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Changing the Equation: Redesigning Developmental Math

Leeward Community College

Contact: Eric Matsuoka

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

Project Abstract

In the traditional format, Leeward Community College (LCC) offered four three-credit remedial and developmental courses that had to be taken in sequence after initial placement: Basic Math through Problem Solving (100 students), Introductory Algebra with Geometry (650 students), Algebraic Foundations I (975 students) and Algebraic Foundations II (950 students). The overall DWF rates for these courses were approximately 47%.

The academic difficulties that these completion rates posed for students were serious. For many students, failure in these courses not only provided barriers in pursuit of their academic goals but also posed financial difficulties associated with repeated enrollments. These low success rates also posed serious resource challenges for the college. With surging enrollments due to the state of the economy, there were both classroom and lecturer shortages.

The goal of the redesign was to reduce the traditional four courses to three courses: Whole Number Operations (one credit), Essential Mathematics for Algebra (three credits) and Accelerated Algebraic Foundations (four credits) utilizing the Emporium Model and the ALEKS software program. As part of this redesign, the faculty worked with college-level math faculty to clearly identify what students needed to know to be successful in transfer-level math. Only those topics found to be essential for success in subsequent courses were included in the new courses. Reducing the number of courses not only reduced the costs to the students and the college but also helped to alleviate the compounded DWF attrition that accompanied long remedial/developmental sequences of courses.

In the redesigned model, each student spent a minimum of three hours per week doing math, one under guidance of the instructor in the classroom lab, one in the math lab with math faculty on hand for assistance, and a third either in the math lab or at another location of the student’s choosing. The ALEKS software provided students with immediate feedback on their progress to reinforce prior knowledge while introducing new content.  In this way, students could be in charge of their own progress with clear goals.  Faculty closely monitored student progress with weekly classroom interactions as well as reports generated by ALEKS. All of these factors enhanced the quality of the remedial and developmental math program and improved student learning.

Because LCC’s redesign restructured the content of four remedial and developmental courses into three courses, while preserving all the necessary components as determined by both the remedial and developmental as well as the college-level math faculty, data was collected “before” and “after” the redesign.  The content of each of the new courses was mapped to the content of the traditional courses, and student learning was assessed using comparisons of common content items selected from exams. Finally, as the redesign included conversations with college-level math faculty, the team planned to measure performance in follow-on courses. 

The redesign involved changes in faculty roles due to coordinated course development and delivery (including standardized tests), substitution of interactive tutorial software for face-to-face class meetings and the use of automated grading and course management software to handle course administration. As a result, each faculty member had more students enrolled in each section. The redesign produced direct cost savings in two ways. First, in the traditional format, 12 credits of remedial and developmental math were offered in the sequence whereas in the redesign only nine credits were required of students needing the entire sequence. The reduction in the number of courses and credits produced savings to the college since fewer faculty were needed to serve comparable numbers of students. Second, larger total class sizes were established so fewer faculty were needed to serve comparable numbers of students. Each section increased from 25 students in the traditional format to 30 students divided into two groups of 15 students in the redesign. The number of sections decreased from 107 traditional sections to 81 redesigned sections, with an accompanying decrease of 245 students. The overall cost of the developmental math program was reduced by 18% after full implementation of the redesign, and the cost-per-student was reduced from $319 to $287, a decrease of 10%.

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

Since the content of the four legacy courses was redistributed among the three redesigned courses, student learning comparisons could not be made by using entire exams. Instead, the comparisons were made by comparing student performance on problems graded using common rubrics. Student mastery of course learning outcomes improved in most areas with some showing equivalent performance and very few showing poorer learning.

  Percent of students demonstrating substantial or full mastery of learning outcome
Whole Numbers        
Topic

Traditional
Fall 2010

Redesigned
Fall 2011
Traditional
Spring 2011
Redesigned
Spring 2012
Addition 84.9% 97.4% 73.9% 100%
Subtraction 73.6% 94.7% 78.4% 100%
Multiplication 74.5% 94.7% 68.2% 100%
Division 70.8% 86.5% 68.2% 100%

 

  Percent of students demonstrating substantial or full mastery of learning outcome
Prealgebra        
Topic

Traditional
Fall 2010

Redesigned
Fall 2011
Traditional
Spring 2011
Redesigned
Spring 2012
Perimeter 72.3% 87.4% 70.5% 91.7%
Translations 54.5% 72.5% 63.2% 90.3%
Order of Operations 57.1% 74.3% 40.0% 54.2%
Solve Proportions 55.4% 77.9% 57.9% 59.0%

 

  Percent of students demonstrating substantial or full mastery of learning outcome
Algebra        
Topic

Traditional
Fall 2010

Redesigned
Fall 2011
Traditional
Spring 2011
Redesigned
Spring 2012
Order of Operations 67.90% 98.80% 62.90% 98.40%
Graph lines 53.70% 83.50% 56.90% 77.70%
Rules of exponents 64.90% 91.70% 69.30% 90.00%
Polynomial Operations 78.40% 90.20% 69.30% 83.40%
Factoring 64.20% 88.70% 60.90% 61.50%
Simplify radicals 67.90% 72.10% 70.80% 87.10%
Solve a 2x2 system 74.10% 93.80% 61.80% 92.70%
Long division 53.70% 82.00% 62.70% 74.40%
Add/subtract rational exp 68.70% 31.20% 71.70% 23.60%
Complex fractions 55.10% 47.80% 59.00% 23.10%
Fractional exponents 72.10% 79.80% 71.70% 64.80%

The three topics in the Accelerated Algebraic Foundations course where redesigned students performed poorly compared to the traditional students were used in only one course (College Algebra) that followed it.  In response, review material was added to the beginning of that course to help students to review those areas more carefully before proceeding with the new material. Additional review material was also integrated throughout the course to provide just-in-time brush-ups as new material was introduced.

Course-by-Course Completion Rates

Course completion rates were higher, although not significantly higher, in the redesigned Whole Numbers course compared to the traditional Basic College Math course. The majority of the students who would have placed into the traditional Basic College Math course now place into the next course in the sequence. 

Completion rates for the redesigned Essential Mathematics for Algebra were significantly higher than those of the corresponding traditional course Pre-algebra in both the fall and spring semesters of full implementation. 

Completion rates for the redesigned Accelerated Algebraic Foundations were significantly higher in the fall semester of full implementation compared to the traditional course rate (pooled from Algebraic Foundations I-II) but not significantly different from the traditional rate in the spring semester. It is important to note, however, that the redesigned algebra course replaced two sequential traditional courses.

Grade of C
or Better

Traditional
Fall 2010

Redesigned
Fall 2011
Traditional
Spring 2011
Redesigned
Spring 2012
Whole Numbers 62% 62% 60% 67%
Prealgebra 45% 75% 54% 67%
Algebra 56% 64% 52% 50%

Improved Course Completion: Making Progress Grades

There are other indications that redesigned students completed at an even higher rate. LCC analyzed fall 2011 and spring 2012 course grades by considering a what-if "Making Progress" (MP) grade. Students receiving an MP grade must have demonstrated mastery of 65% of the objectives in ALEKS. When taking into account MP grades, completion rates were even higher in the redesign.

  Fall 2011
Traditional
C or Better
Spring 2012
Traditional
C or Better
Fall 2011
Redesign
A, B, C + MP
Spring 2012
Redesign
A, B, C + MP
Whole Numbers 62% 67% 62% 67%
Prealgebra 75% 67% 80% 69%
Algebra 64% 50% 84% 75%

Other Impacts on Students

  • Positive and improved student attitudes toward math and the Emporium Model. Many students expressed their surprise at how well they did in the Emporium model even though they did not feel they would do so. Many admitted they felt prior classes were a waste of their time but the policies and procedures used in the Emporium model changed their impression. In addition to direct student comments, there have been many reports from other disciplines and units of students expressing their appreciation of the subject and the redesign.
  • Acceleration potential. In fall 2011, 21 students were initially placed into Essential Mathematics for Algebra and completed that course as well as the next course (Accelerated Algebraic Foundations) in the same semester. In spring 2012, 24 students did so as well. Twenty-one students who were placed into developmental mathematics completed their developmental work early enough in the semester that they were able to register for special part-of-term transfer level math courses; 14 of these students successfully completed the transfer-level course.
  • Improved enrollment distribution. Overall student enrollment in developmental math decreased from the traditional format. Due to the merging of two sequential three-credit courses into one four-credit course, the distribution of students enrolled in a class one level below the transfer level increased and the number of students registered for a class three (or more) levels below the transfer level decreased by more than 90%.

Impact on Cost Savings

Were costs reduced as planned?

The redesign involved changes in faculty roles due to coordinated course development and delivery (including standardized tests), substitution of interactive tutorial software for face-to-face class meetings and the use of automated grading and course management software to handle course administration. As a result, each faculty member had more students enrolled in each section. Larger total class sizes were established so fewer faculty were needed to serve comparable numbers of students. Each section increased from 25 students in the traditional format to 30 students divided into two groups of 15 students in the redesign. The number of sections decreased from 107 traditional sections to 81 redesigned sections, with an accompanying decrease of 245 students after the change in required credits.

Faculty participated in the lab as part of their instructional assignments. For each three-credit course, faculty were assigned to two weekly scheduled hours where they met with students and two open lab hours monitoring and assisting drop-in students. For each four-credit course, faculty were assigned to two weekly scheduled hours where they met with students and four open lab hours. Having faculty maintain open lab hours might appear cost ineffective compared to hiring para-professional tutors; however, since the open lab hours were included in the faculty member’s workload, there was no need for additional tutors.

The redesign also shifted the full-time/part-time ratio of the sections taught. In the traditional format, 60% of the sections were taught by full-time faculty; in the redesign, only 37% of the sections were taught by full-time faculty.

In addition, because of the decrease in the number of credits required by those who started at the beginning of the developmental math sequence from 12 credits in the traditional format to eight credits in the redesign, overall enrollment declined in developmental math by 9% (245 students).The reduction in the number of courses and credits produced savings to the college since fewer faculty were needed to serve comparable numbers of students. The overall cost of the developmental math program was reduced by18% after full implementation of the redesign, and the cost-per-student was reduced from $319 to $287, a decrease of 10%.

Sustainability

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

LCC’s administrators and a majority of the developmental math faculty see the value of the redesign and are committed to its sustained implementation and success. The cost savings analysis completed as a part of the program reporting shows that the adopted redesign is fiscally sustainable as well.

Based on the success of the redesigned developmental math courses established during the period of the grant, redesigned sections of transfer-level courses College Algebra and Accelerated Pre-Calculus were created. The redesign was fully implemented in College Algebra during fall 2012. Further evidence of the college’s and discipline’s commitment to redesign includes repurposing, renovating and furnishing an additional classroom to support the new redesign.

 

 


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