Course Development Using OCW Resources: Applying the Inverted Classroom Model in an Electrical Engineering Course Authors: Kent Chamberlin - Professor of Electrical and Computer Engineering, University of New Hampshire Daniel Carchidi - Manager, Instructional Development Center, University of New Hampshire Abstract Linear Algebra for Electrical Engineers was developed in response to a need identified by Electrical Engineering students at the University of New Hampshire for who were seeking a discipline-specific course in linear algebra. Using MIT Prof. Gil Strang s OCW Linear Algebra course, Prof. Kent Chamberlin was able to adapt Prof. Strang s online courseware so that he could make it available to his students to take as an independent study course. The pedagogical approach selected for the course, the inverted classroom (Lage, et al. 2000; Gannod, et al., 2008), is an instructional method in which pre-recorded lectures are viewed prior to the class session, permitting the students and instructor to focus on clarifying concepts, problem solving, and discussion during the class period rather than the three-times-per-week lecture that is typical for this type of course. The availability of OCW video lectures enabled the inverted classroom method to be used effectively for this course. This paper provides an overview of how a Linear Algebra course for electrical engineers was developed; the identification of student need for linear algebra; the customization of content for the specific needs of electric engineering students and associated course structure; and lessons learned from using OCW content to create an inverted classroom experience that included targeted problem solving and discussion opportunities for the students. Keywords OCW, OpenCourseWare, OER, Open Educational Resources, faculty, linear algebra, electrical engineering, University of New Hampshire, inverted classroom, rapid course development, Gilbert Strang. Introduction The objective of this course was to cover the fundamentals of linear algebra with a focus on topics that are of particular relevance to electrical engineering students. Because this course is not part of the core of electrical engineering curriculum, it was offered as an independent study that satisfied a senior elective requirement. And, because the course was not an existing course within the ECE department, it had to be developed from the ground up. What is noteworthy is that what was perceived to be a tailored, high-quality course was developed with a surprisingly small amount of effort and in a relatively short period of time, particularly considering the time and effort it takes to develop a new, traditional course. As is described in greater detail below, this was accomplished by assembling available content from the internet and combining it with custom made content, assignments and assessments.
The linear algebra, independent-study course addressed here was taught as an overload by the instructor, and it was offered because of a perceived need on the part of students. Had OCW courseware not been available, this course could not have been taught because the participating faculty member would not have had the time to deliver three extra hours of lecture per week in addition to the other duties associated with the course. However, because that workload was reduced through the use of external content, the course was able to be offered. All of the video lectures used for the course are available through MIT's Open Courseware Linear Algebra site: http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/index.htm All of the online material relating to the Linear Algebra course was reachable through a single webpage. That page contained a calendar, partitioned by week, which had links to the video lectures, notes, associated homework assignments and solutions to past assignments. Those links were updated generally one week in advance. The textbook for the course was text used for the original course (Introduction to Linear Algebra by Gilbert Strang), and this book was relied upon heavily throughout the course. The class met in person on a weekly basis to discuss the video lectures and the assignments. It was understood by the students that they were to have watched all of the hyperlink videos on the course website prior to coming to these weekly sessions, and it was clear from their degree of preparedness that they had indeed done so. It was straightforward to determine if the students had watched the videos in this small class of five, although a simple quiz could be used to make this determination for a larger class. The in person meetings lasted about two hours and they were highly interactive, with far more interactions between students than is typical in a traditional classroom. That interaction to a large degree centered around problem solving, where the students and the instructor worked more as team members than as instructor to student. To better align the course for electrical engineering students, homework assignments and projects were assigned that focused on electrical engineering topics. For example, students were asked to use the circuit analysis techniques that Strang describes in section 8.2 of his book to solve for currents and voltages in a specified circuit. Other discipline specific topics that were highlighted in the course were the Fourier transform, polynomial regressions on noisy data and data compression using matrices. Many of these assignments were carried out using Matlab. Recognizing the need Linear Algebra for Electrical Engineers was an independent-study course targeted to the needs of five upper-level undergraduates who had expressed a desire for a customized version of the course that addressed discipline-specific applications. In the past, engineering students wishing to study linear algebra in greater depth would take a course from the mathematics department, which provided a treatment of the subject that was often so abstract as to be unattractive to engineering students.
Desiring a more applied version of a Linear Algebra course, the students approached a faculty member with experience in linear algebra and requested that it be offered as a regular independent study course, where the students would learn about the topic on their own and then meet with the instructor on a regular basis to discuss the material. That initial request was denied, because the faculty member felt that it would be inappropriate to teach an independent study in a subject area where there was an existing course. However, after it was realized that a structured, discipline-specific course could be generated with a reasonable amount of effort, the course was approved for delivery. Although the Linear Algebra course described here has been offered only once, the manner in which it was offered, and the response that it received, indicates that at least some future courses will be developed using a similar approach. This type of course customization may be particularly important in small departments and at the graduate level, where available courses tend to be limited. It is not difficult to envision having one faculty member be able to manage multiple courses of this type, and be able to do so at a higher level of quality and a lower level of effort than to teach a single course in the traditional classroom. Customization and Course Structure The course was structured to fit into a standard, one-semester timeframe of 15 weeks, the same as the original MIT course. And, in the beginning of the course where the foundational material is covered, the UNH course moved at roughly the same pace and entailed the same homework problems as the MIT course. In the first five weeks of the UNH course, there was one homework set per week, with the problems coming from Strang s textbook. After that point in the semester, most of the problems were created by the instructor and were targeted towards electrical engineering applications. The UNH course did not cover all of the 34 video lectures comprising the MIT course, as some of the lectures did not appear to be a relevant as the other 25 that were assigned. Also, during several of the in-person meetings, the instructor gave regular lectures targeting electrical engineering specific topics, such as the Fourier Transform, circuit analysis and data compression. The mix of video lectures and in-class lectures will likely vary in future offerings of the UNH course, and that mix will be based on the interests of the students and the range of topics identified by the participating faculty member. The final grade for students was based on 13 homework assignments, a mid-term, a final project and a final exam. Because of the small size of the class, the instructor performed all of the grading. The in-class exam was given mid-semester, and used to ensure that all of the students were proficient in the basic concepts covered in the video lectures. All of the students in the course were assigned the same final project, and that project was to develop code that would perform compression on an audio file. Strang discusses data compression in lecture #31, and the UNH students were asked to write Matlab code to apply the compression techniques to an actual audio file. This project turned out to be challenging for some of the students, but all were able to produce working Matlab code that met assignment requirements.
Images may help for poster itself? Course Development Lessons Learned Actively assess student needs: By understanding the limitations expressed by engineering students with existing mathematics courses in linear algebra, the instructor was able to identify specific content and instructional methods to address gaps in the curriculum. The UNH Mathematics department offers a general introduction to linear algebra that many engineering students and electrical engineering students in particular, found too abstract to apply to other aspects of their studies. They expressed this as a need for an applied version of the course that linked to other parts of the engineering curriculum and which could be made available prior to the completion of their studies. Adapt existing materials for the context of your course add the details and applications: OERs offered under a CC BY-NC-SA license offer numerous opportunities for adaptation and customization. Gil Strang s MIT OpenCourseWare Linear Algebra course provided a comprehensive set of video lectures that address the foundations of linear algebra. It freed the instructor from having to create lectures for the course, which would have been time consuming and of lower quality than Professor Strang s videos. The instructor could then focus on his subject matter expertise and pedagogical creativity. He was able to develop problems sets that build on the video lectures and textbook using examples within electrical engineering. Vary traditional pedagogy by using video to replace the face-to-face lecture and enhance student review of content: As a result of the OCW video content, students were not constrained to a specific time to attend a face-to-face lecture. Students were assigned to read the textbook and view the video lectures prior to class each week. Unlike a typical face-to-face lecture, students were able to pause and replay the video as often as they liked until they were able to understand the concept being taught. The instructor asked the students to identify particular points of clarification in the video lectures that he could address using electrical engineering applications of the concepts that would tie into examples the students might be familiar with, thus improving understanding.
More rapid course development within existing teaching load: Because of the timing of the student request and restrictions on teaching load, this course was developed and taught in-load. There wasn t enough time for the development of linear algebra course materials that would focus exclusively on electrical engineering applications, which had plagued the instructor in previous attempts to run the course. By mixing available video content with newly developed problem sets and assessment materials, the problem was overcome. Do what you do best coaching, problem solving, application of concepts: The inverted classroom model of teaching using OCW s Linear Algebra course immediately focused the course development process on the value added steps of one-to-one and small group interaction. This freed the instructor to spend in class time reviewing problems, clarifying concepts, and interacting more closely with students in the class, often providing the type of instruction that the students found most effective. OERs provide numerous customization possibilities OERs offered under a CC BY-NC- SA license offer numerous opportunities for adaptation and customization: Gil Strang s MIT OpenCourseWare Linear Algebra course provided a comprehensive set of video lectures that address the foundations of linear algebra. It freed the instructor from having to create lectures for the course, which would have been time-consuming and potentially of lower quality than Professor Strang s videos. The instructor could then focus on area of the course that highlighted his subject matter expertise and pedagogical creativity. He was able to develop problems sets that build on the video lectures and textbook content by using examples within electrical engineering. For example, while Prof. Strang provided an overview of the mathematics describing Fourier Transforms, the tailored UNH course provided students with the opportunity to explore the topic in greater depth using practical applications. Conclusion OER/OCW materials provided a foundation for rapidly developing a customized linear algebra course for University of New Hampshire engineering students. The instructor incorporated openly available MIT OCW linear algebra video content, proprietary textbook material, and customized problem sets and examinations to address a gap in the curriculum. This approach allowed him to utilize an inverted classroom model to focus on areas of his own expertise and provide greater problem solving and discussion opportunities for his students. References Gilbert Strang, Introduction to Linear Algebra, Wellesley-Cambridge press, third edition Lage, M.J., Platt, G.J, & Treglia, M. (2000). Inverting the Classroom: A Gateway to Creating an Inclusive Learning Environment. Journal of Economic Education. 31(1), 30-43. Gannod, G.C, Burge, J.E., & Helmick, M.T. (2008). International Conference on Software Engineering. Leipzig, Germany: May 10-18. 777-786.