Changing the Equation: Redesigning Developmental Math
Manchester Community College
Contact: Joanne Russell
Manchester Community College (MCC), one of the 12 community colleges in the Connecticut Community College system, traditionally offered two developmental mathematics courses: Prealgebra and Elementary Algebra. Students were placed into the sequence based on scores on the Accuplacer test. MCC offered 10 sections of Prealgebra enrolling ~250 students each semester and 20 sections of Elementary Algebra enrolling ~500 students each semester. Full-time and adjunct faculty taught sections of 25-30 students in a standard classroom setting. MCC devoted one-third of its full and part-time math faculty to teaching developmental math courses.
Despite the resources devoted to developmental math at MCC, the pass rates and persistence of students were dismal. Fifty percent of newly enrolled students placed into a developmental math course; 17% of students placed into Prealgebra. Average pass rates were 55% for Prealgebra and 60% for Elementary Algebra, compared to a 65% overall pass rate at MCC. Furthermore, students who began in Prealgebra would take three or more semesters to complete the sequence through Intermediate Algebra. Baseline data collected over five years of study showed that only 8% of students who began with Prealgebra passed Intermediate Algebra.
The developmental sequence did not prepare students for success in Intermediate Algebra. Of the students who took Intermediate Algebra and began their mathematics sequence at the Prealgebra level, only 42% passed with a C or better compared with 58% of students who placed directly into the course. The data more than suggested that mathematics redesign was urgently needed. Improvement in pass rates, persistence and mastery of content were the outcomes used to measure the success of the redesign efforts.
The Emporium Model was the basis for the redesign of the two-course developmental sequence. The content of each course was modularized; a mastery model for progression through the modules was used. Students could, if able, work at an accelerated pace and complete the sequence of modules in one semester. Students were required to spend three hours in a supervised math lab setting with their assigned instructor and one additional hour in the computer math lab each week for a total of four required hours in the lab each week. The college adopted the ALEKS software platform for its redesign. Students progressed at their own pace with the assistance of a faculty member and professional tutors who staffed the lab.
The effectiveness of mathematics instruction was enhanced by standardizing content and assessment strategies across all sections of developmental math. The modular approach supported various learning styles and eliminated difficulty related to beginning a new topic before achieving mastery of the prerequisite skills and understanding. Students were able to progress at their own rate and receive immediate feedback from the software as well as one-on-one assistance in the lab. They were encouraged to work collaboratively as they uncovered mathematical relationships. Students who failed a module were able to pick up at the point at which they did not achieve mastery without repeating the entire course. The Prealgebra and Elementary Algebra modules were blended into a seamless, modularized design.
MCC evaluated the effectiveness of the redesign by comparing learning outcomes in the redesign with outcomes in the traditional course using embedded assessment questions throughout the term. The modular delivery system allowed common assessments for each module, providing opportunity to assess outcomes not only cumulatively but formatively throughout the developmental sequence. In addition, MCC tracked student success through the developmental sequence and into college-level math and compared this data to baseline data.
MCC’s primary cost reduction strategy was to double enrollment in each section. Section size increased from 25 students per section in the traditional format to 50 sections in each redesigned section. Each redesign section was taught by a full-time or adjunct faculty member supported by two to three tutors. The number of sections taught annually was reduced from 60 to 31; the cost-per-student decreased from $255 to $165, a 35% savings. In addition, classrooms have now been freed up for use by other courses, and the department now has the ability to expand its college-level math course offerings.
In the redesign, did students learn more, less or the same compared to the traditional format?
Fifteen common test items were embedded into course assessments, five early in the semester, five at mid-semester and five in the final examination in both the traditional and redesigned courses. The embedded questions were chosen to assess student proficiency with the most import concepts and skills in the 167 specific learning objectives for Elementary Algebra and 178 specific learning objectives for Prealgebra. All questions required students to calculate an exact result. No partial credit was allowed, and there were no multiple-choice questions. Many questions required a number of steps before reaching an answer, and some required plotting points and drawing graphs. The grading criteria were the same for all students.
The results of student scores on the embedded questions showed improvement in learning outcomes in both levels of developmental course work. The traditional scores are from fall 2010 and spring 2011; the redesign scores are from fall 2011.
Course-by-Course Completion Rates
The percentage of students earning a final grade of C or better fluctuated among the traditional and redesigned courses.
Percentage of Students Passing with a “C” or Better
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 MCC’s case, the redesigned courses were more difficult than the traditional course. For example, the redesign students were not allowed to use calculators; the traditional students often were.
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. MCC redesign students had to pass each module independently at an 80% levels 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, MCC analyzed fall 2011 course grades by considering a what-if “Making Progress” (MP) grade. Students receiving an MP grade must have demonstrated 70% mastery and complete the course within four weeks after the end of the semester. When taking into account the MP grades, completion rates improved in Elementary Algebra in the redesign.
Percentage of Students Including MP
Were costs reduced as planned?
The MCC team followed their plan and actually saved more than initially anticipated. Section size was doubled from 25 students in the traditional format to 50 students in the redesigned format. Instructors were able to double the number of students because there was significant reduction in faculty time to grade homework and prepare assessment materials and they were assisted in each redesigned section by two or three tutors. This allowed ample time to provide the assistance needed for all students. There was almost never a time when students had to wait for help, and most instructors felt an improved engagement with their students. MCC reduced the number of sections offered from 60 to 31. In addition, the ratio of full-time to part-time faculty was shifted from about 45:55 in the traditional format to about 25:75 in the redesign. The cost-per-student decreased from $255 to $165, a 35% reduction.
In addition, classroom space has been freed up to accommodate additional sections of other courses. The cost of copying tests and quizzes was also greatly reduced. The mathematics department was able to expand upper-level course offerings and has added sections in Linear Algebra, Calculus III and Differential Equations as a result of the shift in resources from developmental math classes to upper-level science and engineering classes.
The cost of student use of software was less than what was spent by them to purchase textbooks for the class. In addition, students were no longer required to purchase a graphing calculator for their courses.
Will the redesign be sustained now that the grant period is over?
The mathematics department has consistently supported redesign. Although there was initial skepticism and inertia to overcome, the result has been a very collegial process, one which has strengthened the department. Adjunct faculty members are now fully involved in the implementation, having received extensive training and mentoring. The college has hired professional part-time tutors and one full-time tutor specifically for the developmental math lab.
MCC committed major resources to this initiative by building a new math lab specifically designed for developmental math. In addition, the college invested a significant amount of faculty time in designing and implementing the course redesign. These initial investments were key to the success of the initiative. The entire college is exceptionally supportive of this initiative. The impact of redesign has been felt and recognized in sister community colleges, the state university system and local school districts. In addition, the process of creating the math redesign has positioned the college in a leadership role in several statewide initiatives to improve college readiness among high school graduates.