Iowa State University

The Traditional Course

Discrete Mathematics is a gateway course for a large number of students at Iowa State University and is required for all business and social sciences majors, students who may often achieve low mathematics grades in high school. Most of these students continue on to take a required introductory statistics course for which parts of Discrete Mathematics are an excellent preparation.

The university currently teaches its freshman level Discrete Mathematics course in a typical lecture/recitation format. Large lectures (~150 students) are taught by faculty and temporary instructors twice a week. Recitation sections (~35 students) are taught once per week by teaching assistants. Total enrollment in the course is about 1,800 students per year.

The current course experiences the standard academic problems associated with the multi-section large lecture format: over 30% DFW rates; lack of consistency in course objectives, delivery, and testing; low student morale and performance; and insufficient individualized feedback from instructors. In addition, students perceive this course as an obstacle and do not see the connection of the material to subsequent courses and real-world problems. It represents a hurdle before they can enroll in their major of choice. Students lack skills in analyzing problems, data presentation, and graphical analytical skills, and they often have substantial gaps in basic algebra skills that are not addressed properly.

The Redesigned Course

Building on redesign efforts of other math courses, Iowa State will move to a design that is modularized, web-based and self-paced. The main topics of the existing course in Discrete Mathematics (functions and graphing, basic linear algebra, linear programming, counting, and probability and statistics) will remain the same.

The learning goals for the redesigned course require students to

• gain a thorough understanding of basic concepts;
• be able to solve problems and questions by breaking them into manageable parts;
• develop data presentation and graphical analysis skills; and
• connect the content in this course with that of subsequent courses and their future professions.

Important components of the redesign include:

• Self-paced modular approach
• Collaborative learning
• Structured flexibility
• Immediate feedback on quizzes and assessment activities
• Learning options based on student goals
• Integrated and proactive student support
• Expansion of learning and understanding through the use of technology
• Expansion of learning and understanding through "real world" units including guest pages and real world applications.

A Web-based environment will integrate WebCT for presentation of material, management of communications and administration. Available from Wiley and compatible with Web CT, EDU will accept formulas and recognize mathematical equivalent forms and materials in student work for online testing. Content materials by Barnett/Ziegler/Byleen (Prentice-Hall) will also be used.

The course will be divided into five manageable modules, subdivided into weeklong segments, with clearly communicated learning objectives. The course software will suggest different homework problems and case studies for students based on their majors or other group indicators. Guest pages and case studies suggested by faculty in business and other departments will be tailored to the students' main interests and subsequent course and career goals. Expansion of learning and understanding through the application of technology will be achieved through incorporating Microsoft EXCEL spreadsheets for instantaneous graphics and simplification of extensive repetitive calculations. The redesigned Web environment will include a test of basic algebra skills early in the course with suggestions for further study, if necessary.

To prevent students' from falling behind, a problem observed in other math courses and the traditional format for this one, a structured timeline for quizzes, linked with homework completion will be incorporated.

To insure adequate student support, the course will include weekly small recitation sections, additional office hours, availability of a Math Help Room, and a peer-mentoring program. Integrated and proactive support also includes feedback through online tutoring in WebCT chat rooms, a Web-bulletin board for each recitation section, and weekly emails informing students about their progress and, if necessary, suggesting additional materials for study based on their homework, quiz, and exam performance. The online testing software, EDU permits analysis by topic, so that areas of difficulty can be identified easily and included in the recitation sessions and other feedback.

Assessment of the course redesign will be conducted by the Research Institute for Studies in Education (RISE), College of Education, Iowa State University. The general assessment strategy includes a pretest-posttest control group design, student surveys, long-term study of academic success, and measures of student attitudes and reactions to different course modes. Data analysis will be undertaken based on stratified sampling of the student population according to three major lines of demarcation related to differences in student performance and perceptions of course delivery method. Results of student surveys based on the stratified samples will be combined with student performance data to determine which differences in learning outcomes may be attributable to specific course components. A longer-term study of academic success will track students through subsequent courses where Discrete Mathematics is a prerequisite.

Traditional Course Structure

• 15-week term
• 8 lecture sections (fall) and 4 lecture sections (spring)
• 40 recitation sections (fall) and 20 recitation sections (spring)
• 3 contact hours per week: 2 (1-hour) lectures of 150 students and 1 (1-hour) recitation of 30-35 students
  
• Twelve full-time faculty each teach one section of the course. They prepare and deliver two lectures per week, supervise 1.25 TAs per section, create homework and exams, hold two office hours per week, and help grade exams.
• Fifteen TAs assist in teaching the course. They conduct four recitations per week, help create quizzes, proctor and grade quizzes and exams, attend orientation and staff meetings, and hold two office hours per week.

Redesigned Course Structure

• 15-week term
• 1 section each term (1200 students in fall, 600 students in spring)
• 24/7 access to online learning environment
• 1 (1-hour) optional recitation section each week
  
• Two full-time faculty members supervise the course. They enhance the test banks in the online testing software, hold 3 office hours per week, and conduct meetings with TAs and the Online Course Manager.
• Ten TAs assist in teaching the course. They conduct 6 recitations per week and hold 4 office hours per week, and conduct online help sessions.
• One Online Course Manager assists the faculty in teaching the course. The Manager enhances test banks in the online testing software, manages the logistics of web delivery, maintains course software and electronic grade books, holds 7 office hours per week, conducts online help sessions and orientation meetings for TAs and students.

Summary

In summary, the redesigned course will implement the following changes:

• Modularize the content
• Increase active learning by students
• Provide a structured yet flexible learning environment
• Develop a peer mentoring program
• Implement on-line testing
• Link learning options to student goals and future majors
• Integrate proactive student support opportunities
• Include applied learning experiences
• Provide frequent and immediate feedback

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