common with the source of current has a value of 0,2 V (law of Kirchhoff on tensions) lower than the other (law of ohm), Va = 11,8 V. The interpretation of the ...
CONCEPTUAL REPRESENTATIONS OF HIGH SCHOOL STUDENTS CONCERNING THE SOURCE OF CURRENT: THE "MODEL OF THE HIGHWAY" Abdeljalil Métioui1 and Louis Trudel2 1 Université du Québec à Montréal, Canada 2 Université d'Ottawa, Canada Abstract: The international community of the researchers in didactics of the sciences is unanimous to specify that all didactic strategy development must take into account the conceptual complexity of the scientific models and the various conceptual representations of students. The present communication is about this last measure while describing, by means of qualitative research, the representations of high school students' in physics, relatively to the current source and the voltage source. Thus, we were able to verify some hypotheses with respect to the conceptual nature of their reasoning. The majority of students interrogated on situation-problems requiring the understanding of current and voltage sources constructed naive representations. They referred for the most part to an erroneous model that we will call the "model of the highway" where several currents can coexist independently from each other. Keywords: conceptual representation, source of current, qualitative research, high school student, physics
INTRODUCTION The electric phenomena are interpreted using two fundamental concepts, both the concepts of current and voltage (difference of potential). The understanding of this duality forms the basis of learning and is necessary for an adequate performance in this field. However, numerous didactic studies from several countries have the tendency to show that the majority of the conceptual difficulties of pupils, with respect to the theory of the electric circuits, takes its source in the deficiency in the understanding of the notions of current and voltage. Our research belongs to that perspective and in the first section we will recall the results of previous research on representations of concepts of current and voltage. In the second section, we describe the methodology used in order to characterize the representations of high school students in physics class, in the particular case of sources of current and voltage; this will be followed by a description of the target population. Lastly, we will specify the results and the limits of this study, as much from the theoretical perspective as from the methodological one.
THE REPRESENTATIONS OF THE CONCEPTS OF CURRENT AND VOLTAGE: REVIEWED OF THE LITERATURE The problem of the representations of the students, with regard to the concepts of current and voltage, was the subject of numerous researches (Küçüközer and Kocakülah, 2007; Métioui and Levasseur, 2011; Métioui, Brassard, Levasseur and Lavoie, 1996; Métioui and Trudel,
2012); Millar and King, 1993). A synthesis of these researches reveals that, according to most researches, the current and voltage have the following properties: The current is energy. A voltage is the intensity of the current strength. A battery is a reservoir which dilapidated current as it crosses the different components in a circuit. The modifications of a circuit only affect the components situated downstream (sequential model). Every component of a circuit receives its part of the current so that some identical components receive and consume identical currents. Currents flowing in resistors in series are equal; voltages across parallel resistors are equal. It follows that the current in parallel resistors must be different. These results put in light, according to us, an important fact. A considerable gap exists relatively between the explanatory models of the pupils with respect to the concepts of current and voltage and the ideas accepted by the scientific community.
METHODOLOGY AND DESCRIPTION OF THE SAMPLE The representations are complex systems and as such are generally studied by means of qualitative research. Indeed, most authors specify that the representations are constructed from words or actions by the observed subjects. They are inferred, and that means one constructs from these observable demonstrations something that one doesn't understand fully, but that is necessary, in order to give an explanation of it. So we elaborated a written questionnaire (see annex A) in order to guide the student toward two problems whose solution calls on various aspects directly associated with the notions of the current and voltage sources. Let's note that the two retained questions presented neither great theoretical difficulties nor calculations, but they had been selected for their originality. These questions didn't come from manuals, as they were outside beaten trails, while staying simple and transposable to convenient situations. In other words, the elements of the problem were known of the pupil, but the situation presented was unusual, hence the pupil could not answer them mechanically. Thus, deprived of the opportunity to recall a memorized verbal argument or algorithm, the pupil had no other choices than to mobilize his conceptual structure to solve the problem. To clarify the representations of the students, following the distribution of the questionnaire, we have given to a certain number of these students, chosen through randomized sampling, an oral questionnaire (see annex B), to compare their answers with those that have emerged from the written questionnaire. In order to ensure the validity of the findings, we took into account two essential criteria, both the diversification of the sample and the saturation of the speeches. Thus, the written questionnaire had been presented to 168 students of three different high schools. As for the oral questionnaire, it had been distributed to 29 students in semicontrolled interviews. Let's note that all students had previously taken a structural course on electric circuits and that they participated to this research on a voluntary basis. The length of the written questionnaire
was sixty minutes and about thirty minutes for the oral questionnaire. The written questionnaire had been validated by their professors who made us notice that our questions were formulated in an unusual way. Indeed, they mentioned that compared to the problems their students are accustomed to solve where the quantitative aspect is important, our problems were centered on qualitative analysis. However, they assured us that in theory, their students would be able to solve them.
INTERPRETATION OF THE QUESTIONNAIRE WRITES The answers of the pupils have been regrouped by category because the same mistakes constantly come back. The results are presented according to the general diagram below: Y(Y1, Y2, Y3)
CATEGORY X: Number of the category
Typical answer or description of the category
Commentary
Collegiate
Analysis: question # 1 This question (see annex A) has for objective to verify the pupil’s acquisition of the notion of ideal current source. Indeed, the pupil must note that there is not any change of the value of Vc since the current in the C1 capacitor won't be affected; the source of ideal current provides the same current, whatever the value of the equivalent resistance in series. The interpretation of the data of this question (#1) allowed us to identify five categories of answers as illustrated in table 1. Table 1 Categorization (question # 1) Category I
The loading time doubles or increases (false)
Category II
Good answer, justification
incomplete
12 (5, 2, 5)
Category III
The loading time (or the discharging time) decreases (false)
17 (9, 5, 4)
Category IV
No answer or a fuzzy answer
Category V
Good answer, adequate justification
erroneous
or
82 (33, 38, 12)
53 (29, 16, 6) 4 (1, 1, 2)
The table 2 illustrated the hypothesis about the conceptual representations underlying each category:
Table 2 Hypothesis about the conceptual representations (question # 1) Category Question 1 (I) The loading time doubles or increases (false) (II) Good answer erroneous or incomplete justification (III) The loading time (or the discharging time) decreases (false) (IV) No answer or a fuzzy answer (V) Good answer (adequate justification)
Hypothesis about the conceptual representations One can ignore a source of current while considering it like a source of voltage. No explicit conceptual foundation. Idem, Category I and supplementary mistake with respect to the loading rate. No hypothesis A source of current produces a constant current, whatever the circuit.
Analysis: question # 2 The objective of the question 2 was to determine if the pupil is aware that the presence of a source of current in a branch determines the current in this branch which is 2 mA. The last value of current in the branch implies that the tension at the boundary-mark of the resistance in common with the source of current has a value of 0,2 V (law of Kirchhoff on tensions) lower than the other (law of ohm), Va = 11,8 V. The interpretation of the content of this question (#2) allowed us to identify six categories of answers as illustrated in table 3. Table 3 Categorization (question # 2)
CATEGORY I
The current in the resistance is not equal to 2 mA (false)
16 (6, 10, 0)
CATEGORY II
Adequate analysis (good answer)
54 (11, 24, 29)
CATEGORY III
Fuzzy answers, without justification
36 (20, 12, 4)
CATEGORY IV
The source of current is a short circuit or an open circuit (false)
31 (24, 6, 1)
CATEGORY V
Consider that the current in the resistance is 2 mA, but assimilates the difference of potential (d.p) of the resistance (200 mV) to the one of the source or apply the voltage Kirchhoff law inadequately.
23 (13, 5, 5)
CATEGORY VI
Assimilate the circuit to an equivalent resistance whose
9 (2, 6, 1)
current would be 2 mA and deducts from it the difference of potential between the boundary-marks of the source.
The table 4 illustrated the hypothesis about the conceptual representations underlying each category: Table 4 Hypothesis about the conceptual representations (question # 2) Category (question # 2)
Hypothesis about the conceptual representations
The source of current is a component that provides the current; this current can be added to the one produced by the other sources. The current is in reference to a component (running between the boundary-marks of R) and don't necessarily apply to the whole branch. The arrow indicates the real sense of the current; therefore its orientation is not arbitrary. The source of current is not very different from a source of voltage since one uses a source of voltage precisely to provide a current. If one puts a source of current in the electric circuit, it is probably to get a supplementary current. Hence, one can add this current to the one already produced by the source of voltage. The source of current possesses a high resistance, because the (II) Adequate analysis current is weak. (good answer) The source of current is in fact a resistance. All components with two boundary-marks experience a tension between its boundary-marks and a current that crosses it; while dividing this tension by this current, one gets a quantity whose units are Ohms; this quantity is therefore the resistance. It is why the concept of resistance applies universally to all systems of components. The source of current shares the total current and the total tension (III) Fuzzy answers, with the other components; the components that receive a lot of without justification current also receive a lot of tension (the law of ohm shows indeed that the two are proportional). The ideal source of current possesses a very high (IV) The source of current is resistance. While applying Ohm’s law implicitly, one deducts a short circuit or an open that no current circulates in the source of current, which can circuit (false) appear paradoxical. But while replacing the source of current by an open circuit, one arrives to an answer. The source of current being an open circuit ("a tip of thread"), (I) The current in the resistance is not equal to 2 mA (false)
there is no current, therefore no tension (indeed, by Ohm’s law, one knows that when there is no current, there is not any tension). The source of current being (or capable to be replaced by) a short circuit, it doesn't have any resistance; therefore the tension between its boundary-marks is zero. A source of current is only an indicator of the current in a circuit (V) Consider that the current and doesn't correspond to a component. in the resistance is 2 mA, but assimilates the difference of potential (d.p) of the resistance (200 mV) to one of the source or apply the voltage Kirchhoff law inadequately (VI) Assimilate the circuit to an equivalent resistance whose current would be 2 mA and deducts from it the difference of potential between the boundary-marks of the source
A source corresponds to a resistance of which one can calculate the value with the help of Ohm’s law.
INTERPRETATION OF THE ORAL QUESTIONNAIRE We asked the pupils to solve a simple problem concerning a source of tension in series with resistances and a source of current of 2 mA. While making some modifications to the resistances or to the source of tension, the pupil must realize that the current doesn't change. Unfortunately, the majority added merely a current of 2 mA, produces by the source of current, to the one that would be produced by the source of tension, calculated while applying the law of ohm ingenuously. A deep analysis of the set of the data of the oral questionnaire allowed us to put in evidence a set of conceptual difficulties that gives support to our interpretation of the data of the questionnaire: In a circuit, every component has a role to play. The global functioning of the circuit is to certain degree the result of the contributions of each of the components. For example, a resistance serves to decrease the current, a battery to nourish a circuit while running and the current source (as its name indicates) serves to provide a part of the current.
In the current source, a current I pass through and across its electric terminals there is a voltage V. Therefore, one can replace the current source by a resistor R whose value would be V/I, in accordance with Ohm's law. The current sources are abstracts; they don't exist in reality. The current sources are useless: It takes voltage to produce a current. We specified in our theoretical setting that the representations are of the objects of research constructed by the researchers in the interpretation of the speeches of the target populations and that they are complex. Otherwise, in this process of construction of the representations, the researcher cannot give truly an account of the wealth and the diversity of the conceptual structure of the learners. In spite of the inherent limits to the research process, we succeeded in putting in evidence a representation which allows the simultaneous cohabitation of several currents in a conductor. This erroneous representation ensues presumably form the application of the superposition theorem and from the analysis by mesh. This theorem, used to analyze linear circuits including several sources (of current and tension), stipulates that the total current will be equal to the sum of the partial currents, obtained while considering one source at a time and replacing the others by open circuits. The mistake of the pupil consists in lending an independent physical reality to the fictional partial currents by analogy to a freeway, which allows an independent circulation of several rows of vehicles as shown in the following figure. The total current is the algebraic sum of the I1 currents, I2, I3 and I4. I1
Legend I2
Current I1 Current I2
I3
Current I3 Current I4
I4
Figure 1. The freeway model Here is an excerpt of the answers given by a pupil, illustrating this model: Q.1: Calculate the current I, as shown in the figure. R:
I will calculate the current by Ohm’s law.
Q:
How?
R:
First, one computes the resistance, 100 ohms in parallel with 100 ohms that makes 50 Ohms.
Q:
Okay.
R:
That can be divided in two. Adding 50, that makes 100 ohms.
Q:
After?
R:
I equal V divided by R. Twelve volts divided by 100 ohms equal 120 mA.
Q:
Then?
R:
120 mA added to the source of current that you have in series.
Q:
Why?
R:
Because that adds itself. It is a circuit in series.
Q.2: If one doubles the battery, what will happen to the current? R:
It is going to be two times bigger.
Q:
Why?
R:
Because the resistance that leaves, the resistance is seen like two times less. It is two times smaller.
Q:
If one doubles the tension, what will happen to the current?
R:
One doubles the current.
Q:
Why?
R:
In more that by the formula one can see it. The law of ohm, I equal V on R.
Q3. : If one doubles the resistor of 50 Ohms, what will happen to the current? R:
It should lower.
Q:
For what reason?
R:
Because the resistor is bigger and again, according to Ohm’s law, the lower the current, the more the resistance goes up.
Q.4: If one inverts the poles of the battery, what will happen to the current? R:
The current changes direction and it comes to juxtapose itself with the source of current of 2 mA, which it would be necessary to subtract from the 120 mA that I calculated previously.
CONCLUSION In the present research, we have succeeded to put in evidence a representation which dictates that several currents can coexist simultaneously in a conductive material. It is an erroneous interpretation resulting presumably from the theorem of superposition and the analysis by meshes. The theorem used to analyze the linear circuits including several sources (of current and voltage), stipulate that the total current will be equal to the sum of the partial currents when taking into account one source at a time and when replacing the others by open circuits or short circuits. The mistake consists in lending an independent physical reality to the fictional partial currents as on a highway, which allows an independent circulation of several rows of vehicles.
REFERENCES Küçüközer, H., & Kocakülah, S. (2007). Secondary School Students' Misconceptions about Simple Electric Circuits. Journal of Turkish Science Education, 4(1), 103-115. Métioui, A., & Trudel, L. (2012). Acquiring Knowledge in Learning Concepts from Electrical Circuits: The Use of Multiple Representations in Technology-Based Learning Environments. Journal of Systemics, Cybernetics and Informatics, 10(2), 24-35. Métioui, A., & Levasseur, J. (2011). Analysis of the reasoning of pupils on DC and the laws of Kirchhoff. RDST, No 3, 155-178. Métioui, A., Brassard, C., Levasseur, J. & Lavoie, M. (1996). The persistence of students' unfounded beliefs about electrical circuits: the case of Ohm's law. International Journal of Science Education, 18 (2), 193-212. Métioui, A., & Trudel, L. (2012). Acquiring Knowledge in Learning Concepts from Electrical Circuits: The Use of Multiple Representations in Technology-Based Learning Environments. Journal of Systemics, Cybernetics and Informatics, 10(2), 24-35. Millar, R., & King, T. (1993). Students' understanding of voltage in simple series electric circuits. International Journal of Science Education, 3, 339-349.
ANNEX A WRITTEN QUESTIONNAIRE QUESTION 1 In the following circuit, one opens the S1 switch that was closed since one minute. Vc tension evolves in a certain manner. One redoes the same experience with a resistance of 5,5 KΩ. What is the tension difference Vc?
2,75
1 mA
100μF
S1
Va
12V
QUESTION 2
100
In the following circuit, the entry voltage being equal to 12 V, calculate the value of voltage Va between the boundary-marks of the source of current of 2 mA. Explain.
2 mA
Va
ANNEX B ORAL QUESTIONNAIRE 100
Question 1: Calculate the current I1, as shown in figure 1.
I1 100 E = 12 V
50 2 mA
Question 2: If one doubles the battery, what will happen to the current? Question 3: If one inverts the poles of the battery, what will happen to the current? Question 4: If one doubles the resistance of 50 Ω, what will happen to the current?
