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Raising the Bar and Equity? Effects of State High School Graduation Requirements and Accountability Policies on Students' Mathematics Course Taking Author(s): Kathryn S. Schiller and Chandra Muller Source: Educational Evaluation and Policy Analysis, Vol. 25, No. 3 (Autumn, 2003), pp. 299-318 Published by: American Educational Research Association Stable URL: http://www.jstor.org/stable/3699497 Accessed: 29/09/2008 14:02 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=aera. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit organization founded in 1995 to build trusted digital archives for scholarship. We work with the scholarly community to preserve their work and the materials they rely upon, and to build a common research platform that promotes the discovery and use of these resources. For more information about JSTOR, please contact [email protected].

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EducationalEvaluationand Policy Analysis Fall 2003, Vol. 25, No. 3, pp. 299-318

Raising the Bar and Equity? Effects of State High School Graduation Requirements and Accountability Policies on Students' Mathematics Course Taking Kathryn S. Schiller State University of New York at Albany

Chandra Muller University of Texas at Austin In response to the national push to raise academic performance of all students, most states have adoptedpolicies designedto raise academicstandards,monitorprogresstowardthose standards,and hold schools and studentsresponsibleforattainingthem.Giventhe complexnatureof the educational process, thesepolicies are likely to have mixedeffects on both general levels of attainmentand stratificationbased on race or ethnicityand social class. Using nationallyrepresentativelongitudinaldata and hierarchicallinear modeling, this article explored the association betweenstudents'mathematics course work and states' high school graduation requirementsand assessment or accountability policies. Wefound thatstudentsin states withmoregraduationrequirementstendedto enroll in higher level mathematicscourses asfreshmenandpersist to takemoreadvancedlevel courses. Similartrends were also found for studentsin states that link test performanceto consequencesfor schools. Extensive testing, however,had little effect on course takingexcept to increase differencesbased on socioeconomicstatus.In contrast,differencesbetweenracial or ethnicgroups tendedto be smallerin states where testperformancewas linkedto consequencesfor students. Keywords:accountability,educationalstratification,equity,graduation requirements,mathematics achievement,opportunitiesto learn, race and ethnicity,social class, sociology of education

THE No Child Left Behind Act of 2001 brought sweeping changes in the role of the federal government in elementary and secondary schooling through, among other reforms, increased mandated testing and school accountability. The law requires states to almost immediately start administering mathematics and reading examinations based on established state curriculum standards to all students in grades 3-12. In addition to over-

all progress towardmeeting state standards,the law also calls for monitoringthe progresswithin each school of studentswho areeconomicallydisadvantaged,fromracialor ethnicminoritygroups, have disabilities, or have limited English proficiency. Schools thatfail to makestate-definedadequateprogresstowardmeetingthe statestandards will be subjectedto increasinglysevere sanctions over five years culminating with restructuring,

This researchwas supportedby a grantto the first authorfrom the AmericanEducationResearch Foundation,which receives funds for its "AERA GrantsProgram"from the National Science Foundationand the National Centerfor EducationStatistics (U.S. Departmentof Education)underNSF GrantRED-9452861. It was also supportedby fundingfrom the NationalInstituteof Child Healthand HumanDevelopmentundergrantRO1 HD40428-02 (ChandraMuller,PI) andthe NationalScience Foundation undergrantREC-0126167 (ChandraMuller,PI) to the PopulationResearchCenter,University of Texas at Austin. We thankthe reviewers for their comments and suggestions. Opinions reflect those of the authorsand do not necessarily reflect those of the grantingagencies.

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such as state takeoveror conversionto a charter school. The goal of this legislation is to not only raise academicstandardsand, thus, performance for Americanschool children,butalso to decrease gaps in achievementbetweensocially advantaged and disadvantagedgroups. The provisionsin No ChildLeftBehindwere a continuationof efforts over the past 40 years by educationalpolicymakersandpractitioners to raise standardsin mathematicsand science. These reforms have included not only raising expectations for students'masteryof these subjects,but also requiringthat all studentshave exposure to a core curriculumincorporatingthese standards. Approximately20 years ago, statepolicy makers also began implementing examination systems to hold schools accountable for students' academic progress (McDonnell, 1994). Both reform efforts-raising expectations and increasing externalaccountability-redefinewhata high school graduate should know and provide incentives for all students to acquire a minimum level of achievementin orderto earn a diploma. In response to these reforms, schools have raised graduationrequirementsand restructured their academic programs. Between 1980 and 1993, the averagenumberof creditsin core academic subjectsthat schools requiredfor earning a high school diplomaincreasedby over 1.6 years (Stevenson & Schiller, 1999). Over two thirds of this changewas in requirementsfor additional courses in mathematics and science. Another dramaticchange was the softening,if not official elimination, of formal academic tracking systems in favor of a standards-basedcore curriculum in which tracksaremore subjectspecific and based on timing of course enrollments (Lucas, 1999). During the 1980s, public high schools increased the size of their academic tracks by 14%to enroll an average of 46% of their sophomore cohortswhile vocationaltrackenrollments droppedby 12%to an average of less than 19% of theirsophomorecohorts(Stevenson& Schiller, 1999). This shiftingof studentsinto the academic track was most dramaticin states requiringtest score resultsto be widely disseminatedto policy makers,the media, and parents. Complexity of the educationalprocess, however, meansthattheseeffortsto improvestudents' educationalexperiences and academic achievement have had mixed results. High-stakes examinationsfor students,for example, have been 300

relatedto higherratesof droppingout for at-risk students but do not appear to affect levels of achievement (Jacob, 2001). Greaterschool accountabilityappearsto increasethe numberof advanced mathematicscreditshigh school students earn,but does not affect theirprobabilityof earning a diploma(Muller& Schiller,2000). In addition, these stateaccountabilitypolicies also seem to exacerbatethe attainmentgapbetweenstudents of low- and high-socioeconomic backgrounds, suggesting thatpoor studentsmay be negatively impacted by holding schools responsible for theiracademicprogress(Muller& Schiller,2000). Thus, neitherhigh-stakes examinationsfor students nor school accountability are a panacea for helping all students reach higher academic standards. Developing effective policies requiresunderstanding how proposed reforms may influence studentachievementat differentstages of the educationalprocess, with thoughtfulconsideration of potentialnegativeeffects. This studyexplores whetherstudents'mathematicscourseenrollments as freshmen and in high school overall varied as a function of states' high school graduation requirementsand assessment or accountability policies. Drawing from a nationally representative longitudinal sample of U.S. high school students in the early 1990s, we used hierarchical linear modeling (HLM) to examine variation across states in both the level of mathematics coursesstudentstendedto takeanddifferences in course enrollments related to race or ethnicity and social class. We focused on mathematics because studentsplacementsin this highly structured and sequentialsubjectcreates key turning points in their opportunitiesto learn (Schneider, Swanson, & Riegle-Crumb, 1998; Stevenson, Schiller, & Schneider, 1994). The mathematics courses studentstake in high school affect their academic achievement and their admission to competitive postsecondaryschools and preprofessional programs. Opportunities for Learning and State Policies A core goal of schooling has always been to promote students' development of skills and knowledgeimportantfor successas adultsthrough courses of study providing them with basic opportunitiesfor learning.Since the Cold Warand A Nation at Risk (National Commission on Ex-

Raising the Bar and Equity?

cellence in Education, 1983), U.S. high schools have been criticized for failing to producegraduates preparedfor the demandsof highereducation and the workforce.Of particularconcern is that U.S. high school students continually lag behind their counterpartsin other industrialized nations in mathematics and science (Stedman, 1997). The formeris consideredespecially problematic because understandingbasic mathematical principals taught in algebra and geometry are importantfor students' success in science (Schmidt et al., 2002). Graduateswho are weak in these two subjects are consideredunprepared for entry into medicine, engineering, and other technology fields. These concerns have focused policy makers'attentionon whatcoursesstudents take in high school and whetherthey masterthe materialto which those courses are supposedto expose them. In response to policymakers' mounting concernsaboutbothacademicqualityandeducational inequity,educationalreformeffortssince the mid1980s have encouraged"de-tracking"by requiring all studentsto complete a common core curriculum (Wells & Oakes, 1996). These efforts were fueled by sociological research revealing great variation in the academic experiences of adolescents, with some exposed to challenging curriculumin the college preparatorytrackwhile othersreceived only basic instructionin the general track(Gamoran,1987; Oakes, 1985). While intended to allow matching of students' talents andintereststo course content,high school track assignmentswere often based on non-academic criteriasuch as social class and ethnicity (Oakes & Guiton, 1995). Even in schools withoutformal tracking,students'opportunitiesfor learningare often constrainedby systemsof prerequisites,especially in highly structuredsubjectslike mathematics, that create sequences of opportunities for learningthat can span both grade levels and schools (Stevenson et al., 1994). Where students areplacedas freshmencreatesa positionaladvantage for gainingaccess to advancedlevel courses, which are related to greater gains in academic achievementandentryintopostsecondaryschooling (Schneideret al., 1998).Thus,curricularstructures create defacto tracking in that freshmen course enrollments determine to a great extent students'academictrajectoriesin high school. In this articlewe exploredwhetherstates' efforts to raise standardsand increaseaccountabilitywere

relatedto the level of mathematicscoursesfreshmen take and how far studentsprogressedin the subjectduringhigh school. To what extent policymakers can change students' courseenrollments,and thus achievement, is questionablebecausemanyindividualfactorsinfluencethe types andnumberof coursesthey take. Children of college educated parents are more likely to enroll in algebrain 8th grade, allowing themto move on to geometryas high schoolfreshmen, comparedto theirclassmateswhose parents only attendedhigh school (Stevensonet al., 1994; Useem, 1991). Childrenof moreeducatedparents not only receive a head startin the high school mathematicscurriculum,but also tend to persist in takingcoursesincludingexposureto advanced algebraandcalculus.While this situationappears to be changing, girls and minoritystudentshave in advanced been traditionallyunder-represented level mathematicscourses(Oakes, 1985). One of the centralconcernsof ouranalyseswas to determine whetherstatepolicies were relatedto differences basedon social class andethnicityin freshman mathematicscourse enrollmentsas well as accumulationof advancedcoursecreditsin these subjects. During the early 1980s, regulatory changes focusedon raisingacademicstandardsby increasing the numberof credits requiredin academic subjectscomparedto earlierdiplomaholders,in effect alteringthe definitionof a high school graduate (Chaney, Burgdorf, & Atash, 1997; Clune & White, 1992; Stevenson & Schiller, 1999). The logic behind such changes was that requiring students to take more courses in core academic subjects increases their opportunities for learningkey skills and resultsin higherlevels of academicachievement.Basic assumptionsbehind thesepolicies werethatmanyhigh school students are motivatedto take only the minimumnumber of requiredcourses, that the additionalcourses they take will be academicallyrigorous,and that they areable to do the workrequiredto pass these courses. Research finds at least partial support for arguments linking high school graduation requirementsto increased mathematics course taking and academic achievement of students, especially for those who are marginal in their motivation and skills (Chaneyet al., 1997;Clune & White, 1992). This studywas designedto compare differences in mathematicstrajectoriesof similarly able students in states with differing course requirementsfor high school graduation. 301

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Although increased graduationrequirements appearedto raiseenrollmentin academiccourses, many policy makersquestionedwhethercourse titlesaccuratelyreflecttheircontentorthatstudents may be given passing grades without learning the material(McDonnell, 1994). These concerns fueled efforts since the late 1980s to establish performance standards and increase external monitoring of students' progress toward those standards.Initially,mandatingexternalexaminations was a mostly "persuasive"reformstrategy intendedto provideinformationindicatingwhich studentsneed remediation,to establishcommon academicgoals for studentsand teachers,and to promotecommunitygrassrootsmovements supportingacademicexcellence (McDonnell, 1994). The assumption underlying these policies was that regular monitoring of students' academic progresswould improvetheirpreparationfor advanced level work and increase the demandfor rigorous course offerings. Critics of these policies, however, raise concerns that standardized testing creates self-fulling prophecies that limit the opportunitiesfor learning of academically and socially disadvantaged students (Wells & Oakes, 1996). In our studywe examinedwhether more extensive testing of high school studentsin academicsubjectswas associatedwith enrollment in higher level mathematicscourses throughout high school for all students. Many states also have establishedformal systems of rewardsand sanctions linked to performance on mandatedexaminations that are designed to hold studentsand schools accountable for attainingat least minimalacademicstandards. Althoughcontroversial,initial reformefforts established high stakes examinations linking test performanceto consequencesfor individualstudents such as trackplacement,gradepromotion, and high school graduation(Heubert& Hauser, 1999). Critics expressed concern that such policies structurallylimit socially and academically disadvantagedstudents' access to opportunities for learningby allocatingthem to remedial courses and encouraging them to dropout of school (Catterall, 1989; Jacob, 2001). Some research, however, suggests thatmotivatedlowachievingstudentsmay benefitfroman increased emphasison academic achievementand support from teachers(Muller, 1998; Roderick& Engel, 2001; Schiller & Muller, 2000). Because these examinationsareusuallyheldearlyin high school, 302

the policy is more likely to impact the courses taken by freshmen and sophomores to prepare for the tests and might potentially discourage studentsfromtakingmoreadvancedlevel courses asjuniorsandseniors.We exploredin theseanalyses whetherstates'high stakesaccountabilitypolicies affected students'tendencies to enroll in or avoid higher level mathematicscourses at two key points in theirhigh school careers. Statepolicies promotinginstitutionalaccountability by linking tangible consequences for schools to aggregatemeasuresof studentperformance startedbecoming common in the 1990s. Ratherthan directly regulatinginstructionalactivities, these state policies set academic excellence as the goal while giving schoolsthe freedom to determinethe best way to help their students reach the state standards(Elmore, Abelman, & Fuhrman,1996). One way schools might choose to raise student performanceis to increase the numbers enrolled in courses that preparethem forhigherlevel workin key academicsubjectslike mathematics.However, some schools might also marginalizepoor-performing,particularlyminority andpoor, studentsto avoid accountabilityfor their expected failure on the state assessments (Schiller & Muller,2000). We exploredwhether greaterschool accountabilitywas relatedto equity in opportunitiesto learnmathematicsacross social classes or racialand ethnic groups. The decentralizednatureof the nation'sschool systemsmeansthatstatesvarygreatlyin the strategies andpoliciestheyhaveadoptedata giventime. Although most states raised academic course requirementsfor a high school diploma during the 1980s, by 1990 only threestateshad adopted the NationalCommissionon Excellence in Education's recommendationthat all students take at least threeyearsof mathematics(Chaneyet al., 1997). In 1993, states on average required 2.4 years of mathematics (Stevenson & Schiller, 1999). By this time, most states had also implemented some sort of mandatedtesting program, although how often and in how many subjects studentswere tested as well as the consequences for test performancevaried greatly across states (Schiller & Muller,2000). In the analysesfor this articlewe examinedthe impact of greatercourse requirementsfor high school graduation,more frequentmandatedtesting, andimplementationof sanctionsandrewards for either studentsor schools linked to test per-

RaisingtheBarandEquity? formanceon high school students'course taking in mathematics.Using longitudinaldata from a nationally representativecohort of 8th graders, we focused on two key stages of students' academic careers: (a) where they entered the high school mathematicscurriculumand (b) how far they progressedthroughthe curriculum.We used HLM to test the extent to which these policies aimedat raisinglevels of attainmentandincreasing equity were related to differences based on social class andrace or ethnicityin opportunities for learning mathematicsin high school. Controllingfor otheraspectsof students'social backgroundsand middle school mathematicsclasses and grades, we also examined how the relationshipbetweenfreshmanmathematicscourseplacements and students' persistence in the subject varied among states with different policies. Data and Method Thesample The analyses in this articlerequiredthe use of two data sets, one to provide longitudinalinformationon students'social backgroundsand academic experiences,andthe otherto provideinformation on states' assessmentand accountability policies. Both of the studies we used were conductedin the early 1990s. The National Education Longitudinal Study of 1988-92 (NELS:88-92) followed a nationally representativesampleof 8th gradersin 1988 through their high school careers and beyond (Ingles,Scott,Lindmark,Frankel,& Myers,1992). The panel used for these analyses consisted of 10,046 public school students who participated in the firstthree waves of data collection (1988, 1990, and 1992) and for whom high school transcriptswere collected. All 50 states and the Districtof Columbiaarerepresentedin NELS:88-92, with an average of 196 students and 22 high schools per state.1Forthese analyses,the sample was weighted to take into account the complex sample design and nonresponserates so that the results would be representativeof those for the 1988 8th-gradecohort. Informationon states'assessmentandaccountability policies was obtained from the National LongitudinalStudyof Schools (NLSS). One purpose of NLSS was to examine the impactof state policies on changes in school practices (Levine & Stevenson, 1997; Stevenson& Schiller, 1999). In 1993, state departmentsof education were

asked throughthe National CooperativeEducation Statistics System to answer a lengthy questionnaire concerning their testing and accountability policies. Responses were received from all 50 states and the Districtof Columbia. Mathematicscourse enrollments The measuresof students'mathematicscourse taking were constructedfrom the NELS:88-92 course-leveltranscriptfile, whichincludesindicators of the topic and when it was takenfor every course a studenttook duringhigh school. Based on the standardsequencesof mathematicscourses most studentstake, courses were classified into one of the following groups,in hierarchicalorder: (0) no math,(1) remedialmath,(2) generalmath, (3) pre-algebra, (4) Algebra I, (5) geometry, (6) AlgebraII,(7) advancedmath,(8) pre-calculus, (9) calculus (Schiller & Hunt, 2001). The first analysis in this articlepredictedthe highest level mathematicscourse studentstook as freshmen, indicating where they entered the high school mathematicscurriculum.The secondanalysispredicted the number of Carnegie units earned in higherlevel mathematicscourses (geometryand above), which arecommonlyrequiredfor admission to a competitive college or postsecondary academic program.Due to a highly structured sequence of prerequisites,how many Carnegie units students accumulated in advanced level mathematicscourses is a good indicatorof how far they progressed toward calculus. Because where studentsstartedin the sequencewas likely to affecthow fartheyprogressed,freshmancourse placement was also used as a predictor of the second dependent variable. Student-levelvariables This studyfocused on differencesacrossstates not only in students' freshman mathematics courses andnumberof advancedcredits,but also in the variationin these outcomes related to socioeconomic statusandrace or ethnicity.In these analyses,family socioeconomicstatus(SES) was a measure of students' financial and social resourcesfrom outsidethe school based on a composite of parents'education,income, andoccupation createdby NCES. Using HLM,we evaluated whetherthe relationshipbetween SES andmathematics course taking varied across states with differinggraduationrequirementsor assessment policies. 303

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Insteadof the usual four-groupclassification of students'race or ethnicity, our HLM models only included indicators for African American and Latino/a with the comparison group being white or Asian American.We chose not to distinguishbetweenwhiteandAsianAmericanstudents becauseof thelattergroup'ssmallsamplesize and sparsedistributionin many statesthatresultedin unreliableHLMcoefficients.Ourresultsconcerning the effects of raceor ethnicityon mathematics coursetakingandtheirvariationacrossstateswere not significantlyaffectedby this decision. To controlfor otherindividualcharacteristics that might have influenced mathematicscourse enrollments, we included other indicators of students'backgroundcharacteristics(genderand family structure)and prior academic achievement (middle school mathematics grades and 8th-grademathematicscourse enrollments).We used grades,ratherthantest scores, because they measurehow well studentsmet the expectations of their middle school teachers in their classes and are frequentlyused by high schools to place studentsin freshmancourses.2We also included indicatorsfor whetherstudentsattendedan urban or ruralpublic high school, with suburbanas the contrastcategory.For a descriptionof these variables, see AppendixA. Statepolicy measures Our approachto analyzingthe effects of state policies was to develop indicatorsof strategies, or policy levers,thatstatesadoptedto raiseexpectations and increase accountabilityfor students' academic progress. Efforts to characterizestate policies have rangedfrom broadgeneralcharacterizationsof the policy environment(Lee, 1998) to analyses of specific policies such as requiring studentsto pass an examinationto graduate(Catterall, 1989; Jacob, 2001).3 Analyses using the former are difficult to interpretbecause distinctions in the purposesof variouspolicies are lost. The latteroften fail to find significanteffects of policies unless the analyses focus on the subpopulations most likely subject to the policies. Our goal was to develop "mid-level"indicators of statepolicies thatreflectthe variousstrategies statesused to raise expectationsand accountability as well as the extent to which a type of policy lever was employed. The measures used in our analyses were based on statepolicies reportedin 1993, the yearduringwhich most NELS students graduatedfrom high school. 304

In this studywe includedan indicatorof states' academic course requirementsfor high school graduation,the oldest strategy for raising academic standardsby requiring students to take more courses. In the NLSS questionnaire,states were asked to report the number of Carnegie units in various subjects that students were requiredto completeto be eligible for a high school diploma. The variableused in this analysis was the total numberof credits requiredin the four core academicsubjectsof English, social studies, mathematicsand science. (See AppendixB for a full descriptionof the statevariables.)Only three states (Colorado,Massachusetts,andWyoming) reportedsetting no course requirementsfor high school graduation,while the remainingstatesrequiredan averageof 9.96 creditsin these subjects to earna diploma. Our measure of the extensiveness of states' testing programsin 1993 was based on their reportsof the gradelevels andmajoracademicsubjects in which mandatedtests were administered to studentsduringhigh school. Only seven states reported no mandated testing of high school studentsin the major subjects of English, social studies/history,mathematics, and science. The remainingstatesgave on averagefourteststo high school students,althoughtwo states (Minnesota andVirginia)reportedtesting studentsin all four subjectseveryyear.The extensivenessof a state's testing programis an indicatorof whetherexternal examinations were used on a regular basis to monitorstudents'progressthroughthe established curriculum,usually with the intention of raising overall levels of achievement. Although most states tested high school students, they varied in the extent to which performance on those tests carriedmeaningfulconsequences for studentsor schools. Ourmeasureof consequences for studentsbased on test performance was the sum of states' reportsof whether test scoreswererecommendedor requiredforpurposes such as placementin remedialor advanced placementprograms,promotionto the next grade, or awardof a high school diploma. Almost two thirdsof the states had guidelines or mandatory policies specifyinghow test scoresshouldbe used to determinesome aspect of students' academic program or success. Those states with such policies linked test scores to an average of three or four consequences for students. Fewer states linked students'performanceon mandatedtests

Raising the Bar and Equity?

to rewardsandsanctionsfor schools in 1993. The survey asked abouteight types of consequences, such as financialrewardsfor meeting standards or sanctionslike loss of accreditationfor failure to do so. Over two thirds of the states reported thatthey eitherdid not set performancestandards or did not provide incentives for meeting those standards.The remainingthirdof the stateslinked aggregatetest scoresto an averageof threeor four consequencesfor schools. In preliminaryanalyses, the four measuresof states' policies appearedto reflectdistinctstrategies for increasingstandardsand accountability. The four measures of state policies were only moderately related to each other with correlations all less than .36. The strongestcorrelation reflected that the number of consequences for schools and for students linked to test performance was relatedto stateshaving a testing program.However, the extensiveness of testing and how results were used to determinesanctionsor rewardstendedto be unrelated. Analysis technique The questionsof whetherstatetestingpolicies were relatedto students'mathematicscourses in high school requireda multilevel analytic strategy. We were concernednot only with variation in students' mathematics course taking across states with differingpolicies (directeffects), but also with whether the associations of students' outcomes with their social backgroundsvaried across states (interaction effects). A common techniquefor analyzinghierarchicaldata(in this case, students nested within states) and crosslevel effects is HLM, which allows simultaneous considerationof factors from two levels of analysis (Bryk & Raudenbush, 1992; Raudenbush & Bryk, 1986).4 The same student and state policy variables were used for analyses of students' freshman mathematicscourse level and the numberof advancedmathematicscreditsearned,except freshman course level was also used to predict the lateroutcome.The student-levelmodel is shown in Equation1, where ij was the value for a given studentin a given stateandBkjwas the coefficient for students'SES, race and ethnicity,or the control variablesin each state. The effects for some of the student-levelfactors, such as race or ethnicity, were expressedby severalcoefficients,for example B2j for Latino/a and B3j for African-

American.The termeijwas a measureof the random error,which included unmeasuredsources of variationin a particularstudent'soutcome. In our analyses, all the student-levelvariableswere centered aroundtheir grandmeans for the sample, which allowed the intercept(Boj)to be interpretedas the meanoutcomefor each stateadjusted for the characteristics of students in that state (Bryk, Raudenbush,& Congdon, 1996; Willms & Raudenbush,1989). Y, = P,j + By (SESi,) + B2j-3j(Race/Ethnicityij) + B4j-0j (Controls) + ei

(1)

Preliminaryanalysesindicatedthat,in oursample, the associations between the student-level controlvariablesandmathematicscourseseither did not vary significantly across states or those variationswere not related to state testing policies. Either situation meant that assuming the associations were constant across states did not substantiallyaffect the results for SES and race or ethnicity. Thus, for the analyses presented here,the coefficientsfor the student-levelcontrol variables were set to be "fixed effects" and our statistical model assumed that the relationships between these studentcharacteristicsandmathematics course enrollmentswere the same for all states (Bryk & Raudenbush,1992). The state-levelanalyses,in essence, examined the extent to which variationin the coefficients for the intercept,SES, andrace or ethnicitywere related to states' graduationand accountability policies. Equation 2 shows the general model used for estimatingthe effects of these statepolicies.5 Each of the policy variableswas centered aroundits grandmean, which meantthatYk0was the averageeffect of variablek across states and the other coefficients were adjustmentsto those coefficients, or interactioneffects, for states that differed in their testing policies. The effect of a student-level variable was increased when the coefficient for a state policy variablewas in the same direction (plus or minus) as the intercept for the student-levelvariableand reducedwhen the two coefficients were in the opposite direction. The termukjwas the errorterm for estimation of the student-levelcoefficientfor each state. Bkj = YkO + Ykl-k4(State

Policiesj) +ukj

(2) 305

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The combined HLM model is shown in Equation 3. Yi = [Too+ Yoi-o4(State Policiesj)+

oj]

+[710 + Y1-04(State Policiesj)+ +[2-30

+

22-34(State Policiesj)

lj]*SESi +U23j]

* Race/Ethnicityij +

4-100* Control Variablesi

+eij

(3)

Results States vary in their approachesto raisinghigh school students' academic attainmentand promoting equalityof opportunitiesfor learning,but the extentto whichthesepolicies impactstudents' educationalcareersis uncertain.The purposeof our study was to examine variationacross states adoptingdifferentstrategiesfor raisingstandards and establishingaccountabilityin two criticalaspectsof students'mathematicscourseenrollments: wherethey startedas freshmen,andthe amountof advanced-levelcourseworkcompletedby graduation. The goal was to determinewhetherthese statepolicies were relatedto students'mathematics course placementsas freshmenand theirpersistence in advancedmathematicsas well as differencesbased on SES and race or ethnicity. Freshman Mathematics Course Placements

Theresultsfor students'freshmanmathematics courseenrollmentsare shownin Table 1. The top panel of the table containsthe coefficientsfor the interceptand independentvariablesmodeled on the statelevel. The firstcolumn shows the Level2 intercept,or averageeffect, for the student-level variables of interest. The other four columns show the coefficients for state policy variables. The lower panel containsthe coefficients for the student-levelcontrols,which were assumedto be constantacross states. All of the student-levelcontrolvariablesexcept urbanicitywere significantpredictorsof students' mathematicscourseplacementsas freshmen.Students tendedto enroll in a higher level course if they were female, lived with bothnaturalparents, had highermathematicsgradesin middle school, and enrolledin Algebraas an 8th grader.6Eighth graderswho took remedial mathematicstended to be placed in lower level courses as freshmen, 306

even takinginto accounttheirsocial backgrounds andmiddleschool mathematicsgrades.Freshman courseenrollmentsappearedto have been similar acrossurban,suburban,andrurallocations. The first row of Table 1 indicates that states' graduationand accountabilitypolicies were related to differences in where freshmenenter the high school mathematics sequence. On average, freshmen tended to enroll in pre-algebra (coded as 3). In states requiringmore academic coursecreditsfor graduation,freshmentendedto take slightly higher level mathematicscourses. Although statisticallysignificant,this effect was small at less than 7% of a course level per standarddeviation change in the numberof courses required(.077 = .024 * 3.203). This difference, however, was only slightly smaller than those relatedto genderor family structure.Extensiveness of testing was also significantly related to freshman course enrollments, with students in states with more extensive testing tendingto enroll in slightlylower level freshmanmathematics courses (-.059 = -.017 * 3.461). Neither of the state accountabilitypolicy variableswere significantly relatedto freshmancourse enrollments. Extensivetestingwas also significantlyrelated to a somewhat strongereffect of socioeconomic status on freshmanmathematicscourse level. A standarddeviationincreasein the numberof tests was relatedto almosta 20%increasein the effect of SES [.197 = (.018 * 3.461)/.314]. These results indicatethe gaps between poor andrich students were larger in states that test high school students more frequently and in more subjects. The strongereffect of SES in states with more extensive testing was consistentwith analysesof otheracademicoutcomes such as earninga high school diploma(Muller& Schiller, 2000). Our results identified no overall differences based on race or ethnicity after controlling for prioracademicperformanceand SES. However, statepolicieswererelatedto significantdifferences in freshman mathematics course enrollments between African American and white students. The tendency for African American studentsto enroll in somewhat lower level courses comparedto similarwhites was strongerin statesrequiring more academic courses for graduation or linking test performanceto consequences for students. The latter policy strategy more than doubled the effect of being African American for each additionalconsequence.Conversely,the

TABLE 1 Effectsof State Policies on the Level of FreshmanMathematicsCourses State Policy Student-levelVariable

Average Effect

Intercept Socioeconomic status

3.507*** .314***

Race/ethnicity Latino/a AfricanAmerican

-.030 -.074

Student-levelControl Male Living with both parents Middle school mathgrades 8th-grademathclass Remedial Algebra/advanced Urbanicity Urban Rural * =p < .05, ** =p