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Changing the Equation: Redesigning Developmental Math

Pearl River Community College

Contact: Judy Roane

Project Abstract
Final Report (as of 3/1/12)

Project Abstract

Pearl River Community College (PRCC) is a two-year institution, that serves a six-county area in southern Mississippi with a 2009 fall semester enrollment of 4,899. The developmental course sequence at PRCC consisted of Fundamentals of Mathematics, Beginning Algebra and Intermediate Algebra. Over 1,000 students enrolled in these courses each semester (approximately 200 in Fundamentals, 400 in Beginning, 400 in Intermediate.) In the traditional format, less than 50 percent of students were successful (achieved a grade of C or better.) In addition, of the unsuccessful students, only 33 percent returned to school the following semester. Improving these numbers has been a major goal of the mathematics faculty for several years.

The course redesign used the Emporium Model of instruction. Students were required to spend at least two hours per week in the mathematics laboratory. The computer lab schedule was designed to give students considerable flexibility to meet the time requirement. Students also met one hour per week with the instructor in classrooms equipped with computers. During the class meeting, students worked on their assignments and met individually with the instructor to assess their progress and formulate a plan for the coming week. Courses were divided into modules with students expected to complete one or more modules per week. All testing occurred in the classroom or lab.

The redesign actively engaged the students in their learning and made the students more responsible for their learning. From the students’ perspective, immediate feedback and awareness of their progress improved the quality of the course. The modular design required students to attain mastery of each topic before progressing. This allowed students to focus their time and effort on their weakest topics to gain mastery. All the sections of the courses used the same software, which helped the students to progress through the course sequence and helped the faculty maintain consistency across sections.

In order to assess the impact of the redesign on student learning, final exam scores in the redesigned courses were compared to scores on the same final exams from a number of years prior to the redesign.

PRCC increased the number of developmental math sections taught by full-time faculty each term from five to nine for the same workload credit and reduced section size from 24 to 20. Overall, the number of students a faculty member carried increased by ~31%. The cost-per-student decreased from $252 in the traditional format to $168 in the redesign, a 33% reduction. The redesign reduced the number of adjunct faculty needed and eliminated the need to pay full-time faculty overload assignments. The savings remained in the department budget to be used for professional development (travel and training) and for technology needs. Further savings are anticipated due to higher student retention and increased enrollment in college-level mathematics courses.

Final Report (as of 3/1/12)

Impact on Students

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

Improved Learning

Student performance improved significantly in all three developmental courses as measured by comparing mean performance on common final exams.

Course

Traditional

Mean

Redesign

Mean

Fundamentals of Mathematics

Fall 2010

45.2

Fall 2011

83.7

Beginning Algebra

Fall 2009 & 2010

50.5

Fall 2011

74.1

Intermediate Algebra

Fall 2009 & 2010

60.2

Fall 2011

72.3

In addition, PRCC redesigned its College Algebra course. Student performance on the final examination increased from a mean of 64.4 in the fall 2009 and 2010 traditional format to 73.8 in the fall 2011 redesign.

Course-by-Course Completion Rates

Course completion rates (grades of C or better) improved in two of the three developmental courses for the pilot but dropped again with the full implementation:

  • The completion rate for Fundamentals of Mathematics increased from 58% in the traditional format to 67% in the spring 2011 pilot but dropped to 57% during the fall 2011 full implementation. Some adjustments will be made to the course modules to reproduce the pilot rate.
  • The completion rate for Beginning Algebra increased from 38% in the traditional format to 42% in the fall 2011 redesign.  While this is an increase, more work needs to be done on this course to improve the completion rate.
  • The completion rate for Intermediate Algebra increased from 48% in the traditional format to an all-time high of 67% in the spring 2011 pilot but dropped to 44% during the fall 2011 full implementation. Some adjustments will be made to the course modules to reproduce the pilot rate.

The most improved completion rates were in College Algebra which went from 59% prior to the redesign to 76% in the spring 2011 pilot and 67% during the fall 2011 full implementation.

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 PRCC’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 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. PRCC 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.

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

There are other indications that redesigned students, in the majority of instances, are completing at a higher rate.  PRCC analyzed spring 2012 course grades by considering a what-if “Making Progress” (MP) grade. Students receiving an MP grade must have completed at least 50% of modules at 80% mastery. When taking into account the MP grades, completion rates improved in the redesign.

  Traditional
C or Better
Redesign
A, B, C + MP

Fundamentals of Mathematics

58%

73%

Beginning Algebra

38%

63%

Intermediate Algebra

48%

66%

Other Impacts on Students

In the traditional format, developmental math faced as many as three courses before they were eligible to take a college-level mathematics course. The redesign offered students the opportunity to complete one course and begin another within a single semester. The progress made in the one course was retained to the next semester so that students did not have to repeat previously mastered material. The time required to complete the entire developmental sequence has been tremendously reduced. This was a great motivating factor for students.

Impact on Cost Savings

Were costs reduced as planned?

The department has realized significant cost savings as a result of the redesign project.
In the traditional model, PRCC offered 77 sections of 24 students each; 46 sections were taught by full-time faculty and 31 were taught by adjuncts. In the redesign, the total enrollment increased by 91 students; 97 sections of 20 were taught, 82 by full-time faculty and 15 by adjuncts.

As part of the redesign, full-time faculty workload changed. The redesign format allowed one instructor to teach more students than were taught in the traditional format while decreasing class size. PRCC increased the number of developmental math sections taught by full-time faculty each term from five to nine for the same workload credit and reduced section size from 24 to 20.The student load for each instructor increased on average from 134 students each term to over 160 students. In addition, faculty worked five hours weekly in the lab with no change in the overall hours devoted to developmental math. This could be accomplished because the class only met once a week and because no hand-grading was required. Overall, faculty productivity has risen by 31%.

The department was also able to reduce the need for adjunct faculty and overloads for full-time instructors. The cost-per-student decreased from $252 in the traditional format to $168 in the redesign, a 33% reduction. Other savings included reduced copying costs due to online homework and testing.

Pearl River also 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. These savings are not included in the cost-per-student comparisons cited above.

Sustainability

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

The results obtained for College Algebra and Fundamentals of Mathematics show the value of the redesign. More work is necessary to gain the same results in Beginning and Intermediate Algebra. The PRCC team continues to make minor changes to these courses in order to produce better and more consistent results for these students.

 

 


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