Download Engineering Students` Conceptual Understanding of Electro

Progress In Electromagnetics Research Symposium Proceedings, Marrakesh, Morocco, Mar. 20–23, 2011 1661
Engineering Students’ Conceptual Understanding of Electro- and
Magnetostatics
Johanna Leppävirta, Henrik Kettunen, and Ari Sihvola
Department of Radio Science and Engineering
Aalto University School of Science and Technology, Finland
Abstract— At the university level, the teaching of engineering students is often focused mostly
on the development of procedural knowledge, that is, formulating and solving problems mathematically. Another very important factor associated with the enhancement of engineering skills
is the conceptual knowledge, the actual comprehension of the physical concepts and the relations
between them. Prior research has revealed that academically successful engineering students
often lack deep understanding of the basic concepts and principles that underlie their training
areas [1]. The aim of this study was to assess undergraduate engineering students’ conceptual
knowledge of electro- and magnetostatics and examine how these conceptions would change after
instruction. The Conceptual Survey of Electricity and Magnetism (CSEM) [2] multiple-choice
test was administered as a pre- and post-test to students (cumulative N = 233) enrolled on
an elementary course on electromagnetics (Static Field Theory) at Aalto University School of
Science and Engineering, Finland. The study shows that engineering students have considerably more difficulties with magnetostatics than with electrostatics. The instruction, although
extensive, does not produce significant changes on students’ initial conceptual understanding of
magnetostatics. The study also found that the correlation between the students’ conceptual and
procedural knowledge was quite low. The result indicates that basic conceptual knowledge is a
necessary but not sufficient condition for acquiring procedural skills in electrostatics and magnetostatics. The findings suggest that more instructional time should be spent on mathematically
and conceptually demanding magnetostatics. Furthermore, we need to broaden the view of what
type of knowledge is valued and assessed in engineering education. These results encourage us
to develop and introduce new instructional practices for enhancing conceptual understanding of
students during elementary engineering courses.
1. INTRODUCTION
Proficiency in problem-solving and calculation has long been one of the main goals in many domains
of engineering education. Although teachers without doubt acknowledge the importance of the
conceptual base, the approach to teaching and assessment has traditionally been procedurally
dominated [3]. Recent studies, however, show that academically successful engineering students
often have little understanding of the basic concepts and principles that underlie their areas of
training [1].
Conceptual understanding makes the learning of procedural skills easier and frees capacity for
learning more difficult procedures [4]. When skills are learned without understanding, they are
learned as isolated bits of knowledge and it can be difficult to engage students in activities that
help them understand the reasons underlying the procedures. On the other hand, without sufficient
procedural fluency, students have trouble deepening their understanding of the basic ideas or solving
problems mathematically [5].
Byrnes and Wasik [6] distinguish two approaches regarding the relationship between procedural
and conceptual knowledge in the domain of mathematics. In the simultaneous activation approach,
conceptual knowledge is seen as necessary and sufficient for correct use of procedures. This view
argues that enriching students’ conceptual knowledge enables the students to detect errors in their
procedures [5]. Furthermore, if conceptual knowledge is low, procedures will be performed incorrectly. The contrasting view is the dynamic interaction approach [6]. The conceptual knowledge
is seen as a necessary but not sufficient condition for acquiring procedural skills. Conceptual
knowledge forms a basis for learning new procedures, but once acquired, procedures develop independently through proceduralization, discrimination and generalization. Moreover, conceptual and
procedural knowledge seem to interact in diachronic cycles over time rather than simultaneously
when student is engaged in problem-solving.
The aim of this study was to assess undergraduate engineering students’ conceptual ideas of
electrostatics and magnetostatics and examine how their conceptions change after instruction. We
also examine the possible relations and correlations between students’ conceptual and procedural
understanding in electromagnetics.
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2. METHODS
The conceptual learning gains were measured by using the Conceptual Survey of Electricity and
Magnetism (CSEM) test [2]. The CSEM is a broad survey instrument that investigates the understanding of electric charge, potential, electric and magnetic field and force, and Newton’s laws in
the context of electromagnetics. The CSEM consists of 32 multiple-choice questions. In this study,
the last four of these questions (29–32) were omitted since they deal with dynamic field theory,
which was not covered in this studied elementary electromagnetics course focusing only in static
fields. The test was translated into Finnish and was used as a pre- and post-test. The pre-test
was administered to students during the first lecture and the post-test after the final lecture. The
post-test data of autumn 2010 course has not yet been collected at the time this paper is written.
The CSEM test was conducted on students (cumulative N = 233) enrolling in the Static Field
Theory course at Aalto University School of Science and Engineering, Finland, in autumn 2007 and
2010. Electromagnetic field theory is taught in two one-semester courses (Static and Dynamic Field
Theory) to sophomore students participating in the electrical engineering program. The aim of the
Static Field Theory course was to learn the basic concepts of electricity and magnetism: electric
and magnetic field and force, electric potential, conductors, electric currents, and so on. The course
consisted of lectures, complex multi-step homework exercises, a project work, and a final exam.
Students could participate in tutorials, where they solved standard textbook problems with the
help of an assistant. The multi-step homework exercises were compulsory and more complex than
the exercises solved at tutorials. A Finnish textbook [7] about static field theory was used during
the course and the language of instruction was Finnish.
The procedural knowledge of students was measured by assessing their performance in the final
exam. The exam exercises were complex problems and similar to the homework exercises, which
required an ability to identify and formulate the precise problem from the given scenario.
3. RESULTS
The overall success of undergraduate engineering students on the CSEM test was 57% and 59% of
correct answers in years 2007 and 2010, respectively. The pre-test results indicate that the level of
preliminary knowledge of the students was quite equal in both years. The CSEM score increased
to 67% after instruction (2007). The normalized learning gain g, which is defined as the actual
average gain divided by the maximum possible gain,
g=
%post − %pre
,
100 − %pre
(1)
was 0.23. According to cut-off criteria of Hake [8], this score is considered as low-gain (g <
0.30). In traditional courses that have low interactive engagement, the average gain varies generally
between 0.15 and 0.30. The overall results reveal a notable disparity between electricity and
magnetism questions (see Fig. 1). In 2007, the pre-test scores were 62% (electrostatics) and 45%
(magnetostatics), and the post-test scores 72% (electrostatics) and 54% (magnetostatics). In 2010,
the pre-test scores were 64% (electrostatics) and 45% (magnetostatics). The electrostatic questions
were considerably easier to students than the questions relating to magnetostatics. The engineering
students performed 17 (2007) and 19 (2010) percentage units poorer on the magnetism questions
compared to the electricity questions. Furthermore, the learning gain was different in the two
topics: on magnetism questions, g was only 0.17 while on electricity questions the gain was 0.26.
To compare students’ conceptual and procedural performance a scatter plot was constructed for
the data. The graph area was divided into four quadrants (numbered anti-clockwise beginning with
the top right quadrant) splitting the vertical and horizontal axes at the corresponding average value
for all students for the relevant index. The relation between conceptual and procedural knowledge
was investigated with the Pearson correlation coefficient.
The number of participants with matching CSEM post-test- and final exam data was 102 (year
2007). The average CSEM post-test score for this sample was 18.80 (standard deviation 7.54;
scale 1–28) and the average final exam score 14.47 (standard deviation 5.75; scale 1–30). The
correlation between conceptual and procedural performance was 0.49, which, although significant
(p < 0.01), was not very high. The first quadrant in Fig. 2 contains students that perform well
both conceptually and procedurally. One third of the participants entered into this group. An
equal amount of students (33%) were in quadrant 3, which means that they performed poorly
in both aspects. The second quadrant contains students that performed well conceptually but
Progress In Electromagnetics Research Symposium Proceedings, Marrakesh, Morocco, Mar. 20–23, 2011 1663
Figure 1: The average performance (%) in the CSEM conceptual areas.
Figure 2: Comparison of scores on the CSEM post-test (scale 1–28) with scores on the final exam (scale
1–30).
poorly procedurally, and the fourth quadrant contains students performing well procedurally, but
not well conceptually. It is interesting to note that more students were conceptually strong and
procedurally weak (19%) than procedurally strong and conceptually weak (14%). This observation
supports the dynamic interaction view which considers the conceptual mastery to be a necessary
but not sufficient requirement for achieving expertise in the topic.
4. CONCLUSION
The results indicate that there is a relation between conceptual and procedural knowledge when
learning electro- and magnetostatics. The findings of this study can be said to generally favour
the dynamic interaction view that conceptual knowledge is a necessary but not sufficient condition
for procedural knowledge. As seen in Fig. 2, 19% of students performed well conceptually, but
did not succeed in the final exam. Fewer students (14%) lacked conceptual knowledge but were
proficient in procedures and problem-solving. This suggests that some general knowledge of the
basic concepts and relations are needed in order to succeed in complex problem-solving. The
findings reveal, however, that in the context of electromagnetics, it is possible to have conceptual
knowledge without considerable procedural skills but the reverse situation is less common. As
the dynamic interaction view proposes, the conceptual knowledge forms the basis for learning new
procedures but once acquired, procedures develop independently. Our other study [9] shows that
prior conceptual knowledge predicts success in the final exam, but developing students’ procedural
skill with complex problem exercises during the course does not significantly enhance students’
conceptual knowledge.
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Our research findings, as well as prior studies [2], indicate that students have considerably
more difficulties with magnetostatics than with electrostatics. This applies to both conceptual
and procedural understanding. Even though the magnetostatic phenomena are more visible than
the electrostatic ones, consider, for example, permanent magnets and compasses, the procedural
mathematical treatment of magnetic quantities seems to be more problematic. There is, of course,
a certain fundamental difference between electro- and magnetostatics. Whereas the electric field
arises from charges, the magnetic field arises from current, the simplest magnetic source being a
dipole.
The field theory course in the present study begins with electrostatics, which is a common tradition in electrical engineering curricula. The required mathematics, vector algebra and analysis,
is mostly covered using electrostatic examples. Magnetostatics are taught in the end of the course
and also less time is used for covering this topic. Many magnetostatic concepts can be taught by referring to their duality with electrostatics. However, due to the aforementioned difference between
electric and magnetic sources, magnetic fields often are mathematically more complicated, considering, for example, the Coulomb’s law in electrostatics and the Biot-Savart’s law in magnetostatics.
Therefore, the proficiency in manipulating vectors becomes essential. On this particular course,
many students had problems especially with vector algebra. Moreover, considering the CSEM test,
it seems that also the conceptual understanding of magnetic field is more difficult to achieve. In
addition, the learning gain remained lower in the magnetostatics questions.
The study indicates the need for educational practice to broaden its view of what type of
knowledge is valued and assessed in engineering courses. In order to be proficient in mathematics,
science, and engineering, students need to deepen their understanding of the key concepts and relations within their areas of training. We would recommend practitioners to seek ways of introducing
new instructional practices for enhancing engineering students’ conceptual proficiency.
ACKNOWLEDGMENT
This work was supported in part by Aalto University School of Science and Technology, Lifelong
Learning Institute Dipoli and Faculty of Electronics, Communications and Automation, and the
Academy of Finland.
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