double jeopardy: testing the effects of …debdavis.pbworks.com/w/file/fetch/101333737/bahr 2007...

DOUBLE JEOPARDY: TESTING THE EFFECTSOF MULTIPLE BASIC SKILL DEFICIENCIES ONSUCCESSFUL REMEDIATION

Peter Riley Bahr*

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Prior research has established that the depth and breadth of remedial need in basic skills(math and English) exhibited by a student at college entry are strongly and negativelyassociated with the likelihood of achieving college-level competency in those subjects(i.e., successful remediation). This well-documented finding is built upon a body of workemploying either simple bivariate analyses or regression analyses that assume additiveeffects. Yet, there are reasons to suspect that multiple basic skill deficiencies, rather thanexhibiting additive effects alone, may exhibit a negative multiplicative interaction effect onthe likelihood of successful remediation. In this research, I test the hypothesis that thenegative effect of math deficiency increases in magnitude with decreasing Englishcompetency. Although the data support this hypothesis, I find that this interaction does nothave substantive importance in the face of the powerful direct effect of math deficiency onthe likelihood of successful remediation in math.

................................................................................................................................................................................................KEY WORDS: remediation; remedial education; developmental education; basic skills;mathematics; English; community college.

INTRODUCTION

Postsecondary remediation is an issue of considerable controversy oneducational policy agendas, and a subject of increasing focus amongresearchers. One of the topics of greatest interest to researchers is thepredictors of successful remediation, for which there is growing evi-dence that depth and breadth of remedial need play a dominant rolein determining whether a given student will remediate successfully. Toelaborate, although postsecondary remediation ostensibly is intendedto reduce disparities between disadvantaged and advantaged groups,instead it exhibits the ‘‘Matthew Effect’’: those who have the greatest

*Address correspondence to: Peter Riley Bahr, Department of Sociology, Wayne State

University, Detroit, MI 48202, USA. E-mail: [email protected]

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0361-0365/07/0900-0695/0 � 2007 Springer Science+Business Media, LLC

Research in Higher Education, Vol. 48, No. 6, September 2007 (� 2007)DOI: 10.1007/s11162-006-9047-y

need for remediation are the least likely to remediate successfully,while those who require the least remediation are the most likely toremediate successfully.Prior research on the effects of depth and breadth of remedial need

on the likelihood of successful remediation has been built upon anassumption of additive effects. In particular, the methods employed inprior analyses have introduced the assumption that the negative effecton the likelihood of successful remediation of degree of remedial need invarious subject areas accumulates across the subjects in which a givenstudents requires remedial assistance. However, there is reason tobelieve that additive effects may not represent accurately the conse-quences of multiple basic skill deficiencies for the likelihood of success-ful remediation. Instead, multiple skill deficiencies may exhibit anegative multiplicative interaction effect. More specifically, someresearch suggests that poor English skills, especially poor reading skills,hamper the acquisition of other basic skills, such as mathematics. Thus,one would expect that the negative effect of degree of math skilldeficiency on the likelihood of successful remediation in math wouldincrease in magnitude with decreasing English competency.In this research, I use nested logistic regression models to test whether

accounting for the multiplicative interaction of math deficiency andEnglish competency improves the accuracy of prediction of successfulmathematics remediation (defined here as a passing grade in a college-level math course) over models that assume simple additive effects ofmath deficiency and English competency. To accomplish this test, I usedata addressing a population of 55,530 remedial math students enrolledin 107 community colleges, the academic progress of whom I monitorfor a period of 6 years. I find that the magnitude of the negative effectof degree of math deficiency on the likelihood of successful mathematicsremediation increases as students’ English competency declines. How-ever, upon closer examination, I find that this interaction effect does nothave substantive importance in the face of the overwhelmingly powerfuldirect effect of degree of math deficiency on the likelihood of successfulremediation in math.

BACKGROUND

Postsecondary remediation is a subject of increasing interest amongpolicy makers and researchers (e.g., Bahr, n.d.a, n.d.b; Bettinger andLong, 2005; Burley, Butner and Cejda, 2001; Crews and Aragon, 2004;Deil-Amen and Rosenbaum, 2002; Greene, 2000; Grubb and Gardner,2001; Illich, Hagan and McCallister, 2004; Jenkins and Boswell, 2002;

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Mazzeo, 2002; McCabe, 2003; Merisotis and Phipps, 2000; Oudenhoven,2002; Perin, 2004; Waycaster, 2001; Worley, 2003). There are sound rea-sons for this growing interest, as the sheer scale of remedial need inpostsecondary institutions is daunting. To illustrate, Parsad, Lewis, andGreene (2003) found that nearly three in ten (28%) first-time collegefreshmen enrolled in remedial coursework (reading, writing, and/ormath) during the Fall term of 2000. Adelman (2004a), employing a lar-ger window of observation, found that four in ten (41%) college stu-dents enroll in remedial coursework at some point during postsecondaryattendance. The expense, too, is daunting: estimates place the nationaldirect cost of public postsecondary remedial programs at one to two bil-lion dollars annually, and the total direct and indirect public and privatecosts at nearly seventeen billion dollars annually (Breneman and Haar-low, 1998; Greene, 2000; Phipps, 1998; Saxon and Boylan, 2001).In discussing the topic of postsecondary remediation, mathematics

skills are of particular interest, in part because more students requireremedial assistance with mathematics than with any other subject area.For example, in the Fall term of 2000, 22% of first-time college studentsenrolled in remedial math coursework, compared with 14% who enrolledin remedial writing courses and 11% who enrolled in remedial readingcourses (Parsad, Lewis and Greene, 2003). Adelman (2004b), employing alarger window of observation and somewhat different measures, foundthat 34% of ‘‘nonincidental’’ students earn credits in remedial math, while18% earn credits in remedial writing. Comparable data on earned creditsin remedial reading were not provided, but overall 11% of students enrollin remedial reading at some point during attendance (Adelman, 2004a).Thus, mathematics holds an undisputed position as the category ofpostsecondary remediation serving the greatest number of students.More troubling even than the scale of need for remediation in math is

the low rate of successful remediation among remedial math students.While few comprehensive, large-scale, long-term evaluations of remedialprograms have been undertaken (Grubb and Gardner, 2001; Koski andLevin, 1998; Phipps, 1998; Roueche and Roueche, 1999), one recentlarge-scale study found that only 25% of students in communitycolleges who begin the remedial math sequence successfully complete acollege-level math course (Bahr, n.d.a). In other words, three out offour underprepared students who start down the path toward college-le-vel math never arrive at that destination. Given that community collegesare the primary venue in which remediation is accomplished (Adelman,2004b; Day and McCabe, 1997; Parsad, Lewis and Greene, 2003), thislow rate of successful remediation in math is disconcerting and demandsgreater empirical attention.

MATH DEFICIENCY, ENGLISH COMPETENCY, AND REMEDIAL OUTCOMES 697

Among the primary predictors of successful mathematics remediationare depth and breadth of remedial need. Depth of remedial need refersto the degree of deficiency in a given subject area, while breadth ofremedial need refers to the number of basic skill areas in which a givenstudent requires remedial assistance. Both depth and breadth of reme-dial need have been found to be negatively correlated with the likeli-hood of successful remediation (Bahr, n.d.a).The phrase ‘‘Matthew Effect,’’ coined by Merton (1968), has been

extended to describe this finding among remedial students (Bahr, n.d.a),just as it has been used to describe similar stratification processes inother aspects of the U.S. educational system (Kerckhoff and Glennie,1999). ‘‘Matthew Effect’’ refers to the well-known biblical passage, ‘‘toeveryone who has, more shall be given, and he will have an abundance;but from the one who does not have, even what he does have shall betaken away’’ (New American Standard Bible, Matthew 25:29). As itrelates to remediation, the phrase highlights the fact that, althoughintended to reduce disparities between advantaged and disadvantagedgroups, in the end those who need remediation the most are the leastlikely to remediate successfully, while those who require the least reme-diation are the most likely to remediate successfully.The magnitudes of the gaps in successful remediation across degrees

of remedial need are quite large, even after controlling for a host ofother predictors. For example, among first-time students in communitycolleges, Bahr (n.d.a) found that the odds of remediating successfully inmath (successfully completing a college-level math course) for Interme-diate Algebra and Geometry students (the highest level of remedialmath skill) are more than twice the odds for Beginning Algebra studentsand more than three times the odds for Pre-Algebra and Basic Arithme-tic students. He further notes that this problem is exacerbated by defi-cient English skills: remedial math students who are prepared forcollege-level English coursework have odds of successful remediation inmath that are one-fourth greater than the odds for remedial writing stu-dents and one-third greater than the odds for remedial reading students.Although the definitions of ‘‘successful remediation’’ vary somewhat

across studies, other researchers have found similar relationshipsbetween depth/breadth of remedial need and successful remediation.Weissman, Silk, and Bulakowski (1997) found that 69% of degree-seek-ing students who need remedial assistance only with math, and 66% ofthose who need remedial assistance only with writing, successfully reme-diate within 2 years. However, just 53% of those who need both mathand writing assistance remediate successfully, while only 33% of thosewho need assistance with math, writing, and reading do so. Similarly,

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McCabe (2000) found that only 20% of community college studentswho require assistance in all three basic skill subject areas remediatesuccessfully, compared with an overall success rate of 43% among reme-dial students. Likewise, Easterling, Patten, and Krile (1998) found that15% of students who require ‘‘extensive’’ remediation complete a col-lege-level math course successfully, compared with 24% of students whorequire ‘‘moderate’’ remediation and 34% who require ‘‘minimal’’ reme-diation. Thus, we find in the literature a growing body of evidence doc-umenting the negative effects of depth and breadth of remedial need onthe likelihood of successful remediation.A number of explanations for these findings have been suggested.

Some have argued that the stigma of placement in low ability groupsnegatively influences students’ perceptions of themselves and the subjectmatter, and, thereby, academic outcomes (Hadden, 2000; Maxwell,1997). One might extrapolate from this argument that the lower is astudent’s placement in the remedial hierarchy, the greater is the stigmaattached to that placement (e.g., placement in Basic Arithmetic is morestigmatizing than placement in Intermediate Algebra), and, conse-quently, the lower is the likelihood that the student will remediate suc-cessfully. However, this explanation is disputed by Deil-Amen andRosenbaum (2002), who found a shift toward ‘‘stigma-free’’ remediationin community colleges that tends to hide from underprepared studentstheir remedial status. Alternatively, McCusker (1999) suggests thatremedial students become discouraged at the prospect of taking numer-ous courses that do not result in credit towards a degree and/or length-en the time required to achieve personal educational objectives, which isa problem that worsens the further down the remedial ladder onebegins.However, these explanations, and the methods of analysis employed

in prior work on the topic, imply a simple accumulation of disadvan-tage (i.e., additive relationships) with increasing depth and breadth ofremedial need. While the evidence supports this somewhat one-dimen-sional interpretation, there is reason to believe that the relationshipsbetween math deficiencies and English deficiencies are more complexthan they appear initially. In particular, these explanations fail to takeinto account the potential interplay between deficiencies in multiple skillareas and, more specifically, the role that English skills play in mathskill acquisition.Considered in a larger context, English skills are not simply one of

several areas of potential remedial need. Rather, reading and writingskills represent two of the fundamental tools necessary to resolve otherskill deficiencies (Perin, Keselman and Monopoli, 2003; Stanovich,


1986). Adelman addresses this problem in his discussion of the effect ofreading deficiencies on the likelihood of degree attainment. He arguesthat the need for remedial assistance in reading is a sign of ‘‘comprehen-sive literacy problems’’ (1996, p. 56), and that ‘‘[i]f you can’t read, youcan’t read the math problem either...’’ (1998, p. 11). In other words,resolving innumeracy requires literacy.Given that instruction in mathematics is structured in such a way that

it includes the assumption of strong English skills, poor English skillsrepresent an impedance (like a weight on the shoulders) working againstmath skill acquisition at each step of the remedial math ladder. Thosewho face longer distances to travel up the mathematics ladder also facethe weight of this impedance longer. Thus, while the literature indicatesthat the mathematical distance a remedial student must travel is nega-tively correlated with the likelihood of reaching the goal of college-levelmath, it is reasonable to hypothesize further that this correlation willgrow in magnitude with decreasing English skills.

HYPOTHESIS

In this study, I test for a substantively important multiplicative inter-action effect of degree of math deficiency and degree of English compe-tency on the likelihood of successful remediation in math, independentof the direct effects of degree of math deficiency, English competency,and a comprehensive set of controls. I hypothesize that the negativeeffect of degree of math deficiency on the likelihood of successful math-ematics remediation varies systematically as a function of English com-petency. More specifically, I hypothesize that the magnitude of thenegative effect of math deficiency on the likelihood of successful remedi-ation in math increases as English skills decline.

DATA AND MEASURES

Data

My analysis draws upon data collected by the Chancellor’s Office ofCalifornia Community Colleges. The Chancellor’s Office, under man-date from the California Legislature, collects data each term via elec-tronic submission from the 112 community colleges and affiliated adulteducation centers in California. The data maintained by the Chancel-lor’s Office represent a census of community college students in Califor-nia and include transcripts, demographics, financial aid awards,matriculation records, and a variety of other information.

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I selected for this analysis the Fall 1995 cohort of first-time collegefreshmen enrolled in any of California’s 107 semester-based communitycolleges (N = 202,484). Valid course enrollment records were availablefor 93.9% (N = 190,177) of these students. I observed the courseenrollments of these students across all semester-system colleges (with-out regard to a given student’s first institution of attendance) for6 years, through the Spring term of 2001, and then eliminated all stu-dents who did not enroll in any math coursework or whose first mathcourse was not remedial in nature. The resulting remedial math cohort(N = 69,921) represents all of California’s community college freshmenwho first enrolled in a semester-based community college, whose firstterm of college attendance was the Fall term of 1995, whose first mathenrollment was remedial in nature, and who enrolled in this first mathcourse prior to the Summer term of 2001. Of these 69,921 students, Idropped 1,177 students (1.7%) who have missing data on sex, age, orthe ID variable used to track student records across colleges. Of theremaining 68,744 students, I dropped 5,953 students (8.7%) whose firstEnglish enrollment was an English-as-a-Second-Language (ESL) courseand 7,261 students (10.6%) who did not enroll in any English course-work during the 6-year window of observation. The resulting analyticalcohort is composed of 55,530 remedial math students who also enrolledin at least one non-ESL English course during the 6-year period ofobservation.Note that I do not include ESL students in the category of remedial

English because ESL students face substantively different challenges inskill acquisition compared with students requiring remedial writing orreading assistance. As Kurzet (1997, p. 60) explains, ‘‘the assumptionthat the ESL students are illiterate or marginally literate adult educationstudents...fails to recognize that the prior education of ESL studentsranges from primary schooling through university and professionalschool.’’ This distinction is consistent with the bulk of the literatureaddressing postsecondary remediation (Boylan and Saxon, 1999a).

Remedial Mathematics

Remedial math courses are structured to provide a ‘‘ladder’’ ofcoursework leading up to the minimum expected math competency ofentering college freshmen. For the purpose of this analysis, I use thecommonly accepted definition of remedial math as any nonvocationalmath course presenting material below college algebra (e.g., Adelman,2004b; Hagedorn, Siadat, Fogel, Nora and Pascarella, 1999). To catego-rize math courses, I used course catalogs and course characteristics in


the data to determine the skill-level of each math course in which anymember of the cohort enrolled at any point during the 6-year observa-tion period. Through a painstakingly detailed process, I collapsed 2,750substantive math course listings into five categories: basic arithmetic,pre-algebra, beginning algebra, intermediate algebra/geometry, and col-lege-level math. Basic arithmetic represents the lowest level of mathskill, followed in order by pre-algebra, beginning algebra, and interme-diate algebra and geometry (the latter two are parallel courses in theinstitutionalized mathematics progression). The category of college-levelmath encompasses all math courses of a skill equal to, or greater than,college algebra (e.g., college algebra, pre-calculus, calculus, trigonome-try, finite mathematics, statistics). I ignored nonsubstantive math cour-ses (e.g., math ‘‘labs,’’ math tutoring) and vocational math courses (e.g.,basic mathematics for medical applications) when the vocational mathcourse was not part of a larger remedial mathematics sequence or other-wise categorized as college-level math. Note that, while the remedialmath courses are conceptually sequential, the degree of institutionalizedenforcement of prerequisites varies across the 107 colleges included inthis analysis.

Outcome Variable

I consider one central outcome with respect to remedial math: theattainment of college-level math skill, operationalized as the successfulcompletion of a college-level math course within 6 years of initial col-lege enrollment. This outcome, which is one of several possible opera-tionalizations of successful remediation, is among the most widelyaccepted because, as Boylan and Saxon (1999b, p. 6) argue,

[t]he most essential purpose of remedial courses is to prepare students to besuccessful in the college curriculum. If students who are underprepared for successin community college courses can be properly prepared for these courses, thenremediation should be considered successful. The extent to which those who com-plete remedial courses are able to pass college-level courses in the same or relatedsubjects, therefore, should be a key measure of the impact of remediation.

For the purpose of this analysis, a successful math course enrollmentis one resulting in a grade of A, B, C, D, or Credit. Grades of F, NoCredit, or Withdrawal are treated as unsuccessful. Math enrollments forwhich final grades could not be determined (e.g., Missing, Report De-layed, or In Progress with no further notation) were dropped from theanalysis, but math enrollments resulting in grades of In Progress wereincluded when grades on the partial work completed for the courses arenoted in the data.

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Explanatory Variables

The primary explanatory variables of interest here address two facetsof basic skills preparation: degree of math deficiency and degree ofEnglish competency. Ideally, degree of mathematics deficiency would beoperationalized using placement exams given at the commencement ofcollege attendance. Unfortunately, matriculation processes at the 107colleges included in this analysis are quite varied, and the only consis-tent means of categorizing students in terms of math deficiency is theskill-level of a given student’s first math course. Therefore, degree ofmathematics deficiency (an ordinal variable) is set to the skill-level of astudent’s first math course and is treated as a set of dichotomous(dummy) variables, with intermediate algebra/geometry as the excludedcategory.Like math deficiency, English competency is set to the skill-level of a

student’s first English course. However, compared with the mathsequence, the English sequence exhibits much greater inter-school vari-ability and, as a consequence, requires a simpler classification scheme.In total, I collapsed 6,625 substantive English course listings into fourcategories: remedial reading (including courses in basic reading, phonics,vocabulary, and spelling), remedial writing (including courses in basicwriting, grammar, sentence structure, and punctuation), English-as-a-Second-Language (ESL), and college-level English. As noted earlier, Iremoved from the analytical sample all students whose first Englishcourse was ESL in nature and all students who did not enroll in anyEnglish coursework. The result is an ordinal measure of baseline Eng-lish competency that includes three possible values (in order from lowestskill to highest): remedial reading, remedial writing, and college-levelEnglish. English competency is treated here as a set of dichotomous(dummy) variables, with college-level English as the excluded category.Finally, in addition to the measures of baseline mathematics defi-

ciency and baseline English competency, I generated a set of interactionterms of degree of mathematics deficiency and degree of English compe-tency. Each of these is the multiplicative product of a category of mathdeficiency and a category of English competency, excluding intermediatealgebra and geometry on the math deficiency variable and college-levelEnglish on the English competency variable.

Control Variables

I include a substantial number of control variables found in priorresearch to be predictors of academic outcomes among postsecondary


remedial students (e.g., Bahr, n.d.a, n.d.b; Burley, Butner and Cejda,2001; Hagedorn et al., 1999; Hoyt, 1999). Among the control variablesincluded here are sex, race/ethnicity, age, three proxies of socioeconomicstatus (SES), four measures of enrollment patterns, student’s academicgoal, grade in first math class, grade in first English class, referral toacademic advising, and receipt of academic advising. Details concerningthe particular operationalizations of each of these variables follow. Fre-quency distributions for each of these variables, as well as mathematicsdeficiency, English competency, and the outcome variable (successfulversus unsuccessful remediation in math), are provided in Table 1.Sex is treated as a dichotomous variable (female = 1; male = 0).

Race/ethnicity includes nine nominal categories (White, Black, Hispanic,Asian, Pacific Islander, Filipino, Native American, Other, and unre-ported) and is treated as a set of dummy variables, with ‘‘White’’ as theexcluded category. Age is measured in years, was collected at the timeof application for postsecondary attendance, and is treated as a continu-ous variable.While the data do not contain direct measures of SES, which would be

desirable, variables measuring receipt of financial aid can serve as indi-rect measures of SES (Koski and Levin, 1998). Three variables that serveas proxies of SES are included in this analysis. The first is a dichotomousvariable indicating receipt of a fee waiver during the first year of atten-dance (received fee waiver = 1; did not receive fee waiver = 0). Thesecond is a dichotomous variable indicating receipt of any grants duringthe first year of attendance (received one or more grants = 1; did notreceive any grants = 0). The third is a continuous variable indicating thetotal monetary value of any grants received during the first year of atten-dance. Students who did not receive any grants during the first year ofattendance are assigned a value of zero on this latter variable.The four variables that measure differing aspects of enrollment pat-

terns include persistence, a nonlinear persistence term (the square rootof persistence), enrollment inconsistency, and delay of first math courseenrollment (i.e., ‘‘math procrastination’’). Persistence is operationalizedas the number of terms (including summer terms, but excluding winterintersessions) in which a given student enrolled in courses from Fall1995 through Spring 2001. Enrollment inconsistency is operationalizedas the percentage of terms in which a given student did not enroll incourses from Fall 1995 through the last term that the student wasobserved in the system. Delay of first math is operationalized as theterm number (sequentially ordered) of first math enrollment, with theFall term of 1995 assigned a value of one and the Spring term of 2001assigned a value of seventeen. All three variables addressing aspects of

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TABLE 1. Frequency Distributions of the Variables Addressed in this Study

Variable Values N %

Remediation in math Successful 15,545 27.99

Unsuccessful 39,985 72.01

Baseline math deficiency Intermediate algebra

or geometry

12,804 23.06

Beginning algebra 21,774 39.21

Pre-algebra 9,090 16.37

Basic arithmetic 11,862 21.36

Baseline English competency College-level 17,700 31.87

Remedial writing 32,894 59.24

Remedial reading 4,936 8.89

Persistence (terms enrolled) 1–2 6,318 11.38

3–5 13,718 24.70

6–8 15,363 27.67

9–11 12,514 22.54

12–14 6,402 11.53

15–17 1,215 2.19

Enrollment inconsistency (%) <20.1 18,859 33.96

20.1–40.0 19,602 35.30

40.1–60.0 11,123 20.03

60.1–80.0 5,092 9.17

>80.0 854 1.54

Term of first math Fall 95–Spri 96 40,027 72.08

Summ 96–Spri 97 8,124 14.63

Summ 97–Spri 98 3,354 6.04

Summ 98–Spri 99 1,923 3.46

Summ 99–Spri 00 1,189 2.14

Summ 00–Spri 01 913 1.64

Academic goal Transfer 12,231 22.03

Transfer + AS/AA 24,834 44.72

AS/AA 3,459 6.23

Vocational degree 1,464 2.64

Vocational certificate 838 1.51

Other job-related 3,887 7.00

Abstract 2,453 4.42

Remediation 859 1.55

Undecided 5,074 9.14

Not reported 431 0.78

First math grade A 7,065 12.72

B 8,691 15.65

C 9,601 17.29

D 4,426 7.97


TABLE 1. (Continued )

Variable Values N %

F 6,923 12.47

Withdrawal 14,104 25.47

Credit 2,945 5.30

No credit 1,593 2.87

Ungraded 182 0.33

First English grade A 6,445 11.61

B 11,237 20.24

C 9,620 17.32

D 3,387 6.10

F 4,029 7.26

Withdrawal 10,088 18.17

Credit 6,712 12.09

No credit 2,481 4.47

Ungraded 252 0.45

Undetermined 1,279 2.30

Advising Referred for

advising

50,084 90.19

Not referred for

advising

5,446 9.81

Received advising 42,200 75.99

Did not receive

advising

13,330 24.01

Sex Male 24,442 44.02

Female 31,088 55.98

Race White 24,211 43.60

Black 5,634 10.15

Hispanic 17,520 31.55

Asian 3,287 5.92

Pacific Islander 437 0.79

Filipino 2,438 4.39

Native American 590 1.06

Other 637 1.15

Missing 776 1.40

Age Less than 18 5,229 9.42

18–20 40,957 73.76

21–25 4,060 7.31

26–30 1,973 3.55

31–35 1,380 2.49

36–40 919 1.65

41–50 850 1.53

50+ 162 0.29

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enrollment patterns and the nonlinear persistence term are treated ascontinuous variables.Academic goal is a self-reported measure of a student’s primary aca-

demic objective collected at the time of application, which I collapsedinto ten nominal categories:

1. Transfer to a 4-year institution as an exclusive objective,2. Transfer to a 4-year institution with an allied objective of a nonvo-

cational Associate’s degree,3. Associate’s degree (nonvocational) as an exclusive objective,4. Vocational Associate’s degree as an exclusive objective,5. Vocational certificate as an exclusive objective,6. Other job-related goals (e.g., acquiring or advancing job skills,

maintenance of a professional license),7. Abstract educational goals (e.g., discovering educational interests,

personal development),8. Remediation in fundamental academic subjects (including students

seeking credit for a high school diploma or a general educationdiploma),

9. Undecided, and10. Unreported.

Academic goal is treated as a set of dummy variables. The goal of‘‘transfer to a 4-year institution as an exclusive objective’’ is the ex-cluded category.

TABLE 1. (Continued )

Variable Values N %

Fee waiver Received fee waiver 19,537 35.18

Did not receive fee

waiver

35,993 64.82

Grant Received grant(s) 12,710 22.89

Did not receive

grant(s)

42,820 77.11

Total dollar value

of grants received

<$501 826 6.50

$501–$1000 1,633 12.85

$1001–$1500 2,322 18.27

$1501–$2000 1,852 14.57

$2001–$2500 3,355 26.40

$2501–$3000 1,193 9.39

>$3000 1,529 12.03


Grade in first math course includes nine nominal categories: A, B, C, D,F, Withdrawal, Credit, No Credit, and Ungraded. Grade in first Englishcourse includes ten nominal categories: A, B, C, D, F, Withdrawal, Cred-it, No Credit, Ungraded, and undetermined (e.g., ‘‘in progress’’ with nofurther notation). Both are treated as a set of dummy variables, with ‘‘A’’as the excluded category.Lastly, interaction with academic advising services is measured using

two dichotomous indicators of a given student’s experience of being re-ferred to, and/or receiving, academic advising at any time during the 6-year observation period. For both dichotomous variables, the positivecondition (i.e., referred; received) is assigned a value of one, while thenegative condition is assigned a value of zero.

Strengths and Weaknesses of the Data

The data I assembled for this study have a number of strengths andweaknesses. Among the strengths are access to a population (ratherthan a sample), the large size of the population (N = 55,530), thelength of time over which academic careers are observed (6 years), thecapacity to distinguish between temporary breaks in enrollment andlong-term exit from the postsecondary system, and the capacity toobserve course enrollments despite student movement across colleges.However, six weaknesses of the data also must be noted.First, the definition of a remedial math student excludes two groups of

students of interest in questions concerning remediation. It excludes stu-dents who are unprepared for college-level math coursework, yet who donot enroll in such courses. In addition, it excludes students who are mis-placed in college-level math coursework, who subsequently fail these cour-ses, and who then either do not enroll in any other math or enroll inremedial math coursework. However, these expressions of selection biasare of less serious concern than they might first appear. It would be rea-sonable to assume that students who are misplaced in college-level mathcoursework are disproportionately those who have the highest remedialskills, while students who do not enroll in remedial math courseworkdespite poor math skills likely are those who have the lowest skills.Assuming that these errors are otherwise random (i.e., not correlated withother variables), the loss of students at each end of the continuum wouldtend to reduce observed average differences in remedial outcomes acrossdegrees of math deficiency by excluding students who have the highestand lowest math skills, leading to the attenuation of estimated effects.A second weakness of the data is the use of course enrollments as

measures of baseline math and English skill. This is an unavoidable

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consequence of the absence of high school transcripts in the data andvariation in methods of skill assessment across the colleges. However,the use of course enrollments in this manner is not without precedent inresearch on remediation (e.g., Adelman, 1996, 1998, 2004a).Third, in terms of measuring successful remediation (defined here as the

successful completion of a college-level math course), the data do not ac-count for academic progress accomplished outside of California�s semes-ter-system community colleges. More specifically, students who enter oneof the 107 semester-based community colleges, enroll in a remedial mathcourse, and subsequently transfer to one of the five quarter-system com-munity colleges, to a private 2-year college, or to a community collegeoutside of California, effectively are treated as unsuccessful with respect toremediation in math because academic progress occurring outside of thesemester-system colleges is unobserved. Although unobserved remedialprogress accomplished at other institutions is expected to represent only asmall fraction of the total progress, due consideration must be given to thepossible impact of this flaw in the data on the findings presented here. Inparticular, to the extent that basic skills competency and financial re-sources covary positively, competency may be associated with access toother postsecondary alternatives, which would tend to reduce the ob-served rates of attainment at higher levels of basic skills competency.Fourth, because the observation period is truncated at 6 years, some

students may enroll in their first math course so late that completingsuccessfully a college-level math course within the observation period iseffectively impossible. However, such a condition characterizes only asmall percentage of the students in this analytical cohort. Specifically,96.44% of the students included in this analytical cohort enrolled intheir first math course within the first four years following commence-ment of attendance in the Fall semester of 1995, allowing more thansufficient time to remediate successfully regardless of a given student�sinitial level of math skill deficiency. Furthermore, I tested the effect ofexcluding from the analytical cohort all students who enrolled in theirfirst math course later than 4 years following commencement of atten-dance (N = 1,976), and found that excluding these students had noappreciable impact on the analyses presented in this research.Fifth, the data do not address two control variables found to be

important in prior studies of educational outcomes, namely employmentintensity and credit course load (e.g., part-time versus full-time enroll-ment). Employment intensity (e.g., hours worked per week) has beenfound to be moderately negatively correlated with degree expectations,persistence, and other desirable academic outcomes (American Councilon Education, 2003; Carter, 1999; Hoyt, 1999; Toutkoushian and Smart,


2001), although this finding is not entirely consistent across studies(Titus, 2004). The findings concerning the effects of course load on aca-demic success are clearer and generally indicate that part-time studentsare somewhat less likely to experience desirable academic outcomes thanare full-time students (Hoyt, 1999; O’Toole, Stratton and Wetzel, 2003;Szafran, 2001). While a variable measuring course load could be con-structed from the transcript data, it would face many of the same funda-mental problems and complications described by Adelman (2004a, p. 96).The sixth weakness of the data concerns the generalizability of find-

ings. While the use of a population has substantial advantages over theuse of a sample, the population addressed in this study includes onlystudents in California’s semester-system community colleges. AlthoughCalifornia’s community college system, which has annual enrollment of2.9 million students (Turnage, 2003), is the largest postsecondary educa-tional system in the world, and while remediation in California’s systemis much like remediation in the systems of other states in that placementprocedures and exit standards vary from college to college (Boylan, Saxonand Boylan, 1999; Grubb and Gardner, 2001; Hadden, 2000; James,Morrow and Perry, 2002; Jenkins and Boswell, 2002; Koski and Levin,1998; Kozeracki, 2002; Oudenhoven, 2002; Shults, 2000), the generaliz-ability of any findings of this analysis to other states is uncertain.

METHOD

I use nested logistic regression models (Long, 1997) to test the hypothe-sis that the negative relationship between degree of math deficiency andthe likelihood of successful remediation in math increases in magnitude asEnglish competency declines. Stated another way, I test whether account-ing for the interaction of math deficiency and English competency im-proves the accuracy of prediction of college-level math skill attainment, ascompared with a model that does not account for this interaction. How-ever, given that the data address an entire population (rather than a sam-ple of a population), I do not present standard errors or p-values for theregression coefficients because tests of statistical significance lack meaningwhen applied to population data (Berk, Western and Weiss, 1995). In-stead, I use the Bayesian Information Criterion (BIC) and McFadden’sR2 to compare the goodness of fit of the nested models (Long, 1997).

ANALYSES

Bivariate Analyses

I present in Table 2 a cross-tabulation of the unadjusted probabilityof remediating successfully in mathematics (the mean of the outcome

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variable) by baseline math deficiency and baseline English competency,and I illustrate these findings in Fig. 1. The findings presented inTable 2 indicate a sharp decline in the probability of remediating

TABLE 2. Cross-tabulation of the Unadjusted Probability of Remediating Success-

fully in Math, by Baseline Math Deficiency and Baseline English Competency

Baseline math

deficiency

Baseline English competency

College

English

Remedial

writing

Remedial

reading Total

Interm. alg. & geom. 0.571 0.501 0.438 0.535

(6,763) (5,514) (527) (12,804)

Beginning algebra 0.350 0.265 0.219 0.291

(7,553) (12,757) (1,464) (21,774)

Pre-algebra 0.218 0.141 0.109 0.154

(1,980) (6,061) (1,049) (9,090)

Basic arithmetic 0.135 0.078 0.046 0.080

(1,404) (8,562) (1,896) (11,862)

Total 0.403 0.233 0.152 0.280

(17,700) (32,894) (4,936) (55,530)

NOTE: cell sizes are provided in parentheses.

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Interm. Algebra & Geom. Beginning Algebra Pre-Algebra Basic Arithmetic

Baseline Math Deficiency

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ath College English

Remedial Writing

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FIG. 1 Unadjusted probability of successful remediation in math, by baseline mathdeficiency and baseline English competency (from Table 2).


successfully with increasing mathematics deficiency, and this relationshipholds for all levels of English competency. Additionally, at all levels ofmathematics deficiency, the probability of remediating successfully inmath declines with decreasing English competency. These findings con-firm prior analyses, which indicate that the likelihood of remediatingsuccessfully declines both as a function of increasing mathematics defi-ciency and decreasing English competency (e.g., Bahr, n.d.a; Easterling,Patten and Krile, 1998; McCabe, 2000; Weissman, Silk and Bulakowski,1997).

Regression Analyses

In Table 3, I present the results of two nested logistic regressions of thedichotomous indicator of successful mathematics remediation on selectedvariables. In Model 1, I regress the outcome variable on a set of dichoto-mous variables representing degree of mathematics deficiency, a set ofdichotomous variables representing degree of English competency, and acomprehensive set of controls (not shown) including: race, age, sex, threeproxies of SES (receipt of a fee waiver, receipt of a grant, and the dollarvalue of any grants received), persistence, a nonlinear persistence term,enrollment inconsistency, delay of first math enrollment, academic goal,first math grade, first English grade, referral to academic advising, andreceipt of academic advising. As it relates to the effects of math deficiencyand English competency, Model 1 estimates average effects of theseveral categories of English competency across the levels of mathematicsdeficiency, and average effects of the several categories of mathematicsdeficiency across the levels of English competency, net of controls.In Model 2, I add to the independent variables included in Model

1 a set of dummy variables representing the multiplicative interactioneffect of math deficiency and English competency. In contrast to thefirst model, Model 2 estimates effects of each level of English compe-tency that are specific to each category of mathematics deficiencyand effects of each level of mathematics deficiency that are specificto each category of English competency, net of controls. The com-bined net effects of math deficiency and English competency, as esti-mated in Model 1 and Model 2, are presented as odds ratios inTable 4.The results of the regression presented as Model 1 indicate a sharp

decline in the likelihood of remediating successfully in math withincreasing mathematics deficiency. Model 1 predicts that the odds ofremediating successfully in mathematics for Beginning Algebra studentsare 30% of those for Intermediate Algebra and Geometry students,

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holding constant English competency and all of the control variables.Said another way, Intermediate Algebra and Geometry students are238% more likely to remediate in math than are Beginning Algebra stu-dents, net of other variables. The odds for Pre-Algebra and Basic Arith-metic students are 11% and 7% of those for Intermediate Algebra andGeometry students, respectively. In other words, Intermediate Algebraand Geometry students are 792% and 1293% more likely to remediatesuccessfully in math than are Pre-Algebra and Basic Arithmetic stu-dents, respectively. Thus, a very strong relationship is observed betweendegree of mathematics deficiency and college-level math skill attainment.

TABLE 3. Logistic Regression Coefficients for the Direct and Multiplicative Inter-

action Effects of Baseline Math Deficiency and English Competency on Successful

Remediation in Math, Net of Controls (not shown)

Model 1 Model 2

Direct effects of

math skill deficiency

Interm. alg. & geom. Comparison Comparison

Beginning algebra )1.218 )1.200Pre-algebra )2.188 )2.105Basic arithmetic )2.634 )2.464

Direct effects of

English competency

College English Comparison Comparison

Remedial writing )0.349 )0.306Remedial reading )0.599 )0.465

Interaction effects

for remedial writing

Beginning algebra )0.035Pre-algebra )0.129Basic arithmetic )0.198

Interaction effects

for remedial reading

Beginning algebra )0.105Pre-algebra )0.187Basic arithmetic )0.453

Intercept )9.625 )9.623

Model summary Log likelihood )19551 )19547BIC )566988 )566930McFadden’s R2 0.406 0.406

N 55530 55530

NOTES: 1. The control variables included in the two models are as follows: race, age, sex, three

proxies of SES (receipt of a fee waiver, receipt of one or more grants, and the dollar value of any

grants received), persistence, a nonlinear persistence term, enrollment inconsistency, delay of

first math enrollment, academic goal, first math grade, first English grade, referral to academic

advising, and receipt of academic advising.

2. Tests of statistical significance (standard errors and p-values) are not provided because they

lack meaning when applied to data for an entire population.


Low English competency further decreases the likelihood of successfulremediation in math. Holding constant math deficiency and all controls,students who need remedial writing assistance have odds of remediatingsuccessfully that are 71% of those for college-level English students.Likewise, students who need remedial reading assistance have odds that55% of those for college-level English students. Said another way,college-level English students are 42% and 82% more likely to remedi-ate successfully in math than are remedial writing and remedial readingstudents, respectively. Thus, English competency has a much smallerrelationship to college-level math skill attainment than does math defi-ciency, although the relationship between English competency and col-lege-level math skill attainment is still strong.Following the addition of the interaction terms in Model 2, small

reductions are noted in the direct effects of both degree of mathematicsdeficiency and degree of English competency. However, these changes inthe direct effects are balanced by the interaction terms, which indicatethat the magnitude of the negative effect of math deficiency on success-ful remediation in math increases with decreasing English competency.

TABLE 4. Net Odds Ratios of Successful Remediation in Math and Predicted

Probabilities of Successful Remediation in Math, by Baseline Math Deficiency and

English Competency (Calculated Based on the Regression Models in Table 3)

Baseline math

deficiency

Baseline English

competency

Net odds ratios

Predicted

probabilities

Model 1 Model 2 Model 1 Model 2

Interm. alg. & geom. College English 1.000 1.000 0.327 0.322

Remedial writing 0.706 0.736 0.256 0.259

Remedial reading 0.549 0.628 0.211 0.230

Beginning algebra College English 0.296 0.301 0.126 0.125



Pre-algebra College English 0.112 0.122 0.052 0.055



Basic arithmetic College English 0.072 0.085 0.034 0.039



NOTE: Predicted probabilities were obtained by setting all independent variables except math

deficiency and English competency to their respective modes (in the case of categorical vari-

ables) or means (in the case of continuous variables) and varying systematically math deficiency

and English competency.

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When the individual coefficients are combined and transformed intoodds ratios (Table 4), the net result of accounting for the interaction ofmath deficiency and English competency is a narrowing of the gaps insuccessful remediation between college-level English, remedial writing,and remedial reading students at the two highest levels of math skill,and a widening of the gaps at the two lowest levels of math skill. Forexample, the odds of remediating successfully in math for IntermediateAlgebra/Geometry students who need remedial writing assistance in-crease from 71% to 74% of the odds for college-level English studentsat the same math skill level. Likewise, the odds for Intermediate Alge-bra/Geometry students who need remedial reading assistance increasefrom 55% to 63% of the odds for college-level English students. Con-versely, while the relative odds of remediating successfully for BasicArithmetic students who are prepared for college-level English increasefrom 7% to 9%, the odds remain stable for remedial writing students atthe same level of math skill and decrease for remedial reading studentsfrom 4% to 3%. Thus, the regression models presented in Table 3 doappear to support the hypothesis that English skill deficiencies exacer-bate the effect of math skill deficiencies on the likelihood of successfulremediation in math. In other words, the analyses support the conclu-sion of a negative interaction effect of mathematics deficiency and Eng-lish competency on the likelihood of successful remediation in math.However, an examination of the BIC values for Model 1 and Model 2

suggests the opposite conclusion. The difference between the two BICvalues indicates very strong support for Model 1, which means that theaddition of the interaction terms in Model 2 does not increase signifi-cantly the fit of the equation relative to Model 1 (Long, 1997). Addi-tional evidence for this conclusion can be found in the R2 values, whichdo not vary across the two models, leading to a conclusion favoring thesimpler model (Model 1).

Predicted Probabilities

To explore this seeming discrepancy, I calculated predicted probabili-ties of successful mathematics remediation based upon the estimatedcoefficients for each model. These calculations were accomplished bysetting all of the control variables to their respective means (in the caseof continuous variables) or modes (in the case of categorical variables),and then systematically varying math deficiency and English compe-tency. Thus, the predictions are based on what one might call the ‘‘typi-cal’’ or ‘‘average’’ student in the remedial math cohort. The results ofthese calculations are presented in Table 4 (third and fourth columns)


and represented graphically in Figs. 2 and 3. Additionally, in Figs. 4and 5, I illustrate the predicted disadvantage, or gap, in the probabilityof successful remediation in math between college-level English andremedial writing students, and between college-level English and reme-dial reading students, respectively.The predicted probabilities confirm the interpretation of the coeffi-

cients presented earlier. Specifically, the gaps in the predicted probabil-ity of successful remediation in math across the several levels of Englishskill narrow at the two highest levels of math skill and widen at the twolowest levels of math skill, once the interaction of math deficiency andEnglish competency is taken into account. These changes are mostevident between college-level English students and remedial readingstudents, as illustrated in Fig. 5. However, the changes in the predictedprobabilities between Model 1 and Model 2 are quite small and, at firstglance at Figs. 2 and 3, almost indiscernible. Thus, the predicted proba-bilities confirm the conclusions drawn from the model summary statis-tics that the interaction terms do not add substantively to the fit orpredictive value of the model.

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h College English

Remedial Writing

Remedial Reading

FIG. 2 Predicted probability of successful remediation in math, by baseline mathdeficiency and baseline English competency, before accounting for the interaction

of math deficiency and English competency (from Model 1, Table 4).

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DISCUSSION

The findings of this analysis with respect to my hypothesis are mixed.As hypothesized, the data indicate that the negative effect of mathemat-ics deficiency on the likelihood of successful remediation in mathincreases in magnitude with decreasing English competency. The poorerare a student’s English skills, the greater is the negative impact of mathskill deficiency on the likelihood of remediating successfully in mathe-matics. Thus, a need for remedial English assistance compounds theproblem of math skill acquisition as math skills decline, and more sowith decreasing English skills. This effect of poor English skills multi-plies the already overwhelmingly low chances of successful remediationin math for students who have the worst math skills, placing studentswho face the combination of very poor math skills and serious Englishdeficiencies at a severe risk of not remediating successfully in math.However, contrary to my hypothesis, accounting for the interaction of

math deficiency and English competency does not contribute signifi-cantly to the fit or predictive value of the model. Considered globally,this appears to be a consequence of the overwhelmingly powerful directeffect of math skill deficiency and the overall low probability of success-ful remediation in math. To illustrate, the estimates presented in Model

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FIG. 3 Predicted probability of successful remediation in math, by baseline mathdeficiency and baseline English competency, after accounting for the interaction of

math deficiency and English competency (from Model 2, Table 4).


1 indicate that the ratio of the odds of remediating successfully (versusnot) for college-level English students relative to remedial readingstudents is 1.82 at all levels of math skill. The estimates presented inModel 2 indicate that the ratio of the odds of remediating successfully(versus not) for college-level English students relative to remedial read-ing students is 1.59, 1.77, 1.92, and 2.51 for intermediate algebra/geome-try, beginning algebra, pre-algebra, and basic arithmetic, respectively.At the upper and lower ends of the math skill continuum, these differ-ences in the odds between Model 1 and Model 2 are of respectable mag-nitude and consistent with my hypothesis. Just as predicted, the literacygap in the acquisition of college-level math skill narrows at the high endof remedial math skill, and widens at the low end of remedial mathskill, once the interaction effect is taken into account.However, the probability of remediating successfully for basic arith-

metic students is so low at all levels of English competency thataccounting for the interaction effect increases only slightly the absolutemagnitude of the predicted gap between high and low levels of Englishskill. For example, accounting for the interaction increases the gap in

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FIG. 4 Predicted disadvantage in the probability of successful remediation in mathfor remedial writing students versus college-level English students, before accountingfor the interaction of math deficiency and English competency (Model 1) and after

accounting for this interaction (Model 2).

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the predicted probability of remediating successfully between college-level English students enrolled in Basic Arithmetic and remedial readingstudents enrolled in Basic Arithmetic by only 0.01, relative to the modelthat does not account for the interaction. In fact, the predicted proba-bilities for the interaction model (Model 2) converge below 0.04 for stu-dents whose first math course is Basic Arithmetic at all levels of Englishcompetency. In other words, a ‘‘typical’’ student who has very poormath skills is exceedingly unlikely to acquire college-level math skillsregardless of the student’s English competency. The predicted probabil-ity of successful remediation in math for students who have the nextlowest level of remedial math skill (Pre-Algebra) is only slightly morefavorable. A ‘‘typical’’ student whose first math course is Pre-Algebra,and who is prepared for college-level English, has just a 5.5% chance ofremediating successfully, while a similar student who needs remedialreading assistance has only a 2.9% chance (estimated using the coeffi-cients presented in Model 2).Thus, what is most striking about these findings is not the interaction

between math skill deficiency and English competency, but, rather, it is

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FIG. 5 Predicted disadvantage in the probability of successful remediation in mathfor remedial reading students versus college-level English students, before accountingfor the interaction of math deficiency and English competency (Model 1) and after

accounting for this interaction (Model 2).


the terribly low probability of successful remediation in math forstudents who have the poorest math skills. Said another way, the mostimportant effect identified in this analysis is not the interaction of mathdeficiency and English competency. Instead, the most important effect isthe direct effect of math deficiency on the likelihood of successful reme-diation in math. Quite literally, the odds are stacked against studentswho have the poorest math skills. Even students who have the advan-tage of adequate English skills are very unlikely to overcome severemath deficiencies. Moreover, students who have poor English skills havealmost no chance of attaining college-level math skill if they entercollege with math skills that are at the lower end of the remedial mathhierarchy.

IMPLICATIONS

Several important implications for policy and future research can bedrawn from this work. First, the findings presented here somewhat con-tradict implications that might be drawn from Adelman’s work onremediation. In his work on credential attainment among postsecondaryremedial students, Adelman describes remedial reading (the lowest levelof non-ESL English competency) as ‘‘the most serious remedial prob-lem’’ (Adelman, 2004a, p. 87). Although Adelman’s work did notaddress successful remediation as an outcome, one mistakenly mightconclude from this statement that poor English skills are the core prob-lem to be remedied in all matters related to remediation. In fact, that isnot the case. While English competency does play a role in math skillacquisition, it is by no means a dominant one. As far as the acquisitionof college-level math skills is concerned, degree of deficiency in mathclearly is a far more important predictor than is English competency,although this is, to some extent, common sense because the outcomeexamined here is mathematics skill achievement. Whether this effect ofmath skill deficiency is due to stigma (Hadden, 2000; Maxwell, 1997),discouragement (McCusker, 1999), or some other cause remains to bedetermined, but it is clear that few of the students who need the mostremedial math assistance ever achieve college-level math skill.Second, my findings indicate that the problem of extremely poor

math skills is disturbingly pervasive. In the analytical cohort addressedhere, more than one-fifth (21.4%) of remedial math students exhibitedthe worst math skills at college entry (Basic Arithmetic), while morethan one-third (37.7%) were represented in the two lowest levels ofmath skill (Basic Arithmetic and Pre-Algebra). When all levels of Englishcompetency are included (i.e., college-level, remedial writing, remedial

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reading, ESL, and no English coursework), students whose first mathcourse is Basic Arithmetic or Pre-Algebra constitute fully 40.4% of theremedial math cohort. When all levels of math skill are incorporated(including college-level math students and students who do not enroll inmath), students in the two lowest levels of remedial math constitute14.9% of all first-time college freshmen.The prospects of advancing to college-level math for these students

are dismal. In the analytical cohort addressed in this analysis, only onein nine students (11.2%) in the two lowest levels of math completed suc-cessfully a college-level math course within 6 years, compared with morethan half (53.5%) of students in the highest level of remedial math(Intermediate Algebra/Geometry). When all levels of English compe-tency are included, less than one in ten students (9.6%) in the two low-est levels of math skill remediated successfully within 6 years. Given thelimited academic prospects for students who lack fundamental mathskills (Bahr, n.d.b), it is critically important that we identify points ofintervention by which to increase the rate of successful remediation inmath among students who have the poorest math skills.One additional finding is worthy of further discussion. The models

presented here account for a wide range of controls, including race, age,sex, three proxies of socioeconomic status, persistence, a nonlinear per-sistence term, enrollment inconsistency, delay of first math enrollment,academic goal, first math grade, first English grade, referral to academicadvising, and receipt of academic advising. It is somewhat surprising tofind that the effect of math skill deficiency is so strong despite controlsfor other variables. For example, one might assume that students whohave severe math deficiencies fail to remediate successfully because theybecome discouraged and drop out of college. If that were the case,controlling for persistence and enrollment inconsistency would reducesubstantially, or even eliminate, the direct effect of math skill deficiency.However, the direct effect of math skill deficiency remains potent despitecontrols for an array of other variables. So, poorly skilled students donot appear to be simply dropping out of college. Although poorly skil-led students generally are not attaining college-level math skill, they doappear to be ‘‘sticking around’’ in the community college system.A supposition one might make concerning this finding is that reme-

dial math students who have the worst skills are among the most likelyto switch to academic goals that ultimately do not require college-levelmath competency (e.g., vocational degrees or certificates). In support ofthis argument, evidence of goal switching among community collegestudents has been presented in prior research (e.g., Dougherty, 1987;Pascarella, Wolniak and Pierson, 2003; Voorhees and Zhou, 2000).


However, Bahr (n.d.b) found that the most likely academic outcome, byfar, among remedial math students who do not remediate successfully isneither the completion of a community college credential (includingvocational certificates and vocational degrees) nor transfer to a 4-yearuniversity. Thus, while unsuccessful remedial math students appear tobe persisting in the postsecondary environment, there is little conclusiveevidence that they are switching to alternative, institutionally recognizedacademic trajectories. Further research is needed to determine whypoorly skilled remedial math students are remediating at such low ratesand, as a related matter, what alternative academic trajectories unsuc-cessful remedial math students are selecting.

CONCLUSION

In this study, I tested the effect of the interaction of math skill defi-ciency and English competency on the likelihood of successful remedia-tion in mathematics (college-level math skill attainment). I found thatthe decline in the likelihood of successful remediation in math associ-ated with increasing mathematics deficiency increases in magnitude(worsens) as English competency declines. However, the overall proba-bility of successful remediation in math is so low, and the effect of mathskill deficiency on the likelihood of successful remediation in math is solarge, that this interaction of math deficiency and English competencyproves to be comparatively unimportant and ultimately lacks predictivevalue. As a student’s math skills at college entry decline, the effect ofEnglish competency on the relationship between math deficiency andmath skill acquisition decreases substantially in importance.

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Received January 16, 2006.


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