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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. 1662 PIERS Proceedings, Marrakesh, MOROCCO, March 20–23, 2011 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. 1664 PIERS Proceedings, Marrakesh, MOROCCO, March 20–23, 2011 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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