Developmental Mathematics Program Completion: Traditional Instruction
Compared to Computer-Based Instruction
Carrie F . Quesnell and Kristin M . Hadley
Weber State University
Developmental courses assist underprepared college students in their progress toward college degrees. Developmental edu- cation classes are offered at 98% of public two-year institu- tions and 80% of four-year public institutions in the United States (National Center for Educational Statistics [NCES], 2003). Overall, 28% of all entering freshmen enroll in at least one of these courses. Of all developmental courses, mathemat- ics is the most commonly taken subject in two-year commu- nity colleges (NCES, 2008).
Faculties of developmental mathematics programs have investigated many ways to improve the typically low passing rates for developmental mathematics courses. The issue is complex as such courses typically have many nontraditional students, first-generation college students, and students from diverse backgrounds. Many factors influence student success in developmental mathematics courses, including student causal attribution ideas (Dasinger, 2013), mathematics readi- ness, and student course behavior (Li et al., 2013).
To address these complexities, research has investigated promising practices for developmental mathematics courses.
Based on research with students, discussions with develop- mental faculty, and in-depth studies of programs, Boylan (2002) offered best practices for developmental education.
Criteria for inclusion of a best practice were that the practice was cited in several studies as effective in developmental education, cited in studies over time, replicated at several institutions, considered important by experts in developmental education, and supported by sound research and evaluation at the implementing institution. Based on those criteria, Boylan identified 13 instructional practices: (a) develop learning communities, (b) accommodate diversity through varied instructional methods, (c) use supplemental instruction, (d) provide frequent testing opportunities, (e) use technology with moderation, (f) provide frequent and timely feedback, (g) use mastery learning, (h) link developmental course content to college-level requirements, (i) share instructional strategies, (j) teach critical thinking, (k) teach learning strategies, (l) use active learning techniques, and (m) use classroom assessment
techniques. A decade later, Bonham and Boylan (2012) inves- tigated the implementation of these best practices and found successful programs used technology as both a supplement and integrated with the classroom and computer lab. Despite the success of programs using technology as a supplement, many institutions have advocated increased computerization of developmental mathematics courses.
Developmental mathematics instructors and research- ers have used and investigated many instructional strategies using computers, ranging from homework management (Spradlin & Ackerman, 2010; Jacobsen, 2006) to computer- based instruction. The emporium model (Olsen 1999), which factors in many of Boylan’s (2002) best practices has been heralded as one of the best computer-based means to address the high failure rates for developmental mathematics, with some sites reporting passing rates in the 70 to 80% range, with some semesters near 90% (National Center for Academic Transformation [NCAT], 2009). However other researchers have reported mixed results and cautions (Golfin, Jordan, Hull, & Ruffin, 2005; Taylor, 2008) including concerns about increased drop-out rates (Zavarella & Ignash, 2009). Yet, in spite of these cautions, and based on the successes of early adopters of the emporium model, many colleges and universi- ties have implemented such models (NCAT, 2009). Weber State University (WSU) is one such example. The institution embarked on a study to compare the student outcomes for lecture-based (2007 admission) to computer-based (2010 ad- mission) instruction for developmental mathematics courses.
Specifically, the study sought to answer the following research questions:
• Do a greater percentage of students successfully complete the developmental mathematics program when taught using a lecture-based method or when taught using computer-based instruction?
• Students are allowed to take two semesters to fin- ish one developmental mathematics course using the emporium model. How many more semesters
than the minimum did students from each of the two groups take to complete the developmental mathematics course sequence?
• For students who finished the developmental mathematics program taught using the two meth- ods, was there a difference in the pass rate for the next mathematics course? Was there a difference in the grades the two groups earned in the next course?
Method
Developmental Mathematics Course Context
The students participating in the emporium-based redesigned courses at WSU held to the following course schedule and procedures. Students met in small classes 1 hour per week with their instructor and spent at least 2 hours per week at the mathematics lab, where they worked on their individually paced material via computer and received individual tutoring as needed. These students were expected to complete 10 mod- ules of instruction over the 15-week semester, mastering each topic as they progressed. Mastery learning was incorporated and students could repeat assessments as needed until they had demonstrated proficiency. Prior to taking a module assess- ment, students presented their study notes for approval and completed learning activities such as studying the textbook, watching an instructional video, and completing homework.
Participants
Participants in the study were students at Weber State
University. Over the period of the study (2007–2010), students at WSU were 71% Caucasian, 6% Hispanic, 18% unknown,
other ethnicities less than 2% each. The lecture group of students was composed of 761 students admitted to WSU for the fall semester of 2007 who were referred to developmen- tal mathematics based on Accuplacer placement test scores.
Similarly, the computer (emporium model) group contained 931 students whose first semester at WSU was the fall se- mester of 2010 and who also were referred to developmental mathematics based on Accuplacer placement test scores.
The number of developmental mathematics courses needed varied from one to three, depending on placement test scores.
Demographic information for the two student groups is shown in Table 1. For each student, the researchers also obtained a list of the courses taken and the final grades earned for each developmental mathematics course the student took over the five semesters following admittance. To protect student confi- dentiality, only student identification numbers were used and student data was not associated with student names.
Procedure
The researchers collected the data from the university. They conducted random spot checking on the data using the student ID numbers to verify the accuracy of the course and grade data provided. Once the data were spot checked and deemed to be accurate, data analysis began with descriptive statis- tics for each of the two groups of students. From the data, the researchers determined whether the students finished the program by earning a C grade or higher in Math 1010 (Intermediate Algebra), coded that with a data value of 1 or assigned a 0 if the student did not complete the program. The researchers also determined the number of semesters beyond the minimum required for each student who completed the program. The researchers then determined which students
Lecture
Instruction Computer
Instruction t df
N = 761 N = 931
Gender Male 367 371
Female 394 560
Age Mean = 19.44 Mean = 19.45
–0.48 1692
SD = 3.56 SD = 3.78
High School GPA
Mean = 3.16
(N = 735) Mean = 3.03
(N = 931) 4.53
(p < 0.01) 1662 SD = 0.51 SD = 0.64
Table 1: Demographic Data for Students in the Lecture and Computer Developmental Mathematics Programs
enrolled in a college-level mathematics course which satisfied the university’s mathematics general education requirement after completing developmental mathematics. If the student enrolled in a Quantitative Literacy (QL) course, the data value was coded as 1 and if the student did not enroll in a QL course, the data value was 0. The researchers also computed the grade point average for the QL course for each student in the two groups who took QL courses.
Results
Age and high school GPA of the two groups were compared.
There was no significant difference in ages of the two groups but the mean high school GPA was 3.17 for the lecture group and 3.05 for the computer group. Results of the t test for equality of high school GPA shows that the two means were significantly different (t =4.53, p <0.001 ).
To answer the research questions, the researchers con- ducted t tests to compare the variables for sequence comple- tion, semesters over the minimum to complete the sequence, enrollment in a QL course, and QL course grade. The results of these t tests are shown in Table 2. The two programs differed significantly (t =3.52, p <0.001 ) in the number of students who finished the sequence with the lecture condition having more students who completed, both in absolute number of students and as a percentage of all students who partici- pated. The t tests did not show a significant difference in the number of semesters over the minimum required for students to finish the developmental mathematics sequence, the rate at which students enrolled in QL courses, or grades earned in QL courses by students who finished the sequence.
Lecture Computer t test
n Mean SD n Mean SD t df p
Complete 761 0.34 0.48 931 0.26 0.44 3.52 1690 0
Sem . over min . 260 0.28 0.68 245 0.25 0.62 0.48 503 0.63 Enroll in QL 761 0.24 0.43 931 0.22 0.42 0.92 1690 0.36 Grade in QL 182 2.07 1.26 205 2.11 1.26 –.12 385 0.9
Table 2: t tests for Equality of Means for Students in Lecture- or Computer-based Developmental Mathematics Programs Note: Equal variances assumed
Given that the two groups had high school GPAs that were significantly different, the researchers next performed an analysis of covariance (ANCOVA) to control for high school GPA. There was a significant effect of instructional type on program completion after controlling for the effect of high school GPA, F
(
1,1663)
=4.951, p =0.026. Comparing the adjusted group means (Table 3), there was a difference in program completion between students who had lecture instruction and those who had computer instruction, 32%versus 28%.
Discussion
Past research has shown mixed results for computer-based instruction compared to traditional lecture-based instruction for students in developmental mathematics courses (Golfin et al., 2005). The computer-based instruction at WSU is closely modeled after the instruction type provided one of the most successful emporium sites (Cleveland State Community
College, NCAT, 2009) but it has not shown a similar increase in student success. In this study, the percentage of WSU stu- dents completing their developmental sequence with computer instruction was 26% compared to 34% with lecture-based instruction. Part of the difference in success at WSU may be that this study looked at completion of the entire developmen- tal sequence versus single-semester course pass rates (Squires, Faulkner, & Hite, 2009). Another possible difference between this study and others (Squires et al., 2009) is that students at WSU are not automatically dropped from the course due to
Group Mean Std . Error 2007 (Lecture) 0.324 0.016 2010 (Computer) 0.275 0.014
Table 3: Adjusted Means for Lecture and Computer Instruction—Estimates
nonparticipation. This practice could affect the semester pass rates and sequence completion rates.
This study viewed student completion of the develop- mental sequence over five semesters. Topper (2011) presented data which followed students for three years at institutions participating in the Achieving the Dream initiative, which showed that, of the students who needed one level of develop- mental mathematics, 36% completed it. Twenty-six percent of students assigned to two levels of developmental mathematics completed, and 19% of students assigned to three levels com- pleted. The percentages for all developmental students under study at WSU are similar—26% for computer and 34% for lecture, or using the adjusted means from the ANCOVA, 28%
for computer and 32% for lecture. However, in the Topper report (2011), there is no mention of the types of instruction provided at the participating community colleges.
The second research question was whether students took longer to complete the sequence when enrolled in either lec- ture or computer-based instruction. There was no significant difference in the two programs for this variable. On average, it took students a little more than one-quarter of a semester more than necessary to complete their three course developmental mathematics sequence. Under both programs, students had the opportunity to work faster to complete the sequence in fewer semesters. In the lecture program, students could work faster by enrolling in Math 0955, which contained the curriculum for both the prealgebra and beginning algebra courses. In the program based on computer instruction, students could work ahead to complete multiple courses in one semester. A small number of students in each type of instruction completed the sequences faster than the minimum. The Achieving the Dream data (Topper, 2011) showed that 63% of students made multiple attempts to pass at least one of the developmental mathematics courses to which they were referred. This result is consistent with WSU students taking, on average, more than the minimum number of semesters to complete their program.
There was no significant difference in the rate at which students enrolled in QL courses and no significant difference in students’ grades in the QL courses they took after complet- ing the developmental mathematics sequence. This result seems to suggest that both instructional modes produced students who were equally prepared for university-level math- ematics. However, from the computer-based instruction, more students, in total, enrolled in the next mathematics course.
For lecture-based instruction, 182 (24%) enrolled in a QL course while for computer instruction, 205 (22%) enrolled in a QL course. Even though the number of students taking a QL course was higher for computer instruction, as a percentage of the total number of students, it was lower, 22% compared to 24% for lecture courses.
These findings are similar to the findings of Golfin et al.
(2005), which showed that computer-based instruction was less effective in some cases and more effective in other cases.
For this study, there was a difference in the rate at which students completed their assigned developmental sequence, with lecture instruction having the higher rate. However, there was no difference in the number of semesters students took to complete their assigned sequence and no difference in the rate at which students enrolled in QL courses. Finally, this study showed that students taught with either computer instruction or lecture instruction were equally prepared for their QL, col- lege credit-bearing courses.
Limitations and Recommendations for Further Research
This study only included students at Weber State University who are predominately white and middle class. A similar study with a more diverse student population may yield different results.
In this study, the researchers obtained data for student enrollment and grades for only five semesters. A student placed in the lowest developmental mathematics course would require at least three semesters to finish the program.
However, students may delay enrollment in developmental courses for one semester after admission. Looking at student enrollment over more semesters may influence the outcomes.
Of particular interest would be students who failed to com- plete the sequence when taught by lecture who subsequently completed the sequence with computer instruction. Case stud- ies of these particular students may provide insight into which types of students may be best suited to computer instruction.
It may also be useful to study a few students who have not successfully completed developmental mathematics under the computer-based system to understand why they are not completing the courses.
Another area of possible research would be to determine whether the effects of class attendance are the same as what Jacobsen (2005) found previously. In the computer-based system, students attend class only 1 hour per week and receive credit for their attendance. It would be useful to know whether this one class session was valuable in helping students to com- plete their courses.
All WSU students were placed into the developmen- tal mathematics sequence using only their score on the Accuplacer test. The outcomes for these students varied widely and lack of success may be, in some cases, attributed to misplacement. Some research has documented the use of multiple measures, including high school GPA, to make bet- ter placement decisions (Belfield & Crosta, 2012). It may be beneficial to study alternate placement methods.
Developmental education has the task of preparing students to transition to college-level studies and, ultimately, college degrees. The future workforce of the United States will rely more heavily on college-trained workers, so the
importance of developmental education cannot be over- stated. Developmental educators must continue to study their programs and implement change when necessary to ensure students have the opportunity to succeed in college.
Carrie F . Quesnell ([email protected]) is an instructor of mathematics at Weber State University in Ogden, Utah. She teaches both developmental and college- level mathematics. Her primary research interest is developmental mathematics
program effectiveness and her favorite class to teach is pre-calculus.
Kristin Hadley ([email protected]) is an associate professor of teacher education at Weber State University in Ogden, Utah. She teaches courses in mathematics pedagogy and research. Her research interests include mathematics anxiety and mathematics pedagogical content knowledge.
References
Belfield, C. R., & Crosta, P. M. (2012). Predicting success in college: The importance of placement tests and high school transcripts. (CCRC Working Paper 42). Retrieved September 17, 2012 from http://ccrc.
tc.columbia.edu/Publication.asp?UID=1030
Bonham, B. S., & Boylan, H. R. (2012). Developmental mathematics:
Challenges, promising practices, and recent initiatives. Journal of Developmental Education, 36(2), 14–21.
Boylan, H. R. (2002). What works: Research-based best practices in developmental education. Boone, NC: Continuous Quality Improvement Network with the National Center for Developmental Education.
Dasinger, J. A. (2013). Causal attributions and student success in developmental mathematics. Journal of Developmental Education, 36(3), 2–12.
Golfin, P., Jordan, W., Hull, D., & Ruffin, M. (2005). Strengthening mathematics skills at the postsecondary level: Literature review and analysis (IPR 11659). Washington DC: U.S. Department of Education, Office of Vocational and Adult Education.
Jacobsen, E. (2005). Increasing attendance using email: Effect on
developmental math performance. Journal of Developmental Education, 29(1), 18–26.
Jacobsen, E. (2006). Computer homework effectiveness in developmental mathematics. Journal of Developmental Education, 29(3), 2–8.
Li, K., Zelenka, R., Buonguidi, L., Beckman, R., Casillas, A., Crouse, J., et al. (2013). Readiness, behavior, and foundational mathematics course success. Journal of Developmental Education, 37(1), 14–36.
National Center for Academic Transformation. (2009, June 1). Tennessee Board of Regents: Developmental studies redesign initiative. Retrieved November 15, 2009, from http://www.thencat.org/States/TN/Abstracts/
CSCC%20Algebra_Abstract.htm#FinalRpt
National Center for Educational Statistics. (2003). The condition of education 2003. NCES 2003-067. Washington, DC: U.S. Department of Education.
National Center for Educational Statistics. (2004). The condition of education 2004. NCES 2004-077. Washington DC: U.S. Department of Education.
National Center for Educational Statistics. (2008). Community colleges:
Special supplement to the condition of education 2008. Washington DC:
U.S. Department of Education.
Olsen, F. (1999, October 8). The promise and problems of a new way of teaching math. Chronicle of Higher Education, 46(7), A31–A33.
Squires, J., Faulkner, J., & Hite, C. (2009). Do the math: Course redesign’s impact on learning and scheduling. Community College Journal of Research and Practice, 33, 883–886.
Spradlin, K., & Ackerman, B. (2010). The effectiveness of computer-assisted instruction in developmental mathematics. Journal of Developmental Education, 34(2), 12–42.
Taylor, J. M. (2008). The effects of a computerized-algebra program on mathematics achievement of college and university freshmen enrolled in a developmental mathematics course. Journal of College Reading and Learning, 39(1), 35–53.
References continued on page 53.
Developmental Mathematics Program
Completion: Traditional Instruction Compared to Computer-Based Instruction
Continued from page 29.
Topper, A. (2011, January/February). Developmental education: Time to completion. Data notes: Keeping informed about Achieving the Dream data, 6(1). Retrieved from http://achievingthedream.org/news/
data_notes_janfeb_2011
Zavarella, C. A., & Ignash, J. M. (2009). Instructional delivery in developmental mathematics: Impact on retention. Journal of Developmental Education, 32(2), 2–13.
The Casper College Statistics Program:
Making Advanced Statistics Accessible to Undergraduates
Continued from page 34.
Burn, H., Gould, R., Orosz, B., & Parker, M. (2013, October 21). Connection with community colleges. Retrieved from http://www.amstat.org/
education/webinars/ConnectionswithCommunityColleges.wmv Cannon, A., Hartlaub, B., Lock, R., Notz, W., & Parker, M. (2002). Guidelines
for undergraduate minors and concentrations in statistical science.
Journal of Statistics Education, 10(2). Retrieved from www.amstat.org/
publications/jse/v10n2/cannon.html
Davis, E., Aitchison, T., Allen, E., Gomez, C., Laird, S., & Raczyńska, K.
(2015). An investigation of student response to a potential tuition cap increase at Casper College. Community College Journal of Research and Practice. Community College Journal of Research and Practice, 39(2), 192-198.
Tarpey, T., Acuna, C., Cobb, G., & De Veaux, R. (2002). Curriculum guidelines for Bachelor of Arts degrees in statistical science. Journal of Statistics Education, 10(2). Retrieved from www.amstat.org/
publications/jse/v10n2/tarpey.html
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