University of Idaho

The Traditional Course

Intermediate Algebra, Algebra, and Pre-Calculus comprise a group of developmental-level courses that review information offered in high school math. Students in the colleges of engineering and business as well as in the various sciences are required to understand pre-calculus in order to take a number of courses in their majors. With a total of 2,428 students enrolled, all three courses are taught in a traditional lecture format. Students receive support from a Mathematics Assistance Center, a drop-in facility staffed mainly by undergraduate assistants. However, students must seek help on their own; the active learning, immediate feedback, and personalized instruction available from the assistance center are not embedded in the traditional lecture format.

There are five academic problems to be solved:

• The traditional courses suffer from high Drop-Failure-Withdrawal (D-F-W) and repeat rates.
• Students who succeed do not retain their learning; only 67% of the students who receive a C or better in Intermediate Algebra receive a C or better in Pre-Calculus.
• The courses use the same teaching environments in which students have previously failed to learn math skills. Although students realize the need to improve their math skills, they see little hope of success in the lecture environment and thus have a high level of dissatisfaction with the courses.
• Students must often delay taking introductory courses in their major in order to complete the mathematics courses, which contributes to students' high level of dissatisfaction.
• It is difficult to attract and virtually impossible to retain good remedial math teachers due to the existing tenure environment at the university.

To address these problems, faculty initially planned to redesign Intermediate Algebra, the first course in the developmental sequence, as a studio course taught in groups with computer support. However, faculty then decided on a more global redesign of the three courses—and of the way in which math skills are taught at the University—based on the model of Virginia Tech's Math Emporium.

The Redesigned Course

The prime objective in course redesign is to use technology in a math learning center in order to move students from a passive learning environment to an active one in which the student controls and individualizes learning based on personal needs. The three developmental-level courses and the Mathematics Assistance Center will merge into a new learning center called Polya, which will house material and personnel to support student learning.

The goals for the redesigned environment include the following:

• Help students become active learners and effective problem solvers
• Provide diverse ways of accommodating student learning and diverse applications of learning appropriate to the student’s field of study
• Build student confidence in their ability to succeed in mathematics
• Instill a firm basis of mathematical skill and conceptual understanding that enables the student to succeed in subsequent mathematics courses
• Provide a place where students can return for assistance as needed

In order to achieve these goals, faculty will redesign the pre-calculus learning environment using technology. Polya, housed in an easily-accessible building, will contain 72 computers in pods of four that are designed for as many as three students to work together at a single monitor. Students will not required to be in Polya in order to learn since most of the technology will be Web-accessible. Polya will use commercially-available math tutorial software that generates problems and offers immediate feedback. Lectures of about 25 minutes, covering topics in the math textbooks, will be available on streaming video or video-on-demand. Weekly quizzes and tests will be available so that students can repeat them up to three times, with consultation and additional study between attempts. Professors, instructors, graduate teaching assistants (GTAs), and undergraduate teaching assistants (UTAs) will be available in Polya to work with students in groups and individually. Online bulletin boards and e-mail will provide a continuous means of communication between students and instructors.

In line with the new learning environment, faculty will replace the more rigidly-structured traditional courses with a fluid, personalized learning experience for students. Pre-calculus students will be divided into focus groups of 40 to 50 each, with an attempt to group students according to their majors so that the group can emphasize particular applications of pre-calculus. Each focus group will meet once a week to coordinate activities and discuss experiences and expectations. The written portions (20%) of tests will be done in the focus group as well.

Aside from the weekly focus group meeting, students will have the freedom to manage their learning time, types of learning activities, and rate of progress in learning pre-calculus concepts and skills. They may work with textbook exercises and math tutorial software, view taped lectures, attend live lectures in Polya, get individual help from instructors and TAs, and/or work in small or larger seminar groups.

Traditional Course Structure

• 16-week term
• ~60 sections per year of 40 students each (all 3 courses)
• 3 lectures per week
  
• Two to three lecturers each teach three sections per term. They prepare all lectures, learning activities, assignments and exams; deliver three lectures per week; evaluate assignments and exams; and hold office hours.
• Twelve GTAs each teach two sections per term. They prepare all lectures, learning activities, assignments and exams; deliver three lectures per week; evaluate assignments and exams; and hold office hours.

Redesigned Course Structure

• 16-week term
• ~ 60 focus groups of 40-50 students meet weekly to discuss learning issues
• Optional weekly lectures
• Students spend time in Polya depending on need
  
• One senior instructor updates and revises course materials as needed, serves as Lab Director to provide training and coordination, and works as an instructor with instructor responsibilities.
• Two instructors lead focus groups, and as needed, hold individual student conferences, assist with materials development and give live lectures or create digital versions of lectures.
• Eight GTAs lead focus groups, hold individual student conferences as needed, and serve as back ups for UGTAs in answering student questions in Polya.
• UTAs provide assistance to students as needed in Polya.
• One full-time and one half-time Center Manager monitor students and operations in Polya, and provide data management.

Summary

In summary, the redesign will implement the following changes:

• Modularize the content of three developmental, pre-calculus courses
• Offer content in a variety of ways: online math tutorials, video, real-time lectures, person-to-person tutorials, small and large group discussions
• House content modules in a math learning center (Polya) and online
• Create focus groups based on the students' academic majors
• Reduce group meetings to one per week
• Reduce the number of faculty and GTAs involved in the courses
• Offer most testing online to provide immediate student feedback and development
• Provide individual assistance as needed
• Personalize the pre-calculus learning experience for students to foster student learning and success

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