Changing the Equation: Redesigning Developmental Math
Cossatot Community College of the University of Arkansas
Contact: Robbie McKelvy
In the traditional format, Cossatot Community College of the University of Arkansas (CCCUA) offered three developmental math courses--Essential Mathematics, Introductory Algebra, and Intermediate Algebra--with a total average enrollment of 223 students per semester on all three of its campuses.
Although these courses had been somewhat successful, the redesign addressed a number of academic problems in the traditional format: 1) the average failure rate was 36.5%; 2) there was no way to deal with knowledge differences among individual students; 3) all concepts were taught through lecture; 4) the time required for completion of the sequence delayed graduation for many students; 5) instruction lacked consistency among sections; and 6) low-enrollment classes were frequently cancelled at one CCCUA campus.
CCCUA’s course redesign modularized the content of the three courses into one course, Foundations for Mathematics. The new course utilized the Hawkes Learning System and the Emporium Model where student learning was mastery-based and learner-centered. Students were required to master only concept deficiencies indicated by placement and diagnostic testing. The course was structured using content modules to deliver instruction, practice and testing in a lab setting with immediate assistance provided by instructors or tutors. Receiving immediate feedback from instructors or tutors on practice and tests motivated students to work harder and allowed some to complete in less time. Classes met for three scheduled hours per week in the computer labs. Those not completing received an NR (non-recorded) grade, which allowed them to enroll in the next semester and continue where they left off.
Pre- and post-testing were used to compare student learning outcomes data from the traditional and redesigned formats of the course.
The course redesign involved a reduction in the number of sections offered from 32 to 23, an increase of section size from 14 to 18 and the use of alternate adjunct staffing. Cossatot’s cost-per-student decreased from $277 in the traditional course to $225 in the redesign, a 19% reduction. Cossatot used the “one-room schoolhouse” strategy, which meant that all developmental math courses could be scheduled in the same classroom and time slot. This allowed sections to fill and eliminated the need to offer smaller, separate sections of courses with low enrollments. The savings will be used to establish more advanced math course offerings, add more technology in the classrooms and possibly hire another full-time faculty member for the division.
In the redesign, did students learn more, less or the same compared to the traditional format?
Each student was tested using the same test, the nationally normed COMPASS Algebra test, at the start and end of the course or equivalent modules. Students showed a higher gain in all three redesigned courses than in the traditional format, but these differences were not significant.
Course-by-Course Completion Rates
Course completion rates (grades of C or better) appeared to decline under the redesign.
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.
In addition, the redesigned courses were more difficult than the traditional courses. The redesigned courses 1) had more assignments, more quizzes and more tests than the traditional courses and consequently took longer to finish, 2) included more content than the traditional courses and consequently took longer to finish, and 3) required an 80% mastery level, which essentially raised the cut score for a student to earn a C in the redesigned courses.
In the redesign, students were required to master all of the content of all of the courses. CCCUA redesign students had to pass each module independently at an 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.
Overall, the course content for all of the courses was more rigorous for the redesign students than for the traditional courses to better prepare the students for the college-level math courses. The math department chair and several instructors have noticed that students who have completed the redesigned developmental math sequence are better prepared and their knowledge base is more consistent..
Improved Course Completion: Making Progress Grades
There are other indications that redesign students, in the majority of instances, are completing at a higher rate. CCCUA awarded an MP grade to students who completed at least 75% of course modules at 80% mastery. This would have been more than equivalent to a grade of C or better in the traditional courses. Students receiving the grade of MP can pick up during the next semester where they left off; they are not required to start over. When taking into account the MP grades, completion rates were similar or improved in the redesign.
The CCCUA team feels that they can improve on these rates by working with the instructors to intervene with students who are not asking for help in a timely manner.
Other Impacts on Students
The redesigned program has increased student mobility. Some highly motivated students completed more than one level of modules in the same semester and began the next level immediately. This put students on track to complete their certificates or degree programs on time. Students found this aspect of the redesigned program--the possibility of completing more than one developmental course in a semester—to be the most positive aspect of the program.
Many students favored working with an instructional software package and especially the chance to work on the program at home. Others, however, found the computer work very stressful and said they would rather be in a traditional classroom. At CCCUA, there are a large number of non-traditional students who lack computer skills. At the math department’s request, the CCCUA learning center has begun to offer workshops at the beginning of each semester for students who need to learn basic computer skills. Based on a recent survey of students, student attitudes have changed for the better toward the redesigned course.
Were costs reduced as planned?
CCCUA reduced the number of sections taught on its three campuses from 32 to 23 and increased section size from 14 to 18 in the redesign. The traditional average was low because sometimes small sections of 5 to 7 students were needed. CCCUA successfully implemented the “one-room schoolhouse” approach to deal with low-enrollment sections, producing both institutional cost savings as well as clear benefits to students. Previously, when small sections did not “fill”, they had to either be cancelled, (interrupting student progression through the sequence and incurring lost revenue to the college) or offered at a relatively high cost. Using the one-room schoolhouse approach, which was created by the math department at Cleveland State Community College, meant that the college offered multiple developmental math courses in the same computer classroom or lab at the same time. Students worked with instructional software, and instructors provided help when needed. Even though students were at different points in the developmental sequence, they could be in the same classroom. This strategy enabled the CCCUA to increase course offerings and avoid cancelling classes, which, in turn, reduced scheduling roadblocks for students and enabled them to complete their degree requirements sooner. Since fewer sections were needed to accommodate the same number of students, the overall cost-per-student was lowered.
CCCUA also reduced the level of adjunct instructor used in the developmental courses because of the consistency in course content and delivery in the redesign format. In the traditional format, all adjuncts were masters-qualified, whereas in the redesign, bachelors-qualified adjuncts were used. Overall, these changes led to a reduction in the cost-per-student from $277 in the traditional course to $225 in the redesign, a 19% savings.
The savings will be used to establish more advanced math course offerings (CCCUA was able to offer Calculus I and II for the first time in several years), convert a classroom into a second computer lab on the Nashville campus to be used for a humanities redesign and possibly hire another full-time faculty member for the division.
Will the redesign be sustained now that the grant period is over?
After the first semester of full implementation in fall 2011, CCCUA’s redesign is beginning to produce positive results. The math division is planning to develop a few new content modules for the redesigned course, incorporating skills needed for the technical trades. Because of the interest generated by and the success of the math redesign, the humanities division has begun to redesign their developmental writing/reading course similarly.