Web-based Implementation of Discrete Mathematics

Abstract

The Department of Mathematics at Iowa State University teaches a freshman-level Discrete Mathematics course with total enrollment of about 1,800 students per year. The traditional format includes large lectures, with about 150 students each, taught by faculty and temporary instructors in two class sessions per week and recitation sections, with about 35 students each, taught once per week by a teaching assistant. In this format, the course experienced the standard academic problems associated with the multi-section large lecture format: over 30% D/F/Withdraw rates; lack of uniformity and inconsistency in course objectives, delivery, and testing; low student morale and performance; and insufficient individualized feedback from instructors. In addition, students failed to see the connection of the material to subsequent courses and real world problems; spent great effort on repetitive calculations and little or none on computing; lacked skills in analyzing problems, data presentation, and graphical analysis; and often had substantial gaps in basic algebra skills that were not addressed
properly by course content. Discrete Mathematics was redesigned to address these challenges with a Web-based, self-paced model. The Web-based environment integrates WebCT as learning management software, MapleTA as an online testing program, and textbook and related materials by Barnett, Ziegler, and Byleen (Prentice-describes Hall) as the content basis. The redesigned course includes weekly small recitation sections,
additional office hours, availability of the Math Help Room, and peer-mentoring through study groups and Supplemental Instruction. Integrated and proactive student support includes Web-based feedback through online office hours, a Web-bulletin board for each class, and Web-published individual current scores and class standing. The redesigned course syllabus is divided into manageable modules, with clearly communicated learning outcomes and objectives. Expansion of learning and understanding through the application of technology are achieved through incorporating Microsoft EXCEL spreadsheets for instantaneous graphics and simplification of extensive repetitive calculations. The Web environment also includes a new fourth main course topic of basic algebra skills early in the material as preparation for the other sections. Assessment of the course redesign was performed by the Research Institute for Studies in Education (RISE), in the College of Education, at Iowa State University. The general assessment strategy included a pretest-posttest control group design and longterm study of academic success. Student performance data were used to determine which differences in learning outcomes may be attributable to specific course components. Students in the Web-based sections performed no worse, and usually performed better, than did classroom-based students. These results are based on student performance on learning outcomes in Fall 2002, Spring 2003, and Fall 2003. In a straight comparison, the design sections did significantly better than the control sections on eleven out of thirteen exams compared, with comparable results on the remaining two exams. This difference exists despite significantly higher cumulative GPAs for students in the control sections for two semesters and insignificant differences in the third semester. This suggests that the Web-based course design is able to enhance the performance, and hence the chances for retention, of even less-highly achieving students (as determined by their lower GPAs). A longer-term study of academic success has tracked students through subsequent courses for which Discrete Mathematics is a prerequisite. These results are also positive, though less conclusive. The traditional course used 12 faculty and 15 teaching assistants to deliver the course at a cost of $129 per student. The redesigned course is staffed with 3 faculty and 9 teaching assistants. The redesign costs $77 per student, resulting in savings of $93,600 per year.