Changing the Equation: Redesigning Developmental Math
Guilford Technical Community College
Redesign Coordinator: Susan Barbitta
In the traditional format, Guilford Technical Community College (GTCC) offered three courses: Essential Mathematics, Introductory Algebra and Intermediate Algebra. Enrollment in these courses was approximately 3,700 students per semester; 48% of students passed the course in which they were enrolled. About 25% of the sections were taught by full-time instructors, the remainder by adjuncts. Every instructor followed a uniformly defined departmental syllabus and curriculum, used a prescribed textbook and incorporated Pearson’s MyMathLab interactive software into their courses.
The academic problems faced by the course included low student pass rates, gaps in students’ mastery of concepts from previous math courses, the inability of students to move quickly through a course and complete more than one course per semester. Instructor to student face-to-face interaction was not optimal because of the lecture setting of the traditional course. Because students worked on MyMathLab as homework when instructors were not present, it was not being utilized to its fullest capabilities.
GTCC’s course redesign had three primary goals: 1) increase the percentage of students who successfully complete the developmental math curriculum, 2) fill in academic gaps from previous math courses, and 3) permit students to move rapidly through their courses. GTCC redesigned its developmental mathematics curriculum using the Emporium Model. Three existing courses were divided into 13 modules. Students began each module with a pre-test, moved through a module as quickly as their skills allowed using a guided notebook/schedule, took a post-test and, if successful, moved on to the next module. Because testing occurred when the students felt they were ready and because retesting was available, students experienced higher levels of success and less test anxiety. GTCC anticipated that many students would complete more than one course during one semester and that they would miss fewer class sessions than in the traditional class setting since only three of the five required hours interacting with the software had to be done in the lab.
The redesign approach to developmental math enhanced the quality of student learning. The guided module design allowed students to be more active and engaged learners, receive immediate feedback about their work, focus on what they did not know and move quickly through what they did know. A combination of guided content learning, acceleration and remediation as needed meant that more students could successfully complete the course and that the cumulative learning effect from module to module would be greater because the mastery approach was reinforced with regular testing
GTCC is deeply committed to research-based decision-making. GTCC evaluated the effects of the redesign by comparing performance on a common final exam in the traditional and redesign sections. GTCC also looked at comparative success rates as well as persistence and retention rates in the developmental courses.
The redesign allowed GTCC to increase section size from 25 students to a weighted average of 44 students across its three locations. GTCC also increased the percentage of students taught by full-time faculty, thus reducing the need for adjuncts. The increase in section size and the hiring of nine additional full-time faculty members allowed GTCC to reduce the percentage of adjunct-taught sections from 61% to 19%. Overall, the cost-per-student in developmental math at GTCC declined from $148 to $118, a 20% reduction. These savings will be used to pay for faculty release time to work on further course development.
In the redesign, did students learn more, less or the same compared to the traditional format?
Student performance improved significantly in all three courses as measured by performance on common final exams.
Course-by-Course Completion Rates
Course completion rates did not appear to increase in the redesign.
Introductory Algebra students were required to begin with module one and complete or place out of all of the Essential Mathematics work before beginning the true Introductory Algebra modules. The expectation was that these students would place out of these prerequisite modules if they truly were Introductory Algebra students. Most Introductory Algebra students did not place out of prerequisite modules. While this negatively affected success rates for Introductory Algebra, the team feels it addressed and remedied the academic gaps present in their knowledge base. These students were required to work through nine modules instead of the four modules that are truly the Introductory Algebra material.
Success rates in Intermediate Algebra declined from 45% to 36%. While somewhat disappointing, these results were not unexpected. Intermediate Algebra students were required to begin with module one and complete or place out of all of the Essential Mathematics work and all of the Introductory Algebra work before beginning the true Intermediate Algebra modules. The expectation was that these students would place out of these prerequisite modules if they truly were Intermediate Algebra students. Most Intermediate Algebra students did not place out of prerequisite modules. While this negatively affected success rates for Intermediate Algebra, the team feels it addressed and remedied the academic gaps present in their knowledge base. These students were required to work through 13 modules instead of the four modules that are truly the Intermediate Algebra material.
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 GTCC’s case, 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; 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. GTCC 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
Despite these lower course-by-course completion rates, there are indications that redesign students, in the majority of instances, are completing at a higher rate. In fall 2011, GTCC added a “Making Progress” (MP) grade. Students receiving an MP grade must have completed three of five modules or two of four modules at 80% mastery. When taking into account the MP grades, completion rates improved in the redesign.
Other Impacts on Students
Were costs reduced as planned?
In the traditional format, Guilford Technical and Community College (GTCC) enrolled about 7,000 students annually in developmental math and offered 280 sections of ~25 students each. GTCC’s redesign plan was to increase enrollment to 9,300 and offer 186 sections of 50 students each at its three locations. GTCC also planned to increase the percentage of students taught by full-time faculty, thus reducing the need for adjuncts. The projected reduction in the cost-per-student was $148 to $96, a 35% decrease.
This plan was, however, modified during full implementation. Only one location, where about 68% of the students are enrolled, was able to build a lab sufficiently large to accommodate sections of 50; the other two locations offered sections of 35 and 24. Enrollment was less than anticipated because of an improvement in the economy. Many GTCC students had been displaced workers. As new firms moved to the area, these unemployed workers were able to find jobs and consequently reduced their enrollments or stopped attending college. With an actual enrollment of about 7,900 students, the weighted average redesign section size across the college was 44 students, an overall 76% increase of 19 students per section. The increase in section size and the hiring of nine additional full-time faculty members allowed GTCC to reduce the percentage of adjunct-taught sections from 61% to 19%. Overall, the cost-per-student in developmental math at GTCC declined from $148 to $118, a 20% reduction.
The redesign also saved some students tuition dollars since students could complete the developmental requirements in a shorter length of time (i.e., in one term if they were motivated to do so.) In addition, students could adjust their schedules to reflect life changes instead of having to withdraw from the course and lose tuition. Students also realized a significant savings in the cost of course materials since they only needed to purchase one book and online code for all three developmental math courses.
Will the redesign be sustained now that the grant period is over?
The sustainability of the redesign is not in question. The administration at GTCC has supported the redesign from the beginning and continues to support it. North Carolina has recently redesigned the developmental math curriculum into eight one-credit modules. Students will have multiple exit points based on their program of study. The Emporium Model will facilitate this implementation.