Improved Learning By Non Traditional Undergraduate Students In Analytical Methods In Engineering

At the University of Wisconsin-Milwaukee (UWM) most of our undergraduate engineering students work at least half time and about 30% of our students work full time. Analytical Methods In Engineering, a core class required by all the undergraduate engineering departments at UWM, has been modified over the past three years to improve learning by these nontraditional undergraduate students. The evening section consists of two 100-minute lectures per week without any discussion sections. This option is attractive to nontraditional part-time students who work full-time in industry and want to limit their visits to campus. Long traditional lectures, tired students, and large amounts of material do not provide a good learning situation. This paper describes the use of technology to allow more efficient use of class time. Savings in lecture time are invested in alternative teaching techniques and additional examples to help break up the lecture and to improve student learning. Engineering software is used to give the students physical insight into the mathematics and to use as a validation tool. Assessment procedures to verify the success of the project were developed and data has been analyzed. The resulting class structure, which was tailored to meet the needs of nontraditional students, has improved the quality of learning for all students. The study found a modest increase in average student learning with a significant reduction in the class standard deviation. Successful portions of this project have been incorporated into the day section of this course over the past 3 semesters, which consists of three 50-minute lectures taught by faculty and one 2-hour discussion section led by a teaching assistant per week. The use of these techniques in additional courses is being evaluated within the department and college. I. Overview of Project Most engineering curricula require that students take a series of courses from the mathematics department consisting of three semesters of calculus followed by a course in differential equations and linear algebra. The University of Wisconsin-Milwaukee (UWM) is somewhat unique in that this fourth-semester course is replaced by an engineering-math course taught by engineering faculty. This four-unit core course, EE234: Analytical Methods In Engineering (previously named Linear Systems Analysis), is required by all the engineering departments in the college (civil, electrical, industrial, materials, and mechanical). The advantage of this approach is that while the students are learning about these mathematical techniques they can also be introduced to engineering applications. The disadvantage is the large amount of material to be covered in this class. The topics covered in this course include: P ge 867.1 “Proceedings of the 2003 American Society for Engineering Education Annual Conference & Exposition Copyright © 2003, American Society for Engineering Education” 1. First-order Differential Equations 2. Complex Numbers and Functions 3. Linear Algebra and Linear Systems of Equations 4. Linear Differential Equations of Second Order 5. Laplace Transforms 6. Vector Algebra, Dot Products, Cross Products 7. Fourier Series 8. Eigenvalues and Eigenvectors 9. Introduction to Probability and Statistics The mission of the UWM College of Engineering and Applied Science (CEAS) is to serve the needs of students, alumni, industry and the communities of eastern Wisconsin. As part of this mission, the college offers many courses in the evenings, which allows full-time employees at local companies to pursue degrees. EE234 has both a day section and an evening section during the fall and spring semesters. The day section consists of three 50-minute lectures and one 110minute discussion section (taught by teaching assistants) per week and is composed of primarily full-time students. Traditionally homework is assigned but not graded. The discussion section is used to answer questions, to give quizzes, to solve additional problems, and to provide supervised exposure to computer problem solving techniques using commercial software such as Mathcad. The evening section, on the other hand, consists of two 100-minute lectures per week without any discussion sections. This section consists of mainly part-time students, many of which work full-time in industry and want to limit their visits to campus. Due to these time constraints, this class was typically taught in a traditional lecture format. In addition, it is difficult for these students to meet with faculty during set office hours. This project attempted to incorporate the additional learning benefits provided in the day discussion section into the evening section of Linear Systems Analysis (EE234) and to improve the quality of learning for the nontraditional students within the current time constraints. This project was partially funded by an undergraduate teaching improvement grant received from the University of Wisconsin System for 2000-2001. II. Project implementation A. Efficiency of material presentation The first issue that had to be addressed was the efficiency of material presentation. The two 100minute lecture format for the evening section was established especially for students who work during the day. This enables them to limit their trips to campus. Unfortunately, this format does not work well with the traditional lecture. Attention spans of students are quite short for traditional students and even shorter for nontraditional students who have worked a full day prior to attending class. Although alternative teaching techniques, which could help break up the lecture and to promote increased student learning are available, they tend to add to the length of the lecture. Therefore before such techniques can be used, the material must be presented more efficiently. During the spring of 2000, I invested the time during the semester to create powerpoint slides for this course. These power-point slides were made available to students in advance for each lecture on the class web page enabling students to pay attention in class instead of frantically copying notes. This produced a substantial time savings for the course. Shortly after P ge 867.2 “Proceedings of the 2003 American Society for Engineering Education Annual Conference & Exposition Copyright © 2003, American Society for Engineering Education” this project began, the college invested in four media presentation classrooms with built-in computers and video projectors. One of these rooms was utilized for this course. Additional time savings could be obtained if the number of topics in the course could be reduced. The content of this core course for all engineers has been “developed by committee”. Over time topics have been added to the course to meet the needs of specific engineering programs. During the summer of 2000, each department was approached to evaluate the relative importance of each of these topics to their students. Although, some topics were less important to some departments (or to some subspecialties within a department), other departments indicated that these same topics were of importance. The net result was that I did not find any topic that could be cut from the course. On the contrary, one department wanted to add a few additional topics to the material for the course. Therefore the only time savings for this course would be obtained through the use of technology in the classroom. B. Alternative learning techniques Part of the time saved by using computer generated power-point presentations for this class was invested in alternative learning techniques designed to improve the quality of student learning. During my week at the Science and Engineering Education Scholars Program in the summer of 1999, I was introduced to a number of alternative learning techniques. Due to the time constraints of the nontraditional engineering students within this evening section class, some of these techniques involving group projects outside of class will not be applicable. I selected a pair and share technique for use with this course. After presenting the lecture material including an example or two on the board, I had the class break up into small groups of 2 or 3 to solve a problem on their own. Afterwards we discussed the problem as a class. This helped eliminate misconceptions and better enabled the students to complete their out-of-class homework assignments. C. Feedback Feedback is an important element in the improvement of student learning. As a result, homework solutions would be scanned in and posted on the class webpage on a timely basis. Solutions to quizzes would be discussed immediately after completion. Exams would be graded in a timely manner and solutions would be provided in class as part of the lecture. In this manner students can better understand their mistakes and hopefully learn from them. D. Inclusion of computer problem solving techniques The third issue that had to be addressed was the incorporation of the additional learning benefits provided in the day discussion section into the evening section. The day section had introduced students to computer problem solving techniques as part of the discussion section. This was done for two reasons. The first was to introduce students to a computer tool used in industry. The second was to provide a different solution approach that may reach students with a different learning style. During the semester, the day-section students typically have five computer assignments to complete during the discussion section with teaching assistants (TA) there to help them. Mathcad had been selected for this course because of its ease of use and minimal learning curve. Mathcad is also commonly used in industry. In addition, the college of engineering and applied science (CEAS) computer labs also have a Mathcad license for a most of the computers in the college. The problem with introducing application software into a class without a P ge 867