Changing the Equation: Redesigning Developmental Math
Contact: Robert Hall
Formerly, the developmental math course sequence at Cochise College consisted of four four-credit courses: Developmental Math, Fundamental Math, Elementary Algebra and Intermediate Algebra. Intermediate Algebra had the highest average enrollment with roughly 900 students annually. Elementary Algebra usually enrolled around 750 students annually. Annual enrollments for Fundamental and Developmental Math were roughly 350 students and 150 students respectively. Over 60% of all math students (2,200 students annually) were enrolled in these developmental math courses. Students engaged in three hours of traditional classroom/lecture time per week plus one hour of non-lecture learning. Math practice time was usually delivered using cooperative learning techniques or Hawkes Learning Systems software.
The developmental math sequence should be the gateway to success in college-level mathematics, but too often it became an insurmountable barrier to educational attainment. A former departmental review at Cochise showed that, of the 5,782 students enrolled in developmental math courses between 2007 and 2010, nearly 43% received a D, F or W. Almost 25% of the students never completed the developmental math sequence, a rate that had not changed significantly since 2004. Half-measures could not overcome this problem; redesign was needed to improve the success rate of developmental math students. For recent high school graduates, redesign was critical to remediating deficiencies in mathematics skills. For returning adult students, redesign provided critical flexibility by allowing them to progress through the developmental math sequence without being tied to the pace of a single class.
The Cochise developmental math program was redesigned into three courses (Developmental Math I, II and III). Fifteen modules--each corresponding to a desired learning outcome--were distributed evenly across the courses. Students were able to move at their own pace through the courses and were given three semesters to complete them successfully. Students were required to spend four hours per week in class where the focus was on using interactive software and receiving individualized attention to help students actually do math; lecture requirements were eliminated.
The redesign significantly enhanced the quality of the developmental math students’ experiences. They had a high-touch, modularized experience where feedback and assistance were available instantaneously (software) and on-demand (instructors and tutors). Time and attention were directed only where the student needed it, with extra instruction and practice in areas of difficulty and the ability to move rapidly through areas of demonstrated mastery. MyMathLab software engaged the students in every session, and the ratio of instructors/tutors in the lab classrooms was calibrated based on the size of class and level of need. Students had multiple ways to reinforce their learning experiences: online tutorials, individualized instruction, collaborative learning and software-based practice. The use of technology supported immediate feedback on progress (exercise, homework, quizzes, tests, etc.) so that both the students and the instructors knew how students were progressing.
The groundwork had been laid for assessing the impact of redesign on student learning prior to the beginning of the redesign project. The campus and instructors selected for the pilot had experience with implementing new models and assessing impact. The redesign team included members with substantial expertise in developmental mathematics, and they were given the authority to closely examine outcomes. The department as a whole had been involved in assessing developmental math outcomes for over 10 years. A significant element of that assessment was the exit exam; Cochise had four semesters of data on this exam, which allowed the department to perform both parallel and baseline comparisons against the redesigned courses. All students (those taking traditional or redesigned courses) were tested in comparable settings.
Prior to the redesign, Cochise offered 71 traditional sections of developmental math on the main campus with an average section size of 21 students each. After the redesign, the average section size increased to 38 students. The increase in section size meant that each of ten full-time faculty members carried on average an additional 33 developmental students each year. The percentage of full-time faculty teaching the developmental sections increased from 53% in the traditional courses to 73% in the redesign. The cost-per-student declined from $351 in the traditional format to $306 in the redesign, a reduction of 13%.
In the redesign, did students learn more, less or the same compared to the traditional format?
To assess the impact of redesign on student learning outcomes, Cochise compared common items from exams given throughout the semester to both traditional and redesigned cohorts. Each problem was evaluated as right or wrong. The numbers portrayed below represent the percentage of questions answered correctly in each condition.
Redesign students in the first two courses outperformed traditional students, although the difference was not significant. Traditional students in Intermediate Algebra outperformed redesign students in Intermediate Algebra, although again the difference was not significant.
Course completion rates (grades of C or better) were higher under the redesign. In the case of Elementary Algebra, the difference was statistically significant
Improved Course Completion: Making Progress Grades
There are other indications that redesigned students completed at an even higher rate. Cochise analyzed fall 2011 course grades by considering a what-if "Making Progress" (MP) grade. Students receiving an MP grade must have completed at least 60% odf the modules with 80% or better mastery. When taking into account MP grades, completion rates were even higher in the redesign. In the case of the first two courses, those differences were statistically significant.
Other Impacts on Students
Were costs reduced as planned?
Prior to the redesign, Cochise College offered 71 traditional sections of developmental math on the main campus with an average section size of 21 students each. After the redesign, the average section size increased to 38 students. The increase in section size meant that each of ten full-time faculty carried on average an additional 33 developmental students each year. The percentage of full-time faculty teaching the developmental sections increased from 53% in the traditional courses to 73% in the redesign. The cost-per-student declined from $351 in the traditional format to $306 in the redesign, a reduction of 13%.
Cochise also used the “one-room schoolhouse” approach to deal with low-enrollment sections at their extended learning sites, producing both institutional cost savings as well as clear benefits to students. Section sizes did not increase because the labs were too small. 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 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 extended learning centers to offer each level of developmental math each semester 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. These savings are not included in the cost-per-student comparisons cited above.
Will the redesign be sustained now that the grant period is over?
Cochise faculty and staff believe in the redesign project and are committed to continue the new format for students. The labs are in place with plans for continuing improvements to facilities and training for instructors and tutors. Many college-level classes, especially online courses, are now using the same software and parts of the redesign concept.
The administration continues to fully support the math department’s efforts to improve student learning. A 50-station lab was constructed on the Sierra Vista campus at the beginning of fall 2011. A similar lab is now under construction on the Douglas campus. Plans are also being made to construct a lab in the new facilities on Ft. Huachuca. The college’s IT department deserves special recognition in its support of the redesign effort. Without their assistance, this change would not have been possible.
The goal of the math department is to continually improve the redesign effort. Sessions have been scheduled during upcoming faculty and staff convocations to receive feedback from center directors and associate faculty members. Part of the discussion will be devoted to improving the facilities at the extended learning centers.