Missouri Course Redesign Initiative
University of Central Missouri
Course Title: Intermediate Algebra
The department of mathematics and computer science at the University of Central Missouri (UCM) offers 10 sections (35 students per section) of Intermediate Algebra per semester as the pre-requisite for three general-education courses: College Algebra, Contemporary Mathematics, and Basic Statistics. All sections of Intermediate Algebra are currently offered in a traditional lecture format. Graduate teaching assistants (GTAs) are employed to teach all sections. When not enough GTAs are available, adjunct faculty are hired to cover the remaining sections.
The department’s assessment data from 2005 to 2009 show that the DFW rates for Intermediate Algebra are 38.31%, 29.66%, 45.04%, 33.58% and 33.58%, respectively. Furthermore, Intermediate Algebra also suffers from course drift due to inconsistent coverage among sections. The department intends to increase the student success rate as well as create greater consistency throughout the course.
UCM will base its redesign on the Emporium Model. Lecture time will be replaced by online, interactive learning activities provided by commercial software and supported by individualized assistance in a computer laboratory. Students will be required to attend the lab and will be actively engaged in their learning. Students’ understanding of math and confidence in their math ability will increase, and the success rate in Intermediate Algebra will improve. More students will be better prepared as they move on to college-level math courses.
For the past eight years, the department has given common final exams in Intermediate Algebra and will use the same common exam to compare performance of students in the redesigned Intermediate Algebra course.
Intermediate Algebra was a relatively inexpensive course at the university prior to the redesign, yet the new format will produce a 12% savings. Section size will be increased from 35 to 70 students, reducing the number of sections offered annually from 20 to 10. The number of GTAs needed in the course will decline from five to 2.5, and undergraduate learning assistants will be added to help staff in the lab. Overall, the redesign will reduce the cost-per-student from $118 to $104.
In the redesign, did students learn more, less or the same compared to the traditional format?
Final exam scores from fall 2011 traditional sections were compared with those of the fall 2012 redesigned sections. The final exam for the traditional sections was paper-pencil; the redesigned sections’ exam was computer-based. Questions in both formats were on the same topics and the same difficulty level.
Students in the redesigned course performed significantly better. The average final exam score in the traditional sections was 62.65, whereas that of the redesigned sections was 84.97.
It is worth noting that some instructors of the traditional sections curved the grades of the sections they taught, while all the redesigned sections were graded on a straight scale.
Students spent more time doing math. They needed to correct and improve exercises and to take quizzes and tests multiple times in order to meet the prerequisites. For example, a student was required to have a minimum of 90% for homework 1 to do practice quiz 1 and a minimum of 70% for practice quiz 1 to take quiz 1.
Math anxiety was reduced by positive learning experiences. Students appreciated the opportunities to redo exercises and to retake quizzes and tests.
Upon requests of students completing redesigned Intermediate Algebra, two sections of redesigned College Algebra were offered in spring 2013. At this point, the department is not able to offer more redesigned sections of College Algebra.
Were costs reduced as planned?
UCM’s plan was to reduce the number of Intermediate Algebra instructors, all of who were graduate teaching assistants (GTAs), from five to 2.5 by increasing section size from 35 to 70 students and thus reducing the number of sections offered annually from 20 to 10. Although undergraduate learning assistants (ULAs) were added to help staff the computer lab, the redesign planned to reduce the cost-per-student from $118 to $104, a 12% savings.
During full implementation in the fall 2012 semester, the redesign team was surprised by a high enrollment of 497 students in Intermediate Algebra (compared to the estimated average of 375 students). Therefore, eight sections of Intermediate Algebra, instead of five, were offered taught by four GTAs. Despite this modification of the plan, the cost-per-student was reduced from $118 to $103 per student, a 13% savings.
Having fewer GTAs assigned to teach Intermediate Algebra allowed the department to assign the remaining GTAs and adjuncts to teach College Algebra and Contemporary Mathematics previously taught by full-time faculty. This had a strong, additional impact on the department's overall cost savings.
In addition, the department was able to assign more full-time faculty, who taught College Algebra in the past, to teach higher level mathematics and computer science classes due to program expansion and increased enrollment. Thus, the Intermediate Algebra redesign project allowed the department to have the flexibility of assigning more full-time faculty to teach additional classes for majors.
Pedagogical Improvement Techniques
What techniques contributed most to improving the quality of student learning?
Electronic learning resources. The redesign used MyMathLab as the primary instructional resource for its electronic textbook, video lectures, online tutorials and assessment tools, and automatic grading system. In-class lectures were replaced with online lectures and weekly study guides. Students were required to turn in a worksheet of five exercise problems each week. They could learn to solve those problems through the etext and video lectures.
Individualized assistance. Students were given individualized assistance to learn the material. They welcomed the ability to get help when they needed it and the personal attention they received. The computer classroom was open 8-5, Monday through Friday. Students could also use the tutorial service provided by the university’s Student Success Center in the evenings and Trio Services over the weekends.
Mastery learning. Students were required to achieve a mastery level of at least 90% on each homework assignment and at least 70% on each quiz/test before moving forward. Questions were algorithmically generated and randomly selected from a pool to provide a unique quiz/test for each attempt. Hence exercises, quizzes, and tests could be done multiple times to correct and improve learning.
A flexible learning environment. The redesign allowed students to advance through the course ahead of schedule. About 20% of the students completed all work and took the final exam before finals week.
Cost Reduction Techniques
What techniques contributed most to reducing costs?
Consolidating Sections. Two regular size classrooms were combined to create a large classroom/lab equipped with 72 computers for 70 students. Thus, the number of sections offered and instructors needed were cut in half. Grading was done online automatically. It did not take much time for each individual instructor to finalize grades since they were determined on a straight scale provided by the overall scores from the courseware. This allowed the instructors to handle more students.
Shared Resources. MyMathLab made it easy for the faculty expert to course-copy multiple sections with minor modifications. All sections used the same syllabus, lesson plans, worksheets, study guides, online homework, quizzes and exams. This model reduced the impact of adding three more sections with short notice.
Space savings. All redesigned sections met in the same computer lab. This arrangement freed up more space and times to schedule other classes.
What implementation issues were most important?
Changes in the original design. 1) Lecture time was eliminated. Since students were engaging various activities during class time, it was ineffective to conduct in-class lectures. Topics of each unit were introduced through study guides, worksheets, and online lectures. 2) The redesign team replaced the publisher’s workbook with etext reference and weekly study guides/worksheets based on the workbook. The weekly study guide directed students to new topics and examples within the etext. The embedded video lectures helped students complete the five worksheet problems. Worksheets were collected and graded for credits. 3) Due to scheduling difficulties, weekly meetings of instructors and learning assistants were replaced by one meeting before the first day of class, email communications, and individual meetings when necessary. The faculty expert is planning to develop online resources for training instructors and learning assistants.
Prerequisite course competency and placement issues. Some students enrolled in Intermediate Algebra without meeting the prerequisite competency in Introductory Algebra. It was a result of either inappropriate placement or early enrollment before verifying students’ performance of the prerequisite. The math department does not have the administrative right to drop those students. The faculty expert will need to work closely with academic advisers and Introductory Algebra instructors to reduce the breaches before the semester starts.
Personnel issues. The turnover rate among instructors and learning assistants was pretty high. There is a constant need to find the right persons for the job and to develop online training resources for new personnel. Scheduling a training session for all instructors and assistants to attend has been difficult. Online training will solve the problem.
Multitasking classroom issue. For most of the time, students taking a quiz/test were seated close at the front of the classroom. But there were times when a large number of students wanted to take a quiz/test. They had to do it among those receiving help from assistants or engaging in peer discussion. The environment could be rather distracting for both students and assistants.
Student attitudes. Students who did not succeed in this course either lacked basic math skills or did not attempt the homework starting early in the semester. The latter type of student may have had personal problems or an antagonistic attitude toward the subject and/or the redesign format. Most of them did not respond to instructors’ emails or came in for help when it was too late to catch up. Their names were submitted to the university’s Early Alert System for further contacts by the Department of Academic Enrichment.
Will the redesign be sustained now that the grant period is over?
The full implementation of redesigned Intermediate Algebra in fall 2012 occurred just in time when more full time faculty and adjuncts in the math department were needed to teach other courses. This was due to increased enrollment and expanded programs within the department. Meanwhile, a lot more students than expected were required to take Intermediate Algebra. The department had to offer eight 70-seat sections, instead of five sections as originally planned. Without the redesign approach, it would have been impossible to offer three more sections accommodating nearly 200 additional students with short notice.
The higher success rate makes it clear that the redesign approach improves the student learning experience. The two redesigned College Algebra sections were full shortly after they were open for enrollment. It shows that many students were in favor of the redesign model when it was available. At the same time, the department of academic enrichment is seeking to undertake Introductory Algebra redesign with the help of the Intermediate Algebra redesign team.