Teaching College Algebra using Supplemental Instruction versus the traditional lecture method.
Trying to improve students' academic success has been the focus of many universities across the country. The success of a student begins in the classroom. One of the most troublesome and sometimes terrifying course for students is College Algebra. At Valdosta State University we have tried different methods such as a WEB delivery course and teaching with computerized instruction to improve students' success. For the past two years, at Valdosta State University the Department of Mathematics and Computer Science has been teaching College Algebra (MATH 1111) via a Supplemental Instruction (SI) method. The students' performance on the departmental final exam for the treatment group, SI method, versus the control group, traditional lecture method, was compared. The SI method showed no significant difference on the departmental final exam. Then we compared the mean SAT scores for the two groups. The SI method showed significantly lower SAT scores. It is clear that weaker students in mathematics that take the SI courses can perform on the average on the final exam just as well as the students in the traditional courses.
Key Words: teaching college algebra, lecture, supplemental instruction.
Supplemental Instruction (SI) is a model of student academic assistance whose major goal is to help students succeed in courses that are historically difficult. SI was originally conceived by Deanna Martin at the University of Missouri-Kansas City (UMKC) in 1973 to help students in the health science professional schools. An additional goal of the program is the reduction of attrition rates in the targeted classes and, therefore, the improvement of graduation rates of the students in these classes (5).
A key feature of the UMKC model of supplemental instruction is the use of students as SI leaders. These leaders are responsible for holding optional class sessions several times a week. The leader's role is to provide assistance in mastering the course material by helping students form study skills and strategies that will lead to success in the course.
Valdosta State University (VSU) studied the UMKC model as well as models used by other universities across the country. VSU now offers supplemental instruction to provide academic assistance to college algebra students. The research contained in this paper is an attempt to determine the effectiveness of the SI program in this course at VSU.
REVIEW OF LITERATURE
A review of the literature on supplemental instruction revealed numerous (several hundred) publications and research studies devoted to the subject. In addition to published articles, there are numerous electronic articles and web sites strictly devoted to supplemental instruction. Since the subject matter for this study is college algebra, only research dealing with college-level mathematics was of interest to the investigators.
Preliminary research of the late 70's and early 80's indicated that supplemental instruction resulted in positive learning gains and increased retention. Content specific research and experimental design research then began to emerge. Studies in mathematics began in the late 80's. Results from the first study were presented by Kenney (2). She found that the mean final course grade for students taking supplemental instruction as part of their first semester calculus course for business and economics majors was significantly higher than the mean final course grade for students in a non-supplemental instruction control group. A regression analysis for this study found that the independent variable, attendance at SI sessions, had a significant regression coefficient when used to predict the final course grade. The SI treatment group also had a semester grade point average for all of their course work, not just the calculus class, which was significantly higher than the semester grade point average of the non-SI control group. Kenney's research agreed with that of other researchers that appropriate study techniques learned by students in a supplemental instruction class can apply to their other college courses.
In a follow-up study, Kenney (3) tracked the same students in their second-semester of business calculus. No SI instruction was available for this course. Final course grades for these students showed no significant difference between the groups.
Kenney and Kallison (4) studied the effects of supplemental instruction in the entry-level calculus courses for engineering majors. No significant difference was found between the mean course grades for the SI treatment group and the non-SI control group. This research is consistent with the research of others which indicates that supplemental instruction has a stronger impact upon lower-ability learners than it does upon higher-ability learners.
A summary of this study, and additional research on supplemental instruction whose emphasis was on college-level mathematics, was published by Kenney and Kallison in 1994.
Commander and Stratton (1) found that students who participated in adjunct learning support courses for college algebra (a variation of the traditional SI program) were successful at passing college algebra. All students who completed the adjunct course passed college algebra, while only 80% of those not enrolled in the adjunct course and who completed college algebra had a passing grade. The means of the course grades for the two groups were statistically significant.
Extensive research on SI is conducted annually by the Center for Supplemental Instruction at the University of Missouri-Kansas City. Current research findings regarding their institution, and that of other institutions from across the United States, may be found on their web site under Publications and then choose Research Studies (6). Included in the data are studies which demonstrate the effectiveness of supplemental instruction on course grades in the broad discipline of mathematics, as well as courses including algebra, calculus and finite mathematics. The university also maintains a literature review of recent research, both published and unpublished, by content area on the same web site. Under Publications select SI in Content Areas (6).
Every semester, several sections of College Algebra, MATH 1111, were offered with supplemental instruction. The SI sections were identified in the schedule of classes and were open to enrollment by any student. Students weak in mathematics were encouraged to sign up for SI sections. Courses met three times a week for a fifty-minute period with the assigned professor. Twice a week the classes met for a fifty-minute period with the assigned SI leader. Attendance at both lecture and SI sessions was a requirement of the course. It was assumed that the only pedagogical difference between the two methods was the use of the supplemental instruction provided by the SI leader. A job description of an SI leader can be found in Table 1. At the end of the course all students enrolled in College Algebra at VSU took a common cumulative multiple-choice final examination. Data were then collected on all students enrolled in both the SI classes and the traditional method classes, as explained in the next section.
During registration the SI classes were listed under college algebra--5 days a week (MTWRF). The students had a choice of which class to register for, an SI class or a Traditional method class. The SAT-Mathematics scores indicated that weak students in mathematics tend to register for the SI classes.
At the end of each semester, we collected data and reported the sample size (n), the mean ([bar.X]), and standard deviation (sd) on the following variables: Final Exam, the High School GPA (HGPA), and SAT-Mathematics (SAT-M) test scores. Table II summarizes the data.
At the end of each semester we compared the mean on the Final Exam, the High School GPA (HGPA), and SAT-Mathematics (SAT-M) test scores between the two methods. Table III summarizes the comparison of final exam means, Table IV summarizes the High School GPA means, and Table V summarizes the SAT means in mathematics.
Comparison 1 -- Null Hypothesis: There does not exist a statistical difference between the means on the final examination for the two methods.
A departmental final examination consisting of 50 multiple-choice items was administered at the end of the semester. A two-tailed Z-test was used to test the null hypothesis.
Comparison 2 -- Null Hypothesis: There does not exist a statistical difference between the means on the HGPA for the two methods.
Comparison 3 -- Null Hypothesis: There does not exist a statistical difference between the SAT-Mathematics means for the two methods.
From Table III, we failed to reject the null hypothesis for three consecutive semesters, i.e. there does not exist a statistically difference between the means on the final examination for the two methods, SI and Traditional. At first glance one may think the SI Method does not improve the Final Exam test scores. Evidence to the contrary comes from Tables IV and V.
From Table IV, in Spring 2002 and Fall 2002, the SI method had a statistically significant lower HGPA mean than the Traditional method. We can conclude that weaker students in mathematics are populating the SI sections. Stronger evidence about this conclusion comes from Table V. In Fall 2001, Spring 2002, and Fall 2002, the SI method had a statistically significant lower SAT-Mathematics mean than the Traditional method. Again, we can conclude that weaker students in mathematics prefer to take the SI courses.
Table III indicated that there is no significant statistical difference in the Final Exam mean between the SI and Traditional methods. Tables IV and V indicated that weaker students in mathematics take the SI courses. Between the three tables, we can conclude that if weaker students in mathematics take the SI courses and can perform on the average on the final exam just as well as the students in the Traditional courses, then the SI method is successful. Weak students in mathematics might not have the same success on the final exam if the only alternative to them is the Traditional method. We believe that holding the SI course improves the final exam average for weaker students and that we should therefore continue using it.
Table I. Job Description for Supplemental Instructor Leader * For a five-day course the SI Leader was responsible for the course two days a week (two hours). Preferably, Tuesday and Thursday or any other two days that were agreeable to instructor and SI leader. * The SI Leader met with the instructor two to three times a week so the continuation of the class from one day to the next was smooth. The SI Leader could attend the instructor's lectures but it was not mandatory. * The SI Leader made it clear that his or her role was to help students understand concepts and assignments and not to do the assignments for the students. * The instructor gave the SI Leader a clear assignment for each class at least a day before the SI Leader met the class. The assignment was extra problems in addition to the homework. The SI Leader divided the classroom in groups to work on their assignments. * The SI Leader did not grade homework or lecture or do any of the instructor's duties. An exception to this rule was short, multiple-choice quizzes designed to ensure attendance at SI sessions. * The SI Leader was paid on a weekly basis per course (during a regular semester). Instructors managed their expectation consistent with this workload. Table II. Data Collected On the Performance of SI vs. Traditional Methods. Method of Final Exam HGPA SAT-M Semester Content [bar.X]/sd/n [bar.X]/sd/n [bar.X]/sd/n Delivery SI 60.03/14.39/237 2.73/0.68/237 483.45/56.73/237 Fall-2001 Lecture 59.27/19.43/364 2.86/1.06/364 500.23/69.21/364 Fall-2001 SI 55.65/14.42/109 2.54/1.01/109 478.62/62.21/109 Spring-2002 Lecture 54.86/17.01/211 2.87/1.16/211 495.59/63.79/211 Spring-2002 SI 56.09/15.28/174 2.92/0.73/174 479.66/56.14/174 Fall-2002 Lecture 58.56/15.99/503 3.17/0.84/503 499.69/68.91/503 Fall-2002 Table III. Hypothesis Testing for the Final Exam Means between SI vs. Traditional Methods Fall 2001 Spring 2002 Fall 2002 SI Mean 60.03 55.65 56.09 Lecture Mean 59.27 54.86 58.56 Test statistic Z = 0.5498 Z = 0.4363 Z = -1.8159 P-value P = 0.5625 P = 0.6626 P = 0.0694 Note: Positive test statistic indicates the mean for the SI method was higher. * Indicates the mean difference was statistically significant. Table IV. Hypothesis Testing for the HGPA Means between SI vs. Traditional Methods. Fall 2001 Spring 2002 Fall 2002 SI Mean 2.73 2.54 2.92 Lecture Mean 2.86 2.87 3.17 Test statistic Z = -1.8316 Z = -2.6307** Z = -3.7412** P-value P = 0.0671 P = 0.0085** P = 0.0002** Note: Positive test statistic indicates the mean for the SI method sections was higher. ** Indicates the result was statistically significant at [alpha] = 0.01. We have enough statistical evidence to reject the null hypothesis and accept the alternative that the two HGPA means are significantly different. Table V. Hypothesis Testing for the SAT-Mathematics Means between SI vs. Traditional method. Fall 2001 Spring 2002 Fall 2002 SI Mean 483.45 478.62 479.66 Lecture Mean 500.23 495.59 499.69 Test statistic Z = -3.2451** Z = -2.2926* Z = -3.8158** P-value P = 0.0012** P = 0.0219* P = 0.0001** Note: Positive test statistic means the mean for the SI method sections was higher. * Indicates the result was statistically significant at [alpha] = 0.05. ** Indicates the result was statistically significant at [alpha] = 0.01. We have enough statistical evidence to reject the null hypothesis and accept the alternative that the two SAT-Mathematics means are significantly different.
1. Commander NE and Stratton CB: A learning assistance model for expanding academic support. J Develop Ed 20: 8-13, 1996.
2. Kenney PA: Effects of supplemental instruction on student performance in a college-level mathematics course. Paper presented at the Annual Meeting of the American Educational Research Association, 1989.
3. Kenney PA: Effects of supplemental instruction on student performance in a college-level mathematics course: A report of additional results. Paper presented at the Annual Meeting of the American Educational Research Association, 1990.
4. Kenney PA and Kallison JM Jr.: Research studies on the effectiveness of supplemental instruction in mathematics. New Directions Teach Learn 60: 75-82, 1994.
5. Center for Supplemental Instruction, University of Missouri-Kansas City (2003). Overview. Retrieved July 3, 2003, from http://www.umkc.edu/cad/si/
6. Center for Supplemental Instruction, University of Missouri-Kansas City (2003). Publications. Retrieved July 3, 2003, from http://www.umkc.edu/cad/si/
Andreas Lazari*, Professor
Kathy Simons, Associate Professor
Department of Mathematics and Computer Science
Valdosta State University
Valdosta, GA 31698
Corresponding author: Andreas Lazari