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Changing the Equation: Redesigning Developmental Math

Northern Virginia Community College

Contact: Teresa Overton

Project Abstract
Final Report (as of 8/1/12)

Project Abstract

Northern Virginia Community College (NOVA) redesigned all three of its developmental mathematics courses—Arithmetic, Algebra I and Algebra II--into one unified course, Developmental Mathematics. During the summer, spring and fall of 2009-2010, enrollment in the traditional courses totaled 9,392 students. Enrollment has been growing at an annual rate between 5 and 15 percent over the last several years.

The overall success rate in these courses was below 50%. Most classes were taught using a traditional lecture method in which the instructor set the pace of the course. More prepared students often lost motivation while waiting for the class to get to the point where their individual difficulties began. The pace was often too fast for the less prepared student.  Typically, a student who failed the course had to repeat the entire course. With so many instructors involved in the delivery of these courses, it was difficult to maintain consistency in the learning outcomes. 

Concurrent with NOVA’s implementation of its redesign, the Virginia Community College System (VCCS) instituted a redesign of developmental mathematics for all 23 member colleges throughout the Commonwealth of Virginia. In the VCCS redesign, the content of the three prior developmental math courses was allocated into ten modules. A new placement test was also designed, aligned with the new units of material and containing diagnostic features intended to indicate those specific units of material in which an individual student requires remediation. Colleges were given the option of offering each unit as a stand-alone one-credit course with a recommended duration of four weeks or of offering the units using a shell course model to simplify course registration. There were multiple exit points, depending on the student’s planned degree program. NOVA chose to use the shell-course model.  In this model, students registered for a four-credit course (MTT 4) if they needed to complete at least four units to qualify for their desired credit-level math course. Students who needed to complete just 1, 2 or 3 units of material to reach their exit point registered for a 1, 2 or 3 credit shell course. The one-credit courses were scheduled for a four-week session; the two-credit courses for an eight-week session; and the three-credit courses for a 12-week session.

Each NOVA campus established a math computer lab staffed by faculty, instructional assistants and peer tutors to provide one-on-one assistance to students as needed. Each student was required to spend a minimum of two hours per week in the lab, in addition to a scheduled two-hour class in a computer classroom. MyMathLab provided diagnostic and record-keeping functions and immediate feedback to students. The class instructor discussed weekly progress with each student, providing support and encouragement and building a sense of community among the learners.

This redesign addressed students’ varying levels of preparation. The course was more active and learner-centered and was based on a mastery approach, requiring more time-on-task than in the traditional model. Uniform learning outcomes were reinforced through frequent practice and immediate feedback. Students were allowed to focus on the skills they lacked and to progress through the units at their own pace. If a student failed a module, he or she was required to repeat only that module, not the entire course.

During the pilot phase in spring 2011, the college used the parallel sections method of assessment. The student learning outcomes developed for the redesign were shared with instructors of the traditional sections. To assess the pilot, performance on at least 30 common content items from selected exams given to an equal number of traditional and redesigned sections were compared. Comparison of success rates (as measured by course grades) for the two methods was challenging in light of the different standards for assigning grades in the redesigned course compared to the tradtional courses.

In the traditional format, instructors taught 7.5 sections of 25 students each; in the redesign, they taught 10 sections of 25 students each. Adjuncts previously were paid for teaching four credits per course; in the redesign, they were paid for three credits. There was also a 5% increase in the percentage of sections taught by adjuncts. (In the future, NOVA expects the percentage of adjunct-taught sections to increase.) To insure effective coordination of the new course across multiple campuses, NOVA hired a lab manager for each campus and provided some faculty release time as well. Enrollment in developmental math increased from 8,190 to 8,403. The overall impact of these changes was a reduction in the cost-per-student from $323 in the traditional format to $297 in the redesign, an 8% decrease. In the future, NOVA expects faculty to teach more students over the entire term, as some students will only need one, two or three credits (rather than four) in their final term, depending upon the remaining number of modules needed prior to their exit from the program. Savings will be used to offer additional, upper-level math courses.

Final Report (as of 8/1/12)

Impact on Students

In the redesign, did students learn more, less or the same compared to the traditional format?

Improved Learning

Students in the redesign learned significantly more than students in the traditional format as measured by performance on 30 exam questions given to both groups of students. The following table summarizes the percent of students giving correct answers on questions in the three different subject-matter categories during the various semesters.

 

Traditional
Spring 2011

Redesign
Spring 2011

Redesign
Fall 2011

Redesign
Spring 2012

Arithmetic

66.3%

80.4%

84.3%

84.3%

Algebra I

64.7%

91.8%

93.3%

90.7%

Algebra II

57.2%

83.6%

88.7%

87.0%

Overall, for the traditional sections in spring 2011, 60.9% of the answers were correct; for the redesigned sections in spring 2012, 88.3% of the answers were correct. This amounts to an impressive 45% improvement in performance by redesign students over traditional students. 

Course-by-Course Completion Rates

In order to compare individual course completion rates, one needs to look at the percentage of students who complete the same amount of material in the same period of time. In the redesign of their developmental math sequence, NOVA collapsed three courses into one, modularized course. Students enrolled in the new course could be beginning students or students continuing from a prior semester. Consequently, it was not possible to calculate comparative course completion rates for this project.

The team did identify a group of students in the redesigned course where a completion rate could be directly compared to the completion rate of students in NOVA’s traditional Arithmetic course. These were students who did not pass the diagnostic portion of the placement test for at least one of the units 0, 1 and 2, the units that align quite closely with the content of the traditional Arithmetic course. Their failure to pass the diagnostic test(s) indicated that these students truly needed an Arithmetic-level course, and that they would have placed into Arithmetic before the redesign. The following table shows the percent of these students who successfully completed units 0 through 2, a result comparable to earning a satisfactory grade in Arithmetic. The completion rate for the redesign students represents 34% to 39% improvement over the percent of S grades in the traditional Arithmetic course.

 

Total number of students

Percent completing (as defined above)

Spring 2011 Traditional

258

44.6%

Spring 2011 Pilot Redesign

463

59.8%

Fall 2011 Redesign

4213

61.1%

Spring 2012 Redesign

1501

62.0%

Other Impacts on Students

  • Improvement in success rates in credit-level math courses. The two most common entry-level math courses at NOVA are Mathematics for the Liberal Arts and Precalculus. The exit point from developmental math for moving into Math for Liberal Arts is unit 5, while the exit point for moving into Precalculus is unit 9. The following charts summarize the performance for three sub-categories of students in these two courses in spring 2012.

Mathematics for the Liberal Arts

 

Total number of students

Percent with A, B or C grades

All students

2183

67.7%

Students who took no developmental math at NOVA in prior three-year period

1278

66.2%

Students who successfully completed traditional Algebra I in prior three-year period

206

70.9%

Students who successfully completed through unit 5 in redesigned developmental math

523

72.5%

Precalculus

 

Total number of students

Percent with A, B or C grades

All students

1439

57.7%

Students who took no developmental math at NOVA in prior three-year period

845

60.8%

Students who successfully completed traditional Algebra II in prior three-year period

237

38.8%

Students who successfully completed through unit 9 in redesigned developmental math

232

72.0%

Particularly in Precalculus, the improvement in performance of redesign students compared to prior traditional students is impressive.

  • Acceleration. Ten percent of students completed more work in a single semester than they were required to do, which was also more than they would have been able to complete under the traditional model. In the past, they could complete only the content of one of the individual developmental math courses, and then they had to wait for the next semester to move forward. The team will look for ways to further emphasize this positive feature of the redesign to the students.
  • Altered students attitudes. Students are more likely to realize the necessity of taking charge of their own learning and of seeking out assistance when needed. In an attitude survey administered at both the beginning and the end of the semester, they were more likely at the end to disagree with the statements “I dislike going to math class” and “Math is usually my least favorite class.” 76% of the students agreed or strongly agreed with the statement “Overall, I am satisfied with the MASTER Math course”; 69% agreed or strongly agreed with “The way the class is set up helps me stay on task with learning the course material”; 66% agreed or strongly agreed with “Overall, I feel this course is helping me improve my study habits”; and 57% agreed or strongly agreed with “Overall, my attitude toward mathematics is now more positive”.

  • Students needing to work at a slower pace. Under the traditional course structure, students had to maintain the pace set by the instructor. In the redesign, a similar pace is still the expected pace in order for students to complete the shell course in the available time. However, a significant group of students need to work at a slower pace due to learning disabilities or other challenges. These students can progress under the redesign and pick up where they left off in a subsequent semester rather than going back to the beginning of an entire course. Such students account for a sizeable portion of those who receive R (Re-enroll) grades in their course, since this grade requires that students have a 90% attendance grade and complete at least 50% of the required material. A total of 755 students, representing 19.0% of the total, received the R grade in spring 2012. The persistence among this group of students seems to be improving, and the team will study the data over time to see if this perception is confirmed.

Impact on Cost Savings

Were costs reduced as planned?

Institutional Savings

Because the course materials were already developed for the instructor and most grading was done within the software, each faculty member received three workload credits for teaching a four-credit course. In the traditional format, instructors taught 7.5 sections of 25 students each; in the redesign, they taught 10 sections of 25 students each. Adjuncts previously were paid for teaching four credits per course; in the redesign, they were paid for three credits. There was also a 5% increase in the percentage of sections taught by adjuncts. (In the future, NOVA expects the percentage of adjunct-taught sections to increase.) To insure effective coordination of the new course across multiple campuses, NOVA hired a lab manager for each campus and provided some faculty release time as well. Enrollment in developmental math increased from 8,190 to 8,403. The overall impact of these changes was a reduction in the cost-per-student from $323 in the traditional format to $297 in the redesign, an 8% decrease. In the future, NOVA expects faculty to teach more students over the entire term, as some students will only need one, two or three credits (rather than four) in their final term, depending upon the remaining number of modules needed prior to their exit from the program. Savings will be used to offer additional, upper-level math courses.

Student Savings

The redesign has reduced the cost of developmental math for many students. The traditional developmental sequence was 11 credits; the redesigned course has been reduced to 10 credits. It was possible for students to complete fewer than 10 credits since they could be exempt from individual units via satisfactory unit-by-unit scores on the placement test. Students could also complete more than four units during the semester but pay for only four credits if they worked hard.

Sustainability

Will the redesign be sustained now that the grant period is over?

The team has no question about the sustainability of the redesign. NOVA’s administration was supportive from the beginning and continues to offer support. The Virginia Community College System now requires a modular approach to the developmental math curriculum, and for a school the size of NOVA, an emporium and technology-based approach is the only realistic delivery method that is available for a modular curriculum.

Students are becoming increasingly aware that the redesign offers significant benefits compared to the traditional course structure. They no longer have to spend time on units of material where they demonstrated competency via the placement test; they can move more quickly through the required units to qualify for their required credit-level math course; and they have a great deal of flexibility in scheduling and study times, with individualized assistance available upon request, six days a week. There is a good possibility that they can complete their developmental math requirements in less time and with less cost. However, for those students who need to go slowly through the material because of special learning needs, the redesign structure works for them as well, since the student, not the teacher, sets the pace.

 

 


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