar to Shipstone’ s (1984) ’ sequence
model’ and to Osborne’ s (1983) ’ attenuation model’ . It implies a compromise between the notions that a current circulates the circuit and that it is
used up as it goes through each component of the circuit.
Constant current source model: It encompasses bipolar circuit elements,
the circulation of current in a cycle and the need for a closed circuit.
However, the battery is seen as a source of constant current. that is, the
current supplied by the battery is always the same regardless of the circuit
features. It is recognized that the battery ’ wears out’ with time and that this
is the only source of current variation. According to this model, two bulbs
share the current, whether they are connected in series or parallel. A similar
model is described by Cohen et al. (1983) and it shows most of the features
of Shipstone’ s (1984) ’ sharing model’ . According to Shipstone (1984) this
model results from the assimilation of some rules about circuit functioning
into children’ s models. For instance, the rule that identical bulbs connected
in series (or parallel) shine equally brightly.
Ohm’ s model: A current flows around the circuit transmitting energy.
Current is conserved and well differentiated from energy. The circuit is
seen as a whole interacting system, such that a change introduced at one
point of the circuit affects the entire system. This corresponds to the ’ scientific view’ and has also been found by Osborne (1983) and Shipstone (1984).
This model becomes increasingly popular as students grow older, perhaps
as a result of instruction.
Mental models of electricity
Most studies of children’ s models of electricity so far have been mainly concerned
with the functioning of simple circuits. Only a few have examined the nature of
electric current, resulting in only a partial picture of students’ mental models of the
domain. Many of these studies make use of quite similar probes, leading to very
similar outcomes. While this improves the reliability of the findings, it tends to
turn them into a standard form of conceptualizing such models. It is possible to
infer from such studies, for instance those of Osborne and Freyberg (1985) and
Shipstone (1985), that children’ s understanding of simple electrical circuits
improves with age and instruction, from simple intuitive mental models towards
some version of the consensus, socially agreed, model. Only a few studies, by
White and Frederiksen (1987) and by Eylon and Ganiel (1990), address the
issue of possible model progression within the context of cross-age studies. Both
the studies by Osborne (1983) and by Shipstone (1985) show the popularity of
different mental models as a function of age, but they both do not address explicitly what is changing in these models.
The problem with the word ’ model’ as it is used in most previous research is
that it refers to the content of children’ s knowledge about electricity or is a synonym for particular conceptions of how a circuit works, that is, to refer to the mental
models of current circulation. A model of electricity involves several interrelated
concepts and science teachers may have little empirical basis on which to decide
which concepts are more important and why. There is no doubt that such studies
provide priceless information on how students reason about the functioning of
simple electric circuits and about their knowledge of scientific vocabulary.
However, very little is provided concerning causal or explanatory models in the
sense used by Harré (1970), White and Frederiksen (1990), or Brown and Clement
(1989). This must be understood as a consequence of the researchers’ purposes.
There does seem now to be a growing consensus that, if science education is to
provide more than simple knowledge of science content, that is, of specific facts
and laws of science, then it must elicit how students acquire and use mental models
to think of the physical world and how these models evolve with age.
What has emerged from such studies is that children’ s mental models of electricity involve a number of different aspects. These are the:
(1) differentiation of basic terms used to speak about electricity, like current,
electricity and energy;
(2) recognition of the bipolarity of batteries and other circuit elements;
(3) recognition of the necessity of a closed circuit if a current is to circulate in
(4) issue of the conservation or non-conservation of current;
(5) effects of electrical resistance on current;
(6) models for current circulation;
(7) nature of electric current.
Most of the proposed models of electricity deal with only few of such aspects.
For instance, items 1, 3 and 5 predominated in the early studies (Osborne 1983,
Tiberghien 1983). With the use of slightly more complex circuits, the other aspects
were considered a little later (Shipstone 1984, Kärrqvist 1985, McDermott and
van Zee 1985). Some aspects are likely to occupy a more central place in children’ s
mental models so that instruction may affect them to different degrees. A child
who cannot differentiate between current and energy properly is unlikely to adopt
a view in which current is conserved, for instance. Research findings also suggest
that children are more prone to change their views about some of the above mentioned points after instruction than about others (Osborne 1983, Shipstone 1984,
Arnold and Millar 1987). Thus children can, after instruction, recognize batteries
and other circuit elements as bipolar devices and the need for a closed circuit if
current is to circulate in it (Osborne 1983, Psillos et al. 1987, Cosgrove 1995). That
suggests that their models of current circulation have changed, as has been found
in a number of studies (Shipstone 1984, Osborne and Freyberg 1985).
Other aspects of children’ s models of electricity, however, are more resistant
to change, for instance those involving the conservation of current. This becomes a
really critical difficulty as students progress in their studies to consider more
complex situations, such as those involving combination of resistors in series
and parallel (McDermott and van Zee 1985, Shipstone 1985), and when they
start to learn about the microscopic processes going on in a circuit (White and
Frederiksen 1987, Eylon and Ganiel 1990). Some researchers point out that the
problem is with the lack of differentiation between current and energy (Arnold and
Millar 1987), while others suggest that what needs to be addressed is how children
think of the nature of current (White and Frederiksen 1987, Eylon and Ganiel
The nature of electric current and electric processes as well as the role of other
circuit components are addressed in a few studies to a varying degree. Eylon and
Ganiel’ s study (1990), although not aiming to describe students’ mental models of
electricity, produced a large amount of evidence regarding reasoning about electricity. The emphasis was on the microscopic processes taking place in a circuit
passing through transient states and the relationship of such processes to the
macroscopic behaviour of the circuit. Stocklmayer and Treagust (1996) focused
on the images and metaphors that novices and experts evoke to speak and think of
electricity. They found that teachers held a mechanical model of electricity in
which electrons are seen as minute hard balls moving along ’ tunnel-like’ wires.
Apparently these teachers rely on a functional vocabulary to describe the circuit
functioning and do not refer to electric fields. This picture contrasts with the more
’ global and holistic’ views of experts. This study indirectly lends support to our
thesis that subjects’ mental models progress as they acquire more conceptual
knowledge of the field.
In conclusion, while aspects related to how a circuit works are well understood, more emphasis needs to be put on the study of how subjects’ mental models
of electricity evolve as they acquire experience and conceptual knowledge of the
subject. That is important for the purposes of informing curriculum planning and
the devising of more efficient teaching strategies and assessment. it involves the
study of how subjects go about understanding valid scientific explanations of it, for
instance, by relating the microscopic processes taking place in a circuit to the
observed behaviour of its components or by explaining electric and magnetic interaction in terms of fields. In a certain sense, this calls for an exercise of stretching
the notion of model (Gilbert and Boulter 1995) being used in science education
The study
The study reported here involved Brazilian 15- to 17-year-old secondary students
and three groups of professionals whose daily jobs involved electricity. The first
group comprised physics teachers, the second a group of electrical engineers and
the third a group of practitioners. The practitioners were electricians or schoollaboratory assistants, most of whom were partially schooled and had no formal
instruction in the subject. They had attended school for four years on average and
only two of them have completed their primary education. Table 1 gives the details
of the sample population. The younger students were attending the first year of
secondary education. In the eight years of elementary and middle school, which is
normally called the first grade or primary school in Brazil, they had only met
general notions about electricity, but had received no instruction about electric
circuits. Electricity and electromagnetism are taught at the second year of secondary education (age 16). The other two student groups differed in the purposes and
orientation of their study of electricity.
Data were gathered by means of semi-structured interview which consisted of
a number of simple experimental situations involving prediction–observation–
explanation (White and Gunstone 1992). This type of probe has been shown to
be a useful way of uncovering individuals’ understandings of concepts and beliefs
Table 1. Population details.
First-year secondary students (age about 15). Had not studied
electricity and magnetism yet
Third-year secondary students (age 17–18). Had studied
electromagnetism in the year before
Third-year technical school students (age 17–18). Had studied
electromagnetism in the year before
Partially schooled practitioners in areas related to electricity. No
formal instruction in the subject
Electrical engineers with more than two years of work experience
Secondary physics teachers, most with long teaching experience
Number of
(Champagne et al. 1985). The same set of questions (see Appendix) was presented
to all the interviewees, but the follow-up depended on the responses given. The
interviews were audio-recorded and transcribed soon after the event. In designing
the research probes we were confronted with the need to think of interesting
situations which could be answered by all the interviewees independently of
their level of schooling. For this reason, only very simple circuits were used. All
the interviews were conducted in the Portuguese language, as was the entire analysis. In translating pieces of conversation with particular interviewees, the standard
form of English was adopted. We have attempted to portray what the respondents
might have meant by particular responses and actions.
Four models of electricity were identified among the population studied: electricity as flow, electricity as opposing currents, electricity as moving charges and
electricity as a field phenomenon. The models identified in this study are somewhat different from the models of electricity reported in previous research
(Osborne 1983, Shipstone 1984, Kärrqvist 1985, Heller and Finley 1992). A number of reasons seem to account for the differences. In first place, the subjects in
previous studies were typically secondary students with ages ranging from 11 to 16
years, although students at the end of primary school have also been studied
(Tiberghien 1983). None of these studies inquired into how adults, both
unschooled and professionals with an university degree, thought about electricity,
except those of Stocklmayer and Treagust (1996), and of Heller and Finley (1992).
This latter piece of research was exclusively into how elementary and middleschool teachers at rural schools in the USA conceptualize electric current. The
study only concerned those individuals holding alternative views of it: it did not
include in the sample teachers who already have ’ an essentially correct model’
(Heller and Finley 1992). The study by Stocklmayer and Treagust (1996) involved
adult apprentices and technical-school students as well as physics teachers and
university lecturers. Their findings support some of the models identified in the
present study.
Electricity as flow
This model is characterized by a poor differentiation between the scientific notions
of current, energy, electricity and voltage. Current is seen as ’ something’ flowing
through the circuit, from the battery to the bulb very much like water in a hydraulic circuit. This thing flowing through the circuit is sometimes referred to as
energy, sometimes as electricity or simply as the current. Subjects frequently
refer to its unseen nature. The battery is the source of the energy/electricity
which flows through the circuit. The need for a physical link between the source
of agency and the object which is acted upon was obvious it is suggested by a
number of everyday situations, for example a bulb only lights when properly
connected to a battery. Students usually adopted views similar to Andersson’ s
(1986) ’ experiential gestalt of causation’ . Practitioners, on the other hand, tended
to see the situations from the point of view of what is required for their function.
They emphasized some operative rules which contain the knowledge applicable to
specific situations and elements for troubleshooting. For instance, the rule that
’ only a complete circuit functions’ .
Terms like ’ energy’ and ’ electricity’ were used to designate the material substance flowing in a circuit. The battery was imagined as a passive container that
only stores electricity and wears out as its content is used up in the circuit elements. Current travels quickly around the circuit and is used up in the bulb.
Subjects holding this model did not describe a circuit’ s behaviour in terms of
internal mechanisms and processes. Their descriptions were rather based on the
association of perceived events and effects. This model was found exclusively
among first year secondary students (age 15) and partially unschooled practitioners. All the first-year students holding this model tried to connect the bulb
to the battery using only one wire, which indicates some form of ’ unipolar’ or
’ sink’ model. They required some support during the interview in order to light
the bulb. For instance, when an interviewee faced difficulties he/she was given a
bulb socket. The existence of two separated terminals suggested the way to complete the task and all of them succeeded in lighting the bulb in this way. This
indicates that the major difficulty for some of them was to recognize the bulb as a
dipolar device. None of the practitioners required any kind of support in presenting their ideas.
Luiz’s interview
Luiz started to work as an electrician some 15 years before these interviews were
conducted (1994), after working for some months as an apprentice. He had gone to
primary school for two years and he says that he can ’ read, more or less’ . He used
to live in a rural area before migrating to a city, where he worked as a labourer on
building sites. Luiz has never had any formal instruction in electricity, and has
only hands-on experience. He associated electric current with circuits, and with
the notion that there is something passing in the conducting wires of a circuit.
S: I understand that current . . . is a circuit . . . It is the positive wire . . . the live wire.
I: Is there something in the wire?
S: Only electrons and copper, isn’ t it? The wire is copper.
I: And what is this electron?
S: It’ s the voltage that runs . . . It comes from the power station and passes along the
I: How is that?
S: Oh, that’ s hard to explain. I haven’ t studied this.
Luiz was asked to light a torch bulb using a battery and some pieces of wire,
but he did not feel confident to do so. He did manage, however, to light the bulb
with relative ease. Luiz explained that what causes the bulb to light is the existence
of a complete circuit. Current and electricity do not take part in this explanation.
S: I have to use two wires, haven’t I. I never tired this before.
I: Is this different from a house wiring?
S: The voltage is different because this is DC. But the wiring is the same . . . To install
a switch I have to do the same as I’ m doing here . . . that is, I think I have [he
I: What is it that makes the bulb light?
S: What lights it up is the neutral and the live . . . they go into the bulb, then to the
switch and returns to the bulb
I: do you have neutral and live in here?
S: Here? I must have.
I: which one is the neutral?
S: This, the bottom of the battery . . . but I’ m not sure, ’ cause I have no experience
with this.
In Luiz’ s view, the battery only connects one wire to the other. Although he
thought of it as a reservoir of electricity, it has only a passive role. The bulb lights
up because it completes the circuit, putting the ’ neutral’ wire in contact with the
’ live’ wire. He appeared to suggest that he bulb is short-circuiting the neutral and
the live, and in this way producing light. Luiz appeared to think in terms of what is
needed for lighting the bulb, which is more effective in practical problem-solving
situations. He mentioned a number of technical terms, like current, energy and
voltage, as interchangeable.
I: What is going on in the battery while the bulb is lit?
S: One end is meeting the other and providing passage, or else it wouldn’ t light up.
There are two parts here in the battery – top and bottom. If I connect them I’ m
closing a short.
I: And in the wires, what is going on?
S: It’ s passing current through them.
I: How is that?
S: Electricity . . . the electric part.
I: Is there anything passing in this wire?
S: Yes, there is electricity.
I: Is it the same in both wires?
S: No, one is neutral and the other is live.
I: What happens when they arrive at the bulb?
S: It lights because it closes . . . closes one with the other.
I: Where does this electricity come from?
S: From the battery . . . it’ s charged but is going to discharge and to wear out.
I: How is that?
S: Its power will die out. Then it has no more use, it doesn’ t light the bulb any more.
Finally, Luiz was asked to consider a normal lighting situation, like in a room
in which an incandescent bulb lamp can be turned on and off by means of a switch
located in the wall. Luiz explains the switch functioning in terms of completing the
S: The live goes into the switch and form the other end comes out the returning wire
that connects to the bulb . . . when you turn it on, you close the live and returning.
The neutral is up there in the bulb, then the circuit is complete.
I: Why does the bulb light immediately when one turns the switch on?
S: Because it’ s closed there, then if you close here it lights quickly. It must light up
quickly or else there’ s some problem . . . in the bulb or in the switch.
Luiz’ s thinking was procedural. That is, he was concerned with the rules for
wiring electrical circuits properly and with safety procedures. His knowledge of
the lighting circuit functioning already includes elements for troubleshooting.
That is the kind of knowledge that is vital in his work.
Electricity as opposing currents
In this model current is not clearly differentiated from energy: both terms are
sometimes used as equivalents. Current is seen as energy or electricity flowing
through the wires in a circuit from both terminals of the battery towards the bulb.
It is assumed that positive and negative currents travel along separate wires and
that they meet at the bulb to produce heat and light. Thus, this model explicitly
assumes a non-conservation of current. The battery is still seen as a reservoir of
electricity/energy, which wears out with time as a result of energy consumption in
the bulb. A closed circuit is necessary to light the bulb, and current is assumed to
travel fast through the circuit. The role played by a switch in the circuit is not
clear: some individuals suggest that it produces current.
Students sometimes mention protons and electrons, suggesting that electric
current consists of electrical particles moving through a circuit. There is a tendency for students to adopt explanations in the form of a time sequence of events.
This seems to arise from the form of system modelling noted by de Kleer and
Brown (1981), and by Gutierrez and Ogborn (1992). Practitioners, on the other
hand, often refer to a short circuit occurring in the bulb which causes it to light. All
the students holding this model attempted to light the bulb using only one connection to the battery. However, all of them succeeded in making it light after
being given a bulb socket. Apart from two third-year students, all the other subjects holding this model had not studied electricity before. This model agrees with
the well documented ’ clashing currents’ model (Osborne 1983, Shipstone 1984,
Kärrqvist 1985).
Lucio’s interview
Lucio had been working as a electrician for the previous eight years. This involved
doing electrical wiring and maintenance of the electrical network in the university
buildings. He had worked for some time as a bricklayer helper and then spent
about six months as an apprentice electrician on building sites. He had no formal
instruction in electricity, only the help of an experienced electrician. Lucio had
attended the four initial years in primary school and then dropped out. For him,
electricity is a good area to work with:
S: . . . But one has to be careful. It’ s a job in which you cannot make mistakes.
I: What is electricity for you?
S: It’s something that nobody sees. It’ s passing there and no one sees it.
I: What comes to your mind when you think of electric current?
S: There’ s high and low current. High current is dangerous, depending on the
voltage . . .
I: You were taking about something that no one can see in the wire. What is it?
S: I can’ t explain it rightly . . . because it’s energy we don’ t see it . . .
Lucio had no difficult in connecting the torch bulb to the battery. He
explained that the bulb lights when it is short-circuited. He meant that the positive
and negative wires have to go into the bulb so as to make it light. He thought of
current as a sort of energy coming through the wires – positive in one and negative
in the other. When asked about what is going on in the battery he answered that he
thought that the carbon rod existing within a dry cell is a small generator. Lucio
did not refer to any processes taking place inside the battery and so this idea
appears to account for the production of electricity in the battery.
I: What is it that makes the bulb light?
S: For it to light we have to close a short in it.
I: what do you mean by closing a short?
S: The positive and the negative come together, and then it gets in short . . .
I: What is going on in the battery while the bulb is lit?
S: I think it has a tiny generator inside . . . which is that carbon stick it has within.
I: Have you opened a battery?
S: Yes . . . it has carbon which comes right here [at the positive terminal].
I: And in the wires?
S: In the wires . . . the current comes from the battery to the bulb.
I: Is it the same thing in both wires?
S: No . . . It’ s not the same. One is positive and the other is negative.
Lucio did not refer to processes taking place inside the battery and the wires,
except that current is passing trough. He thought of a switch in a circuit as a device
controlling the passing of current, which feeds the bulb with electricity. He recognized that when the bulb is off there is ’ energy’ in the switch, and thus it may be
dangerous to touch it. He explained what happens in the switch in a lighting circuit
that causes the bulb to light.
S: The bulb lights because the switch sends energy to it . . . When it’ s off it doesn’t
send energy.
I: Is there electricity in the bulb when the switch is off?
S: No, because it is that which sends energy
I: Can I handle the circuit without danger?
S: No, there’ s energy in the switch. If the bulb is on, then you must turn the switch
off before touching the bulb.
Electricity as moving charges
A number of third-year students, some technicians, and a few engineers, held the
view that current consists of electric charges in motion through a conductor. The
battery was seen as an active source of electricity, that is, it produces energy which
is delivered to the charges by means of a chemical reaction. Bipolarity of circuit
elements and the need for a closed circuit were evident. The circuit behaviour was
explained in terms of a time-dependent sequence of events, which is likely to have
arisen from reasoning in terms of a chain of causes and effects (Gutierrez and
Ogborn 1992). The emphasis is on the behaviour of individual components, so
that it appeared that subjects holding this model were not able to perceive of the
circuit as an interacting system.
Energy transformations were frequently described and current was assumed to
be conserved. The battery supplied energy to the particles to keep them circulating, and this energy was consumed on passing through resistive elements. This
model incorporated simplified mechanisms to account for processes taking place in
a circuit. A number of mechanical and anthropomorphic analogies were mentioned
to explain the interactions of the particles with the atoms of the circuit components, such as collisions and movement through a viscous medium.
Rui’s interview
Rui (TAC-09) was in the last year of a secondary technical school doing electronics. He thought of electricity in more practical terms and associated the idea of
electricity with devices and apparatus he dealt with in laboratory classes and at
home. His view of electric current were operational, that is, related to the kind of
knowledge one should have in order to quantify it.
S: What comes to my mind when I think of electricity are its everyday uses, mainly in
lighting . . . and also its use in electronics in things like a video recorder, compact disc
players and liquid-crystal displays . . . When I’ m trying to organize how a given
device works . . . then I think of it in terms of components, that is, of coils, transistors
and so on . . .
I: What comes to your mind when you think of electric current?
S: Electric current? . . . It’ s measured in amps. There’ s a definition we use: it’ s the
ordered motion of electrons. But I really think of the measuring unit, the amp . . . It’ s
important to know if a given current is large or small and whether it’s AC or DC.
Rui completed the practical tasks with ease. He drew on the idea of an electric
current as electrons moving through the circuit as being much like cars travelling
in a road, one behind the other. His view of electric current implied that electrons
move to occupy the place which other electrons have just left. The bulb filament
has a capacity of emitting light when crossed by a current. The battery is an active
source of electric charges, however Rui only mentioned the chemical reaction
occurring in a later part of the interview.
S: There’ s a current passing through the filament. Tungsten has the ability of giving
off light when circulated by an electric current.
I: What is going on in the battery while the bulb is lit?
S: It releases negative charges that go on to the positive terminal . . . This current
flows through the bulb and goes back to the battery.
I: And in the wires?
S: The current that just left the battery.
I: How do you imagine this?
S: Oh, it’ s like lots of cars in a traffic jam, only that they are electrons instead of cars,
moving one after the other all over the circuit and returning to the battery.
I: What happens when the reach the bulb?
S: They reach the bulb . . . then there’ s a swap, that is, while some are coming out
others are coming into their place . . . and the whole thing start again in a cycle.
I Is it the same thing in both wires?
S: Yes, there are electrons in both wires, but they keep moving around the circuit.
Rui explained that a switch changed the circuit resistance. This is infinitely
large when the switch is open, and then current cannot flow. In this view a bulb
lights instantly after the switch is closed because current travels at the speed of
light. By this he meant that electrons actually move at the speed of light, as he did
not employ the notion of an electric field being established in the whole circuit.
S: The switch has a metallic slab which links the two wires connected to it. When it’ s
turned off, the slab moves aside and there’ s no contact. Thus the resistance becomes
infinite and there’ s current.
I: Why is it that the bulb lights immediately when the switch is turned on?
S: It completes the circuit and current start to circulate from the positive to the
I: Why is it so fast?
S: Current travels at the speed of light and then reaches the bulb quickly.
I: Do electrons move at this speed?
S: Yes, I think they do . . . I cannot remember it but I know it’ s very high.
Electricity as a field phenomenon
This model comprises some knowledge characteristics of the models presented
above. Current is distinguished from energy and it is understood as the movement
of electrically charged particles under the action of a potential difference. Current
only circulates in a closed circuit and is conserved: the bipolarity of the circuit
elements is recognized. The battery maintains a deference of potential between its
terminals which creates an electric field. This, in turn, causes electric charges to
move along the conductor. People holding this model also referred to energy
transformations, but they explained the processes going on in a circuit in terms of
an electric field acting on the charges.
The circuit was perceived as a whole interacting system, and when a change is
made in it an electric perturbation propagates through the circuit establishing a
new steady state situation. Although subjects still thought of electric current as
motion of charges, they were able to recall field-like explanation when prompted.
This model was found to be held by half of the physics teachers and a few technical
school students.
Almost all the engineers and some teachers and a few students held a different
version of this model. It is similar to the ’ field model’ in most of its aspects.
However, these subjects preferred to adopt a functional description of the circuit
behaviour in terms of energy and voltage. Thus, these subjects frequently referred
to energy transformations, but were not able to describe them. Energy transformation seemed to be a process that does not require further explanation. Individuals
holding this model variation were likely to see the circuit in a holistic way, in that
they did not use time sequence descriptions of the circuit, nor focus on each
component’ s behaviour. Nonetheless they did not explain circuit functioning in
terms of electric field. For this reason they could not properly explain why the
bulb lights immediately on turning the switch on.
Valdo’s interview
Valdo had concluded his university course in electrical engineering two years
previously. He had little experience in the profession, but has worked for some
time as an electronic technician and during his university course. During his
university years he worked as a teacher, in an evening course for unschooled
electricians. he was now studying for a MSc in electronics. Valdo associated electric current to something flowing in a circuit, which may be treated in mathematical terms as a flow variable.
S: when I think of current, two different sorts of ideas emerge . . . Firstly there is the
idea of something flowing . . . something which is passing. Current has no meaning –
it’s only something flowing. A sort of water flow. That is, the analogy that everybody
mentions is that electric current is like water flowing . . .
I: It is like that then?
S: It’ s similar, but it’ s not the same thing. On the other hand, you can think of it as a
mathematical representation of the thing . . . In general terms, it’ s a flow variable,
similar to those used to represent fluid and heat flow.
He clearly distinguished current from electricity and energy, and had no difficult in completing all the tasks. He explained how the bulb lights up when
connected to a battery in terms of electrical energy being transformed into heat
and light. The bulb filament functions as a hindrance which the current has to
I: What is it that makes the bulb light?
S: have an energy source, this battery . . . There’ s a potential difference between the
two terminals. When you create a conducting path between the two potentials where
energy is stored . . . It’s as if you had a water reservoir and pipes that allow this water
to flow through . . . It goes from the higher to lower potential energy . . . If a path
exists then a current is created. the bulb is an obstruction in this path . . . In it electrical energy is transformed into light.
I: How does this transformation come about?
S: By heating. When the current pass across the bulb filament it transforms electrical
energy into light and heat. first the filament heats a lot, somewhat close to a thousand
degrees, I think.
Valdo though of the battery as an active reservoir of charges. When a closed
circuit is provided, the battery transfers charges from one terminal to the other,
supplying them with energy. His model of the battery included an internal resistance which increases with time. To explain what is happening in the battery
during the operation of the circuit, Valdo used a simple model in which electrons
are treated as small hard particles injected by the battery into a tunnel-like wire.
This is similar to the type of description encapsulated in the model of electricity as
moving charges, used by some of the third-year secondary students. But he was
able to describe the situation in more abstract terms, without resource to such
concrete images.
I: What is going on in the battery while the bulb is on?
S: It’ s leaking charge. There’ s a chemical reaction which moves charges across the
battery and where the charges acquire energy from.
I: Is there energy stored there?
S: It’s stored as chemical energy. When a viable path exists the battery
discharges . . . It moves charges from one terminal to the other, that is, from one
potential to the other . . . With time the resistance of this battery grows because the
carbon electrode oxidizes . . . That is, the battery also offers resistance to the passage
of current and for this reason it heats.
I: And what is going on in the wires?
S: They carry energy.
I: Why is that?
S: The potential difference causes it . . . It causes charges to circulate. You can think
of this in terms of a simple model: imagine that there are many small billiard balls, one
behind the other and pushing each other. When more balls are injected at one end of
the wire, those in the opposite end move out immediately . . . But there’ s a hindrance
in the circuit. In it they must be pushed harder and because of friction that produces
heating. Thus the filament gets incandescent and lights up.
I: You said that this is a simple model. Is there another more sophisticated model?
S: I can describe it mathematically . . . You have to think of electrons is an electric
field, created by that potential difference. This electric field is transmitted through
the wire and makes the charges to move instantly through the circuit . . . I don’ t need
to inject charges into the circuit.
Valdo coped well with the remaining situations. He again used the billiard-ball
model to distinguish the processes of matter and energy transport in a circuit. He
was asked why the bulb lights immediately when the circuit is switched on.
S: Let’ s imagine the wire as a tube full of small billiard balls, one after the other.
When you close the switch you’ re allowing the energy source to apply an ’ effort’ ,
available as electrical energy. This push is transmitted through the balls quickly – you
push the first ball and this impulse propagates instantly through the whole circuit. In
this way, energy is transferred to the bulb . . . Electrons’ speed is very low and is quite
different from the speed which energy travels.
The present study inevitably raises the issue of the extent to which the form and
substance of the questioning used to elicit people’ s views about science topics
affects the forms of explanation produced. Individuals apparently can hold different views or ways of explaining things, and can hold different mental models with
which to cope with events and states of affairs (Viennot 1994). A particular view or
form of explanation is triggered by the specific question posed. In this way, it does
not make sense for an individual’ s response to be analysed without reference to the
question he/she was asked. That would explain why a ’ sharing model’ (Shipstone
1984, Kärrqvist 1985, Heller and Finley 1992) was not found in this study. This
model is only needed to explain the behaviour of more complex circuits. In this
study more complex questions were deliberately avoided, given the varied prior
experience of the subjects with electrical matters. It was decided to ask simpler
questions so that everyone would have something substantive to say about them.
It was found that some features of an individual’ s model of electricity are
linked. The differentiation of current and energy, alternative views of the way
that current circulates through a circuit and the lack of conservation of current
are always associated with less developed models of the nature of the electric
current. Such ideas seem to have little or nothing to do with the practical ability
to wire a circuit correctly. Most practitioners, for instance, do not have knowledge
of the principles governing the working of circuits, although they can cope with
their daily tasks. On the other hand, all those subjects holding more sophisticated
models of the nature of the electric current were able to make the connections in
order to light the bulb and explain the functioning of simple circuits. That suggests that science teachers should try to help students to develop better models for
the nature of current.
The mental models of electricity identified in this study exhibit a pattern of
changes along several dimensions as individuals’ models evolve over time. In particular they show changes in the scope and limitation of models, in the differentiation of basic notion, in the adoption of a richer vocabulary, in the use of more
abstract notions, and in the introduction of new entities (Borges 1996). The case
studies reported exhibit many instances of such changes. The distribution of models across the population (see table 2) suggests a rough progression from simple
phenomenological models up to the culturally accepted scientific models. This
progression suggests that individuals develop simple initial models for some
aspects of a given domain. These are constructed from everyday knowledge of
how things work in that domain. Initially subjects are likely to hold different
models for specific situations and, for this reason, when responding to different
probes, their knowledge may appear incomplete and inconsistent. They do not
master the specific vocabulary used in that domain and basic concepts are likely
Table 2.
Distribution of models of electricity across groups.
Electricity as
to be little differentiated. In this way, initial models make few claims about the
nature of the systems dealt with and have little predictive and explanatory power.
As subjects acquire knowledge about that subject matter, new aspects are
incorporated to his/her initial models. The vocabulary related to such models
becomes progressively richer and the basic concepts differentiated. New ontological entities are introduced in the model for that class of phenomena. They may
reclassify the ontological status of existing entities (Chi et al. 1994). Therefore
subjects are able to tell more complete and sophisticated stories about the events
and phenomena in that domain. Underlying such a progression are changes in
individuals’ reasoning. They initially focus on the objects forming a situation
which are unproblematic and salient. With time, the focus changes to the consideration of interactions between those objects and to the internal structures and
entities that give rise to such interactions. These are posited to account for the
observed behaviour. It appears that only with deliberate instruction can learners
come to adopt more sophisticated models. This trend has been found in other areas
of science education (Driver et al. 1994).
In a number of cases it was not possible to assign a model of electricity to each
of the respondents. In such cases, the responses appear fragmented and the set of
conceptions of particular subjects appears to support more than one kind of model.
These may be thought as cases of ’ mixed models’ , or even cases of subjects holding
a set of fragment ideas, perhaps strongly dependent on the context. This is not,
however, an issue specific to this study. It seems to be a general problem when one
attempts to elicit others’ mental models, and has been discussed by a number of
researchers (see Shipstone 1984, Gott 1985 and Vosniadou and Brewer 1992). In
any case, it is not always possible to trace a sharp line delimiting a model’ s or a
category system’ s boundaries.
Table 2 shows the distribution of models of electricity among the study population. It suggests that models ’ electricity as flow’ and ’ electricity as opposing
currents’ are acquired without the need of explicit instruction. On the other
hand the models ’ electricity as moving charges’ and ’ electricity as field’ are associated with physics instruction at secondary school and at university level, respectively. A surprising finding is the number of practitioners holding a moving charges
model compared with first years, for only two of the former had concluded primary education. Secondary students should have been taught some notions of
electricity at primary school. However, this is not actually the case, because
most middle school (ages 11–14) Brazilian science teachers usually have a background in biology or related areas and avoid dedicating much time to topics on
physics and chemistry. This also explains why so many 15 year olds faced difficulties in lighting the bulb and appeared initially to hold na¨õ ve models for current
circulation, when compared with previous research findings (Shipstone 1984,
Osborne and Freyberg 1985).
Some of the practitioners revealed their curiosity about electricity during the
interview. This had led them to read about electricity in books and magazines. All
the three practitioners holding such a model have been working in close co-operation with teachers and engineers. Therefore, knowledge of electricity resulted from
their personal engagement and motivation, and was not related to previous academic experience with the subject matter. Mechanical images of electric current,
such as the view of electricity as moving charges, predominated among 17-year-old
students and is the main outcome of physics instruction in the subject. The five
remaining subjects were found to hold mixed models of electricity.
The models ’ electricity as flow’ and ’ electricity as opposing currents’ represent
an aggregate view in which the entities assumed to form an electric current are not
treated individually. They both make little claim concerning the nature of electricity and are essentially descriptive models and predominate among those who
have not studied the subject yet. They are both too limited to raise further questions about the behaviour of electric current and they do not require experimentation. This is different from the other models, ’ electricity as moving charges’ and
’ electricity as field’ , which are more popular among those who have already studied
electricity. These models suggest that a number of phenomena related to electric
current have to be explained and are amenable to empirical testing. For instance,
that there is a relationship between the intensity of current, the potential difference
of the battery, and the conservation of current throughout a circuit. The images
and metaphors that subjects use to speak about a circuit suggest issues to be
inquired into. For instance, how is it that electricity is transformed into heat
and light? What parameters affect the electrical resistance of conducting wires?
The distribution of models across the groups suggests that the first two models
arise from everyday encounters with electricity and from knowledge already available in the common culture, while the other two models are acquired through
deliberate instruction.
Implications for science teaching and research
The findings of this study suggest that what is referred to in the literature as
’ sequential reasoning’ or ’ causal sequential reasoning’ needs be studied in more
detail. It has been characterized in different ways, for example by Closset (1983),
and Rozier and Viennot (1991), and appears often in the form of explanations
involving a time sequence of events. It has been explained as the consequence of
the adoption of chains of cause and effect (Rozier and Viennot 1991), and from a
view of time being a discrete variable instead of being continuous (de Kleer and
Brown 1983). However, it may result from a broadly standard form of discourse
adopted by science teachers and textbooks. In this study it was hardly found
among practitioners and 15-year-old students.
As discussed earlier in this paper, the acquisition of a scientific understanding
of a given aspect of the natural world is best conceptualized in terms of developing
a mental model of it. Such a model can be run in the mind’ s eye to generate
explanations and predictions related to the behaviour of that system. Any strategy
intended to help students to generate better mental models of a consensus model
must give consideration to the dimensions along which an individual’ s model
progresses. The present study suggests (Borges 1996) that models progress by a:
change in the scope and limitation of models. More sophisticated models
address a larger database of empirical observations in each domain. Models
may expand to account for novel phenomena and may specialize to exclude
anomalies. In this way, old models may still provide adequate explanations
in a narrow domain. This indicates an ability to transform an ill-structured
problem into a better structured one;
differentiation of basic concepts and the adoption of a richer vocabulary.
The basic notions and concepts become better defined and differentiated in
the process of acquiring a common language to speak about phenomena in
that domain;
shift from qualitative to quantitative models. This is accompanied by the
use of more sophisticated notions, amenable to mathematical representation. More sophisticated models do not refer to phenomena as they are
perceived, but rather to constructs and entities more detached from everyday experience. Grosslight et al. (1991) suggested that students’ notions of
’ model’ themselves evolve;
change in ontology. New models often introduce new entities to account for
novel aspects of a given domain. In many situations this implies a move
from macroscopic to microscopic models;
change in the forms of explanation adopted. Initial models tend to be
descriptive in character – knowledge of what happens – and no causal
mechanisms are involved.
Teachers, instructional material, and activities designed to teach electricity, should
give special attention in exploring such aspects. Thus, the model of a system or of a
domain should introduce the appropriate vocabulary, define the entities involved
in producing the system’ s behaviour, and also define how the parts which form the
system are interrelated. Otherwise, learners will find it difficult to construct productive models of that system and to speak meaningfully about it.
Model progression seems to be a general feature of learners in different science
domains (Driver et al. 1994). On the other hand, recent research suggests that
students would profit from learning to see a given domain from different perspectives (Eylon and Ganiel 1990, White and Frederiksen 1990). In particular, they
should be able to interpret physical phenomena from a phenomenological or
macroscopic, point of view and from a microscopic perspective, and to relate
one to the other. The identified mental models could serve as a basis for constructing simple teaching models to introduce younger students to a domain. For
instance, the model ’ electricity as flow’ appears to be the basic idea underlying
most people’ s models of electricity. Initially, teachers can build upon such a notion
to explore simple electrical systems. This view of electricity as a kind of fluid may
allow younger students to avoid the traps of attempting to adopt a microscopic
model too early without the necessary background. Likewise, simple models for
batteries, bulbs and other circuit components may be devised. This sort of model
works well for practitioners and by itself it is not an impediment for students to
acquire hands-on experience and more developed models later on.
This is equivalent to the use of ’ bridging conceptions’ (Clement et al. 1989).
The idea is to build upon intuitive models that even young students can accept and
help them to develop such models. In a later phase a microscopic model will have
to be introduced. The early introduction of such kind of model creates an overload
for learners because a great number of processes are involved even in simple
situations. Therefore, attention should be given to teachers’ own models and to
the ’ teaching models’ (Gilbert and Boulter 1995) they choose to use in classroom
because of the impact they have on children’ s ideas about a subject matter. In a
teaching situation, the terms used to refer to that class of phenomena, the entities
and structures that form the system and the way they interact should be explicitly
introduced. Students must make sense of why the different parts of the system
they are learning about interact in that particular way. that will allow them to
develop their mental models about the mechanisms acting to produce the system’ s
behaviour and to generate explanations for phenomena and events associated to it.
This study has found four models of electricity among a quite heterogeneous
population, both in terms of schooling and of hands-on experience with the subject
matter. These models attempted to capture the progression in individuals’ models
along a number of dimensions: changes in the scope and limitation of models;
differentiation of basic notions and adoption of a richer vocabulary; use of more
abstract notions and introduction of new entities. In such a view of progression,
individuals start with a general model of ’ electricity as flow’ . It pictures electric
current as a material stuff flowing form the battery to the elements of a circuit
where it is used up. This is referred to as ’ electricity’ , ’ energy’ , or ’ voltage’ . The
battery delivers a ’ substance’ to the circuit and for this reason wears out with time.
Subjects holding this view do not refer to unseen entities or mechanisms to
account for electrical phenomena.
The model ’ electricity as opposing currents’ comprises the notion of two distinct types of electricity flowing in opposite directions towards a light bulb, where
they meet to produce light. This view suggests that electric current is not conserved. Terms like ’ current’ and ’ energy’ are not differentiated. The model ’ electricity as moving charges’ appears to be the more likely outcome of secondary
instruction about electricity. It comprises a description of electricity as electrons
moving under the action of a potential difference. Subjects holding this view
normally use mechanistic and anthropomorphic analogies to refer to electric current and electric resistance. This model includes new entities and mechanisms to
account for some of the microscopic processes taking place in a circuit. Finally, the
model ’ electricity as on field phenomena’ includes all of the previous model.
However, individuals use on the notion of an electric field or an electric signal
which travels through the circuit to explain how a change at a point in a circuit
achieves a new steady state and why electric current travels so fast.
The approximate sequence of models identified corresponds to different views
of the nature of electricity. Model progression appears to be a general trend in
other areas of science as well. It exhibits the evolution of learner’ s sense of how
things work and why they behave in the ways they do. That suggests that teachers
and science educators may profit from knowing typical forms of mental models
about each science topic in order to develop new teaching models and teaching
sequences to help students to acquire more productive models.
This study would not have been possible without the sponsorship of the Brazilian
Educational Agency (CAPES) and from the Universidade Federal de Minas
Gerais for A. Tarciso Borges. The people and the organizations involved in this
study are warmly thanked for allowing their daily routines to be disturbed in order
to conduct the interviews.
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Interview schedule
(1) What comes to your mind when you think of:
(a) Electricity?
(b) Electric current?
(c) Electrical energy?
(2) You have a bulb, a D-size battery and some wires, I want you to light the bulb
up using this material.
makes the bulb light?
is going on in the battery while the bulb is lit?
is going on in the wires while the circuit is on?
is it that sometimes makes bulbs break?
(3) Here you have another battery (AA size) which you are going to use in the
place of the first battery.
(a) What do you expect to happen to the bulb’ s brightness on replacing the
(b) Why do you think that?
Change the batteries.
(c) Does the outcome agree with your prediction? Why is that?
(d) What is in the battery that is affected by its size?
(4) In a common lighting situation an incandescent lamp is fixed in the ceiling and
can be turned on/off by means of a switch on the wall.
What does the switch do to make the lamp light when you turn it on?
Is there electricity in the lamp when the switch is off?
Why do you think so?
What is it that makes the lamp light immediately after one closes the
(5) What comes to your mind when you think of:
(a) Electricity?
(b) Electric current?
(c) Electrical energy?