Changing the Equation: Redesigning Developmental Math
Robeson Community College
Contact: LaRonda Lowery
In the traditional format, Robeson Community College (RCC) offered a three-course sequence of developmental math courses. During AY 2009-2010, 1,654 students were served: 864 in Essential Mathematics, 751 in Introductory Algebra and 39 in Intermediate Algebra. Developmental math courses consisted of a three-hour lecture and two-hour laboratory component for a total of four credit hours. Traditionally, the courses were taught in a lecture format with four hours devoted to lecture and one hour of online homework using MyMathLab, resulting in minimal student-faculty interaction.
Students needed to earn a grade of C or higher before taking the next developmental math course or moving into college-level mathematics. Essential Mathematics and Introductory Algebra served as the primary gatekeepers for college-level math. Based on data collected during AY 2009-2010, the overall success rate (grades of C or better) was 46% in developmental math courses, and the retention rate was 66%. Therefore, many students never enrolled in college-level mathematics and did not meet their educational goals. RCC wanted to improve student success, increase retention and persistence through course redesign so students could fulfill their educational goals.
Before redesign, students in developmental math were placed in a structured environment where they were required to work at the same pace. RCC’s redesign of developmental math utilized the Emporium Model of instruction with emphasis on modularization, mastery and flexible pacing. Math classes were scheduled using a fixed laboratory model.
The impact of the redesign on student learning was assessed using common final examinations administered to both traditional and redesigned sections. Student success rates and retention rates in the traditional and the redesigned models were compared. The team also administered surveys to students regarding their perceptions of learning in the redesigned environment.
RCC increased section size from 25 to 42 on the main campus. (At satellite campuses, eight smaller sections were taught, due to space limitations, with a section size of 25.) The number of sections needed declined from 66 to 40, even though enrollment increased by 211 students. Course redesign allowed the college to accommodate enrollment growth without hiring additional math faculty. The cost-per-student declined from $246 in the traditional format to $177 in the redesign, a 28% reduction.
In the redesign, did students learn more, less or the same compared to the traditional format?
Student performance improved significantly in Essential Mathematics and Introductory Algebra as measured by a common final exam.
The team discovered that the traditional Intermediate Algebra hard-copy exam did not adequately cover the concepts that were included in the redesigned online exam. Thus, only approximately one-third of the exam was common to both exams. Interestingly, the redesigned Intermediate Algebra students had a higher mean final exam score (82.04 vs. 80.67), even though the redesigned final exam was at a higher level.
Course-by-Course Completion Rates
Course completion rates (grades of C or better) appeared to decline in both developmental math courses:
Comparisons between the fall 2010 and fall 2011 Intermediate Algebra course were not valid because of small sample size. Historically, Intermediate Algebra has enrolled approximately 20 students a semester. Enrollment in Intermediate Algebra increased from 21 students in fall 2010 to 79 students in fall 2011. Pass rates were 51% in 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.
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. RCC redesign students had to pass each module independently at an 85% 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.
Improved Course Completion: Making Progress Grades
There are other indications that redesigned students, in the majority of instances, are completing at a higher rate. In fall 2011, RCC analyzed fall 2011 course grades by considering a what-if “Making Progress” (MP) grade. Students receiving an MP grade must have completed 10 of 14 mini-modules in Essential Mathematics and 9 of 14 mini-modules in Introductory Algebra, both at an 85% mastery level. 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, RCC offered 66 sections of 25 students each, 38 of which were taught by full-time faculty and 28 by adjunct faculty, for a total enrollment of 1,635 students. The redesigned format included 25 sections taught by full-time faculty and 23 sections taught by adjuncts with an enrollment increase of 211 students. RCC’s redesign plan was to increase section size to 45 students; however, actual section sizes were smaller. On the main campus, section size was increased to 42 students. The availability of a professional tutor and instructor in each developmental math class made it possible to increase the section size. At the smaller, satellite campuses, eight sections of 25 were offered due to space constraints. Thus, annually the average section size was ~40. The cost-per-student declined from $246 in the traditional format to $177 in the redesign, a 28% reduction.
RCC used 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” (particularly at smaller campuses and sites or during certain class times), 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 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 institution 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.
When several programs changed their math requirement to College Algebra, the number of seats needed for Intermediate Algebra increased. To meet this need, RCC was able to adjust seating to accommodate the demand. For example, if the seating capacity had not been reached for Essential Mathematics or Introductory Algebra in a particular section, those seats could be used for Intermediate Algebra students.
Will the redesign be sustained now that the grant period is over?
Robeson Community College is one of 58 community colleges in the North Carolina Community College System (NCCCS). In fall 2010, the State Board of Community Colleges, working in association with leaders from the North Carolina Association of Community College Presidents and the North Carolina Association of Community College Trustees, endorsed a planning initiative, SuccessNC, to foster guiding goals that will positively impact student success. One of the initiatives to improve student success was to redesign developmental education courses. The Developmental Education Initiative (DEI) is a state-policy initiative to redesign the NCCCS developmental education curricula, accelerate student completion, implement diagnostic assessments, increase the number of students who successfully complete developmental education and enroll in college-level courses, and implement supporting policies. The DEI Task Force for Developmental Mathematics revised and modularized developmental math courses so that students could complete the developmental math course sequence in one year. The three four-credit developmental math courses that the college redesigned have been replaced with eight one-credit developmental math courses.
Effective fall 2013, all community colleges in North Carolina will offer the eight one-credit courses. The NCCCS has not prescribed an instructional delivery method but rather will allow each community college to select an instructional delivery method that is appropriate to the needs and resources of the college. One of the goals of the DEI Task Force was that the curriculum would be flexible enough to allow students to complete at a pace appropriate to their individual needs. RCC is one of 18 institutions piloting the new developmental math courses for the NCCCS. RCC is in a position to provide leadership to sister institutions who desire to deliver instruction using the Emporium Model. As a result, other community colleges are requesting advice on how to implement modularized instruction using the Emporium Model.