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Combining DoV framework and methodological preconceptions
to improve student’s electrical circuit solving strategies
Raoul Sommeillier, Frédéric Robert
Bio- Electro- And Mechanical Systems (BEAMS), Brussels Faculty of Engineering,
Université libre de Bruxelles, Belgium.
Abstract
Our research studies about student’s prior knowledge acting as learning
difficulties (referred to as preconceptions) in electricity courses at university
level led us to define knowledge as the association of two elements: a model
and a domain of validity (DoV). This statement is the core of the DoV
framework. This framework reveals its powerfulness in the way it helps
teachers to map students’ cognitive structures, to identify their preconceptions
as well as to derive effective teaching strategies. Quantitative
experimentations we carry out indicate a lack of global circuit solving strategy
among students. Especially, they highlight the fact that the difficulties
encountered by those students in network analysis are not that much relying
on the mastering of solving methods but on the method selection process. This
lack of solving strategy prevents the students to grasp the domain of validity of
the solving methods they master, so to associate the relevant methods with the
suitable circuits. This paper depicts how the application of the DoV framework
to this problem-solving process reveals to be a great tool to identify and tackle
students’ (methodological) preconceptions as well as to formalize, rationalize
and simplify complex solving strategies making them easier to explain, teach
and learn.
Keywords: Preconception; domain of validity (DoV); electricity; network
analysis; problem-solving process; solving strategy.
5th International Conference on Higher Education Advances (HEAd’19)
Universitat Polit`
ecnica de Val`
encia, Val`
encia, 2019
DOI: http://dx.doi.org/10.4995/HEAd19.2019.9458
This work is licensed under a Creative Commons License CC BY-NC-ND 4.0
Editorial Universitat Polit`
ecnica de Val`
encia 361
Combining DoV framework and methodological preconceptions to improve circuit solving strategies
1. Introduction
It is widely acknowledged that students come to courses with difficult-to-change prior
knowledge (referred to as preconceptions in this paper) at both pre-university and university
level, in particular in general physics education. Since several years, we are studying this
phenomenon in circuit theory. Various experimentations led us to propose an original and
formalized conceptual framework based on the concept of Domain of Validity: the DoV
framework. This DoV framework reveals its usefulness and its powerfulness such as a frame
of reference to better understand, identify and assess students’ preconceptions or as a tool
from which effective teaching strategies can be derived. The application of the DoV
framework through experimentations (preposttest design, interviews, case study, etc.) with
different research questions and objectives offered promising results (Sommeillier & Robert,
2017).
We go further in this paper by applying the DoV framework to complex problem-solving
processes and by introducing the concept of methodological preconception. This new
perspective is motivated by quantitative past examination and laboratory test analyses
revealing that the difficulties encountered by the students are at least as much relying on the
method selection process (i.e. the ability to select the most relevant and efficient method(s)
to solve a circuit) as the mastering of solving methods themselves. This application of the
DoV framework reveals to be a great tool to formalize, simplify and so to more effectively
teach complex solving strategies. Several authors among have provided very interesting
analyses about students’ reasoning in circuit solving (Andre & Ding, 1991; Langlois & Viard,
2014; Viennot, 1979), but – according to us – with different perspectives and contexts.
Section 2 depicts briefly the seminal ideas of the DoV framework and how it integrates the
concept of “preconception”. Section 3 introduces the “methodological preconception” as an
expression of a students’ lack of global circuit solving strategy. Section 4 highlights the
benefits of transposing the DoV framework to the network analysis process.
2. Domain of Validity framework
We study students’ learning difficulties caused by prior knowledge in an engineering school.
This approach prompted us to model the observed phenomena and derive an explicit teaching
strategy to address these difficulties. We present in this section a conceptual framework we
call the DoV framework, whose key concept is the domain of validity (or DoV) of a
knowledge. This framework is based on two main assumptions (Subsections 2.1 and 2.2).
2.1. Knowledge is the association between a model and a DoV
We analyzed and summarized seminal ideas from existing constructs about prior knowledge
(Sommeillier, Quinlan, & Robert, 2019): misconceptions, alternative conceptions, anchoring
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Raoul Sommeillier, Frédéric Robert
conceptions, phenomenological primitives (p-prims), threshold concepts, cognitive obstacles
and conceptual changes (Posner, Strike et al., 1982; Smith, diSessa et al., 1994; Vosniadou,
2012) – to mention a few authors among many others. In most of those constructs, knowledge
(or conception or model) is the central – if not sole – element of the cognitive structure.
Discussion across the various constructs then tends to center on how valid that knowledge is
in relation to expert views. We will refer to this these assumptions (knowledge is “atomic”,
and its validity is the focus of debate) as the monolithic view of knowledge.
Instead, we hypothesize that knowledge consists of two connected elements: a model and a
domain of validity (DoV). Both the model and the DoV are part of an individual’s cognitive
structure, hence their knowledge. The DoV is the bounded area within which the model
properly describes “real-life experiences”. Figure 1a illustrates this view: a piece of
knowledge is the association of a model M1 and a domain of validity DoV1 (represented by
the rounded-corner box). The dots represent real-life experiences. Some of the dots are inside
DoV1 (white dots), while others are outside DoV1 (black dot): M1 properly describes the
three “white-dot” real-life experiences, but not the “black-dot” experience. These
“experiences” include situations students may face in everyday life (observations,
experiments, etc.) as well as situations created by the teacher (exercises, labs, problems, etc.).
(a) (b)
Figure 1. (a) Knowledge is a model associated with a domain of validity (DoV)
(b) Graphical formalization of the DoV framework
As a consequence of this hypothesis, there is no single “right” model surrounded by “false”
models; models just coexist, having different DoVs. As a simple example, the model of the
flat Earth is extremely useful and highly accurate when building a house, but disastrously
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Combining DoV framework and methodological preconceptions to improve circuit solving strategies
inaccurate when launching a satellite. The coexistence of the classical mechanics (Newton)
and the theory of relativity (Einstein) is another well-known illustration.
Introducing the DoV concept allows us to capture the fact that a model is sufficient in many
circumstances, but not all circumstances. This situation is depicted at the top of Figure 1b
(representing the teacher’s cognitive structure) where two models M1 and M2 are both valid
but in different DoVs. It leads us to abandon the idea that a conception is “right” or “wrong”
and opens the door to multiple valid conceptions coexisting. According to us, explicit
recognition of DoVs is today lacking in existing teaching strategies.
2.2. Preconception is the association between a model and an overgeneralized DoV
The second DoV framework hypothesis is that very nature of a preconception consists of an
overgeneralized DoV (or ODoV): a domain of validity too wide relative to what the associated
model can really represent. This simple hypothesis explains many phenomena related to prior
knowledge. It also suggests that the typical blocking situation experienced in learning is due
to the monolithic view of knowledge itself, held by the teacher and/or student.
Referring to the cognitive structure depicted on the top half of Figure 1b, this teacher has two
models in mind, with different DoVs, both coexisting without contradiction. One black-dot
experience (launching a satellite into orbit) is properly described by M2 (round Earth) but
not by M1 (flat Earth). The bottom part of Figure 1b depicts the cognitive structure of students
who possess a preconception related to M1: the students possess the same model M1 as the
teacher but associated with an ODoV (including the black-dot experience covered by M2).
When the teacher presents the students with a black-dot experience for the first time (for
which M2 is a better fit), students will use M1 according to their own cognitive structure
(especially if the student is not conscious of a structural difference between this black-dot
experience and the white-dot experiences). The student is confident in M1 because using it
in the past has resulted in positive feedback from the teacher.
Our hypothesis also explains why, even when students understand M2, they may continue to
apply M1: it is different to remember, understand, explain or even apply a model (which
involves only the model itself) than it is to select an appropriate model when facing a real-
life experience (which involves both the model and its DoV). Students could have learned
and remembered a model M2 without having modified the DoV of a model M1.
3. Network analysis and methodological preconception
In the considered electricity course for 2nd year engineering students, the main learning
outcome is to be able to solve electrical circuit problems, more specifically to perform
efficient network analyses. Network analysis is the process of finding the voltages across,
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Raoul Sommeillier, Frédéric Robert
and the currents through, every (passive and linear) component in an electrical circuit. The
circuits covered in this course include all circuit types from the most basic DC circuits with
purely resistive components in steady state to the most complex AC circuits with reactive
components and transient (Figure 3). When looking at solving any circuit, a number of
methods and theories exist to assist and simplify the process. There are many different
techniques for calculating these values, from electrical laws to mathematical tools.
We analyzed the answers provided by 796 students in past examinations (Sommeillier &
Robert, 2017). This examination analysis indicates the difficulties encountered by the
students are at least as much relying on the method selection process (i.e. the ability to select
the most relevant and efficient method(s) to solve a circuit) as the mastering of solving
methods themselves. In other words, when facing a new problem (or felt as if), students tend
to improvise, which consists in ignoring what they fully master. This phenomenon is
enhanced by the absence of a global solving strategy.
A laboratory test analysis we are undertaking leads to the same outcome. Figure 2 shows an
example of those laboratory tests submitted to each student at the beginning of lab sessions.
The aim of this question is basically to solve an AC circuit with a reactive component in
steady state (Circuit type 7 in Table 1). The data analysis reveals that among the 156 students
having passed this test, only 46 students (29%) answered a voltage amplitude of 5V which is
the right answer. 76 students (so 49%) answered 7V and 34 (22%) didn’t provide a numerical
answer. This is due to the fact they – almost half of all 156 students – tried to solve it in the
time domain (3 + 4 = 7 by simply adding the voltage amplitudes) instead of in the frequency
domain (�3² + 4² = 5 by using adding the corresponding phasors) as explicitly defined in
all the course material and already practiced during exercise sessions. Thus, having no global
solving strategy, students tend to apply a solving method outside of its relevant DoV.
Figure 2. Laboratory test example with a reactive circuit with AC source in steady state (Circuit type 7 according
to Table 1) – Translated from French
Regarding the DoV framework, this lack of strategy can be expressed in terms of
methodological preconceptions. A methodological preconception is defined in the DoV
framework identically to a classical preconception (Subsection 2.2): the association of a
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Combining DoV framework and methodological preconceptions to improve circuit solving strategies
model with an overgeneralized DoV, with the particularity that the model referred to as a
solving method and the DoV as a set of circuit types.
4. DoV framework applied to electrical circuit solving strategy
Being able to select the relevant methods for any circuit seen in this electricity course is not
trivial. Indeed, the different circuits the students can face is infinite, the solving methods are
numerous, and they can present slight differences in solving efficiency depending on the
considered circuit types. Formalizing the method selection process and the steps required to
solve any type of circuit illustrates the intricacy the students have to face.
By splitting the analysis in terms of DoVs on one hand and in terms of models on the other
hand, the DoV framework reveals its powerfulness in its ability to formalize, simplify and
categorize the constitutive elements of the global circuit solving strategy we are seeking for.
First, focusing on the DoVs – and so on the different circuit types seen in network theory –
it’s worth to note that each of those circuits can be characterized by three binary parameters:
the nature of the passive components (resistive or reactive), the type of power supply (DC or
AC) and the fact that the circuit is permanently in steady state or that it presents a transient
(absence or presence of a switch). Three parameters having each two possibilities give 2³=8
possible circuits. They are listed in Table 1. Figure 3 gives two basic examples of circuits of
type 1 and type 8, while Figure 2 above presents a circuit of type 7.
Table 1. Eight type of electrical circuits depending on three criteria
Circuit type index 1 2 3 4 5 6 7 8
Component type
Res.
Res.
Res.
Res.
Rea.
Rea.
Rea.
Rea.
Power supply
DC
DC
AC
AC
DC
DC
AC
AC
Switch presence
Yes
No
Yes
No
Yes
No
Yes
No
(a) (b)
Figure 3. Examples of electrical circuits: (a) Circuit type 1 and (b) Circuit type 8
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Raoul Sommeillier, Frédéric Robert
This circuit characterization allows to apply easily the DoV framework. Following the
formalization depicted in Subsection 2.1, the idea is to identify for which circuit types each
method is relevant or not. For instance, independently of the power supply type and of the
presence or the absence of a switch, the “classical” solving method is suitable for circuits
with purely resistive components (circuit types from 1 to 4). The fact this classical solving
method is relevant for some circuit types and not for the others can be modelized by the
graphical formalization of the DoV framework (Figure 1a). In this transposition (Figure 4a),
the considered solving method is what we called the model in Subsection 2.1 and this model
M1 is associated to the DoV in which its use is relevant: a set of circuit types 1 to 4 (i.e. a set
of “real-life experiences”).
(a) (b)
Figure 4. (a) First assumption of the DoV framework applied to one solving method.
(b) DoV framework as a tool to formalize and rationalize a global circuit solving strategy
In this framework, a methodological preconception consists in applying the model outside
the appropriate DoV. For instance, referring to the example illustrated in Figure 2, applying
the model M1 (classical solving method) to the real-life experience 7 (AC circuit with a
reactive component in steady state) reveals the presence of this preconception. Processing
similarly for each solving method allow us to radically simplify and rationalize the network
analysis process which make it easier and more effective to teach. This study leads to a
powerful formalization of a global circuit solving strategy illustrated in Figure 4b.
Combining the DoV framework and the methodological preconception to efficiently map
students’ erroneous method selection in a formalization including only four models (solving
methods) for eight circuit types. Confronting the DoVs appropriated to a model to the
(potentially erroneous) DoV associated by the student to this model enables to easily identify
the nature of the obstacles and to build a teaching situation helping to make the student aware
of this obstacle and to overcome it efficiently. More generally, this formalized result widens
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Combining DoV framework and methodological preconceptions to improve circuit solving strategies
the possibilities in rethinking the ways circuit theory and network analysis are taught from
the identification of students’ difficulties to the development of teaching strategies.
5. Conclusion
Network analysis is a fundamental learning outcome of any electricity course for which
students encounter strong difficulties. Our experimentations indicate the difficulties
encountered by the students are at least as much relying on the method selection process as
the mastering of solving methods themselves. Applying the DoV framework to this problem-
solving process enables to formalize and simplify this process. Combined with the
methodological preconception, the DoV framework is a powerful tool to better identify
students’ difficulties in circuit solving and it offers a useful perspective to conceive efficient
teaching strategies. This way to apply the DoV framework is not bounded to network
analysis, to circuit theory or even to physics. More investigations have to be done to
implement this approach in other fields and education levels. We are currently working on
the development of a science-learning app in which a DoV-based teaching strategy is
implemented in order to help students from all around the globe overcoming their
preconceptions in different scientific fields. Finally, we recommend to any science teacher to
adopt an approach combining the DoV framework and (methodological) preconceptions as a
tool to better understand, evaluate, target and overcome students’ learning difficulties.
References
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conditions, and problem solving in basic electricity. Contemporary Educational
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Langlois, F., & Viard, J. (2014). Raisonnements dans la résolution de problèmes
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