University of Thessaloniki, Greece
The teaching and learning of electricity, a topic often included in primary and secondary curricula, has been the object of many investigations, books and conferences (Duit et al, 1985; Calliot, 1992). The emerging picture world-wide is not promising given that an adequate knowledge of, for example, electrical circuits has rarely been acquired by students by the end of secondary education. Research results provide a fairly clear view of a variety of students' topic-specific alternative ideas (an extensive review is presented in Section C of this volume). Moreover, it emerges that students encounter deep-level conceptual and reasoning difficulties in understanding introductory electricity which the usual or innovative teaching tends to ignore rather than explicitly take into account.
Briefly stated, students demonstrate learning difficulties with regard to:
i) Developing systemic reasoning
Linear causal reasoning is employed by students to account for the functioning of electrical circuits. In simple circuits, causal models are of a source-consumer type resembling, from the scientific perspective, an energy view of simple circuit operation. Often, following the teaching of resistance, sequential models develop, according to which any disturbance travels in one direction affecting circuit components in succession. Linear causal reasoning is fundamentally different from the systemic reasoning which is necessary to understand the electrical circuit as a closed system in which all components interact with each other and any disturbance extends in all directions.
ii) Conceptual differentiation
Students confuse features of current and energy; voltage being considered a property of "current" indicating its "strength". All the scientific concepts collapse under the global-undifferentiated notion of "current/energy".
iii) Establishing phenomenological relations
Students do not relate the phenomenologically different areas of electrokinetics and electrostatics (Frederiksen & White, 1992). For the students, there are no obvious common features between the attraction/repulsion of electrified bodies and the lighting of a bulb.
iv) Linking different models
The establishment of relations between several models - qualitative with quantitative ones, macroscopic ones with underlying microscopic mechanisms - is another source of difficulty for the students (Eylon and Ganiel, 1990).
It is worthwhile noting that students' difficulties such as the above are not specifically limited to electricity but appear across several other topics involving physical processes (Driver et al, 1994; Viennot, 1993).
1. Pathways for teaching electricity
It appears that the consensus which has been achieved gradually among researchers concerning students' learning difficulties has not brought about a consensus on the appropriate pedagogy. Thus in the search for remediation, several research-based pathways have emerged following a constructivist perspective on teaching and learning, according to which the learner is an active agent of his own knowledge construction and the learners' domain-specific prior knowledge is a crucial factor in acquiring new knowledge.
In one pathway, proposals question the feasibility and the educational value of pursuing understanding of the mechanism of the electrical circuit by the students. Since adequate understanding of electrical circuits is difficult, the argument goes, teaching of electricity should focus on important applications, for example electricity at home and/or electrical energy saving ( Berg & Grosheide, 1993 ). In another pathway, however, several proposals focus on effective strategies to render learnable the essential features of more traditional subject matter such as that of understanding of function of electrical circuits.
Within the second pathway, some proposals rely on analogies and analogical reasoning as a vehicle for inducing conceptual change in the students. For example, water analogies are suggested in order to facilitate understanding of the electrical circuit as a closed system (Schwedes, 1995). Yet other approaches use confrontation strategies (Scott et al, 1993) as a means of facilitating conceptual change in the students (Shipstone et al, 1988; Licht, 1991). The above categorisation does not entail the mutual exclusivity of strategies and means employed in several pathways. For instance, the use of some type of analogy seems unavoidable in order to render intelligible current conservation. The differences lie in the relative emphasis put on these strategies as well as in the purposes they serve.
In this context, the present paper outlines key aspects of one approach to teaching basic electrical concepts in secondary general education utilising confrontation strategies. This is one of the teaching sequences developed in a research and innovation programme, concerning various aspects of teaching electricity, carried out over a peroid of several years by the Science Education Group at the School of Education in the University of Thessaloniki (Psillos et al, 1987; Koumaras, 1989).
2. Scientific knowledge
Any approach to teaching and learning science is influenced by epistemological considerations concerning the structure and the object of the scientific knowledge to be taught. We accept here that modelling of the real world is a main function of scientific knowledge (Hestenes, 1992). The core of scientific knowledge comprises models of real objects and processes that are elaborated and shared by the scientific community in order to interpret nature. Models are embedded in theories and are testable in an experimental field (Bunge, 1973). The process of creating theory and models does not consist of an extraction of the common factors from a set of observations, as empiricists would claim (and as has been adopted in several physics curricula and teaching practice). According to constructivist epistemology there are strong links between the questions asked of nature, observations and the theoretical framework.
Questions that are relevant within one theoretical framework are meaningless in a different one. In electricity, enquiry into the nature of the electrical fluid (Stoclmayer and Treagust, 1994) is irrelevant in the context of the Drude model. Any theoretical approach refers to one experimental field and is instrumental in structuring it. For instance, the unification of electrostatic and electrokinetic phenomena was possible only after the work of Ohm and Kirchoff and the employment of surface charges in electrical circuits. Explanations are embedded in a theoretical framework the evolution of which implies a change in the type of explanation and causality accepted by the scientific community. Following Faraday and Maxwell, the electromagnetic field provides the basis for explaining the unified electromagnetic phenomena in classical electrodynamics.
In the development of scientific knowledge, there is a continuous interplay between experimental field, models and theory which shows the need for validating and establishing links between these different levels. Such a creative process requires considerable intellectual effort and is usually the product of collaborative activity producing objective models in the sense that they have been validated and are publicly accepted. Thus scientific models and theories transcend personal idiosyncratic views which students hold as products of everyday interaction with phenomena and ideas. They become part of a shared culture implying a particular way of "seeing" nature.
3. Assumptions about science teaching and learning
Briefly stated, the following assumptions have been taken into account for the development of the teaching sequence on electricity which is outlined in the present chapter. These assumptions do not make up for a comprehensive model regarding the teaching and learning of science, but concern important issues in matching students' learning difficulties with our epistemological perspective.
First, we consider that teaching science should involve all levels of scientific knowledge, namely theory, models, experimental field (Tiberghien et.al,1995). However, scientific models are different in scope and structure from students' personal views of the world. On the one hand, this means that comprehension of scientific models and involvement in modelling activities may imply a conceptual change for the students. On the other, scientific models must not be too distant from students reasoning in order to be intelligible. This implies that a transformation of scientific knowledge in order to be adapted to students' causality is necessary in several cases.
Second, in science teaching, there should be a coherence between the models to be taught and the corresponding experimental field which provides the experiential basis for meaning making. A corollary of this thesis is that the enlargement of the experimental field to be taught should imply the successive presentation of more powerful conceptual models.
Third, in science teaching models should be treated as hypothetical constructs. This, in turn, necessitates a validation process as an essential ingredient for the development of scientific knowledge.
4. The development of models
We outline key aspects of a teaching sequence in introductory electricity, demonstrating the gradual enlargement of the experimental field as well as the successive development of the corresponding models. Various versions of this sequence have been used with samples of students at the end of compulsory secondary education in Greece (15yrs). At this level, physics is taught as a compulsory single subject for two years. Electricity is also taught at primary school, in the context of a two-year course in natural sciences.
The conceptual objectives of this sequence included description and interpretation of circuit behaviour and electrostatic phenomena in terms of the physical quantities V, I, R, E, Q and t. The cognitive objectives included the differentiation of the concepts of V, I and E, the development and use of appropriate models to account for electrical phenomena, the linking of electrostatic to electrokinetic phenomena and the development of a systemic view for the electric circuit.
The sequence has been structured in four parts. The parts form a developmental hierarchy in terms of the questions raised, models which are taught and the corresponding experimental field. Subsequent models are self consistent, but are linked with each other leading to deeper levels of understanding electricity. For example, the concept of resistance is not introduced in the first, phenomenological, part. It is introduced qualitatively in the conceptual macroscopic part, then is related to a microscopic mechanism in the third, the microscopic, part and finally is studied quantitatively at the fourth, quantitative, part.
i) The Phenomenological part
The Phenomenological part has been designed as a long familiarisation period which is characteristic of constructivist approaches in electricity and elsewhere. The Phenomenological part, deals with questions meaningful for the students. These are formulated at the level of phenomena which refer to familiar objects and events and are in line with students' source consumer model, e.g., how does a bulb shine or what do we pay to the electricity board.
Batteries, bulbs and familiar applications such as a torch or Christmas tree lights make up the experimental field. Our research results (Koumaras, et.al) led us to an important decision concerning the experimental field; namely, to include events related not only to the intensity of lighting but also to its duration. This choice enlarges the experimental field, which usually includes only steady state situations in both traditional and constructivist curricula. As a consequence, events such as the duration of lighting or the "life" of a battery, which are familiar to students, are extensively treated in the sequence. We call these situations evolutionary ones.
In our case, scientific concepts are not introduced at this level. At the end of the phenomenological part students are expected to have become familiar with electrical phenomena and experiments, understand the closed circuit, construct causal relationships with respect to 'instantaneous' events referring to the brightness of the bulb and with events extended over time regarding the duration of lighting, for instance " batteries in parallel imply illumination for a longer time".
From the beginning of the sequence students are offered opportunities to experiment with batteries, bulbs and several materials in order to understand the closed circuit and classify materials as conductors and insulators. The knowledge gained about the continuous pathway is further validated for the students when they attempt to interpret familiar but not obvious situations. Thus, for example, a real bicycle is brought in the classroom and students are asked to predict and interpret the circuit of its dynamo.
In the next step, students are involved
in experiments in which they manipulate the number as well as the type
of connections between batteries and the bulbs. Teaching at this level
is limited to the establishment of relations between observable variables,
namely the number of batteries and bulbs, the circuit configuration and
variation of lighting. Students learn that lighting depends not only on
the number of batteries and bulbs but also on the configuration of a circuit.
Both the intensity and the duration of lighting are considered as important
effects. This facilitates the intelligibility of the new knowledge and
the construction of causal models for circuit functioning, as the following
extract from one classroom shows.
Task 1 (Fig.1) was presented to the students during the teaching of parallel connection of batteries and bulbs which followed the treatment of closed circuit and the series connection of batteries and lamps.
Bulb 1 Bulb 2
|The bulbs, batteries and wires
in both figures are similar.
Will bulb 2 shine more, less, or equally brightly than bulb 1?
Initially the students were asked to make their predictions.
Most of them answered that Bulb 2 will be brighter than Bulb 1:
"because in the second circuit there are two batteries while in the first there is only one".
After carrying out the experiment the students in one classroom were asked to provide their interpretations of the equal brightness. In the course of discussion with the teacher, several students introduced the duration of the lighting as follows:
".. With this kind of connection we do not have much brightness but it (lighting/battery) must keep on for more time."
".. With this connection of the batteries we gain time, that is the bulb will be on for double the time than if it were connected with only one battery".
Similar responses were noted in other classrooms, suggesting that when the experimental observations were different from their predictions, several students used the evolution of the functioning of the circuit in their interpretations of the data. By reasoning in terms of time/duration, these students managed to provide plausible, for them, explanations about steady-state tasks. Our research suggests that this is an ingenious reasoning strategy which students use effectively to reduce the conflict between their predictions and experimental results (Koumaras et al).
Finally, It may be noted that it is anticipated that students will persist with their source-consumer model by the end of the phenomenological part. For example, the bulb remains a consumer in students' minds; it has not acquired the status of a resistor.
ii) The Conceptual Part
Once the students have acquired an understanding of electric circuits at a phenomenological level, our results suggest that they are expected to raise conceptual questions of the type "what(quantity) changes when the connection of two bulbs changes?
More powerful models corresponding to an enlarged experimental field and capable of providing answers to conceptual questions are developed at this level. Our choice is on the one hand to repeat a set of phenomena encountered in the phenomenological part such as series and parallel connections of batteries and bulbs so on. On the other to enlarged the experimental field to include, voltmeter and ammeter readings and resistors. Domestic electric appliances such as hair dryers are among the several applications students deal with.
In our case, the conceptual part is based on the modelling of electrical phenomena at a macroscopic level including the concepts of voltage (V), current (I), energy (E), resistance (R), time (t). Simple use of microscopic entities (charged particles, electrons) is made only in response to students' questions regarding "what is flowing". With regard to the conceptual structures we may note that at this level domain knowledge has to be adapted to students' reasoning in order to be intelligible. Taking into account students' causality, the domain knowledge is decomposed into two partial causal models in order to account for brightness and duration of lighting. The first is the flow model, which puts into play the physical quantities V, I, R and their interrelationships. The second is the energy model, which puts into play the physical quantities E and t.
The starting point for conceptual modelling of electrical circuits is an issue on which not all researchers agree. In the present case, voltage and energy are presented as the entrance to the cluster of concepts V, I, E for two reasons. First, we consider that the reconceptualization of "current" towards a scientifically acceptable concept involves conceptual differentiation mainly between the concepts I and E which has a considerable cognitive cost for the students. Such a conceptual change requires substantial preparation in order to occur and may be assisted by the acquisition of preliminary knowledge about voltage and energy (see also Episode 1). Second, the early development of a voltage concept may assist a causal account of electric circuits, render students more "voltage than current minded" and facilitate the formation of links between electrokinetic and electrostatic phenomena at both a macroscopic and microscopic level (Psillos, Koumaras and Tiberghien, 1988). Following voltage, the next step is to introduce current and then resistance. Our data suggest that facilitating the construction of the concept of resistance plays a prominent role in the development of a macroscopic flow model and provides a bridge towards the microscopic model. This is why emphasis is put on the teaching of resistance.
As a first step towards the development of conceptual models, students are involved in various activities, presented in Episode 1. In the next step, students are involved in experimentation with bulbs and ammeters taking qualitative and semi-quantitative data. In addition to bulbs, ammeters are used as current indicators, their readings suggesting that current along the circuit remains the same. Conservation of current alongside the circuit is discussed with the students thus pursuing further the I, E differentiation.. The well known experiment with bulbs and ammeters in series is used to indicate equal readings across the circuit. However, our results lead us to speculate that several of the students consider the ammeter as a consumer of energy like the bulb and thus may assimilate equal ammeter readings in their source consumer model (Psillos, et. al. 1987). A water analogy including a pump, water circuit and a mill provides a useful visualisation of a closed system in which one quantity (water) is circulating and conserved while energy is transferred from the pump and used in the mill. At this point the flow model of current starts progressively developing. Ammeters, even zero point ones, are not used to show current unidirectionality, they are not convincing for the students. The same applies to magnetic needles. Elsewhere we have argued that magnetic effects are interpretable in terms of the source consumer model and should be used only after the development of a current concept ( Psillos, et.al 1987) . Metaphors are utilised for inducing unidirectionality such as "in the rivers the current travels only towards one direction". In addition to the above, students are also experimenting with batteries of different volt indication which show them that for the same circuit current depends on voltage.
In the next step the students are engaged in activities and experiments regarding resistors. They are confronted with a difficult task, namely to relate resistors to bulbs and ascribe two functions instead of one to these two objects i.e. users of energy and regulators of current. This is a crucial step where the flow model of current may acquire meaning for the students, i.e., the flow of "something" may develop into the flow of invisible "material" particles. Students often develop a sequence model and this signifies their conceptual progress. In Episode 2, aspects of a confrontation strategy regarding the teaching of resistance are presented.
At the end of the conceptual part students develop a new relation between E, I. They are involved in a series of experiments which suggest that the rate of energy transferred depends not only on the amount of current in a circuit but also on voltage. For example, in one experiment one torch bulb is connected to one 4.5V battery and one house bulb is plugged plugged to a socket. The ammeters in both circuits have the same readings but the bulbs light differently.
iii) The Microscopic Part
Questions regarding microscopic entities and mechanisms emerge when students start developing the concept of current conservation and particularly the double function of resistors as both energy users and current regulators. For example, the following dialogue has been recorded during a classroom discussion:
Ss Sir, if we measure the current just before a bulb (in a battery-bulb circuit), the ammeter should read more.
Ss Because the electrons accumulate as they to pass through the
resistor. After the resistor the current is less because fewer electrons pass through.
This model has been called a "packed crowd" model for current and is in line with the sequential treatment of changes in an electrical circuit. What matters for our argument is that the students seek an explanation at the level of a microscopic mechanism in order to account for the function of a resistor and current circulation. In the microscopic part, qualitative causal models are developed which provide answers to such questions, enhance macro-micro links and pursue an understanding of the electric circuit as a system.
The experimental field is enlarged considerably to include the interaction of electrically charged bodies, electrostatic machines and conductivity in liquids. Teacher-led experimental demonstrations and discussions are carried out regarding charging, attraction and repulsion of charged bodies, and electrostatic machines as well as about the function of a prototype battery.
A crucial issue at this level is how to
relate electrostatic and electrokinetic fields, seemingly separate for
the students. Experiments, analogies and metaphors, concepts and conceptual
structures are used to establish links at both the phenomena and the model
For example, in one experiment the measurement of voltage between the arms of the Wimshurst machine is related to the measurement of voltage between the battery terminals. Another experiment (see Fig. 2) is used to facilitate links between charging, charged body movement, lighting and ammeter reading. The explanation offered is that an electrostatic machine can accumulate different charges on its poles and hence establish a voltage value between them. Under the appropriate conditions, i.e. one closed circuit consisting of one bulb, the machine and one light movable body between the poles, an electric current may be created.
Crucial aspects of the microscopic mechanisms for battery function are illustrated by analogies, for example the charge separation and accumulation in the arms of the Wimshurst machine are related to the charge separation and accumulation in the battery terminal. Voltage and charge are presented as unifying concepts of electrostatic and electrokinetic phenomena both at the micro and macro level. Voltage is linked to the differential charge accumulation at both the battery poles and the terminals of a Wimshurst machine. Causal explanations are provided for the students in order to make processes intelligible. For example when somebody turns the Wimshurst machine crank, one can observe the deviation of the voltmeter needle; the faster you turn the lrger the voltage indicated.
A simplified causal microscopic model is used to provide an explanatory mechanism for the operation of an electrical circuit. This model is battery centred and voltage corresponds to the surplus and lack of electrons created by chemical reactions on battery terminals. Attraction and repulsion forces are consequently exerted on the free electrons setting them into movement and thus current is established. Lack of space does not permit detailed description of the model. It is important to note however, that such a model is appealing to students because it provides a causal explanatory mechanism of what happens in the circuit. The macroscopic variables I, V, R acquire a microscopic representation which facilitates macro-micro relations.
iv) The Quantitative Part
In the previous parts students have acquired a strong qualitative basis, have obtained semi-quantitative measurements and have explored covariations of the physical quantities V, I and R. At the quantitative part are taught quantitative relations among V, I, R in order to answer questions such as "if we double the resistance value how much will the current decrease in one circuit containing one ammeter, resistors in series and one 4.5 V battery ? ".
The experimental field is enlarged in the quantitative part to include series and parallel connection of resistors, ohmmeter readings and specific resistance. A quantitative macroscopic model is introduced including Ohm's law and the relation R = ñ.l/s. Variation of resistance changes with temperature, are also presented.
Students are engaged in activities in which they use instrument readings to investigate quantitatively various aspects of the functional relation V = I.R. For example, having acquired a qualitative concept of resistance and a microscopic representation of this concept students are involved in direct measurements of resistance obtained by an ohmmeter. Then they compare these data with calculations about the same resistance value which derive from voltmeter and ammeter readings in a circuit consisting of one battery and two resistors in series. Measurements are also taken in order to construct a graphic representation of the I = V/R relationship.
One specific feature of this part is that students are involved in experiments designed to facilitate realising that a local change such as increase in resistance value implies a global change in the whole circuit - for example the value of current in the circuit - thus enhancing the systemic view of the circuit. For example, students are involved in experiments in which they are asked to predict and interpret variations in ammeter readings when a parallel branch including one resistor is added to a circuit containing one battery connected to one resistor:
When we add the resistance the ammeter shows more because there is a parallel connection...we have two circuits the battery has to give more (current).
5. Teaching Strategies
Several teaching strategies and techniques have been applied to facilitate students' constructive activities aiming at understanding the above models. Normally students were involved in collaborative guided experimentation and discussions in order to elicit their views, predict and interpret phenomena. Aspects of two confrontation strategies which have been applied are presented in the next session.
5i). Episode 1: Facilitating conceptual differentiation
In introductory electricity the development of scientific concepts implies students' differentiating the features of current, voltage and energy from the initial global notion "current/energy". Essential steps in facilitating conceptual differentiation by students may be the upgrading of those conceptual features that are weak in students' initial knowledge; the discrimination between the features of different concepts; the establishment of new relations among the concepts (Kariotoglou et al. 1995). This strategy has been applied in the case of voltage which is a weak concept subordinate to current. A teaching unit on voltage and energy has been included in the conceptual part, aiming at upgrading the voltage concept and commencing current-voltage and current-energy discrimination. Aspects of this teaching unit are presented below.
Changing the level of questioning
By the end of the phenomenological part students potentially raise conceptual questions such as : 'What changes occur in a circuit when we connect two batteries in series or in parallel?' The introduction of the voltage and energy concepts aims at facilitating students' use of features of voltage and energy to provide answers to such questions.
Enlarging the experimental field
The experimental field includes batteries and bulbs, as mentioned before. In addition to this, the field is enlarged to include voltmeters and their readings.
Validating new knowledge
In this unit students take and use qualitative and semi-quantitative data to validate the conceptual models. Thus they have the opportunity to use and relate the unknown voltmeter readings with familiar objects or events. For example, the students read 4.5V on a battery and check that a voltmeter indicates 4.5V, or they note that two batteries connected in series might imply 9V and check it with a voltmeter. Measurements are not related to a formal definition of the physical quantities voltage and energy but are utilised as a means to describe the attributes of these concepts.
Introducing meaningful models
As mentioned in section 4ii, the two partial models of energy and flow are gradually put into play at the conceptual level. The level of causal relations changes; from dealing with objects and events students are asked to describe and interpret similar phenomena in terms of physical quantities. In the flow model voltage is introduced as a primary concept with direct reference to the battery, signifying its potential to establish 'current' in a circuit. Voltage is causally related to the generation of current. In the energy model, energy is introduced as a primary concept too by the property of 'storability'. Energy is related to the volume of the battery (for batteries of the same type), in the sense that a battery is a container of energy. In terms of the energy model, energy stored in the battery is causally related to the duration of the lighting. This approach is radically different from several traditional ones in which voltage and energy are introduced by relational equations and is in line with research suggesting that students understand properties of objects better than relations between concepts.
Elaborating the models
The new knowledge about voltage is introduced by using what is familiar to the students, namely, volt indication on batteries. At the beginning of the unit students compare the brightness of identical bulbs connected with batteries of different volt indications. At this point the students are informed that volts measure a new quantity voltage. Then they compare variations in brightness by using batteries connected in series and in parallel and repeat the same experiments using the voltmeter. Essential steps in the evolution of their reasoning are presented below.
Classroom results show that initially, the number of volts indicates for several students the quantity of "current" stored in a battery, either functioning in a circuit or not:
T: After all you have seen in this lesson up to now what do you think that volt indicates?
S3: It is the quantity that a battery has
T: What quantity?
T Do the others agree?
It seems that the students conceptualise only the "quantity stored" in a battery, the amount of which determines how much "current" is "given" to the bulb. A possible schema applicable for the students is " the more I have, the more I give, ". Thus two batteries in series have more "current" therefore they may "give" more "current" to the circuit hence brightness increases. In this way experimental results are interpreted in terms of students' source consumer model.
In a second step two teacher-led demonstrations are used to facilitate discrimination between voltage/energy and voltage/current. The first involves two batteries of the same voltage but different size. These are connected to similar bulbs. In this experiment, students are asked to predict and interpret the brightness of each bulb and the duration of its lighting. Classroom data show that in step two, some students (see S3) relate the volume of a battery to the "quantity stored", which they distinguish from voltage
T: If we connect these two batteries (same V, different size) with two similar bulbs will the brightness be the same?
T: Are you sure, this one is very big?
S3: It does not matter since the volts are the same the batteries have the same force. This one (the small) will finish quickly, the big one will finish later.
S2: Both (batteries) will finish at the same time.
S3: The big one has got more energy it is bigger.
S2: If it has more energy the bulb will bright more.
S3: Quantity, eh, not force.
Here the students conceptualise voltage as determining the "strength/force" of the "current given" by the battery to the bulb. These conceptions are more elaborate than the previous schema and are partially correct. However, the students do not quite distinguish the use of these conceptions as a second variable which conditions the interaction between the battery and the bulb, when they function in a circuit. Students still relate voltage to "current" and, possibly, the volt is a unit of "current" measurement.
In the second experiment, a voltmeter is connected in series with a bulb and a battery. Classroom data show that the students ascribe voltage to battery when trying to interpret the reading of a voltmeter connected in series to a battery and a bulb which, in this case, does not glow.
T: Do we have current in the circuit
T: How do you know this?
S3: The bulb does not bright
T: Does the volt measure the current?
S2: If the volt measured the current the bulb would bright
Voltage now indicates the "strength/force" of the battery. It appears that, in a third step, voltage is conceptualised as a permanent characteristic of the battery which holds when it either functions in a circuit or not. With the help of metaphors (employing the Greek term for voltage, "tassi" which also means tendency, disposition to do), the students relate Voltage to the disposition of the battery to "give current" to the bulb and not to the "current" it "has" or "gives", in line with the objectives of the unit:
T: Okay, can any of you tell us what you think you have learned today.
S1: We learned that voltage is first and then current, the voltmeter does not measure the strength of the current, it does not measure the quantity, it measures the volts.
T: What does this voltage mean? Whose feature is it?
S3: The battery, which gives energy to the bulb.
S4: Disposition of the battery to give current to the bulb.
This step is a difficult one which takes time to become meaningful, so reversals between the steps have been noted in students' conceptions during and after the unit. In the next teaching units conceptual discrimination is enhanced while new relations are developed between voltage, energy and current so that students are helped gradually to differentiate and develop the scientific meanings of these concepts.
5ii) Episode 2: Inducing meaningful cognitive conflict
We present here aspects of a cognitive conflict strategy aiming at facilitating students' construction of a model for resistors and resistance. As we have argued elsewhere (Koumaras et. al, 1995) this strategy is based on: the acquisition of preliminary knowledge by the students; the confrontation with recognisable counter-evidence; the concurrent presentation of a better alternative explanation; the application of new knowledge. One crucial feature for the effectiveness of such a strategy concerns what may count as counter-evidence for the students.
An essential part of this strategy comprises the gradual acquisition of initial knowledge regarding resistance. Students, for example, are involved in experiments observing the co-variation of the length of a resistor, ammeter readings and bulb brightness connected in series to one battery. Also they touch and feel that the temperature of a resistor, such as a nichrome wire, increases as current passes through but not that of a conductor, such as copper wire. This approach is different from usual teaching, which often treats the thermal effects of current separately from resistors. Students realise that a bulb is a resistor by experimenting, problem solving, discussing and exchanging views in group work. Our results suggest though that such knowledge is still interpretable in terms of the source- consumer model. For example, in the above experiment, the resistor warms up not because it is an obstacle but because it consumes more energy. Hence both the brightness of the bulb and ammeter reading decrease:
"In the nichrome wire experiment, the current becomes lower because it is consumed in order to get the wire hot, so less current arrives to the bulb, which gets dimmer. In the copper wire experiment, the brightness of the bulb and the reading of the ammeter remain the same, while the copper wire doesn't get any hotter. The (copper) wire does not consume any current and all of the current gets to the bulb which lights a lot." (typical response from 28/56 students)
Having acquired the prerequisite knowledge,
students are then involved in a conflict situation, in which they are asked
to predict the duration of lighting in two circuits. One circuit includes
one battery and one bulb and the other circuit includes one battery connected
in series with two bulbs. This experiment is counter-intuitive because
results cannot be predicted nor can it be interpreted in terms of students'
causality. If students had been asked to compare the brightness of the
bulbs, the result could have easily been predicted. With regard to duration,
one bulb has a constant capacity to receive current, two bulbs are predicted
to have double capacity and, hence, they will go out earlier. Taking into
account the diminished brightness, students' predictions might go as far
as to suggest the equal duration of lighting in the two circuits as classroom
data have shown.
.S: "... (this result) cannot be explained. Normally, the other battery should finish first (the one connected to two bulbs), or, at least, they should finish simultaneously".
The above experiment satisfies the following criteria. First, it is meaningful for the students since it is based on questions arising from the source- consumer model. Second, experimental results are recognised as challenging because they are not consonant with students' causal reasoning according to which two bulbs should consume more, hence lighting should continue for less time. We argue that the extension of the experimental field in the teaching sequence to include duration of lighting i.e. evolutionary tasks, made it possible to change one conventional experiment into a recognisable counter-intuitive one (Koumaras et.al).
An integral part of the strategy is the presentation, concurrent with the dissatisfaction created in the students, of a resolution provided by a better alternative explanation for the two functions of the resistor, as a pathway for current and user of energy, in terms of a unifying microscopic mechanism. (The mechanism is simple at this level; electrons are presented as particles moving around and warming up the wires by friction). The construction of the desired knowledge about resistance is further facilitated by the interpretation of previous results and extensive new applications in terms of new knowledge.
6. Some results
A range of techniques, such as semi-structured interviews, classroom recordings and written questionnaires have been applied to monitor students' conceptual evolution during and after teaching. In this section, we briefly present comments based on results from post tests administered to 156 students who were taught the sequence during several years. Some comparisons are also made with results obtained from a large reference sample comprising 313 students who attended the official curriculum (Koumaras et al 1991).
The great majority of the students answered correctly tasks on the closed circuit. Tasks focusing on the value of current in circuits including batteries and bulbs were given to the students. Over half of the students utilised the scientific model of current, discriminating current from energy and accepting current conservation. However, about one-fifth of the subjects still reasoned in terms of the source- consumer model in many tasks and did not differentiate current from energy. The majority of the students answered correctly questions regarding what is the volt, what does the quantity voltage indicates and how is it measured. The correct answers to propositions concerning voltage-current relationship were from half to two- thirds of the students.
Concerning reasoning patterns we may note that about half of the students recognised that a change in one circuit implies changes in all circuit parameters in circuits involving change of resistance values. It worth noting that several of our subjects developed a local view of the electric circuit when they were taught about resistance. Later during teaching, they abandoned local in favour of a systemic view but over one- third kept the instruction originated local view. Similar achievements were obtained in tasks regarding series and parallel connections of batteries and bulbs in which experimental subjects used the taught knowledge instead of causal rules based on the source consumer model, which were used prior of the teaching. All these results were significantly better than the ones obtained in the reference sample comprising students attending the lower and the upper secondary school in Greece. For example, the majority of upper secondary students demonstrated sequential models after instruction but did not show systemic reasoning.
The experimental results allow for two views to be taken. The pessimistic one takes into account that alternative conceptions appeared to a number of students despite their involvement in an extended specially designed constructivist teaching sequence. Also some of the alternative conceptions were possibly created by the interaction of the teaching with students' knowledge. The cautiously optimistic view takes into account two results. First, considerable progress was made during and after teaching. Second, the results are significantly better if compared with existing practises, at least in Greece, even when compared with upper secondary school students.
7. Concluding remarks
Teachers and researchers are concerned with the teaching of electricity since this topic appears in primary and secondary curricula world wide. Diagnostic research has been fruitful in identifying students' learning difficulties. Research on teaching is based on a constructivist approach and has focused on alternative pathways which may facilitate the construction of scientific knowledge by students. A notable shift of emphasis is that the teaching of electricity attempts to make up for students' difficulties, not simply to present content in appropriate ways.
In our case we decided to extend the experimental field to include not only steady states but evolutionary situations as well; to link electrokinetik and electrostatic phenomena; to develop causal models adapted to students' causal reasoning; to commence conceptual modelling by voltage and energy, introducing these concepts as primary and not relational ones; to present a hierarchy of models capable of answering progressively sophisticated questions and leading to increased levels of understanding. Research results allow for a cautiously optimistic view to be taken regarding the effectiveness of this sequence.
We suggest that traditional representation of knowledge which is content based should change towards a representation of knowledge that is pedagogical valid to be taught in introductory electricity. Such a process, though, may imply a conceptual change on the part of curriculum designers, teacher trainers and teachers in order to materialise and to render instruction in electricity intelligible for their students.
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Section E4, Teaching Introductory Electricity
from: Connecting Research in Physics Education
with Teacher Education
An I.C.P.E. Book © International Commission on Physics Education 1997,1998
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