success in algebra among community college students

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Success in Algebra AmongCommunity College StudentsCzarina Reyes aa Mathematics/Science Division , BrookhavenCollege , Farmer's Branch, Texas, USAPublished online: 08 Feb 2010.

To cite this article: Czarina Reyes (2010) Success in Algebra Among CommunityCollege Students, Community College Journal of Research and Practice, 34:3,256-266, DOI: 10.1080/10668920802505538

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SUCCESS IN ALGEBRA AMONG COMMUNITYCOLLEGE STUDENTS

Czarina Reyes

Mathematics=Science Division, Brookhaven College, Farmer’s Branch,Texas, USA

College algebra is a required course for most majors, but is viewed bymany as a gatekeeper course for degree completion by students. Withalmost half a million students taking college algebra each year, facultyare experimenting with new course lengths of time that might result inhigher success, completion, and retention rates for college algebra stu-dents. This article reports on a study of the traditional 16-week versusan 8-week course length in college algebra at a two-year MetropolitanCommunity College (MCC) in the United States. The study was to deter-mine which course length of time, 8 weeks or 16 weeks, results in a higherproportion of students successfully completing the college algebra course.Also investigated were success rates among ethnicities, genders, and agegroups. The study included 231 students in college algebra. Data wereanalyzed on four sections of the traditional 16-week courses and four sec-tions of 8-week courses. In this study, success was measured as earning agrade of A, B, or C in the course. Understanding more about courselengths of time for college algebra can aid in increased understandingof time as a factor and, ultimately, may determine if students are moresuccessful in 8-week or 16-week courses of instruction.

College algebra, one of several entry-level undergraduate mathematicscourses, enrolls a larger number of students than other college math-ematics courses in the nation’s community colleges. In the fall of2000, 400,000 students enrolled in college algebra at communitycolleges throughout the country (Small, 2002b). Many studentsidentify this course as one of the toughest courses they take in their

Address correspondence to Czarina Reyes, Brookhaven College, Mathematics=Science

Division, Farmers Branch, TX 75244-4997. E-mail: [email protected]

Community College Journal of Research and Practice, 34: 256–266, 2010

Copyright # Taylor & Francis Group, LLC

ISSN: 1066-8926 print=1521-0413 online

DOI: 10.1080/10668920802505538

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undergraduate careers. Although college algebra remains a criticalcomponent in the core curriculum of American community colleges,little research is available that identifies success, retention, and com-pletion rates for students participating in this course. Small addressedthe 40% to 60% attrition rate in college algebra in his comment,‘‘Because of college algebra’s gateway position in undergraduateprograms, traditional college algebra courses block the academicopportunities and plans of approximately 200,000 students persemester. As educators, we cannot accept this cost’’ (2002a, p. 3).

Community college student enrollment in algebra depends on sev-eral factors: the completion of a developmental mathematics pro-gram, assessment scores that meet the requirements and completionof Algebra I and Algebra II in high school, assessment in trigon-ometry or another higher-level mathematics course, or failing to passadvanced mathematics course when placed in them. Consequently,some students enroll in college algebra for a review of mathematicalconcepts. In view of the fact that large numbers of students enroll anda large number of students repeat college algebra three, four, five, oreven six times, this study attempted to determine if an eight-weeklong course might increase success and retention rates.

There are initiatives that mathematics departments are applyingin order to improve success rates such as: offering courses in 8weeks, supplemental instruction (SI), math lab tutoring, graphingcalculator, and online courses. However, few efforts have been madeto explore and research the volume of students taking collegealgebra and their success rates in 8- and 16-week courses. This sug-gests a need to compare and contrast traditional 16-week versus8-week courses.

Texas has an educational initiative titled Closing the Gaps. Thisinitiative is to ensure that by 2015, the state will expand its educatedpopulation and workforce. Two of the main objectives of this initiat-ive are to increase the enrollment of students by 500,000 and toincrease by 50% the number of degrees and certificates (Texas HigherEducation Coordinating Board, 2008). Therefore, as more studentspursue a college education, college algebra is needed for graduationor entrance into technical programs. To achieve this end in Texas,community colleges continue to explore innovative means to makecollege algebra, along with all courses, more available and accessible.One option for doing this involves offering courses in more concen-trated periods of 8 weeks. Over time, math faculty have argued thata more concentrated time on task such as 8 weeks in college algebramight indicate higher success rates based on the assumption thatgrades are the single indicator of success. Even so, little is known

Algebra Success Among Community College Students 257

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about success rates for different course lengths of time offerings forcollege algebra, 16 weeks and 8 weeks.

Johnson, Johnson, and Smith (1998a) indicated in their meta-analysis that meeting more often in college algebra classrooms pro-motes time on task and higher-level reasoning. Cooperation amongstudents and faculty produces greater mathematical achievement.The traditional 16-week college algebra course has dominated highereducation for years; however, shortened course lengths of time havebecome increasingly popular in the last 15 years among highereducation institutions.

To that end, this research reports on the need to know the outcomesbetween the traditional 16-week versus an 8-week college-level math-ematics courses and the resulting success rates at a two-year college ina metropolitan college district in Texas.

Even though placement in college algebra is mandatory at themajority of community colleges throughout the United States, thereis still a large number of students who are not placed correctly. Shawstates: ‘‘If the student is not initially placed into a mathematics classappropriately, then the student is at an immediate disadvantagebefore other factors have the opportunity to influence success’’(1997, p. 6). Taking college algebra without the proper prerequisiteskills increases the probability of failure for students regardless ofthe length of a course.

The literature does not present unequivocal research demonstrat-ing that 8-week courses have greater success rates than 16-weekcourses. In most cases, studies involving different course lengths oftime have been conducted on small groups of students but not in col-lege algebra courses. A review of the literature reveals that no studyhas yet compared and contrasted different course lengths of time intraditional classroom settings for college algebra courses in Americancommunity colleges. Many of the studies found in the literature onboth the traditional 16 weeks and shortened course lengths of time,such as 8 or 10 weeks, have focused on courses such as business, Eng-lish, theater, biology, accounting, and psychology. None of the stu-dies specifically involved college algebra courses.

Grimes and Niss (1989) conducted a study that compared whetherstudents enrolled in a 15-week economics course learn at the samelevel and achieve the same results as students enrolled in a modifiedmastery class of 8 weeks or 10 weeks. Student performance in thetwo course lengths was measured using standardized techniques suchas the revised Test of Understanding College Economics (TUCE)(Grimes & Niss, 1989). Grimes and Niss (1989) used t test forindependent group means to test for statistical differences between

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the performance scores of the control group, which was 15-weeks,and the modified mastery group (p. 135). Grimes and Niss (1989,p. 136) found no significant differences between the control groupand either of the modified mastery groups (8-week and 10-weekcourses).

RESEARCH QUESTIONS

This study was designed to address the following research questions:

1. Are there greater numbers of students in 8-week college algebracourses who earn grades of A, B, and C than students enrolledin traditional 16-week college algebra courses?

2. Are there greater numbers of White, Non-Hispanic; African-American; Hispanic, Mexican American; and Asian, PacificIslander students in 8-week college algebra courses who earngrades of A, B, or C than those same ethnicities enrolled intraditional 16-week college algebra courses?

3. Are there greater numbers of males=females in 8-week collegealgebra courses who earn grades of A, B, or C than those samegenders enrolled in traditional 16-week college algebra courses?

4. Are there significantly greater numbers of students in the agegroups (18–22), (23–30), and (31–40þ) in 8-week collegealgebra courses who earn grades of A, B, or C than those sameage groups enrolled in traditional 16-week college algebracourses?

METHOD

The data for this study were gathered from a centralized data sourcemaintained by the college. Archival data were acquired from theOffice of Institutional Research at the college. All students fromthe eight college algebra sections selected who had taken collegealgebra at the college were included in the study. These data were div-ided into course length of time: 8 weeks and 16 weeks. Approximately415 students at the college were enrolled in college algebra each sem-ester. Eight sections of college algebra courses were included in theresearch. The population for this study consisted of students enrolledin either one of the four sections of 8- or 16-week college algebracourses at the college. Data were analyzed on four sections of thetraditional 16-week courses and four sections of the 8-week courses.All students enrolled in the eight college algebra sections were taught


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by the same instructor. The 8-week courses taught had one variabledifference, viz., course length of time. Again, success was defined asearning grades of A, B, or C in the courses of instruction.

ANALYSIS

The data analysis consisted of examining the grade distributions inthe 8- and 16-week college algebra courses and the grade distributionsby ethnicity, gender, and age. To determine whether there were stat-istical significance between the 8- and 16-week college algebracourses, grades were analyzed using non-parametric Chi-Square(v2) tests of independence. To determine whether differences existamong ethnicities, grades were analyzed using nonparametric Chi-Square (v2) tests of independence. The same procedures were usedto estimate differences among genders. To determine whether differ-ences exist among age groups, grades were analyzed using a one-wayanalysis of variance test (ANOVA).

FINDINGS

Of the 79 students who took college algebra in 8 weeks, 54 earned agrade of A, B, or C and were considered successful; 13 earned a gradeof D or F and were unsuccessful. Twelve students withdrew from the8-week college algebra courses. Withdrawals, those students who vol-untarily removed themselves from the course before the semesterended, were not included in the data analysis.

In the 16-week college algebra courses, 119 students were success-ful; 13 were unsuccessful. There were 16 withdrawals. In the 16-weekcourses, four grades of N were given. An N meant that students failedthe course due to nonparticipation in class, i.e., nonattendance afterthe institution’s official drop date, not turning in assignments, or nottaking tests. A grade of N was an effort to separate those who failedto attend and complete from those who participated and earned agrade of F. Grades of N were not included in the data analysis.

As Table 1 illustrates, the findings from the research indicated nodifference in the success=completion rates between 8-week and 16-weekcourses. The Chi-Square (v2) results were not significant, v2(1,N¼199)¼ 3.57, with a p value of .059. Several factors may have influencedwhy there was no difference in the two course lengths of time. Forexample, sample size may have been too small for the power of the stat-istical analysis; or concentrated learning time may be just as importantand equivalent to learning in longer course lengths; or the pacing of the

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content of different course lengths have the same effect, and studentsadapt to whichever course length of time in which they are enrolled.In any case, the result for these courses and students is that learningoutcomes appear to be no different based on length of course.

It is interesting to note that out of the 231 students enrolled, 75(32%) were repeating college algebra in the two course conditionsof lengths of time. Examination of these repeaters indicated thefollowing: 47 students, or 20%, had taken college algebra twice; 19students, or 8.2%, had taken college algebra three times; 4 studentsor 1.7% had taken college algebra four times; 3 students, or 1.3%,had taken college algebra five times; and 2 students, or approximately.9%, had taken college algebra six times. The study did not seek toexamine students who were repeating, but it is evident that it shouldbe determined how many of the participants completed collegealgebra for the first time in these courses and if the number of thosewho completed differed in the 8-week from the 16-week course. Thisincidental data suggests that the number and success of repeaters incollege algebra may be an issue second only to the issues of successand attrition in college algebra.

In this study, only 5.2% withdrew from the 8-week course and6.9% withdrew from the 16-week course, which results in a combinedtotal of a 12.1% drop out rate in these college algebra courses. Thisdrop rate is atypical for college algebra. What is known aboutattrition in college algebra is that it is high. Table 2 illustrates theattrition rates for all college algebra courses at the college. This result

Table 1. Successful and unsuccessful grade distributions for

8-weeks and 16-weeks

Successful A, B, C Unsuccessful D, F Total

8 weeks

Frequency 54 13 67

Percent of grand total 27.1 6.5 33.7

Percent of row total 80.6 19.4

Percent of column total 31.2 50.0

16 weeks

Frequency 119 13 132




Total 173 26 199

86.9 13.1 100.0

df¼ 1, Critical value for v2¼ 3.57, p> .05.


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suggests that, for whatever reason, these sections were not typical ofthe normal attrition rates for college algebra in community colleges.

Ethnicities were categorized by White, Non-Hispanic; African-American; Hispanic, Mexican-American; and Asian, Pacific Islander.All ethnicities were divided by course length of time, 8 weeks or 16weeks. Ethnicities were analyzed separately. There was no evidence thatWhite, Non-Hispanic; African-American; and Hispanic, Mexican-American students’ success rates differed significantly.

Table 3 contains information on the number of students classifiedas Asian, Pacific Islander in each course length of time for collegealgebra. The Chi-Square (v2) results were significant, v2 (1,N¼ 34)¼6.08, with a p value of .014. There was a difference in success rates forAsian, Pacific Islander students between the 8-week and 16-weekcollege algebra courses. The 16-week course length of time producedmore completers with 65%, while the 8-week only had 21%.

Table 2. Status of attrition for college algebra courses

Percent Successful completion In-course attrition

Fall 2006 58 29

Spring 2007 60 27

Summer I 2007 80 14

Summer II 2007 67 23

Fall 2007 56 29

Source: (Brookhaven College, 2008a, 2008b).

Table 3. Successful and unsuccessful for Asian, Pacific Islander

students in 8 weeks and 16 weeks

Successful

A, B, C

Unsuccessful

D, F Total

8 weeks

Frequency 7 4 11




16 weeks

Frequency 22 1 23




Total 29 5 34

85.3 14.7 100.0

df¼ 1, Critical value for v2¼ 6.08, p< .05.

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Reported enrollments for females in both the 8-week and the16-week courses were larger than the male enrollments: there were38 females to 29 males in the 8-week courses and 82 females and 50males in the 16-week courses. The Chi-Square (v2) results did notconfirm a significant difference in success rates for males or femalesbetween the 8-week and 16-week college algebra courses.

The age group categories tested were the following: 18–22 years,23–30 years, and 31–40þ years. There was no difference in successrates for the age groups 18–22 years and 31–40þ years. Table 4 pro-vides the ANOVA summary table for the age group 23–30 yearsbetween course length and success rates.

The percent of variance for overall success rates yielded a moder-ate 7.7% g2 effect size; the ANOVA results were statistically signifi-cant; F(1,74)¼ 6.154, with a p value of .015. There was a differencein success rates for the age group 23–30 years in 8-week and 16-weekcollege algebra courses. The 16-week course produced more comple-ters with 59%, while the 8-week course had only 25%.

The quantitative results of this study were not surprising sinceresearch on other topics involving shortened course length did notfind significant differences. However, because of limited study ofinstances of student outcomes in 8- and 16-week college algebracourses, it can be assumed that there might be differences in outcomesin the two course lengths. We had assumed that more concentratedtime on task, 8 weeks rather than 16 weeks, with the same numberof clock hours in mathematics classrooms should increase successand retention rates. This did not prove to be true when examiningthe course lengths of 8 weeks and 16 weeks.

DISCUSSION

The findings may create a quandary for community college math-ematics departments. More time on task is a tenet of learningpsychology, but in this case one would assume there is the same

Table 4. Analysis of variance summary table for the age group (23–30)

Source SS df MS F Sig. g2

Between groups 1.343 1 1.343 6.154 0.015 0.077

Within groups 15.937 73 0.218

Total 17.280 74

Note. N¼ 75; p¼ .05.


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amount of time on task. What differs is the concentration of time ontask; the learning effort is concentrated into 8 weeks instead of 16.

In general, the 8-week college algebra courses enroll a lower numberof students compared to the traditional 16-week course. Thirty-fourpercent of college algebra students were enrolled in an 8-week course;66% were enrolled in a 16-week course. Given the choice of 8 weeksversus 16 weeks, it appears that students two to one prefer the 16-weekcourse. Given that no effort was made to explain students’ motivationto enroll in the 8- or 16- week course, this needs to be examined. It isinteresting that students in the age group 23–30 years completed at ahigher rate in the 16-week course. Several factors might indicate whythis was the outcome. For example, students in this age group are morelikely to be attending school, raising children, and working part- orfull-time. Meeting four days a week can be too overwhelming, and stu-dents in this age group are not able to keep up with the demands of thecourse. The results of these data suggest that for this age group to besuccessful in college algebra, it should be taught in 16-week courses.This suggestion needs to be studied.

Why do community colleges offer 8-week courses? Eight-weekcourses are offered for various reasons: flexible schedules createaccess for more students, students have the option of taking twocollege-level mathematics courses in one semester, and studentswho fear mathematics want to finish the course quickly. Even thoughno statistical difference was found between the 8- and 16-week collegealgebra courses, no assumption is made that 8-week college algebracourses do not need to be offered. Course length of time is consideredarbitrary, because we do not know whether students actually learncollege algebra material better.

Based on these data, the course length of time appears to make nosignificant difference in grades; however, the use of course gradesmight not be the most important sole criterion when comparing8-week versus 16-week courses. Additional research needs to be donethat tests whether there are differences in the performance in math-ematics courses for which college algebra is a prerequisite. Do 8-weekstudents, for example, do as well in trigonometry as the 16-week stu-dents? This might indicate if course compression hampers retention.However, while grades and passing represent obvious outcome indi-cators for assessment of academic success of students and courses,an understanding of any differences in outcomes in eight- andsixteen-week courses should include examination of additionalindicators. For example, what is the extent of the mastery of conceptsby students in each time period, and how many students completeadvanced mathematics courses?

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This study supports the literature that there is not a studentachievement difference between 8-week and 16-week college algebracourses. And there is no research that states why this is true. Thisimplies that course length of time, 8- or 16-weeks, do not improve passrates; it is an arbitrary period of time to take a course in 16-weeks.

IMPLICATIONS FOR PRACTICE

What can mathematics departments at community colleges in theUnited States learn from this study when it comes to offeringshortened course lengths in place oftraditional course lengths? Theoutcome criterion of length of course appears not to enhancecompletion rates, but it must serve other ends valued by communitycolleges and students.

Anyone who has tried to implement a change in practice is facedwith this question: Will this new change increase student success?Since shortened course lengths have become increasingly popularfor college algebra within the last five years, shorter course lengthsare quickly being built into course selection schedules by a numberof institutions. Instead of 14 weeks, Florida’s Valencia CommunityCollege offered in spring 2008 prealgebra, beginning algebra, andmath for the liberal arts courses in a condensed 7-week format thatmet four days a week (Valencia, 2008). Since 2003, BrookhavenCollege in Dallas, Texas has offered developmental mathematics, col-lege algebra, developmental reading, and various business courses in8 weeks or other compressed lengths of time (Brookhaven College,2008a, 2008b). The purposes that short courses serve include allowingmore access, creating flexible course offerings, providing convenienceto students and faculty, and allowing students to finish courses inshorter time periods.

Since mathematics is a subject feared by many students, educatorsmust embrace this challenge and find ways to diminish this fear whileincreasing student success. Thus, an implication of the findings ofthis study is that it makes no difference which course length (8 weeksor 16 weeks) students are enrolled in to have successful completion incollege algebra. Many other questions also deserve attention: Why arethere so many repeaters in college algebra? How many repeaters inthe 8- and 16-week courses pass, fail, or fall into the ethers?Which course length of time benefits different populations of adultstudents, traditional-age students, and students with special servicesrequirements? Additional exploration of these questions throughfuture research may offer insights for community college


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practitioners. If course length makes no difference, why not offer bothlong and short and let students choose for themselves? If a 16-week jobcan be done in 8 weeks, why not do it in 8 weeks?

REFERENCES

Brookhaven College. (2008a). Office of institutional research.

Brookhaven College. (2008b). Retrieved July 1, 2008, from http://www.brookhaven

college.edu/course-schedules/

Grimes, P., & Niss, J. (1989). Concentrated study time and improved learning

efficiency: An experiment using economics U$A. The Journal of Economic Edu-

cation, 20(2), 133–138.

Johnson, D., Johnson, R., & Smith, K. (1998). Cooperative learning returns to

college: What evidence is there that it works? Change, 30, 26–35.

Shaw, P. (1997). An analysis and evaluation of policies and practices of student place-

ment into college algebra classes at paradise valley community college. Unpublished

doctoral dissertation (p. 6.), Nova Southeastern University, Fort Lauderdale-

Davie, FL.

Small, D. (2002a, May=June). An urgent call to improve traditional college algebra

programs. MAA Focus (Summary of the Conference to Improve College Algebra

held at the U.S. Military Academy, West Point, NY, February 7–10, 2002).

Retrieved June 12, 2008, from http://www.contemporarycollegealgebra.org/

national_movement/an_urgent_call.html

Small, D. (2002b). College algebra: A course in crisis. Contemporary College Algebra.

Retrieved June 12, 2008, from http://www.contemporarycollegealgebra.org/

national_movement/a_course_in_crisis.html

Texas Higher Education Coordinating Board. (2008). Closing the gaps initiative.

Retrieved March 10, 2008, from http://www.thecb.state.tx.us/ClosingtheGaps/

Valencia Community College. (2008). Retrieved on April 22, 2008, from http://

www.valenciacc.edu/students/courses.asp

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success in algebra among community college students

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