Download The notion of modeling among the students of technical

THE NOTION OF MODELING AMONG THE STUDENTS
OF TECHNICAL COLLEGE
Abdeljalil Métioui1 and Louis Trudel2
1
Université du Québec à Montréal, Canada
2
Université d'Ottawa, Canada
Abstract: The main objective of this study is to present, in a first time, the impact of the
laboratory activities on the scientific formation of the students. Then, we will present the
results of a qualitative research on the conceptual representations of 169 students coming from
three colleges, with respect to the principles of the electric instruments that are used to
measure the electric current and tension. To this end, a paper-pencil questionnaire and a
clinical interview were used to uncover their representations. The results showed that the
majority of the students interviewed have difficulty to understand the underlying models that
explain the workings of the above mentioned devices.
Keywords: representation, electric instrument, current, voltage, student, technical college,
qualitative research
STATE OF THE QUESTION
The conceptual representations of the students with regard to the electric concepts of current
and voltage were the subject of intense activities of research (Cohen, Eylon and Ganiel, 1983;
Millar & King, 1993; Millar & Beh, 1993; Métioui, Brassard, Levasseur & Lavoie, 1995;
Guttwill, Frederiksen & White, 1999; Paatz, Ryder, Schwedes & Scott, 2004; Métioui,
2012). However, the research on the representations of the students with regard to the
instruments of measure of current and voltage were not the object of systematic survey, in
spite of the central place that the instrumentation occupies in the teaching of
electricity. However, we identified some studies on the impact of the laboratory manuals
(especially in biology and chemistry) on the acquisition of the scientific method and its
associated skills as well as the different epistemological conceptions shared among students
(Métioui and Trudel, 2007). These studies indicate that an important proportion of students
experience serious difficulties to construct the underlying explanatory models of the
experiences achieved at the laboratory and that they are often satisfied with recording the
measurements obtained, without being much concerned about the reality of these measures , as
well as the acceptability of these these measures.
In spite of the wealth of these works, one must note that the students’ conceptions with regard
to the models used to explain the working of the instruments to measure the fundamental
electric quantities (intensity of the current, electric tension, electric power, electric resistance,
inductance and capacity) were not the subject of systematic survey, in spite of the central place
that the instrumentation occupies in the teaching of electricity and electronics (Métioui &
Trudel, 2008).
The present research appears in this perspective and aims to put in evidence the conceptual
representations of students frequenting the technical colleges, with respect to the equivalent
models of electric measure devices. This research tries to explicit their capacity of modeling
and to understand the limits and the insufficiencies of the models that underlie the working of
the electric devices of measure. This study especially concentrates on the ammeter and the
voltmeter. In the following sections, we are going to specify the methodology used to
characterize the conceptual representations of the students as well as the results of our
experimentation.
POPULATION AND METHODOLOGY
In a qualitative research, the population studied is necessarily limited with respect to the
number of the topics selected. However, in order to insure the variability of the representations
and the validity of the findings, we generally took into account the two criteria admitted in this
type of research, that is the diversification of the sample and the saturation of the answers. We
worked with students registered in various representative schools in the technologies of the
electricity and electronic in Quebec, in order to avoid that our findings apply only at a specific
institution. The target population was composed of students coming from the electric
engineering technologies in three colleges and they participated in this survey on a voluntary
basis. The experimentation has been led in two stages: first of all, a paper-pencil questionnaire
had been distributed to 169 students who had sixty (60) minutes to answer. Then, an
individual semi-directive interview of about twenty minutes has been conducted with 32
students chosen among our greater sample in order to target better the conceptual mistakes
identified in the written problems.
Construction of the written questionnaire
We retained three problems (see annex A) to raise the veil on the notions of model and
equivalence among the students of the professional college.
Objective of the problem 1: This situation arises itself when one must measure a current and a
tension, having ideal multimeters used as voltmeters, simultaneously but not as ammeters. The
purpose of this question was to verify if the double role of a device (as a device, with respect
to the point of view of the user and as component, with respect to the point of view of the
circuit) will cause some difficulties to the students. The intensity of the current read by the
ammeter is also the intensity of the current of the power supply; because the ideal voltmeter
behaves like an open circuit, therefore the electric charges don't cross it, as we indicated
previously. Thus, the common boundary-mark of the voltmeter is well on the boundary-mark
of reference of the power supply, and the electric charges of IS intensity come out of the
common boundary-mark of the ammeter, so that the polarities are respected.
Objective of the problem 2: Let's note that all measurement process implies an interaction
between the circuit under test and the device used. One has to model the measurement device
to describe its behavior and its influence on the circuit under test. The circuit presented here is
the one that has the most practical importance since it corresponds to the internal working of
the modern numeric multimeter, used sometime as voltmeter (with a resistance of entry R
typically equal to 10 MΩ) or as ammeter (with a weak shunt resistance, whose value depends
on the scale of the current intensity wanted).
Objective of the problem 3: The expected answers relative to the parts A and B are the
following:
A. Yes, because the circuit presents itself merely like a resistance for the ohmmeter. The
portion "ideal voltmeter" doesn't disrupt in anything the resistor.
B. Yes, the voltmeter indicates the tension presently developed by the source imposing the
current. Therefore, one can evaluate this source of reference (I1) since the resistance of
the voltmeter is known because it is displayed by the ohmmeter:
I1 = 1,032 V / Re = 0,105 μA = 0,105.10-6 A with Re = 9,81 MΩ.
ANALYSIS OF THE DATA OF THE WRITEN QUESTIONNAIRE
The analysis of the data with respect to each of the three problems of the written questionnaire
will take place in two stages. First, we are going to regroup the answers [Total for the three
years N = 169: N1 (First year) = 76; N2 (Second years) = 63; N3 (Third years) = 30] by
category, because the same mistakes constantly come back. Then, we will analyze the set of
the data, followed by the conceptual representations identified.
Analysis of the data: problem 1
The data of this problem permitted to identify eight answer categories (see table 1). These
categories are described briefly and followed by an example of an answer of a student as
illustrated in table 2. Then, percentages of answers for every year in college are provided. The
analysis that follows will bring some information on some of these categories.
Table 1
Categories extracted of the problem 1
CATEGORY
INTERPRETATION
Correct
answer
(fig.1/Table 2)
I
II
Bad polarity of the ammeter (fig. 2/Table 2)
III
The ammeter and the voltmeter are plugged in
parallel (fig. 3)
IV
Ammeter short-circuited (fig. 4/Table 2)
V
Voltmeter short-circuited (fig. 5/Table 2)
VI
No answer
VII
Incomplete answer
VIII
Indecipherable answer (fig. 6/Table 2)
%
6
30
6
(c1, c2, c3)*
(7, 5, 7)
(14, 40,47)
(0, 0,10)
3
3
12
22
18
(7, 1, 0)
(7, 1, 0)
(30, 19,10)
(20, 19,16)
(15, 15,10)
*(c1, c2, c3) are respectively the percentages of the first students, second and third years
Table 2
Quelques exemples de branchements donnés par les étudiants
A
A
Power
V
Load
Power
V
Load
Fig. 2
Fig. 1
A
A
Power
V
Load
Power
A
A
V
Fig. 5
Load
Fig. 4
Fig. 3
Power
V
Load
Power
V
Load
Fig. 6
The majority of the answers are classified in the VI categories (no answer), VII (incomplete
answer) and VIII (indecipherable answer). It is surprising that there are as many students in
these categories. Several hypotheses are possible:
- They didn't understand the electric diagram.
- The characterization task of the problem is completely new for them.
- They are unable to take into account the disruption of the measure devices.
The last hypothesis may be valid for some first year students, but surely not for those in
second and third years. Indeed, the students in later years did more laboratories on the electric
measures of the intensity and voltage in the context of more advanced courses in electricity
and electronics. In spite of that, nearly half among them has the difficulty to plug an ammeter
correctly (figure 2).
The students classified in the III; IV and V categories encounter some difficulties to plug an
ammeter and a voltmeter adequately.
In the case of the first problem, we identified five conceptual representations:
(1-1): confusion between the internal resistance of an ammeter and a resistance of measure
(shunt);
(1-2): if the voltmeter is positioned before the ammeter, then it is not affected by this one
(sequential reasoning);
(1-3): confusion between the notion of ideal and non ideal instrument;
(1-4): confusion at the level of the voltage concept;
(1-5): confusion between current and voltage.
Analysis of the data: problem 2
The answers that are too vague prevent us to draw a clear conclusion with respect to the nature
of the difficulties. In spite of that, the analysis of the data permitted to discover six illustrated
categories of answers in table 3.
Table 3
Categories extracted of the problem 2
CATEGORY
INTERPRETATION
%
(c1, c2, c3)*
I
II
III
IV
V
Correct answer
No answer
Indecipherable answer
Incomplete answer
It is the value of the R resistor that makes
the difference
Application of the Ohm law to the boundary marks
of
the resistance and blockage
0
20
23
40
15
(0, 0, 0)
(20, 18,10)
(30, 36, 32)
(32, 35, 35)
(18, 11,13)
2
(0, 0, 10)
VI
*(c1, c2, c3) are respectively the percentages of the first students, second and third years
In the case of the problem 2, we identified three conceptual representations:
(2-1): The nature of a device depends on the way it is used, that if it is plugged in series, it is
an ammeter and if it is plugged in parallel, it is a voltmeter.
(2-2): The degree of disruption of a device seems to be associated with the absolute value of
the internal resistance instead of its relative value with respect to its context of use.
(2-3): Confusion between the representation of a voltmeter in the proposed model and a
movement of Arsonval or galvanometer that one uses to build a voltmeter or an
ammeter.
Analysis of the data: problem 3
Analysis of the data: part A
The analysis of the data permitted to identify four categories. These categories are presented in
the table 4.
Table 4
Categories extracted of the problem 3 (Part A)
CATEGORY
I
II
III
IV
INTERPRETATION
%
(c1, c2, c3)*
Correct answer
5
Good conclusion, but erroneous justification
14
No answer, incomplete answer or indecipherable
37
Implicit or explicit refusal of the model proposed. One 44
finds, for example, allusions to the battery that is
inside the ohmmeter, and that lets believe that this one
should behave like a source of tension. The functional
models proposed in the problem are seen as unreal
and they are rejected.
(7, 5, 0)
(17, 14, 7)
(38, 41,30)
(38, 38,63)
*(c1, c2, c3) are respectively the percentages of the first students, second and third years
Some answers formulated by students are illustrated below:
"No, because a voltmeter it is like a tip of thread. It doesn't have a resistor. "(First year,
Category IV)
"No, because the efficient resistance of an ohmmeter is 0Ω because one plugs it in parallel,
and it is not necessary that there is a big resistance so that the current passes easily (First year,
Category IV)"
"No, because this number appears too high according to me. Also, I cannot say why"(Second
years, Category III).
"No, because one never plugs in series a voltmeter"(Second years, Category III).
"No, because the instruments have all their mistakes. Either absolute or relative"(Third years,
Category III).
"If the galvanometer is ideal, the measure is good; otherwise, the ohmmeter would measure
the value of the internal resistance of the galvanometer (Re)"(Third years, Category II).
Analysis of the data: part B
The analysis of the data allowed us to identify four categories. These categories are presented
in table 5.
Table 5
Categories extracted of the problem 3 (Part B)
CATEGORY
INTERPRETATION
%
(c1, c2, c3)*
I
Correct answer
10
(7, 13, 7)
II
Refute the model, erroneous findings
15
(14, 18,10)
III
Out topic, disjointed or indecipherable
60
(63, 57,60)
IV
The ohmmeter "clears" a tension
15
(16, 11,13)
*(c1, c2, c3) are respectively the percentages of the first students, second and third years
Some answers formulated by students are illustrated below.
"Yes, because in the ohmmeter there are some batteries"(First years, Category IV).
"These are good devices"(First year, Category III).
"Yes, if it is not well adjusted"(Second years, Category III).
"It is that it measures the voltage of the small source of the ohmmeter"(Second years,
Category IV).
"It is about the tension that the ohmmeter produces to take its measure"(Third years, Category
IV)
"If the voltmeter indicates 1,032 V, then the ohmmeter must indicate the same value, but it is
necessary to interpret it as being in ohm." (Third years, Category III)
As in the case of the previous problems, a majority of respondents encountered a certain
number of difficulties to reason from the proposed models. The modelling and the equivalent
representation do not seem to be t functional concepts at all.
In the case of problem 3, we identified two conceptual representations:
(3-1): Association of the proposed model to a realization of elementary instruments from a
movement of Arsonval (or galvanometer) with a battery and resistors.
(3-2): Association of the proposed model to a realization of elementary instrument from a
movement of Arsonval (or galvanometer) and resistor shunt.
CONSTRUCTION OF THE QUESTIONNAIRE OF THE INDIVIDUAL
INTERVIEWS
We asked the students to solve two simple situations (see annex B). The first questioned the
influence of a non ideal voltmeter on the measure of voltage of a circuit of high impedance. In
this situation, the V1 voltage is also divided between the two electrical resistance of 10 MΩ,
producing a voltage of 5 V shown on voltmeter readings; therefore, V1 = 10 V. Once device is
disconnected, the intensity of the current will be zero in the external resistance of 10 MΩ, so
that tension across its boundary-marks will be also zero. Therefore, one will measure 10 V
between has and b. The second situation required to make a choice between two devices
modulated in a different way but essentially equivalent. . The student had to ask some
questions on the nature of the "dial"; the goal of the question was to see his reaction before the
problem. In the device (b), one doesn't see the role of the resistance of 2 Ω, except possibly to
adjust the resistance of the device. On the other hand, in the device (a), it acts obviously as
resistance of shunt and determines the scale of the device.
ANALYSIS OF THE DATA OF THE INDIVIDUAL INTERVIEWS
First situation
This question was well succeeded; the pupils applied the recipe known of the divider of
tension, without taking into account the model of the voltmeter. Thus, 60% of the respondents
mentioned the influence of the resistance of the voltmeter correctly on the measure
obtained. Among those not answering adequately (40%), one identified three categories of
answers:
1. Voltage is the same with or without the device: this category let us suppose that one didn't
assimilate the concept of disruption.
2. Voltage is null: this category adheres to the prejudice "null current, tension is null."
3. Voltage is equal to the source, but one cannot determine the value of it: this category doesn't
seem to be able to conclude from the elements of the results, following a modification of
circuit. The analysis of a circuit cannot conclude that from the knowledge of the elements
the constituent.
Second situation
For this situation, the majority of the respondents chose the model implying some elements in
series. They extrapolated the use of the device that one plugs, either in series for an ammeter,
either in parallel for the voltmeter. Among those having chosen the model device by parallel
elements, one can distinguish a transposition of the model proposed in a construction of
constituted ammeter of a galvanometer and a resistance shunt of deviation.
POSSIBLE SOLUTION
The teaching of the circuits and electronics should be inspired among others by the systemic
approach that was developed exactly for complex systems. This approach essentially rests on
the notion of model by opposition to the traditional approach that tries to explain the systems
by their internal construction and by the infinitely small. In the case of the measure of the
intensity of the voltage and resistance, this teaching must allow the students to construct the
following conceptual representations:

An electric measurement device plays always two complementary roles: the one of a
sensor that gives us an indication and the one of an ordinary component (often
modelised by a resistance and a capacity in parallel) from the point of view of the
circuit under test.

A measurement device can only measure what are presents at it's its boundary-marks,
without any exception nor interpretation. The user interprets the result. Of the point of
view of the circuit, a device of measure is only a component as the other.

To measure the current in a branch, one inserts an ammeter wherever in the branch, the
common boundary-mark being on the side of the end of the branch.

To measure tension between two nodes, one plugs a voltmeter between these two nods,
the common boundary-mark on the reference node of.

A voltmeter having to plugged between two nodes, it won't never disrupt the circuit
under test if it acts like an open circuit, that is if its intensity of the current is zero or
negligible.

An ammeter having to be inserted in a branch, for and on behalf of a conductor, won't
disrupt the circuit under test if it acts himself as a conductor, which is if tension across
its boundary-marks is negligible.

To represent an ammeter by a voltmeter plugged in parallel on a resistance of shunt (of
known value).

The voltmeter behaves like a simple plain resistance (at least for slow signals), that an
ohmmeter measures without any difficulty.

Most modern numeric ohmmeters possess an active circuit that produces a" stationary
test current (of intensity more or less big according to the scale)." It is therefore normal
to represent them by a source of current in parallel with a voltmeter.

An ohmmeter functions while submitting the component to a trial current, while
measuring voltage across its boundary-marks and while displaying the report between
the two.
CONCLUSION
The use of instruments implies inevitably modeling. This research allowed us to note that the
notion of model is practically inexistent among the majority of the students questioned. They
confound model and internal construction. Their reasoning is very "materialistic" and they
don't conceptualize the circuits. The diversity of the technical tasks and the quick progression
of the technology require a capacity of abstraction and more and more conceptualization. The
technologist must establish conceptual ties between the different systems; he cannot refer
constantly to the internal construction because it is too complex. The didactics of the theory of
the circuits should be inspired by the systemic approach that was developed exactly for
complex systems. This approach essentially rests on the notion of model by opposition to the
analytic approach (or traditional) that tries to explain the systems by their internal construction
and by the infinitely small.
BIBLIOGRAPHY
Cohen, R., Eylon, B. & Ganiel, U. (1983). Potential difference and current in simple electric
circuits. American Journal of Physics, 5, 407-412.
Guttwill, J. P., Frederiksen, J. R., & White, B. Y. (1999). Making their own connections:
Students’ understanding of multiple models in basic electricity. Cognition and
Instruction, 17(3), 249-282.
Métioui, A., Brassard, C., Levasseur, J. & Lavoie, M. (1995). The persistence of students'
unfounded beliefs about electrical circuits: The case of Ohm's law. International Journal
of Science Education, 3, 193-212.
Métioui, A. & Trudel, L. (2007). Analyse critique des expériences proposées dans les manuels
destinés aux jeunes de 8 à 12 ans: Magnétisme, électrostatique et circuits électriques
(Analysis critical of the experiences proposed in the manuals destined to the young of 8
to 12 years: Magnetism, electrostatic and electric circuits). In Critical Analysis of School
Science Textbooks, IOSTE International Meeting Tunisia Hammamet, 7 to 10,
February, CD-ROM, 764-778.
Métioui, A. (2012). Analysis of Secondary Professional-Stream Students' Conceptions of the
Operation of Reversed and Forward Biased Diodes. International Journal of Arts &
Sciences, 5(7), 75-87.
Métioui, A. & Trudel, L. (2008). Utilisation du multimètre en ampèremètre et en voltmètre :
formation des enseignants. In Proceedings of the Paris International Conference on
Education, Economy and Society, Tchibozo, G (Editor), Paris, 17 - 19 Juillet, CD-ROM:
Vol. 2, 556-573.
Millar R. & King T. (1993). Students' understanding of voltage in simple series electric
circuits. International Journal of Science Education, 15(3), 339-349.
Millar R. & Beh K.L. (1993). Students' understanding of voltage in simple parallel electric
circuits. International Journal of Science Education, 15(4), 351-361.
Paatz, R., Ryder, J., Schwedes, H. & Scott, P. (2004). A case study analysing the process of
analogy-based learning in a teaching unit about simple electric circuits. International
Journal of Science Education, 26 (9), 1065-1081.
ANNEX A
WRITTEN QUESTIONNAIRE
Problem 1: One wants to make to vary the current provided by the power supply under test
and to measure the corresponding voltage; for it, one must plug an adjustable load (for
example, a variable resistance).
To do the measures, one has an ideal voltmeter and a no-ideal ammeter, as shown in the figure
below. While completing the diagram, show how it is possible to connect all the circuit
elements to get the ideal values of IS and VS simultaneously. Please comment.
A
IS
POWER SUPPLY
UNDER TEST
VS
ADJUSTABLE
LOAD
V
Problem 2: The ammeter and the voltmeter
being very different devices, in a way
contrary to each other, how could it be that
one can use the same diagram, either a R
resistance and an ideal voltmeter in parallel
as shown ith the opposite figure, to represent:
- a no-ideal voltmeter,
- a no-ideal ammeter.
R
V
Problem 3: To measure the resistance of entry of a voltmeter, a technician plugs it directly on
his ohmmeter. On the opposite schema, one sees the equivalent circuits of the two devices.
A. On the ohmmeter, the technician reads a value that sounds reasonable to him, such as
9,81 MΩ. Do you believe that it is indeed the resistance of entry of the voltmeter? Why?
B. To his surprise, the voltmeter also indicates a value such as 1,032V. Can you draw
information of these facts about the properties of the electric devices?
Re
V
V
I1
Voltmmeter
Ohmmeter
ANNEX B
ORAL QUESTIONNAIRE
Situation 1
Let's consider the circuit of the face below. Suppose the reading of the voltage between a and
b is done with a voltmeter and indicates 5V, if one disconnects the voltmeter, what will the
tension be between a and b?
a
V1


V
b
Situation 2
Let's consider the circuit of the face below. Which of the two devices (a) and (b) is the most
suitable to measure the intensity of the current?


(a)
(b)