Changing the Equation: Redesigning Developmental Math
Northwest-Shoals Community College
Redesign Coordinator: John McIntosh
At Northwest-Shoals Community College (NWSCC), the transitional studies math program strives to remediate basic arithmetic and algebraic skills as well as provide sufficient mathematical proficiency necessary for selected curricula. In the traditional format, traditional lecture-based forms of instruction encouraged primarily passive student learning, few graded homework assignments and unproductive assessments based on lecture material. In 2009, NWSCC redesigned its transitional math courses using the Emporium Model; however, the redesign did not generate the desired results. In reaction, the college sought further improvements. Changing the Equation offered the math faculty the opportunity to reevaluate its initial redesign of the transitional mathematics courses and make needed adjustments.
Prior to implementing the Emporium Model, student success rates (grades of C or better) in Basic Mathematics, Elementary Algebra and Intermediate Algebra were 58%, 52% and 54% respectively. Data also showed that students who began their education in transitional math had a small chance of completing the mathematics course required for a certificate or degree. After implementing the Emporium Model in 2009, success rates in fall 2010 were 46%, 44% and 33% respectively. The college was confident in the changes made in the initial redesign but recognized that necessary improvements were needed to ensure positive results. After NWSCC implemented the strategies recommended by Changing the Equation, student success rates significantly increased. Fall 2011 saw student success rates of 56% in Basic Mathematics, 59% in Elementary Algebra and 56% in Intermediate Algebra.
NWSCC’s initial redesigned courses consisted of five modules and a comprehensive final exam. Modules contained a pretest, content videos, homework and a module test. Students progressed through the content with mastery scores of 80% for homework and 70% for tests and exams. During Changing the Equation, math instructors replaced the five large modules with eight to 10 mini-modules per course. Homework assignments contained 10 to 15 questions per assignment, and quizzes consisted of 10 questions composed from the material of approximately three homework sections. This change alleviated student pressure and test anxiety once students perceived module assessments as “only quizzes.” The math faculty agreed to include a midterm exam as a benchmark to ensure student comprehension of material as well as a comprehensive final exam, which the college uses for data purposes. Students could retest on all quizzes and exams if needed.
NWSCC employed a fixed-flexible method to confirm student attendance. Students met with an instructor in a small 25-computer classroom one fixed day and time per week. Instructors discussed course progress, verified notes and answered individual student questions. The small computer classroom helped instructors reinforce weekly deadlines, increased student accountability and promoted learning communities. Instructors also found an increase in one-on-one communication that allowed them to feel more involved in students’ progress. Students spent an additional period working in the large math lab or student support service area at the students’ convenience. The College utilized the AccuLite tracking system to monitor class and lab attendance for the purpose of participation scores.
The redesign ensured the consistency of all courses by standardizing syllabi and content, thereby eliminating discrepancies among instructors. The smaller modules assisted students and instructors in pinpointing students’ weaknesses. The redesign also encouraged active learning as students took control and responsibility of their own learning. The math lab provided students with individual assistance. The college employed qualified math lab aides to give individualized help to students who struggled with course content, and the computerized component supplied on-going assessment and prompt feedback.
NWSCC measured expected/intended learning outcomes for each redesigned course by comparing common final exam questions. Each math course put forth a general course syllabus which defined the expected learning outcomes for enrolled students. Assessment measures compared completion rates before the redesign to completion rates after the redesign. Qualitative assessment surveys, administered at the beginning and end of each course, showed that math anxiety decreased throughout the semester.
Increased class sizes and greater reliance on part-time instructors led to the college’s cost savings. NWSCC originally sought to increase section sizes to 44 students. The Muscle Shoals campus reached the average section size of 43, while the smaller, rural Phil Campbell campus averaged a section size of 26. Average section size increased from 31 students to 33 students per section. The cost-per-student decreased from $123 to $115, a reduction of 7%. The college also doubled, sometimes tripled, the number of courses offered at a specific class time by utilizing the one-room schoolhouse approach.
In the redesign, did students learn more, less or the same compared to the traditional format?
Student performance significantly improved in Basic Math, Elementary Algebra and Intermediate Algebra as measured by performance on common exam items. Student performance listed is the average percentage of correct answers on a common course final exam.
Course-by-Course Completion Rates
Course completion percentages (final grade of C or better) improved in two of the three courses; in Basic Algebra, the completion rates were similar:
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. The majority of Changing the Equation teams discovered that pass rates in the traditional format were inflated by prior inconsistencies in grading practices. Unlike redesign students who were assessed on common outcomes using common assessment methods, those in the traditional courses were assessed in a variety of ways which led to overall grading differences. Contributors to prior grade inflation in the traditional course included 1) having no clear guidelines regarding the award of partial credit, 2) allowing students to fail the final exam yet still pass the course, 3) failing to establish common standards for topic coverage (in some sections, entire topics were not covered, yet students passed), and, 4) failing to provide training and oversight of part-time instructors. Thus, the C or better rates for the traditional courses were almost universally inflated.
At NWSCC, this phenomenon was especially prevalent in the Basic Mathematics course. In summer 2012, math instructors reviewed the course material to determine if coursework properly aligned with the intended objectives. Math lab staff also offered training workshops at a higher frequency to allow needed faculty/staff preparation for the fall courses. In fall 2012, NWSCC math department launched a custom-made transitional math book that will be used by the three redesigned courses. This compilation will allow Basic Mathematics students to continue into Elementary Algebra without purchasing a new book/access code. The college hopes that this change will encourage more Basic Math students to complete the material and begin the next course’s objectives.
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, NWSCC analyzed fall 2011 course grades by considering a what-if “Making Progress” (MP) grade. Students receiving an MP grade must have completed the mid-term exam, earned a minimum of 70% participation grade and enrolled in spring 2012 semester. When taking into account the MP grades, completion rates improved in the redesign.
Other Impacts on Students
Were costs reduced as planned?
In the traditional model, NWSCC offered 63 sections on two campuses in the fall and spring with an average section size of 31 students. Twenty-seven sections were taught by full-time faculty at a cost of $190,683, and 36 sections were taught by adjuncts at a cost of $48,600. The traditional cost-per-student was $123. NWSCC originally sought to increase section size to 44 students. The Muscle Shoals campus reached the average section size of 43, while the smaller, rural Phil Campbell campus averaged a section size of 26. During the implementation of the redesigned model, enrollment at NWSCC increased by 19%. The College offered 71 sections on two campuses in fall and spring with an average of 33 students per section. Full-time faculty taught 24 sections; adjunct faculty taught 47 sections. In addition, the college hired lab aides and tutors for the fall and spring semesters. The cost-per-student in the redesigned model decreased to $115, a modest 7% reduction as a result of the redesign.
NWSCC 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.
Will the redesign be sustained now that the grant period is over?
Since Northwest-Shoals’ participation in Changing the Equation, its implementation of the Emporium Model has shown increased student success. Due to the success of the project, the math department is considering the redesign of Pre-Calculus with Algebra, Introduction to Technical Mathematics and Mathematical Applications. The continued success of the Emporium Model strengthened faculty and administrator commitment to the mathematics redesign project. This commitment now extends throughout the transitional studies division to include redesigns of English and reading courses.