Changing the Equation: Redesigning Developmental Math
Stark State College
Contact: Aaron McClure
Stark State College (SSC) completely redesigned its three developmental math courses—College Math, Introduction to Algebra and Intermediate Algebra—using the Emporium Model. The enrollment in all three courses for the 2009-2010 academic year was approximately 5,050 with 2,000 in College Math, 2,900 in Introduction to Algebra and 150 in Intermediate Algebra. Intermediate Algebra was only required for a small percentage of majors until recently. In the traditional format, all three courses were offered as traditional, lecture-style classes. There was a common homework set using MyMathLab, common syllabus, common midterm and common final for each course. College-wide enrollment has increased by 30% for the past three years and is expected to continue to do so. Developmental math has seen an even bigger annual increase.
Stark State is a 100% open-enrollment institution. As such, completion rates in each course were below the national average. Completion rates in College Math were 32% to 36%); rates in Introduction to Algebra and Intermediate Algebra were usually in the mid 40’s. Until recently, Intro and Intermediate were part of degree programs of study. Therefore, students could not be required to get above a D to pass.
In the redesign, the three courses were split into 18 modules covering the same material. Originally, the college planned to use the “shell course” model. However, because many programs were still using Intro and Intermediate as program requirements at the time of the redesign, the department was forced to keep the old course names and numbers. Therefore, the 18 modules were split into three sets—with six modules in each course. Doing so eliminated quite a bit of overlapping material. The redesigned courses required 80% mastery on everything—homework, quizzes and tests. This essentially made all three courses A/B courses.
There were two goals for the redesign: 1) to better prepare students for College Algebra and Statistics, and 2) to increase the number of students exiting developmental math and entering college-level courses. To do this in a traditional system would be next to impossible. The mastery learning approach improved student success since math is a building-block subject. Self-pacing and the ability to move ahead in modules and courses helped students who needed less remediation to accelerate.
To measure the success of the redesign, the team looked at student learning outcomes and course-completion rates. Student learning was measured using common assessment items. The team compared questions and problems on the traditional midterm and final with the same or similar items on the redesign’s module post-tests. Success rates in Intro and Intermediate Algebra were compared as A/B rates since the redesign allowed only A’s and B’s to be passing grades.
Stark State reduced the cost of developmental math by increasing section size from an average of 24 to ~48 on the main campus and ~40 students overall. A significant 81% enrollment increase (from 4,400 to 8,000 students) occurred also, yet the total cost of offering the developmental math sequence only increased by 36%. Stark State also reduced the number of contact hours per developmental math course from four to three. In the traditional format, SCC had to pay an additional one hour per section and faculty could only teach eight sections annually. In the redesign, faculty could teach nine courses per year as part of their load. Together, these two actions reduced the cost-per-student from $238 in the traditional format to $178 in the redesign, a decline of 25%.
In the redesign, did students learn more, less or the same compared to the traditional format?
The math department measured learning outcomes using common content items on departmental midterms and finals in traditional courses with similar questions on module posttests in the redesign. The improvement was dramatic.
Under the redesign format, students could only pass the three courses with a B or better. Therefore, completion rates in the two formats measure A/B rates.
In conducting an extended analysis of the discrepancy between increased learning outcomes and decreased course completion rates in Changing the Equation, NCAT has discovered a variety of reasons why course-by-course completion comparisons are not a true measure of the success or lack of success of the program. The majority of Changing the Equation teams discovered that pass rates in the traditional format were inflated by prior inconsistencies in grading practices. Unlike redesign students who were assessed on common outcomes using common assessment methods, those in the traditional courses were assessed in a variety of ways which led to overall grading differences. Contributors to prior grade inflation in the traditional course included 1) having no clear guidelines regarding the award of partial credit, 2) allowing students to fail the final exam yet still pass the course, 3) failing to establish common standards for topic coverage (in some sections, entire topics were not covered, yet students passed), and, 4) failing to provide training and oversight of part-time instructors. Thus, the C or better rates for the traditional courses were almost universally inflated. For example, at SCC completion rates in sections taught by adjuncts averaged 5% higher than those taught by full time instructors.
Further, the redesigned courses were more difficult than the traditional course. The redesigned courses 1) had more assignments, more quizzes and more tests than the traditional courses and consequently took longer to finish, and 2) included more content than the traditional courses and consequently took longer to finish. In the redesign, students were required to master all of the content of all of the courses. SCC redesign students had to pass each module independently at a 80% level before being able to progress to the next module, showing mastery in homework assignments, practice tests and module exams. In the traditional format, students exited the course by simply attaining a total cumulative score of at least 70% or 75%. Based on averaging grades, students were able to earn a C or better by passing enough tests and learning enough competencies but not necessarily all. In traditional sections, students would often continue on to the next topic without having demonstrated mastery of the previous topic.
Mastery learning thus meant that students were doing more work and learning more, which often took longer to do so. That meant that many students did not complete a particular course by the end of the term. They were able to start where they left off in the subsequent term. But because course completion statistics were calculated as the number of students finishing the course at the end of the term, they missed counting students who were still enrolled and progressing. Mastery learning, while sometimes taking longer to accomplish, ensured that students were well prepared to take on college-level work.
Other Impacts on Students
Were costs reduced as planned?
Prior to the redesign, SSC taught 184 traditional sections with an average section size of 24 students and a total developmental math enrollment of about 4,400 students. Full-time faculty taught 52 (28%) of the 184 sections. In the redesign, the total enrollment grew to 8,000 students, almost double the number of students in the traditional format, taught in 200 sections, 39% by full-time faculty. However, the total cost to offer the developmental math sequence did not double; it only increased by 36% while the enrollment increased 81%. This was accomplished by increasing the average section size to ~48 on the main campus and an average of 40 students across all campuses.
In the traditional format, developmental math courses were three credits but four contact hours. This meant that SCC had to pay an additional one hour per section and faculty could only teach eight sections annually. In the redesign, the courses were three credits and three contact hours; faculty could teach nine courses per year as part of their load. Mixing personnel (tutors, students, etc.) allowed the lab coordinator and department chair to create a more efficient combination of people depending on the time and day of the course. Overall, the cost-per-student at Stark State decreased 25%, from $238 in the traditional format to $178 in the redesign.
Will the redesign be sustained now that the grant period is over?
All indications are that Stark State is committed to the Emporium Model for the foreseeable future. While the transition has certainly not been easy, this is seen as the first step toward increasing students’ overall success in math and in college. There is quite a bit of improvement still to be made, but the process itself is significantly better than the traditional format. The process allows for more quality control and for changes to be enacted more quickly and easily. The redesigned program is also a better product for community college students.