Toward Reforming Non-Credit-BearingRemedial Mathematics Courses in Four-YearUniversitiesBy Gregory V. Larnell

EXECUTIVE SUMMARYOver the past several decades,there has been a considerableincrease in enrollments in non-credit-bearing remedial (NCBR)mathematics courses in both two-and four-year colleges anduniversities. These coursesrepresent an important experiencefor many students entering college—proponents view these coursesas critical for helping studentswho are unprepared for collegemathematics courses make asuccessful transition from highschool to higher education. Thesecourses also serve two centralhigher-education policyobjectives: mission differentiationand institutional access forstudents from underrepresentedracial groups. However, recentscholarship indicates that Black-and Latina/o-identified studentsare continually overrepresented inNCBR mathematics courses.Moreover, such research revealsthat these courses have negative

effects on students’ mathematicslearning experiences andthreatening psychosocial impactson students. NCBR courses,particularly in four-yearuniversities, accordingly should beimproved in two primary ways: (1)The curriculum of NCBRmathematics courses should bealigned with contemporarypractices in mathematicseducation at large, and (2) Highereducation institutions should takethe shift to “developmental”courses seriously and coordinateinstitutional support services(compensatory education) withNCBR mathematics courses.

education.uic.edu/ruepi

ABOUT THE AUTHOR

Gregory V. Larnell isan AssistantProfessor in theCurriculum andInstructiondepartment in theCollege of Education

at the University of Illinois atChicago.

policyBRIEFUIC Research on Urban Education Policy Initiative

June 2013

Vol. 2, Book 2

2 UIC Research on Urban Education Policy Initiative

INTRODUCTIONOver the past several decades, therehas been a considerable increase inenrollments in non-credit-bearingremedial (NCBR) mathematicscourses in both two- and four-yearcolleges and universities. Thesecourses represent a cruciallyconsequential experience for manystudents entering college –proponents view these courses ascritical for helping students whoare unprepared for collegemathematics courses makesuccessful transitions from highschool to postsecondary education.However, recent scholarship hasclearly indicated that Black- andLatina/o-identified students arecontinually overrepresented inNCBR mathematics courses.1 Theimportance and relevance of thebroader issue can hardly beoverstated. As Astin stated:

Let me begin by asserting whatmay seem like a radicalproposition: The education ofthe “remedial” student is themost important educationalproblem in America today,more important thaneducational funding,affirmative action, vouchers,merit pay, teacher education,financial aid, curriculumreform, and the rest. Providingeffective “remedial” educationwould do more to alleviate ourmost important social andeconomic problems than most

any other action we could take.2

While many have pointed to K-12educational systems as the primarydriver of the proliferation of NCBRcourses, there has been very littleattention to the ways thatpostsecondary institutionsthemselves participate in thisenterprise. Moreover, the influenceof these courses on students’academic learning experiences hasbeen remarkably absent in highereducation policy. This briefaccordingly considers the followingquestions: What are the purposes ofNCBR courses in mathematics?What is the role(s) of these courseswithin higher education policy andfour-year higher educationinstitutions in particular? Do NCBRmathematics courses “work” (andwhat does it mean for them to doso)? For whom are these coursesworking or not working? Whatinfluence do NCBR mathematicscourses have on the students whoare required to experience them?

The primary focus of this brieftherefore is to review the researchon NCBR mathematics courses andthe higher education policyenvironment in which it is situated.In doing so, the brief aims toincorporate new and emergingevidence of the effects of thesecourses on students’ learningexperiences. Given the highereducation policies at play, thefunction and scale of NCBRmathematics courses are explored,

with particular attention to theworryingly and disproportionatelyhigh enrollments of AfricanAmerican and Latina/o students inthese courses in recent decades. Indoing so, this brief also discussesthe influence of NCBR mathematicscourses on students’ mathematicslearning experiences and thethreatening psychosocial impact ofthese courses on students. Lastly,recommendations are offeredbased on contemporary researchand commentary.

WHAT ARE NCBRMATHEMATICS COURSES?Non-credit-bearing remedialmathematics courses are offered infour-year universities to “providebeginning college students withanother chance to learn (or relearn)the mathematics supposedly taughtto them in high school.”3 Thismotive has engenderedconsiderable controversy among adiverse assembly of direct andindirect stakeholders (e.g.,educators, administrators,economists, sociologists,legislators). On the one hand,NCBR mathematics courses areindispensable tools for equalizingaccess to postsecondaryinstitutions. On the other hand, thecredits for these courses are non-additive;4 that is, while students arerequired to enroll, pay for, andsuccessfully pass NCBR courses inorder to proceed to credit-bearing

policyBRIEF

1 See: Paul A. Attewell, David E. Lavin, Domina Thurston, and Tania Levey, “New Evidence on College Remediation,” The Journal of HigherEducation 77, no. 5 (2006): 886-924; Peter Riley Bahr, “Preparing the Underprepared: An Analysis of Racial Disparities in PostsecondaryMathematics Remediation,” The Journal of Higher Education 81, no. 2 (2010): 209-237.

2 Alexandar W. Astin, “Remedial Education and Civic Responsibility,” National Crosstalk, Summer 1998, www.highereducation.org/crosstalk/pdf/ctsummer98.pdf, 12.

3 Sally Andrea Lesik, “Appling the Regression-Discontinuity Design to Infer Causality with Non-Random Assignment,” The Review of HigherEducation 30, no. 1 (2006): 2.

4 Clifford Adelman, Principal Indicators of Student Academic Histories of Postsecondary Education, 1972-2000 (Washington, DC: U.S. Department ofEducation, Institute of Education Sciences, 2004).

courses, NCBR courses do notcount toward a credential(graduation). In this way, they serveas institutional gatekeepers. Andtoo often, student placements inthese courses produce a familiarresult: a repetitive cycle ofenrollment in NCBR courses beforemoving forward.

In most cases, four-year universitiesrequire new students to complete amathematics placementexamination; students with scoresbelow predetermined levels arethen placed into remedialmathematics courses.5 There isconsiderable variation, however, inthe specific content of thesecourses and the policies acrosshigher education institutions thatdictate placement and coursecontent.6 While some universitiesoffer multiple NCBR mathematicscourses, these courses tend to focuson the basic and procedural skills ofalgebra. In addition, some of thesecourse sequences begin with thefundamentals of middle-schoolarithmetic.

According to the National Centerfor Education Statistics (NCES),NCBR mathematics courses arelisted in nearly 80% of four-yearuniversities’ course catalogs.7 Morethan 90% of all “traditionalundergraduates” take at least oneNCBR course in reading, writing,mathematics or some other contentarea.8 This figure has risenconsiderably from the 22% reportedby the NCES in 1989.9 NCBRmathematics courses are also themost frequently taken among allcontent areas.10

NCBR courses have become a highlycontroversial and political topic ineducation.11 At one end of thecontinuum, opponents contend thatinstitutions offering these courseshave lowered their standards andessentially “dumbed down” theircurricula.12 At the other end, punditspoint to the expense of NCBRmathematics course offerings atpublic universities13 some assertingthat “[students] are paying twice foreducation that [they] should havelearned in high school”.14 Combinedwith the fact that these courses are

typically filled with students, aretaught by either graduate studentsor adjunct faculty, and are on thewhole, “cheaper per student thanregular college coursework,” someNCBR math courses and programsbecome de facto financial assets foruniversity mathematicsdepartments.15

THE HIGHER EDUCATIONPOLICY CONTEXT OF NCBRMATHEMATICS COURSESNCBR mathematics coursesgenerally serve two central higher-education policy objectives:mission differentiation andinstitutional access.16 Althoughboth objectives are aimed atensuring excellence and quality oncollege campuses withinsometimes-sizable universitysystems, the two are not alwayscommensurable. NCBRmathematics courses in highereducation reflect the potentialconflict between these two policyobjectives.

NCBR Mathematics Courses 3

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5 Eric Jacobson, “Higher Placement Standards Increase Course Success but Reduce Program Completions,” The Journal of Higher Education 55, no.2 (2006): 138-159.

6 Eric P. Bettinger and Bridget Terry Long, Addressing the Needs of Under-Prepared Students in Higher Education: Does College Remediation Work?No. w11325 (Cambridge, MA: National Bureau of Economic Research, 2005).

7 As cited in Lesik, “Appling the Regression-Discontinuity Design to Infer Causality with Non-Random Assignment”; National Center for EducationalStatistics, Remedial Education at Degree-Granting Postsecondary Institutions in Fall 2000, NCES 2004-010 (Washington, DC, U.S. Department ofEducation, Institute for Education Sciences, 2003).

8 Attewell, et al., “New Evidence on College Remediation”, 886; Linda Serra Hagedorn, M. Vali Siadat, Fogel F. Shereen, Nora Amaury, and Ernest T.Pascarella, “Success in College Mathematics: Comparisons between Remedial and Nonremedial First-Year College Students,” Research in HigherEducation 40, no. 3 (1999): 261-284.

9 Jan M. Ignash, “Who Should Provide Postsecondary Remedial/Developmental Education?,” New Directions for Community Colleges 1997, no. 100(1997): 5-20.

10 Basmant Parsad, Laurie Lewis, and Bernard Greene, Remedial Education at Degree-Granting Postsecondary Institutions in Fall 2000 (Washington,DC: U.S. Department of Education, Institute of Education Sciences, 2003).

11 Attewell, et al., “New Evidence on College Remediation”; Bettinger and Long, Addressing the Needs of Under-Prepared Students in HigherEducation; Mary Soliday, The Politics of Remediation (Pittsburg, PA: University of Pittsburgh Press, 2002).

12 Attewell, et al., “New Evidence on College Remediation”, 886.13 Bettinger and Long, Addressing the Needs of Under-Prepared Students in Higher Education.14 Jeff E. Hoyt and Colleen T. Sorenson, Promoting Academic Standards? The Link Between Remedial Education in College and Student Preparation in

High School (Orem, UT: Utah Valley State College, Department of Institutional Research and Management Studies, 1999).15 Attewell, et al., “New Evidence on College Remediation”; Dennis Redovich, [Review of the book Increasing Access to College: Extending Possibilities

for All Students], Teachers College Record 105, no. 1 (2003): 50-54.16 Michael N. Bastedo and Patricia J. Gumpert, “Access to What? Mission Differentiation and Academic Stratification in U.S. Public Higher

Education,” Higher Education 46, no. 3: (2003) 341-359.

Mission differentiation refers to theneed for and capacity of publicsystems of higher education todistribute resources on campusessystem-wide to achieve specificaspects of their varied missions.17

The higher education policyenvironment has become “acomplicated mosaic, a richlydifferentiated tapestry, revealing ahierarchically arrayed system ofinstitutions and programs”.18 Asingle institution can feature anumber of intersecting aims:research-intensiveness, land-grantmissions, region-servinginstitutional goals, and specificpopulation-serving institutionalgoals. Serving diverse purposeswithin an institution—a necessarytask for many colleges anduniversities—makes it difficult tomaintain systemic mission diversityor to promote missiondiversification. This crisscrossing ofinterests necessarily complicatesthis seemingly straightforward,overarching policy objective.Paradoxically, mission diversity is amajor factor in the effectivefunctioning of higher educationsystems.19

The goal of mission differentiationor diversity is connected to the goalof institutional access inasmuch aseach provides for the social mobilityof students. Despite the importanceof social mobility and the relativelyrecent attentiveness to rates ofcollege attendance and graduation

among students fromunderrepresented racial groups(primarily, African American,Latina/o, and Native Americans),there is a general lack of scrutiny toissues of student access. Instead,mechanisms that enhanceinstitutional efficiency,accountability, and effectivenesshave predominated academic policyinitiatives during recent decades.20

As curricular tools of highereducation policy, NCBRmathematics courses represent aunique point of tension between thetwin goals of mission differentiationand institutional access. NCBRmathematics courses both serve andperceivably compromise missiondiversity and mission differentiationby vetting student entry to certainkinds of pathways within highereducation systems. NCBRmathematics courses serve missiondiversity by marking certaininstitutions within the system asmore or less rigorous or selectivethan others—and allows others todifferentiate themselves as eliteinstitutions. In either case, however,the case for offering NCBRmathematics courses does notcompromise the central policyobjectives; that is, these coursesshould not be considered as “anappendage with little connection tothe mission of the institution butrepresents a core function of thehigher education community that ithas performed for hundreds of

17 Bastedo and Gumpert, “Access to What? Mission Differentiation and Academic Stratification inU.S. Public Higher Education,”; Carnegie Commission on Higher Education, The Purposes andthe Performance of Higher Education in the United States (New York: McGraw-Hill, 1973); FransVan Vught, “Mission Diversity and Reputation in Higher Education,” Higher Education Policy 21,no. 2 (2008): 151-174.

18 Scott Davies and Neil Guppy, “Field of Study, College Selectivity, and Student Inequalities inHigher Education,” Social Forces 75, no. 4 (1997): 1417-1438.

19 Van Vught, “Mission Diversity and Reputation in Higher Education”.20 Bastedo and Gumpert, “Access to What? Mission Differentiation and Academic Stratification in

U.S. Public Higher Education”.

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A single institution

can feature a

number of

intersecting aims:

research-

intensiveness, land-

grant missions,

region-serving

institutional goals,

and specific

population-serving

institutional goals.

NCBR Mathematics Courses 5

policyBRIEFyears”.21 So, in terms of missiondifferentiation and with respect toone of this brief’s organizingquestions, NCBR mathematicscourses “work”—that is, theyperform their intended function toallow systems of higher education todemarcate their constituentinstitutions.

In contrast, NCBR mathematicscourses are a contentious lever forinstitutional access. On the onehand, the courses are regarded asindispensable for students who needadditional exposure to concepts andprocedures that are fundamental topostsecondary mathematics. On theother, these courses constrictinstitutional access for many (whilepossibly serving missiondifferentiation), given the attritionrates for students who are requiredto enroll in NCBR mathematicscourses. It is therefore unclearwhether the courses “work” withregard to institutional access—thatis, whether students are able to gainthe exposure to the rigorous andpreparative mathematics contentand pedagogy that will help them toadvance fully to the postsecondarycurriculum.

NCBR MATHEMATICSCOURSES AND ISSUES OFTEACHING AND LEARNING Currently, there are no agreed-upon

guidelines, standards, expectations,or benchmarks that guide or informcurriculum articulation orimplementation in NCBRmathematics courses. In this way,the largely decentralized highereducation policy environment isstructurally disconnected from theK-12 educational policy context.Instead, these courses tend to followa time-honored tradition: thecurriculum focuses narrowly onarithmetic, the proceduralunderpinnings of introductoryalgebra (high-school algebra I andII), and sometimes, selections ofgeometry content.22 Although NCBRcourses are intended to bridge thecurriculum from K-12 to highereducation (in terms of policy), thisnarrow content focus insteadexacerbates the divide and supportsthe autonomy of four-yearinstitutions over NCBR courses.

Although the higher educationpolicy context is appreciablydifferent from K-12 policy, thesystemic use of algebra as a gate-keeping mechanism is not new tothe mathematics educationenterprise,23 and it is shared acrossboth K-12 and postsecondarycontexts. Algebra is traditionallyregarded as a “tightly integratedsystem of symbolic procedures, eachof which is closely connected with aparticular problem type”.24 In NCBRmathematics courses, thecurriculum typically obliges

Currently, there are

no agreed-upon

guidelines,

standards,

expectations, or

benchmarks that

guide or inform

curriculum

articulation or

implementation in

NCBR mathematics

courses.

21 Jamie P. Merisotis and Ronald A. Phipps, “Remedial Education in Colleges and Universities:What’s Really Going On?”, The Review of Higher Education 24, no. 1 (2000): 67-85.

22 Hagedorn, et al., “Success in College Mathematics: Comparisons between Remedial andNonremedial First-Year College Students”.

23 Robert P. Moses and Charles E. Cobb, Radical Equations: Math Literacy and Civil Rights (Boston,MA: Beacon Press, 2001); Elizabeth D. Phillips and Glenda T. Lappan, “Algebra: The First Gate,”in Mathematics in the Middle ed. Larry Leutzinger (Reston, VA: National Council of Teachers ofMathematics, 1998) 10-19.

24 John P. Smith and Patrick W. Thompson, “Quantitative Reasoning and the Development ofAlgebraic Reasoning,” in Algebra in the Early Grades, eds. James J. Kaput, David W. Carraher, andMaria L. Blanton (New York, NY: Erlbaum, 2007), 4.

students to “interpret variouscommands—‘solve,’ ‘reduce,’‘factor,’ ‘simplify’—as calls to applymemorized procedures that havelittle meaning beyond theimmediate context”.25 In terms ofmathematical content—specifically, the narrow andprocedure-driven focus on lowcognitive-demand skills26—NCBRmathematics courses are generallystuck in the past.

Similarly, the general pedagogy ofNCBR mathematics courses is,oftentimes, very traditional. Thecourses follow a lecture format inwhich the instructor is regarded asthe expert and students areexpected to acquire by rote themathematical knowledge that theinstructor presents anddemonstrates on the board (or,perhaps, an overhead transparencyprojector or series of worksheets).Depending on the institution andthe resources apportioned to NCBRprograms, a discussion-orientedcourse add-on is sometimesrequired for students to practicetheir skills and seek additionalassistance from teaching assistants.In other cases, the institution mayappoint smaller seminar-stylesections for NCBR mathematicscourses. However, the pedagogy insmaller courses is usually similar tothe larger lecture formats.

The personnel who are appointed toteach NCBR mathematics coursesgenerally reflect the teaching and

learning philosophies of the coursesas well. Although some full-timefaculty members teach NCBRmathematics courses, many otherinstitutions and their mathematicsprograms rely on part-time faculty(e.g., adjuncts) and graduatestudents to staff NCBR courses.These paraprofessionalinstructors—while possibly moreproficient than full-time, tenure-track faculty—are not systematicallyexposed to emergent effective or“best” pedagogical practices.Combined with the fact that thesecourses are typically filled withstudents across multiple sections,NCBR courses are on the whole,“cheaper per student than regularcollege coursework, and in mostinstitutions, [NCBR coursesconsume] a quite modest part of thebudget”.27

Overall, this particular combinationof the issues (narrow curriculumand pedagogy and under-resourcedcourses and instructors) limits theopportunities that students mayhave to (re-) gain confidence withmathematics, especially if theirexposure is limited to topics andexercises that are directlyreminiscent of high school algebracourses and curricula. Arguably,this is true for all students—eventhose for whom any exposure to theadded support of NCBRmathematics would yield somebenefit. Furthermore,straightforward repetition of high-school level tasks does not support

or advance students’ capacities tosee mathematics as something thatis both worthwhile and perenniallyuseful, because there are typicallyfew opportunities to apply themathematics to real-world andstage-appropriate contexts, issues,and problems. Lastly, the kind ofcurricular focus that is typical ofthese courses does not helpstudents to shore up skills anddispositions that will help them touse mathematical reasoningsuccessfully throughout theirpostsecondary trajectories.

EVIDENCE ON THE IMPACTOF NCBR MATHEMATICSCOURSES: PSYCHOSOCIALEFFECTS ON LEARNINGRecent evidence on NCBRmathematics courses suggests thatNCBR mathematics courses maybring about unintended andthreatening effects on studentlearning and, more broadly,students’ mathematical proficiency.The National Research Council(NRC), the arm of the NationalAcademy of Sciences and NationalAcademy of Education that ischarged with offering objectivepolicy advice, has published severalreports that raise issues directlyrelevant to NCBR mathematicscourses.28 Although many of theseand other related policy documentsdecry the growth of remediation inmathematics amid the transition to

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25 Ibid.26 Gregory V. Larnell and John P. Smith, III, “Verb Use and Cognitive Demand in K–8 Geometry and Measurement Grade-Level Expectations,” in

Variability is the Rule: A Companion Analysis of K–8 State Mathematics Standards, ed. John P. Smith, III (Charlotte, NC: Information Age Publishing,2010).

27 Attewell, et al., “New Evidence on College Remediation”, 889; Redovich, [Review of the book Increasing Access to College: Extending Possibilities forAll Students].

28 These reports include Everybody Counts: A Report to the Nation on the Future of Mathematics Education (1989), From Analysis to Action:Undergraduate Education in Science, Mathematics, Engineering, and Technology (1996), and Adding It Up: Helping Children Learn Mathematics(2001).

postsecondary coursework, therecommendations of thesedocuments have had modestdiscernable influence on thebroader debate. The tensionregarding NCBR mathematicscourses is typically centered oncompletion rates, costs, andinstitutional missions, whereas thequestion of whether these coursesinfluence students’ learning ofmathematics—and students’ much-needed proficiency in the subject—is largely absent.

As the NRC Adding It Up reportasserts, however, it is cruciallyimportant for all students tosuccessfully learn mathematics—and that it is much more than justthe accumulation or rehashing ofmathematical skills and concepts.29

The report’s framework specifies fiveinterwoven strands that contributeto proficiency in mathematics:conceptual understanding,procedural fluency, adaptivereasoning, strategic competence,and productive disposition.30 Alongwith conceptual understanding andprocedural fluency, adaptivereasoning and strategic competencedescribe aspects of mathematicalprocesses in which students shouldengage. Productive disposition,however, describes the affectiveaspect of mathematics learning,emphasizing that learners shoulddevelop a “habitual inclination tosee mathematics as sensible, useful,and worthwhile, coupled with thebelief in diligence and one’s own

efficacy.”31

Typically, NCBR mathematicscourses tend to place unusuallyburdensome emphasis onprocedural fluency, or the capacityto carry out computational methodsflexibly, accurately, and efficiently.32

The underlying assumption is thatstudents who exhibitunderperformance on placementexams and are subsequently placedin NCBR mathematics coursesnecessarily lack the requisiteprocedure-driven skills that arefoundational to algebra. To a lesserextent, these courses mayincorporate the other conceptual orprocess-oriented aspects ofproficiency, but there has been noattentiveness in research or practiceto the influence of NCBRmathematics courses on students’dispositions or their identities asmathematics learners. Specifically,we know little about the potentialpsychosocial threats or damage thatNCBR mathematics courses maypose for students who eithersucceed or struggle. In short, manyask if the courses are effective—ifthey work. But we have generally notasked whether the very experiencesof these kinds of courses aredamaging for students in other ways.

A series of recent studies has begunto unpack the experiences thatstudents actually have in thesecourses—that is, the extent to whichstudents enrolled in NCBRmathematics courses may

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NCBR Mathematics Courses 7

Recent evidence on

NCBR mathematics

courses suggests

that NCBR

mathematics

courses may bring

about unintended

and threatening

effects on student

learning and, more

broadly, students’

mathematical

proficiency.

29 Although the main charge for the Committee on Mathematics Learning, the group ofmathematics education scholars appointed by the NRC to produce the report, was to synthesizeresearch on mathematics learning at earlier levels (and not at the transition to postsecondarystudy), the framework for mathematical proficiency represents theories on mathematicslearning at large, not only for young (K-8) learners.

30 National Research Council, Adding It Up: Helping Children Learn Mathematics (Washington,DC: National Academy Press, 2001).

31 Ibid, 5.32 Ibid.

encounter affirmation or threat vis-à-vis their mathematics learningexperiences.33 These studies havefocused particularly on AfricanAmerican students, taking as causethis group’s overrepresentation inNCBR mathematics courses athigher education institutionsaround the country. These studiesare part of a “new wave” of researchin mathematics education that findthat and explore the ways in whichmathematics courses (NCBR andotherwise) serve as contexts aboutwhich students actively make senseof both mathematics learning andother kinds of identities like raceand gender.34

A major finding of these studies isthat students enrolled in NCBRmathematics courses—especiallythose who were successful in highschool (e.g., high-grade earners,salutatorians, honor students)—were experiencing what socialpsychologist Claude Steele and hiscolleagues have termed “stereotypethreat.”35 Stereotype or identitythreat is evoked in situations wherea certain identity that a person hasis cued up or signaled in ways thatcause the person to feel pressure.This psychosocial phenomenongives a person an additional task (inaddition to learning), akin to “tryingto slay a ghost in the room.”36 Forthe students in NCBR mathematicscourses—specifically, the African

American students for whom theoverrepresentation of studentsfrom the same group was anapparent and chronic feature—thehuge task of disproving thestereotype of African Americanstudents’ underperformance inmathematics changed the nature oftheir experience.

Consider the following excerptsfrom Cedric, one of the primaryparticipants in of these studies:

It just; okay, when [theinstructor] explained that thiswas—[the instructor] basicallysaid that this was a remedialcourse. [The instructor] waslike, um, this is the lowestcourse that you will take at [thisuniversity]. [The instructor]said that it doesn’t get anyeasier than this. And then Ikinda looked around, youknow, and I see that most of—even when I go to the [mathhelp sessions]—I see that mostof the students there in [theremedial course] are AfricanAmerican….

I mean I see it. I walk these hallseveryday. I see who’s in theseclasses. I’ll see calculus on theboard, and no black students inthe seats. Sometimes one ortwo... Okay. I just feel like [...] it[...] I don’t know, it kinda hurts

me to see so many blackpeople, like me, in theclassroom. I just feel like we’re[.........] I feel like we could dobetter. [......] Like, if we’re goingto come to [this university],then um, and just be put in the[remedial] class, and then tosee people, like um, just dropout of it; that just, kinda like,hurts me, because it, kinda like,says to me, ‘okay, AfricanAmerican students can’tsucceed in this class, you know.’And it’s remedial, the lowestclass, so [...] So, it’s kinda [...] Idon’t know.

Put differently, some of thestudents—for Cedric and many ofhis peers, the NCBR mathematicscourse experience was about muchmore than mathematicalprocedures and concepts; itbecame stocked with stress anddistraction, inefficient strategiesand rigidities, and ultimately, anissue of college survival versusdiscontinuity.37 Even amongstudents who did not identify assuccessful mathematics students,who had spotty mathematicsbackgrounds and for whom themathematics content of NCBR wasa needed refreshment—studentsfor whom this course could wouldotherwise interpreted as a benefit—there is evidence that they alsoencounter identity threat in

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33 Gregory V. Larnell, “The Product of Many Factors: Exploring Remedial Mathematics Education through One Student’s Background andExperience” (Unpublished Manuscript, Michigan State University, 2008); Gregory V. Larnell, “More Than Just Skill: Mathematics Identities,Socialization, and Remediation among African American Undergraduates” (PhD diss, Michigan State University, 2011); Gregory V. Larnell, “On‘New Waves’ in Mathematics Education: Identity, Power, and the Mathematics Learning Experiences of All Children,” New Waves—EducationalResearch and Development, 16, no. 1 (2013): 146-156; Gregory V. Larnell, “More than Just Skill: Mathematics Identities, Inequity, and Agency AmidTransitions to Postsecondary Mathematics” (Under Review, Journal for Research on Mathematics Education); Gregory V. Larnell, “Project REMATH:Investigating the Mathematics Learning Experiences of Students Enrolled in a Non-Credit Bearing Remedial Mathematics Courses at an UrbanUniversity” (in progress).

34 Larnell, “On ‘New Waves’ in Mathematics Education: Identity, Power, and the Mathematics Learning Experiences of All Children” 35 Claude M. Steele,Whistling Vivaldi: And Other Clues to How Stereotypes Affect Us (Issues of Our Time) (New York, NY: W.W. Norton & Company,

2010).36 Steele,Whistling Vivaldi, 110-110.37 Ibid.

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NCBR Mathematics Courses 9

relation to their course experience.More related studies are underway,and additional study is needed.

PRIMARY ISSUES ANDRECOMMENDATIONSAlthough many have challenged therole of NCBR mathematics coursesat four-year universities, they areindispensable policy levers forinstitutions to address their twinobjectives of missiondifferentiation and institutionalaccess. Nevertheless, manyinstitutions are cutting them out(which places more pressure ontwo-year institutions) or areconverting the courses to online-only environments. From a policyperspective, this may allowuniversities to maintain their statusand sufficiently differentiatethemselves, but it also mayexacerbate inequities regardinginstitutional access for populationsof students that continue to beunderrepresented at thepostsecondary level. From ateaching and learning perspective,these broad changes in NCBRmathematics courses alsoexacerbate the already narrowcurricular focus on proceduralfluency and cognitivelyundemanding skills. In an onlineenvironment, it may be even easierto emphasize and assess highlyprocedural mathematics content,and the pedagogical intervention—although more individualized—would simultaneously becomeeven less personal.

NCBR mathematics courses areamong the most important coursesat a university, and as such, theyneed more resources, not fewer. Asit is, the courses are often stripped-

down, bare-bones teaching andlearning experiences in whichstudents are expected to acquirebasic facts and skills. They are oftentaught by relatively inexperiencedparaprofessionals (e.g., graduatestudents who are often in their firstteaching appointment) orprofessional adjunct instructors towhom professional development isnot routinely or systematicallyoffered. Based on the research andpolicy dimensions presented in thisbrief, there are three mainrecommendations that mayeffectively lead to reforming NCBRmathematics courses at four-yearuniversities.

Universities should modifyplacement processes to take intoaccount other measures of students’mathematics performances.Mathematics is used as a measureof quantitative aptitude throughoutstudents’ transitions topostsecondary education. Studentscomplete PSAT exams, SAT or ACTexams, and/or university-specificplacement exams, depending onthe institution’s given role within ahigher education system and theextent to which institutional access(or selectivity) is central to thatinstitution’s mission. Furthermore,students complete mathematics-specific, standardized assessmentsthroughout more than ten years ofprior schooling before applying forpostsecondary study. And in thenew era of Common Core StateStandards for Mathematics, theseassessments will become evenmore broadly standardized thanever before, producing scores atintervals throughout students’ K-12trajectories. These assessmentshave and will continue to producemany arrays of data available fromwhich to determine a students’

performance over time formathematics assessments.

Despite all of these differentmeasures, only one score—on onetest taken on one occasion andoften with little preparation—isused to determine students’mathematics placements at a singleinstitution. Simple changes likeconsidering a students’ ACT or SATscore along with placement examscores could also be effectively usedto place students into mathematicscourses. A more sophisticatedmodel would include points of datafrom previous years of assessments,particularly in high school, alongwith other precollege tests. Such amodel would effectively involvedigital data records for studentsand the capacity to share thoserecords between school districtsand universities.

Universities should shift themathematical focus of NCBRmathematics courses from roteprocedural skills to emphasizemathematical problem solving thatconnects to other disciplines.Instead of focusing exclusively onrote skills and procedures, NCBRmathematics courses shouldforeground complex mathematicaltasks, mathematical problem-solving skills, modeling real-worldsituations with mathematics, andotherwise unpacking mathematicalconcepts and procedures. In doingso, NCBR courses would achieveboth the goals of repairingstudents’ mathematicalbackgrounds as well as offeringstudents scenarios through whichthey may learn to viewmathematics as an instrumentallyuseful discipline. Furthermore,expanding the scope of NCBRmathematics courses in this way

would improve the alignment ofthese courses withrecommendations from well-regarded organizations such as theNational Research Council and theNational Council of Teachers ofMathematics.

A more promising approach toreforming NCBR mathematicscourses would not only expand themathematical scope of these coursesbut also situate the activities of thecourse in an interdisciplinarycontext. A curriculum that featuredrichly multilayered, group-basedtasks could include the concepts andprocedural topics that are includedin typical algebra courses andembed those skills within real-worldproblem contexts. Following recenttheoretical approaches to teachingand learning mathematics, thesekinds of problem-solving contextscan enhance students’ engagementand participation—and possiblymitigate the potential effects ofidentity threats related tomathematics learning experience.

Universities should offer holisticacademic programming tocompliment NCBR mathematicscourses that aim to militate againstidentity threats. Unlike the reform ofteaching and learning mathematicsat the K-12 level, there is much lessknown about the psychosocialeffects of course experiences inmathematics. This is slowlyimproving. However, there currentlyseems to be a push to strip awayresources from NCBR mathematicsprograms in ways that enable the“outsourcing” of these courses toonline environments. If four-yearinstitutions are serious aboutproviding institutional access andworld-class educational experiences(as is often the slogan), then

apportioning the professionaldevelopment resources for NCBRmathematics course instructors isimperative. Furthermore,coordinating resources andstrategies among curricularstakeholders and extracurricularprogram administrators to moderatethe psychosocial threats aboutspecific groups posed by NCBRmathematics courses is a much-needed but underdeveloped effort atmany four-year universities.

CONCLUSIONNCBR mathematics courses are oneof the most important educationalissues in higher education policy.Each year, scores of students leaveuniversities each year because theyare unable to jump through thehoop that has become introductorymathematics. As many of thestudents have claimed, they aspireto be doctors, nurses, lawyers, andall-too-frequently, first-generationcollege students, African Americans,and Latinos. Still, there must be thewill to implement the best practicesthat have developed in the fieldduring the past few decades. As itstands, NCBR mathematics coursesare not just a slippery rung on theladder of institutional and societalaccess, they are broken andthemselves in need of remediation.In order to do this, we muchapportion the resources to bolsterinstruction, support cross-campuscollaboration among institutionalstakeholders, and fundamentallyalter the ways in which mathematicsinstruction is conceptualized inthese course settings.

10 UIC Research on Urban Education Policy Initiative

policyBRIEF

If four-year

institutions are

serious about

providing

institutional access

and world-class

educational

experiences (as is

often the slogan),

then apportioning

the professional

development

resources for NCBR

mathematics course

instructors is

imperative.

ABOUT USThe Research on Urban Education Policy Initiative (RUEPI) is an education policy research project based inthe University of Illinois at Chicago College of Education. RUEPI was created in response to one of the mostsignificant problems facing urban education policy: dialogue about urban education policy consistently failsto reflect what we know and what we do not about the problems education policies are aimed at remedying.Instead of being polemic and grounded primarily in ideology, public conversations about education shouldbe constructive and informed by the best available evidence.

OUR MISSIONRUEPI’s work is aimed at fostering more informed dialogue and decision-making about education policy inChicago and other urban areas. To achieve this, we engage in research and analysis on major policy issuesfacing these areas, including early childhood education, inclusion, testing, STEM education, and teacherworkforce policy. We offer timely analysis and recommendations that are grounded in the best availableevidence.

OUR APPROACHGiven RUEPI’s mission, the project’s work is rooted in three guiding principles. While these principles are notgrounded in any particular political ideology and do not specify any particular course of action, they lay afoundation for ensuring that debates about urban education policy are framed by an understanding of howeducation policies have fared in the past. The principles are as follows:

• Education policies should be coherent and strategic

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RUEPI policy briefs are rooted in these principles, written by faculty in the University of Illinois at ChicagoCollege of Education and other affiliated parties, and go through a rigorous peer-review process.

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