Changing the Equation: Redesigning Developmental Math
Oakton Community College
Redesign Coordinator: Bob Sompolski
In the traditional format, developmental mathematics students at Oakton Community College (OCC) who placed at the lowest academic levels had to complete 10-11 credit hours before they could take a college-level math course. Data for the 2009-2010 academic year showed that, of the 3,035 developmental mathematics students enrolled during the fall and spring semesters, 60% managed to pass their course.
The goals of the redesign (called ROAD Math--Redesign Of All Developmental Math courses) was to decrease the amount of time needed for unprepared students to reach the Intermediate Algebra level and to increase the passing rates of Intermediate Algebra students. This would increase the number of students who could take a mathematics course that satisfies OCC’s general-education requirement for the bachelor’s degree.
The department replaced all existing developmental courses with a sequence of four, four-credit hour courses, each of which used instructional software, the Emporium Model and a modular design. The redesign allowed students to proceed at a faster pace through the courses whenever possible and provided opportunities to work on modules from their future course(s) during the current semester.
Required attendance in class and engagement outside of class provided a common grade component throughout the department and helped students identify milestones in course progress that indicated success. Utilizing department-wide course development and organization responsibilities provided time for faculty to monitor student progress more closely and just-in-time individual tutoring precisely when the students required it. Delays caused by working the problems at home, turning the work in at a later date and receiving the graded materials at an even later date were minimized.
The redesigned courses used MyMathLab-based post-tests to determine knowledge gained within each module that students completed. Working at a finer granularity, the department used common rubrics to assess student work in order to determine stumbling blocks and strategies to further assist students. The ability to provide immediate feedback on work and position within the grading scheme allowed students to see a direct relationship between their efforts and their results.
OCC’s cost reduction strategy was to reduce the total number of developmental sections offered annually from 137 to 98 by increasing section size from 21 students to 30 in three courses and 26 students to 35 students in Intermediate Algebra. The redesign also provided opportunities for course section compression between past alternate course paths at the Prealgebra and Elementary Algebra levels. In addition, prior to the redesign some of the developmental math courses were three credits and some were four. After the redesign, all courses were four credits. Overall the redesign reduced the cost-per-student by 9%, from $262 in the traditional format to $239 in the redesign.
In the redesign, did students learn more, less or the same compared to the traditional format?
Student learning improved significantly in Prealgebra, Elementary Algebra, Elementary Plane Geometry and Intermediate Algebra as measured by performance on common exam items. All assessment scores are normalized out of 100%.
Comparisons of course completion data (grades of pass/C or better) showed that students enrolled in the redesigned courses in the last half of the sequence of OCC developmental courses (Elementary Plane Geometry and Intermediate Algebra) completed at a higher rate than students in the traditionally taught courses in former semesters. The department does seem to have achieved its goals of improving the success rates of students in these two courses.
Students enrolled in the redesigned courses in the first half of the sequence (Prealgebra and Elementary Algebra) performed less when than students in the traditionally taught courses in former semesters. Data analysis showed that over 83% of passed module exams for Prealgebra were for Modules 1 and 2. That along with only that fact that only two students passed the Module 3 exam before November 1 led the team to suspect that at least Module 3 and perhaps higher numbered modules need to be reworked. Preliminary examination by a team of faculty led to the following recommendations: fewer topics/sections should be required for each module, fewer module post-test review questions be generated for each module and more rudimentary exercises be represented in homework, quiz and module assessment activities. For Elementary Algebra, it was more difficult to detect patterns in the data. Nonetheless, the designers of that course are committed to some adjustments similar to the work to be done on the Prealgebra course.
Data analysis showed that over 83% of passed module exams for Prealgebra were for Modules 1 and 2. That along with only that fact that only two students passed the Module 3 exam before November 1 led the team to suspect that at least Module 3 and perhaps higher numbered modules need to be reworked. Preliminary examination by a team of faculty led to the following recommendations: fewer topics/sections should be required for each module, fewer module post-test review questions be generated for each module and more rudimentary exercises be represented in homework, quiz and module assessment activities.
For Elementary Algebra, it was more difficult to detect patterns in the data that were radically different than Intermediate Algebra. None the less, the designers of that course are committed to some adjustments similar to the work to be done on the Prealgebra course, although the data analysis does not seem to clearly identify a single module that is serving as a barrier to success.
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. In OCC’s case, the redesigned courses were more difficult than the traditional course.
In the redesign, students were required to master all of the content of all of the courses. OCC 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.
Other Impacts on Students
Were costs reduced as planned?
As planned, cost savings were realized as a result of the redesign project. In fall 2010, OCC offered 63 traditional sections of developmental math; in 2011, OCC offered 49 redesigned sections of developmental math by increasing the section size from ~21 to 30 in Pre-algebra, Elementary Algebra and Elementary Plane Geometry. Section size in Intermediate Algebra increased from 26 in the traditional classes to 35 in the redesign. Cost savings were slightly less in the actual redesign than initially planned because the team decided to include tutors in all developmental math sections for one-half of the semester rather than using the tutors only for Intermediate Algebra for the entire semester. After full implementation, the cost-per-student was reduced 9%, from $262 in the traditional course to $239 in the redesigned course, slightly less than the planned $236 cost-per-student and 10% savings.
In addition, some developmental math courses were offered for three credits prior to the redesign while others were offered for four. In the redesign the credit value of all developmental courses was standardized to four credit hours, which increased tuition and fees revenue paid to OCC. Before the redesign, approximately 49% of all developmental students enrolled in a three-credit-hour course, with the remainder enrolling in four-credit-hour courses. The average enrollment in redesigned developmental math during the AY 2011-2012 was 1104, which meant that 541 students paid an additional $95.60, increasing revenues by approximately $51,720 each semester.
Finally, increases in section sizes allowed OCC to decrease the number of developmental math sections offered annually. This decrease had a significant impact upon the space used by the department. Prior to the redesign, a total of 240 contact hours per week were required; after the redesign, only 180 contact hours per week were needed, a decrease in facilities use of 25%.
Will the redesign be sustained now that the grant period is over?
Now that the labs for the redesign have been established and configured, the department is working to finalize IT support for the program and ensure the stability of working conditions for faculty. The department intends to redesign College Algebra and Precalculus to provide a means for calculus-bound students to continue their work in a given semester once they have completed Intermediate Algebra. Historical course success rates in College Algebra average 55% and 65% in Precalculus.
Oakton’s commitment to supporting the redesign has included the efforts of staff from 1) student affairs, who not only advised students but also provided guidance on the use of the student database; 2) facilities, who helped design and implement the computer classrooms that support the program, 3) information technology, who provided logs of open lab use and support and guidance on the use of the Pearson products; and, 4) academic affairs who provided support for the faculty. Those faculty who developed and taught the materials for the redesigned courses represent the best efforts in the reform of teaching mathematics at the college.