Learning and Cost Effectiveness in an Elementary Algebra Redesign

Author Information
Sheila Pisa
Riverside Community College
Institution(s) or Organization(s) Where EP Occurred: 
Riverside Community College
Effective Practice Abstract/Summary
Abstract/Summary of Effective Practice: 

Riverside Community College's elementary algebra course, redesigned to incorporated student interaction, helps students to learn more effectively.

Supporting Information for this Effective Practice
Evidence of Effectiveness: 

Elementary Algebra Student Learning Outcomes for Fall 2001

Data for analysis of Fall 2001 student learning outcomes were gathered via administration of a pre-test and a 45-question common final. The pre-test, administered at the beginning of the course, consisted of 20 questions taken directly from the common final. Due to the fact that five questions differed on the common finals for Fall 2000 and Fall 2001, a sub-score based on 40 questions (SCORE40) was calculated. This 40-item score was used as the basis for comparisons of learning outcomes between Fall 2000 (all traditional) and Fall 2001 (all redesign) courses. In addition, a post-test score (POSTTEST) was calculated using the twenty items that corresponded to the pre-test questions.

Six learning objectives from the elementary algebra course outline mapped to specific pre-test and post-test questions. Thus, sub-scores (SS1, SS2, etc.) were calculated for the learning objectives that follow:

  1. Perform arithmetic operations on real numbers and polynomial, rational, and radical expressions. (9 questions)
  2. Evaluate algebraic expressions. (1 question)
  3. Solve equations involving linear, quadratic, rational, and radical expressions. (3 questions)
  4. Graph linear equations and inequalities given the equation and find equations given the graph. (2 questions)
  5. Factor polynomials. (3 questions)
  6. Use the symbols and vocabulary of algebra to clearly communicate mathematical concepts. (2 questions)


In Fall 2000, all elementary algebra courses were taught in the traditional format. Common final results for Fall 2000 are shown in Table 1.

Table 1. Fall 2000 "Traditional Elementary Algebra Common Final Results"

In Fall 2001, all elementary algebra courses were taught in the redesigned format. Common final results for Fall 2001 are shown in Table 2.

Table 2. Fall 2001 "Redesigned Elementary Algebra Common Final Results"

Eight t-tests were run comparing traditional and redesign common final scores and sub-scores. With the exceptions of learning objectives 4 and 5, redesign student scores were significantly higher than traditional student scores. The topics corresponding to learning objectives 4 and 5, graphing linear equations and factoring polynomials, respectively, are covered near the end of the course. In the shortened lecture format of the redesign course, these topics may not have had as much lecture time devoted to them as the earlier topics had. T-test results for Fall 2000 and Fall 2001 common final scores are displayed in Table 3.

Table 3. T Test Results for Fall 2000 (Traditional) and Fall 2001 (Redesign) Common Final Scores

Trad. Mean
Trad. n
Redesign Mean
Redesign n

Table 4 displays pre-test results for Fall 2001.

Table 4. Fall 2001 "Redesigned Elementary Algebra Pre-test Results"

For Fall 2001, learning gains were calculated utilizing sub-scores of the pre-test and common final. Overall learning gain and learning gains for each of the six learning objectives are shown in Table 5. Table 5 also displays paired difference t test results comparing pre- and post-test measures. In all cases, learning gains were statistically significant.

Table 5. Fall 2001 "Redesigned" Elementary Algebra Learning Gain Results

Overall, it appears that, based on data collected during the fall 2001 semester, learning gain in the redesigned courses (mean = 7.66) was significantly higher than students' learning gain in the traditional course (mean = 6.38, t = -3.77, d.f. = 618, p<.001) and overall, based on available data, students in the redesign format were learning more than students in the traditional format for four of the six learning objectives. There was no significant difference in the means for the other two learning objectives. Data is not yet processed for the spring 2002 semester.

How does this practice relate to pillars?: 

learning effectiveness: Riverside Community College (RCC) redesigned Elementary Algebra, a four credit-unit course, enrolling 3,600 students annually on its three campuses. Elementary Algebra is the college's highest enrolling math course and is the lowest level math course meeting associate degree requirements. For the past decade, the success rate (a grade of C or better) for RCC's Elementary Algebra students has hovered around 50%. This, combined with the fact that the course is required for numerous degree paths, results in at least a 30% repeat rate. Compounding these factors is a very low retention rate, with many students simply giving up and dropping out. These factors, along with a desire to offer a Math Lab service for all of our students enrolled in math courses were the motivations for redesigning the course. The characteristics of RCC's traditional Elementary Algebra course are as follows:

  • Four-unit class
  • Meets for 4 hours each week for 16 weeks
  • Taught exclusively in didactic lecture format
  • 72 sections offered each year (36 per semester)
  • 50 students in each section
  • 50% of sections taught by part-time faculty, 50% of sections taught by full-time.
  • No teaching assistants
  • No established tutorial system
  • No technology component

Faculty felt that this format limited student interaction with materials, instructors, and other students and sought a redesign that would improve on these conditions. The redesigned course reduces the traditional four hours of weekly lectures into two hours of lecture. The course requires a 2 hour participation in lab activities weekly, on a drop-in basis. It also requires participation in an online homework/tutorial program that can be accessed 24 hours a day, 7 days a week from either the lab, home, or anywhere internet service is available. The lecture class sizes were increased from 50 to 75 students, and testing was moved out of the classroom into a lab setting. Testing is taken on computer, using a local server-based program, which grades the test and allows students to print a report that gives feedback on incorrect questions. In the lab, besides using computers for the interactive tutorial software, students have opportunities to interact with faculty, tutors, and other students on their math work. Math faculty, in conjunction with the college's Tutorial Services, developed a math tutorial and counseling support system. This program includes optional workshops for students for extra practice in math topics and study skills. The intent of the redesign is to shift the "locus of control" of the learning process from teacher to learner and allow students to select from an array of services that are offered in a flexible timeframe. Student learning was assessed, comparing traditional and redesigned formats with respect to Elementary Algebra course performance, and gains in knowledge measured by pre- and post-tests. In the coming semesters, we will gather data on student performance in subsequent Mathematics courses, to see if redesigned courses significantly impact students' persistence in math courses. Data has been collected for the spring 2002 semester, but processing is not yet complete.

Estimate the probable costs associated with this practice: 

During the Fall 2001 semester 26 sections of redesigned Elementary Algebra are being offered at the three campuses. The maximum number of students that can be served by these courses is 1890 (19 sections have a cap of 75, 6 sections have a cap of 70, and one course is capped at 45), with sixty-nine percent of these sections being taught by full-time faculty. If the same number of students was to be served with traditional courses capped at 50, 38 sections would be necessary. Since we offer 12 fewer sections in the redesigned format, if 69% of these sections were taught by full-time faculty, roughly 8 sections would be taught by full-time and 4 sections by part-time. I am assuming that an average full-time salary is $64,000 and the average hourly rate for part-time is $42. Using this information I came to the following conclusions: strong>Total Cost Savings $ 68,275 Full-time salaries ($32,000 x .2667 x 8 sections) $ 12,096 Part-time wages (72 hrs. x $42/hr x 4 sections) $ 80,371 Total savings In addition to these cost savings, there were over 200 students enrolling in Math 96 and Math 97 who utilized the lab and brought in funds for 6.30 FTES (full-time equivalent students). This translates to approximately $19,000 income that was not realized until the Math Labs were formed as part of the course redesign. Taking this into consideration, the cost saving was approximately $99,371. We were interested also in the costs required to staff and run the Math Labs, since they were necessary to run the redesigned courses. To calculate these costs, I disregarded those teachers who taught the redesigned courses (since their lab time is part of the Math 52 course load) and included those teaching a Math 96 or 97 load. The hours for the 96 and 97 instructors are accurate, and the amount paid for Coordinators and clerical/tutorial is the exact amount spent. "Costs for Math Labs Fall 2001" Spring 2002 $ 102,629 Coordinators $ 37,546 Tutors/Clerical $ 45,150 Full-time (16.5 hrs x 30 weeks is approximately 1.0 load ($60,200) x .75 for lab rate) $ 45,990 Part-time (36.5 hr. x 30 weeks x $42) $ 231,225


Dividing this figure in half (to approximate the cost for one semester) it costs Riverside Community College approximately $115,613 to operate the Math Labs at the three campuses. Even though the cost was slightly more than the money saved through the redesign ($99,371), the labs were needed even if the course redesign had not taken place. The redesign almost offset the costs, making the labs possible.

Contact(s) for this Effective Practice
Effective Practice Contact: 
Sheila Pisa
Email this contact: