Computer-assisted Learning Of Electromagnetics Through .

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Received: 17 June 2018DOI: 10.1002/cae.22073 Accepted: 9 September 2018RESEARCH ARTICLEComputer-assisted learning of electromagnetics throughMATLAB programming of electromagnetic fields in thecreativity thread of an integrated approach to electricalengineering educationBranislav M. Notaroš Ryan McCullough Sanja B. Manić Anthony A. MaciejewskiDepartment of Electrical and ComputerEngineering, Colorado State University,Fort Collins, ColoradoCorrespondenceBranislav M. Notaroš, Department ofElectrical and Computer Engineering,Colorado State University, 1373 CampusDelivery, Fort Collins, CO 80523.Email: notaros@colostate.eduFunding informationNational Science Foundation, Directorate ofEngineering, Division of EngineeringEducation and Centers, Grant number:EEC-1519438AbstractThis paper discusses an integrated approach to electrical-engineering education thatincorporates computer-assisted MATLAB-based instruction and learning into thejunior-level electromagnetics course and newly created learning studio modules(LSMs). In this model, creativity class sessions are followed by two comprehensiveand rather challenging multi-week homework assignments of MATLAB problemsand projects in electromagnetic fields. This is enabled by a unique and extremelycomprehensive collection of MATLAB computer exercises and projects, reinforcingall important theoretical concepts, methodologies, and problem-solving techniques inelectromagnetic fields and waves, developed by one of the faculty team members.These tutorials, exercises, and codes constitute a modern tool for learningelectromagnetics via computer-mediated exploration and inquiry, exploiting thetechnological and pedagogical power of MATLAB software as a general learningtechnology. The novel approach introduces students to MATLAB programming ofelectromagnetic fields, as opposed to just passive demonstrations of MATLAB's toolsand capabilities for computation and visualization of fields. MATLAB programmingtutorials and assignments are designed to deepen student engagement andaccommodate different learning styles so students can learn more effectively. Inaddition to improving students’ understanding and command of MATLAB use andprogramming within the electromagnetics context and beyond, these exercisesincrease their motivation to learn and appreciation of the practical relevance of thematerial, and equip them with the tools and skills to excel in other courses andprojects. The results of this project were qualitatively analyzed through feedbacksurveys given to the students at the end of each MATLAB assignment. TheElectromagnetics Concept Inventory was also used.KEYWORDScomputers and education, computer-assisted instruction and learning, computer exploration inelectromagnetics, electromagnetics teaching and learning, MATLAB-based instruction and learning,MATLAB tutorials, exercises, and codesComput Appl Eng Educ. 2018;1– 2018 Wiley Periodicals, Inc. 1

2 1 INTRODUCTION1.1 Overview of pedagogical approachSupported by a 5 year REvolutionizing engineering andcomputer science Departments (RED) grant from theNational Science Foundation (NSF), a diverse team ofeducators at Colorado State University (CSU) are implementing a new approach to teaching and learning that reimaginesthe roles of the faculty and moves away from the traditionalcourse-centric structure [5]. As described in the IEEE Accessarticle “A Holistic Approach to Transforming UndergraduateElectrical Engineering Education” [25], our pedagogicalmodel builds on the concept of “nanocourses” to facilitateknowledge integration (KI), a learning model grounded ineducation pedagogy and supported by research. The approachblurs the lines between courses because the faculty take asystems view of the curriculum to identify the fundamentaltechnical concepts of an electrical and computer engineering(ECE) education, independent of courses. These concepts arethen rearranged and organized into cohesive learning studiomodules (LSMs) to lay the groundwork for real-worldapplications. Each LSM is self-contained and addresses oneanchoring concept and a set of sub-topics in a given corecompetency area [5,25]. Although a departure from thetraditional course structure, LSMs still provide a path forstudents to learn all the intended topics in a rigorous fashion.Aiming to connect abstract concepts to the real world ofengineering, KI activities are then created to put learning incontext and illustrate the societal relevance of engineeringknowledge [5,25]. Serving as a mechanism for helpingstudents grasp the commonality and correlations betweencore concepts across the curriculum, KI activities showstudents how LSM fundamentals are integrated to form thebuilding blocks of a complex piece of ubiquitous technology.1.2 Creativity in the technical core of thecurriculumWhile our 5-year RED project spans the entire undergraduateprogram, special attention is given to the technical core, orjunior year, of the ECE curriculum. In addition to instillingdeep technical knowledge of the discipline, faculty areworking in partnership to interweave the following threadsthroughout the curriculum to help students develop skills thatwill allow them to thrive as engineers [25]:1. Creativity thread—integrates research, design, andoptimization.2. Foundations thread—illustrates why math matters in theworld of engineering.3. Professional formation thread—emphasizes professionalskills deemed important by industry.NOTAROŠET AL.This paper dives into the creativity thread of the project,sharing details about how the department is using learningtechnology tools, in this case MATLAB, to enrich and assesslearning.1.3 Challenges of electromagneticsinstruction and learningFor the RED project, technical core material encompassessignals and systems, electromagnetics, and electronics. Thispaper focuses on the role and importance of electromagneticsin the undergraduate curriculum, and the challenges of itsinstruction and learning. It has been noted by severalresearchers [2,6,19,41] that students have an opinion thatintroductory electromagnetics is a difficult subject, andinstructors also find it a difficult subject to teach. Indeed,while electromagnetic theory or theory of electromagneticfields and waves is a fundamental underpinning of technicaleducation, it is often perceived as the most challenging anddemanding course in the electrical engineering (EE) curriculum. The material is extremely abstract and mathematicallyrigorous, and students find it difficult to grasp, which is notunique to any particular school/department, country, orgeographical region.Researchers attribute the difficulty to three main factors:(i) the use of vector mathematics, which some students canview as rather abstract; (ii) introductory classes frequentlyonly cover very idealized situations that do not have truephysical applications; and (iii) realistic electromagneticsexamples in a laboratory setting are difficult to create.These three issues create various problems derived fromcommonly researched factors in engineering studentattrition and achievement. Dinov et al. [9] also point outthat classes that rely heavily on mathematics tend to missother learning modalities such as visual and active learning.If the difficulty related to visual and active learning is notaddressed, it becomes an issue with the instructor/studentlearning styles mismatch, as has been reported in multiplestudies [3,12–14,24]. In addition, if the realistic examplesand true physical applications are not presented in a waythat is both rigorous and relevant, students tend to losemotivation [15].1.4 Understanding student learning stylesLearning styles are characteristic preferences for alternativeways of taking in, and processing, information. The theory oflearning styles has been studied for decades, beginning withKolb's learning styles model in 1984. There are differentvariations on learning styles, but Felder and Silverman's indexof learning styles (ILS) [13] is commonly used in engineeringeducation. They categorize five pairs of complementarylearning styles: sensing and intuitive; visual and auditory;

NOTAROŠ ET AL.inductive and deductive; active and reflective; and sequentialand global.1. Sensing and Intuitive: Sensing learners deal with theoutside world through observing and gathering datathrough the senses, while intuitive learners indirectlyperceive information through speculation and imagination.2. Visual and Auditory: Visual learners use sights, pictures,and diagrams, whereas auditory learners prefer sounds andtext.3. Inductive and Deductive: Inductive learners prefer areasoning progression from observations, measurements,data, etc., to generalities, that is, governing rules, laws, andtheories. Deductive learners prefer the opposite progression of inductive learning, going from the governing ideasto explaining new observations.4. Active and Reflective: Active learning takes place whenexperimentation involves discussions, explanations, ortesting in the outside world. Reflective learners, meanwhile, prefer to go through these processes moreintrospectively. Kinesthetic learning is another commonlyacknowledged modality of learning, where learners preferexploring through touching and interacting, but Felder andSilverman consider this to be part of the active learningstyle.5. Sequential and Global: Sequential learners prefer thestandard layout of class content where the concepts areintroduced and learned systematically. Conversely, globallearners prefer to learn in fits and starts, needing to see howall the pieces fit together before they can make sense of anysmall part.1.5 Importance of adapting instructionalmethods to motivate learnersAlthough there is some debate on the effectiveness ofmatching instructional methods to a student's assessedlearning style, there have been significant studies showingthat a mismatch in learning styles leads to decreasedperformance and a higher attrition rate [3,12–14,24]. InSeymour and Hewitt's study “Talking about Leaving” [39],the data showed that grade distributions of students who leavetechnical curricula are essentially the same as the distributionsof those who continue. Their findings revealed that some ofthe higher performing students leave because of dissatisfaction with their instruction. This fact was also recorded byBernold et al. [3] in their three-year, 1,000 —student study,where they systematically tested the learning style preferences and behaviors of the students and tracked theirsuccesses, failures, and paths throughout 3 years of theengineering program. They found that students who had thegreatest mismatch in learning style preference versus the3standard teaching style preference (lectures) had the largestattrition rate and the poorest grade point average (GPA), evenwhen the comparison was done through a ScholasticAssessment Test (SAT) mathematics covariation. However,as Litzinger et al. [24] note, students with any learning stylepreference have the potential to succeed at any endeavor.Learning styles and modalities are simply preferences thatdictate the ways in which people feel the most comfortablelearning. Felder and Brent [12] note that how much a studentlearns in a class is governed in part by that student's nativeability and prior preparation but also by the compatibility ofthe student's attributes as a learner and the instructor'steaching style.A large part of student performance is tied to theirmotivation. College students, like all adults, have an issuemotivating themselves to study material if it is not applicableto their lives or their future professions [31,42]. Ulaby andHauck [41] observed that students learning in the standardlecture-style environment tend to doubt the usefulness oflearning the subject of electromagnetics as they cannot seehow it can be applied directly to other parts of the curriculumand how it will benefit them once they graduate. Thecognitive science based study “How People Learn” [31]recommends a model to mitigate this issue, which calls forinstructional activities to focus on the most importantprinciples and methods of a subject while building on thelearner's current knowledge and conceptions. The activityshould also utilize techniques known to promote skilldevelopment, conceptual understanding, and metacognitiveawareness rather than simple factual recall.1.6 Background on computer-assistedlearning and programming in technicaleducationComputer software has been used to aid student learning inelectromagnetics for quite some time [1,4,7,8,11,16,17,20–23,26,32–38,40]; although this use has expanded in recentyears, it is not widespread yet and is not universallyimplemented. As Mias [26] notes, computer-assisted learningsignificantly improves the teaching of electromagnetics. Hegoes on to discuss some of the currently utilized methods ofincorporating computer-assisted learning including: educational graphical interfaces for electromagnetic field visualization, the use of spreadsheet programs in solvingelectromagnetic problems, the use of university and/orindustry-developed computational electromagnetics softwareto solve real life problems and gain an insight onelectromagnetic field phenomena, and virtual laboratories.These solutions, although they can be shown to improveteaching, lack one specific task: programming. Mias [26] andRead [35] discuss the advantages of utilizing programming inelectromagnetics instruction. They both note that the benefit

4 of writing computer code is that it increases the students’ needto understand fundamental field concepts of the probleminvolved and the need to be able to obtain the conventionalanalytical solutions of simple problems. Programming, aswell as the other methods of computer-assisted learning, alsobrings in the possibility for design work, a core aspect of thecreativity thread within the RED project, in a way that was notpossible through traditional methods.As another example of the effectiveness of computerassisted learning in engineering/science education, generally,we look to the work by Dinov et al. [9]. In instructing severalstatistics courses of various levels, these authors experimented with a statistics online library provided by the NSFcalled statistics online computational resource (SOCR).While integrating this resource into their classrooms andpost-work did not result in statistically significant gains incomparison to the traditional classroom, they did receivemuch more positive feedback for the course through aqualitative survey, and the retention rate of the supplementedclasses was significantly higher. This shows that even ifstudents do not learn more through programming, which iscontrary to what Mias and Read suggest, they still enjoy thecontent matter more and are more willing to stick with theclass.The use of programming in the current EE curriculumgenerally follows the same trend in that students arefrequently only required to take a single programming courseat the beginning of their program. These courses, which aregenerally offered through the university's Computer Science(CS) department, teach students topics more related to CS,such as sorting and searching, rather than topics that are bettersuited to EE, such as matrix manipulation [19]. The studentsare then expected to use these rudimentary, unrelatedprogramming skills to later program concepts such as vectoralgebra and calculus, multivariable functions, three-dimensional (3-D) spatial visualization, numerical integration,optimization, and finite-difference and finite-element methods. This can be a struggle for many students without astronger background in matrix manipulation and calculusrelated programming.1.7 Utilizing MATLAB to deepen learningand inspire creativityTo adapt our instructional methods to motivate students, andaddress the learning considerations outlined previously, wehave chosen MATLAB (by MathWorks, Inc., Natick, MA)as the learning technology and modeling software languagefor the creativity thread of the RED project. Evidence showsthat students find MATLAB easy to use [35], and it isconsidered an important tool that ECE students and futureengineers need to use effectively. By having a single softwareplatform that is consistently used throughout the curriculum,NOTAROŠET AL.students gain proficiency with the programming environment, allowing them to shift their focus from learningprogramming to understanding the technical content of whatthey are programming.This paper presents inclusion of computer-assistedMATLAB-based instruction and learning in the electromagnetics course and LSMs of the RED project, where thestudents are implementing the core LSM concepts theylearned into a “virtual electromagnetics testbed” usingMATLAB, as part of the creativity thread. The students aretaught “hands-on” electromagnetics through MATLABbased electromagnetics tutorials and assignments of exercisesand projects in MATLAB. To enable this, the lead author ofthis paper has developed a unique and comprehensivecollection of approximately 400 MATLAB computerexercises, problems, and projects, covering and reinforcingpractically all important theoretical concepts, methodologies,and problem-solving techniques in electromagnetic fields andwaves [29], as a modern tool for learning electromagnetics viacomputer-mediated exploration and inquiry. These tutorials,exercises, and codes are designed to maximally exploit thetechnological and pedagogical power of MATLAB softwareas a general learning technology. Similar to the study done byDinov et al. [9], the results of this work are qualitativelyanalyzed through a survey given to the students that recordedtheir feedback about the integration of MATLAB in theircoursework. A preliminary report on this work appears in aconference proceedings [30].When MATLAB has previously been chosen as a platformfor computer-assisted learning [1,4,7,8,11,16,26,32,37,38], theinstructors frequently have created a graphical user interface(GUI) or some similar interface that the students interact withas opposed to writing their own programs. As discussed above,programming forces students to think about the problemlogically and to pay attention to the details, while still having abig picture of the problem at hand. Simply letting a GUI do thecalculations and imaging the results is not as conducive to thelearning process as the active process of programmingelectromagnetics.Note that the “creativity” term within this study should beconsidered and appreciated in a broad sense. The “creativitythread” of our RED project is an umbrella for a variety ofresearch, analysis, and design related activities that studentsperform individually and in teams within the individualcourses and through projects at different stages in thecurriculum. Through this thread, we are attempting to inspireand enhance not only students’ creativity but also a number ofother related, abilities and skills essential for their preparationfor the real world of engineering. Likewise, the link betweenthe “creativity” and the inclusion of computer-assistedMATLAB-based instruction and learning in the ECEelectromagnetics course and LSMs as presented anddiscussed in this work should be understood broadly, in

NOTAROŠ ET AL.multiple ways. Foremost, the “creativity” term linked to theuse of MATLAB in electromagnetics classes here comes fromthe context of this presented implementation, namely, as partof the creativity thread of the RED project, and practically allreferences to “creativity” in this paper are within this context.In addition, MATLAB exercises can help the studentsdevelop a stronger intuition and a deeper understanding ofelectromagnetic field theory, examples, and problems, whichis a prerequisite for reaching other (higher) categories oflearning, including analyzing, evaluating, and creating.Through MATLAB-based computer-mediated explorationand inquiry, students can also invoke and enhance theiranalytical, evaluative, and

surveys given to the students at the end of each MATLAB assignment. The Electromagnetics Concept Inventory was also used. KEYWORDS computers and education, computer-assisted instruction and learning, computer exploration in electromagnetics, electromagnetics teac

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