Virginia Tech

Project Abstract

Virginia Tech is in the midst of redesigning its Linear Algebra course, which is taken each year by 2000 first-year students majoring in engineering, physical science, and mathematics. Approximately 1500 students enroll in the fall and 500 in the spring semester. A mix of tenure-track faculty (10), instructors (13), and graduate teaching assistants (15) teach 38 sections of the course with about 40 students each. Each section meets twice a week for fifty-minute lectures. Students receive individual assistance during one-to-one office hours and review sessions for the tests if the individual instructor chooses to offer them.

Like many large-enrollment, introductory courses, Linear Algebra suffers from a number of academic problems. First, the old format does not take into account the range of academic preparation and learning styles that students bring. For many, the material is easily learned; for others, difficulty arises either due to weak backgrounds in math or problems with the lecture format. Second is the problem of student retention: typically one group of students drops the course early on while another group stays registered but essentially gives up and stops working. Third, a remarkable lack of uniformity in learning outcomes has been reported. Course grades across sections bear surprisingly little statistical relation either to SAT profiles or to scores on a common final exam. Finally, teachers in advanced math, engineering, and mechanics courses have expressed frustration at the inability of students who have passed Linear Algebra to retain certain skills or recall material.

The course redesign will eliminate all class meetings and replace them with Web-based resources developed by experienced faculty, such as interactive tutorials, computational exercises, an electronic hypertextbook, practice exercises with video solutions to frequently asked questions, applications, and online quizzes. The course material is organized into units that students cover at the rate of one or two per week, each one ending with a short, electronically graded quiz. Multiple sections will be treated as one course. Faculty will point students toward appropriate resources and strategies. Students can communicate on a completely flexible time schedule through e-mail or in person with faculty, GTAs, and peer tutors at Virginia Tech's Math Emporium, a 500-work station computer lab open 24 hours per day, 7 days per week. The redesigned course allows students to choose when to access course materials, what types of learning materials to use depending on their needs, and how quickly to work through them.

Quality will be enhanced as students actively choose methods and resources to direct their own learning. Computer-based practice quizzes and tests will provide instant feedback to students, so grading should more accurately reflect student activity and ability. Computer-based testing also provides comprehensive, continuous data collection for faculty, so they can adjust instruction and give individualized help as the course proceeds. In this way, the system offers a personalized dimension that cannot be maintained in the old format. The electronic system also enables students to review course materials later on, when they need it for other courses.

The impact of the redesigned course on student learning will be assessed by looking at final exam grades, statistics on retention and success, the ratio of initial enrollees to completers, and the ratio of no-shows for the final exam to students still registered in the course. Uniformity will be assessed by comparing grade outcomes with standard predictors and with results of the common exams. Feedback will be gathered from faculty via opinion surveys and discussion with math and other partnership faculty who teach courses requiring the retention of math skills. Student perceptions will be assessed by pre- and post-surveys. Evidence already exists that the Math Emporium is having a positive impact on the academic performance of mathematics students in general as well as on the morale of faculty members. Most strikingly, the university reports that scores in mathematics in general have risen 17.4 percent while the failure rate has dropped by 39 percent. The data shows that courses utilizing the Emporium the most are those most likely to show positive changes in student improvement.

Although changes and adjustments are being made each semester, the university expects the long-term configuration to involve only two faculty members for the entire 1,520-student enrollment. One instructor and one tenure-track faculty member will share duties in approximately a 2:1 ratio of hours. The instructor will handle most of the day-to-day activities in course delivery, while the tenure-track faculty member will take the lead in planning and preparation. The new cost structure associated with the redesigned course also includes the graduate and undergraduate Math Emporium helpers, as well as two technical support people for database management and software upkeep.

Redesign will result in a cost-per-student reduction from $91 to $27, resulting in a projected annual operating cost reduction of $128,180.

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