Algebra and the Underprepared LearnerBy Timothy Stoelinga and James Lynn

education.uic.edu/ruepi

ABOUT THE AUTHORS

Timothy Stoelinga isa Senior ProgramAssociate at theLearning SciencesResearch Institute atthe University of

Illinois at Chicago. He is also a partof the UIC Office of High SchoolDevelopment.

James Lynn is theVisiting Director ofthe Office of HighSchool Developmentat the University ofIllinois at Chicago.

He is also a part of the LearningSciences Research Institute at theUniversity of Illinois at Chicago.

policyBRIEFUIC Research on Urban Education Policy Initiative

June 2013

Vol. 2, Book 3

EXECUTIVE SUMMARYAlgebra acts as a gatekeeper forhigh school graduation and post-secondary success. Students whopass Algebra 1 by the end of ninthgrade are more likely to takeadvanced mathematics courses,graduate from high school, andsucceed in college. Yet persistentinequities in access to rigorousalgebra due to issues ofplacement, preparation, andquality of instruction have keptthe gate closed for a largeproportion of students,particularly minority and low-income students. In response,“Algebra for All” policies have beenimplemented whereby all studentsare required to take Algebra 1 by adesignated grade level—typicallyeighth or ninth grade. While suchpolicies are on target in theirintention to increase the numberof students who successfullycomplete Algebra 1 in a timelyway, evidence also shows that fortoo many students, these policiesby themselves have neitherincreased mathematicsachievement nor advanced greateropportunity. Rather, they oftenresult in the watering down ofAlgebra 1 content and significantly

increase the number of studentswho fail the course. Theseconsequences are concentratedamong underprepared students,whom the policies were designedto serve in the first place. As such,the worthy goals of Algebra for Allmay only be realized when arigorous approach to Algebra ismaintained for all students, andwhen necessary systems are inplace to prepare and support allstudents to be successful. TheCommon Core State Standards forMathematics (CCSS-M) nowprovides clearer and morerigorous expectations for thealgebra content all studentsshould learn, but the articulationof such standards is only a startingpoint. Algebra policy, therefore,should include provisions forequitably maintaining this level ofrigor for all students, whileproviding a system of supports to:(1) better prepare students tosucceed before taking Algebra 1;(2) enhance learningopportunities for underpreparedlearners during Algebra 1; and (3)enhance teaching capacity tosupport all learners, particularlythose who are underprepared tosucceed in Algebra 1.

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INTRODUCTIONFor students who are underpreparedto succeed in Algebra 1, passing thecourse can represent anoverwhelming challenge. Yet,success in Algebra 1 is no less crucialfor these underprepared studentsthan it is for students who are betterprepared to succeed. A dilemmaemerges: policies that promotesuccessful completion of Algebra byall students are weighed againsttheir potential to increase failurerates for underprepared students,and the consequences failure canhave on these students’ academictrajectories. In the current context ofsecondary education and in light ofthe relationship of Algebra to collegeand career readiness, however, wehold to the position that all studentsshould take algebra in a timelymanner.

WHY IS SUCCESSFULCOMPLETION OF ALGEBRA 1IMPORTANT FOR ALLSTUDENTS?

Education policy nationwidecontinues on a trend toward raisingmathematics requirements for highschool graduation. In 2013, 42 states,including Illinois, requiredsuccessful completion of at leastthree years1 of mathematics, and 16

of these states required completionof four years. These numbers willlikely increase in the next few yearsas pending legislation is enacted inseveral states. By contrast, in 2001only 28 states required three years ormore of mathematics for graduation,and only 4 states required fouryears.2 Whether or not Algebra 13 isexplicitly stated as a courserequirement (it is in 23 states), thecompletion of the course—and inmany cases the passing of a relatedend-of-course exam—tends to bethe critical step in meeting theseincreasingly rigorous graduationrequirements. In addition, 45 states,also including Illinois, have adoptedthe Common Core State Standardsfor Mathematics (CCSS-M)—writtenspecifications of what studentsshould know and be able to do inmathematics in various grades. Thealgebra standards in CCSS-Mprovide a clear and coherentarticulation of algebra studentsshould learn—in elementary gradesas well as in high-school Algebra 1and Algebra 2 courses.4 Incomparison to previous statestandards, CCSS-M has increasedthe rigor of Algebra 1 by positioningsome content earlier in the overallsequence of Algebra topics.Together, these policy trends raiseboth the stakes and the expectations

policyBRIEF

The algebra

standards in CCSS-

M provide a clear

and coherent

articulation of

algebra students

should learn—in

elementary grades

as well as in high-

school Algebra 1

and Algebra 2

courses.

1 The term “years” is used for clarity in place of Carnegie Units, in which the data was originallypresented. One Carnegie Unit generally equates to credit received for successful completion of atwo-semester, credit-bearing course in secondary school.

2 National Center for Educational Statistics, Digest of Education Statistics, http://nces.ed.gov/programs/digest/d01/dt153.asp; Kyle Zinth and Jennifer Dounay, “Aligned to the Research:Science and Mathematics Graduation Requirements,” State Notes: Mathematics and Science,www.ecs.org/clearinghouse/74/52/7452.pdf.

3 In some settings, a sequence of Integrated Mathematics replaces the traditional high schoolmathematics sequence. This Integrated sequence is currently being proposed by the IllinoisState Board of Education as one model for implementing CCSS-M in grades 9-12. BecauseIntegrated Mathematics 1 includes a concentrated focus on many of the concepts similar tothose found in Algebra 1, the issues discussed in this brief can be similarly applied to IntegratedMathematics 1.

4 National Governors Association Center for Best Practices, Council of Chief State School Officers,Common Core State Standards—Mathematics (Washington D.C.: National GovernorsAssociation Center for Best Practices, Council of Chief State School Officers, 2010).

for Algebra 1, with the intention ofincreasing students’ preparednessto take more advancedmathematics courses and helpingstudents obtain the skills needed tosucceed in college and theworkplace.

In light of these trends, Algebra 1retains its role as a gatekeeper forhigh school graduation and post-secondary success, and the urgencyof passing through continues tointensify.5 High school algebra iswidely considered a key step alongthe path to college and careerreadiness. Because of increasedgraduation requirements, failingAlgebra 1 puts students atsignificant risk of not completinghigh school. In Chicago PublicSchools (CPS), students who earned5 credits and failed no more thanone course in ninth grade were over3.5 times more likely to graduatefrom high school in four years thanstudents who did not achieve thisbenchmark.6 Thus, the widespreaddifficulties faced by many studentsin passing Algebra 1 establishes it asa critical link related to success ratesin high school.

THE CHALLENGE OFALGEBRA

Yet, in CPS and elsewhere, Algebra 1continues to generate the highest

failure rate of any high schoolcourse.7 The reasons for this arecomplex and difficult to isolate, butseveral themes have emerged fromongoing research in mathematicseducation that can provideguidance in the design of policyand practice. With respect to coursecontent, Algebra 1 has historicallyrepresented an importanttransition point in the learning ofmathematics, requiring the use ofgeneralized models, mathematicalabstractions, and understandingsof variables and symbols, all ofwhich are particularly challengingfor many students.8 Simply stated,content associated with Algebra 1 isnotoriously difficult compared withthe number and operationsconcepts concentrated in earliergrades. Research has also indicatedthat many eighth and ninth gradestudents who are required to takeAlgebra 1 are also underpreparedand need more support to succeedbecause of weak foundations inprerequisite concepts.9 As many ofthese students enter their firstalgebra course, they experienceearly, reinforcing patterns of failure,which can lead to the belief theywill not be able to earn a highschool diploma. Without effectiveforms of intervention and support,these patterns of failure can causestudents to fall further behind andeventually drop out of school. But

what kinds of support are neededfor under-prepared students tosucceed in this high-stakes course?How can algebra policy helpprovide these supports as a way tonot only increase graduation rates,but to truly help prepare studentsfor college and post-secondarysuccess?

To investigate these questionsamidst these current challenges,this brief examines evidence relatedto algebra policies and their effectson students, particularly those whoare underprepared to succeed.First, the policy landscape ofalgebra is examined. This sectionfocuses on both the mathematicscontent that students are requiredto learn and research on the effectsof these requirements. Second, thisbrief analyzes additional researchon mathematics education andoffers three principles that beardirectly on improving students’success in algebra: (1) Studentsneed systematic exposure toalgebra beginning early in theireducation and extending throughhigh school; (2) underpreparedstudents need targeted, structuredsupport to succeed in a rigorousAlgebra 1 course; and (3) increasingstudents’ success requiresenhanced teaching capacity thatneeds to be addressed in teacherpreparation programs as well as in

Algebra and the Underprepared Learner 3

policyBRIEF

5 Clifford Adelman, The Toolbox Revisited: Paths to Degree Completion from High School through College (Washington, DC: U.S. Department ofEducation, 2006).

6 Elaine M. Allensworth and John Easton,What Matters for Staying On-Track and Graduating in Chicago Public High Schools: A Close Look at CourseGrades, Failures, and Attendance in the Freshman Year (Chicago, IL: Consortium of Chicago School Research at the University of Chicago, 2007).

7 Chicago Public Schools Department of Evaluation, Research, and Accountability, Two-Yearm Course Taking Patterns and Pass Rates of CPS HighSchool Students in Math and Science (Chicago, IL: Chicago Public Schools, 2003).

8 E.g., Dietmar Kuchemann, “Children’s Understanding of Numerical Variables,” Mathematics in School 7, no. 4 (1978): 23-26; Carolyn Kieran,“Concepts Associated with the Equality Symbol,” Educational Studies in Mathematics 12, no. 3 (1981): 317-26; Sigrid Wagner and Sheila Parker,“Advancing Algebra,” in Research Ideas for the Classroom, High School Mathematics, ed. Patricia S. Wilson (New York, NY: Macmillan, 1993): 119-39.

9 Elaine Allensworth and Takako Nomi, “College-Preparatory Curriculum for All: The Consequences of Raising Mathematics GraduationRequirements on Students’ Course Taking and Outcomes in Chicago” (Paper presented at the Second Annual Conference of the Society forResearch on Educational Effectiveness, March 2009, Arlington, VA), www.educationaleffective-ness.org/conferences/2009/conference.shtml; TomLoveless, The Misplaced Math Student: Lost in Eighth-Grade Algebra (Washington, D.C.: The Brookings Institution, Brown Center on EducationPolicy, September 2008).

in-service professionaldevelopment. Finally, this briefposes a set of recommendations forimproving mathematics educationpolicies and practices in algebra.

THE ALGEBRA POLICYLANDSCAPEIn order to graduate from highschool, Illinois currently requiresthat students must complete threecredits in mathematics, includingAlgebra 1 and a course ingeometry.10 This requirement is theresult of legislation enacted in 2005,which increased overall graduationrequirements in core disciplineswith the intention of ramping upthe academic preparation of Illinoisgraduates. Algebra 1 is theintroductory course in a typicalsecondary mathematics sequenceof Algebra 1, Geometry, and Algebra2. Most students take Algebra 1 inninth grade, though increasingnumbers of students take it ineighth grade, and some as early assixth grade. Guidance from theIllinois State Board of Education(ISBE) on implementing thegraduation requirements citesevidence that high school studentswho take rigorous courses are moreprepared to graduate, succeed incollege, and participate in theworkforce.11

One response to this requirementhas been to delay underpreparedstudents’ enrollment in Algebra tobeyond ninth grade in order toprovide more coursework in pre-algebra skills. Evidence, however,shows that this approach does notwork. Students typically continueto struggle learning the same pre-algebra skills from the middle-grades curriculum, taught using thesame approaches. Consequently,they continue to fall further behindand eventually disengage frommathematics altogether.12 Anotherapproach has been to slow the paceof algebra for underpreparedstudents by stretching thecurriculum over a two-year spanacross ninth and tenth grades.While this approach does moveunderprepared students forward inthe high school curriculum, it doesso at the cost of setting them backby a full year, rather than allowingthem to catch up to their peers.

ALGEBRA FOR ALL:INTENTIONS ANDCHALLENGES

To further ensure access tochallenging mathematics for allstudents, some state and districtpolicies require that Algebra 1 betaken by a specified grade level—typically ninth grade, but in somecases eighth grade—as a measure

to ensure students’ preparednessfor more advanced mathematics.13

Such districts notably include largeurban districts, such as Chicago,Philadelphia, Los Angeles,Baltimore, and Milwaukee, wherelarge inequities exist in the numberof minority and low-incomestudents taking advancedmathematics classes. Research onthe effects of these policies,however, points to both positiveand negative consequences.14 Onthe positive side, Algebra for All hasallowed more students to enrolland successfully complete Algebra1, which in turn opensopportunities for challengingcoursework in mathematics, andincreases the likelihood ofgraduation, college enrollment, andpostsecondary success.15 On thenegative side, these policies do notprovide for the supports needed byunderprepared students to succeedin Algebra 1.

A policy that has been in place inCPS since 1997 mandates that allstudents take Algebra 1 by the endof ninth grade. The policy’s aim is toraise the bar on mathematics for allstudents on the premise thatramping up to a college-preparatory curriculum levels theplaying field and improvesachievement, particularly amongminority and low-income students.

10 Illinois State Board of Education, State Graduation Requirements (105 ILCS 5/27-22, 27-22.05, 27-22.10), November 2012 Guidance Document(Springfield, IL: November, 2012).

11 Illinois State Board of Education, State Graduation Requirements.12 Allensworth and Nomi, “College-Preparatory Curriculum for All”; Adam Gamoran, Andrew Porter, John Smithson, and Paula White, “Upgrading

High School Mathematics Instruction: Improving Learning Opportunities for Low-Achieving, Low-Income Youth,” Education Evaluation andPolicy Analysis, 19, no. 4, (1997): 325-338; Jeannie Oakes, Keeping Track: How Schools Structure Inequality (2nd ed.) (New Haven, CT: Yale UniversityPress, 2005).

13 E.g., Chicago Public Schools Department of Policy and Procedures, “Chicago Public Schools High School Graduation Requirements,” (Chicago, IL:Chicago Public Schools, 2012).

14 Allensworth and Nomi, “College-Preparatory Curriculum for All”; Matthew Rosin, Heather Barondess, and Julian Leichty, Algebra Policy inCalifornia: Great Expectations and Serious Challenges (Mountain View, CA: EdSource, Inc., 2009).

15 Adelman, The Toolbox Revisited; Allensworth and Easton,What Matters for Staying On-Track; Chicago Public Schools Department of Evaluation,Research, and Accountability, Two-year Course Taking Patterns.

policyBRIEF

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Algebra and the Underprepared Learner 5

policyBRIEFResearch indicates, however, thatthe policy has neither raisedstandardized test scores inmathematics nor increased thelikelihood of students attendingcollege. In addition, Algebra 1 hascontinued to produce the highestfailure rate of any single course inthe years following the enactment ofthe policy.16

In the state of California, Algebra forAll has been a major focus ofstatewide policy since the late 1990s,which established as one of itscentral goals the enrollment of allstudents in Algebra 1 by eighth grade.The result has been a drastic increasein the percentage of Californiaeighth-graders taking Algebra 1: from16% in 1999, to 32% in 2003, to 51%in 2008. Pass rates of eighth-graderson the Algebra 1 California StandardsTest (CST) assessment, however,reveals a mix of positive results anddire consequences. While 1.8 times asmany eighth-graders passed theAlgebra 1 CST in 2008 as compared to2003, 1.5 times as many eighth-graders failed the test—about 76,800total students in 2008. On the onehand, the policy opened theopportunity of success for largenumbers of students, particularlyminority and low-income students,who are often denied access toadvanced tracks even when they areprepared to succeed. On the otherhand, it also set a large number ofstudents on a course for failurewithout the adequate preparation orsupports they would need to succeedin Algebra 1. Furthermore, students’

failure on the Algebra 1 CST tendedto continue in subsequent attempts.In 2011, for example, only 20% ofstudents who repeated the Algebra 1course in ninth grade passed the teston their second attempt. Thisrepeated failure may have convincedsome students they are “unable” tounderstand and use mathematics, orever complete the graduationrequirement of passing the Algebra 1CST.17

Another central question in thepolicy debate in California iswhether eighth grade is theappropriate target for enrollment ofmost or all students in Algebra 1.Enrolling students in Algebra 1 ineighth grade effectively requires“compressing” middle-grades topicsinto fewer grade levels ofinstruction. This may putunderprepared students at a furtherdisadvantage, as they have less timeto learn the mathematics skills andconcepts needed to becomeprepared for success in Algebra 1.Careful, equitable, and data-informed designation of whichstudents are prepared to succeed inAlgebra 1 in eighth grade isconsequential. California schoolsthat implemented such placementpractices showed higher eighth-grade mathematics achievementoverall.18

Another consequence of mandatingAlgebra for All is its effect ofreducing the academic rigor in manyninth-grade algebra classrooms.There is evidence that under policies

Enrolling students

in Algebra 1 in

eighth grade

effectively requires

“compressing”

middle-grades

topics into fewer

grade levels of

instruction.

16 Takako Nomi, “The Unintended Consequences of an Algebra-for-All Policy on High-SkillStudents : Effects on Instructional Organization and Students’ Academic Outcomes,”Educational Evaluation And Policy Analysis 34, no. 4 (2012); Allensworth and Nomi, “College-Preparatory Curriculum for All”; Chicago Public Schools Department of Evaluation, Research,and Accountability, Two-year Course Taking Patterns.

17 Rosin et al, Algebra Policy in California.18 EdSource, Needed: Careful Evaluation of Algebra I Placements in Grade 8 (Mountain View, CA:

EdSource, 2011).

where all students are required totake Algebra, students are typicallygrouped according to ability, andmost lower-track “Algebra 1”courses more closely resemble theremedial, pre-algebra courses thatthe policies were intended toeliminate in the first place.19

Students in these lower-achievingclassrooms are typically exposed towatered-down curriculum, moreslowly paced instruction, feweradvanced mathematics topics, andless emphasis on problem-solvingapproaches compared to theirhigher-achieving peers.20 Further,students of color and economicallydisadvantaged students aredisproportionately placed into suchclassrooms, where they typicallyexperience reinforcement ofnegative perceptions about theirability and low expectationsregarding their achievement.21

COMMON CORE STATESTANDARDS

The adoption of the Common CoreState Standards for Mathematics(CCSS-M) by 45 states since 2010has introduced a change in thealgebra policy context. The CCSS-Mdescribe the skills and knowledgethat mathematics educators at allgrade levels should seek to developin their students. One of the majorgoals of the developers of theCommon Core State Standards wasto articulate fewer, more focusedexpectations for K-12 mathematics,which in turn resulted in somesignificant repositioning of content

from previous grade-level andsecondary-course standards.

Several of these changes areconsequential for the curriculumscope of Algebra 1. For example,much of the content previouslyaddressed in Algebra 1 has beenmoved downward into the Grade-8standards (see Table 1 for asummary of major shifts in algebra-related content in CCSS-M). Inaddition, the model Algebra 1course outlined in CCSS-Mincludes a treatment of a limitednumber of advanced topics nottypically addressed until Algebra 2in previous state standardsdocuments and curriculummaterials. The combined resultmight be characterized as a slightlyreduced, more focused scope ofcontent for a ninth-grade Algebra 1course, but with some increase inthe level of advanced algebracontent. On the one hand, the“slightly reduced” aspect may

provide less-prepared learners theadvantage of being able to focus ona somewhat smaller set of algebraconcepts in ninth grade. Inaddition, as students progressthrough the mathematicscurriculum over time, they may bebetter equipped to succeed inAlgebra 1 because the standardsalso articulate a coherent set ofalgebraic and pre-algebra conceptsthroughout elementary and middlegrades. On the other hand,downward positioning of algebracontent means students arerequired to learn more demandingalgebra content earlier, potentiallyincreasing the challenge.

A final important issue related toCCSS-M is the articulation ofexpectations about mathematicalpractices—including sense-making, reasoning, constructingarguments, modeling, usingappropriate tools, attending toprecision, discerning patterns, and

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policyBRIEF

Table 1: Major Shifts in Algebra Content in CCSS-M

CCSS-M Grade-8 Topicspreviously taught in a typical Algebra 1 course

CCSS-M Algebra 1 Topicspreviously taught in a typical Algebra 2 course

• Linear functions – meaning andrepresentations

• Linear equation-solving

• Analyzing and solving systems oflinear equations

• Quadratic functions

• Quadratic equation-solving

• Exponential relationships

• Formal function notation

• Transformations of functions

19 Diversity in Mathematics Education (DiME) Center for Learning and Teaching, “Culture, Race, Power and Mathematics Education,” in SecondHandbook of Research on Mathematics Teaching and Learning, ed. Frank Lester (Charlotte, NC: Information Age, 2007), 405-433.

20 Jeannie Oakes, “Can Tracking Research Inform Practice? Technical, Normative, and Political Considerations,” Educational Researcher, 21, no. 4,(1992): 12-21.

21 Gamoran et al, “Upgrading High School Mathematics Instruction”; Danny Martin, “Hidden Assumptions and Unaddressed Questions inMathematics for All Rhetoric,” Mathematics Educator, 13, no. 21, (2003): 7-21.

expressing regularity. The blueprintof the CCSS-M-alignedassessments, which are targeted tobe implemented by 2014-15,indicates that these practices willbe assessed at a level surpassingwhat has been seen in the past.22 Aswe will discuss later, the integrationof these mathematical practicesinto Algebra curriculum will requirean expansion from the traditionalmodels of teaching Algebra 1.

Overall, it is still uncertain howimplementation of CCSS-M andassociated assessments will affectmathematics outcomes forstudents in grades eight, nine, andbeyond, but they are cause for bothoptimism and concern about thereadiness of students to succeed inAlgebra 1, particularly those whohave not traditionally beensuccessful in mathematics underthe previous, often less-rigorousstandards and assessments.

PRINCIPLES FORIMPROVING STUDENTSUCCESS IN ALGEBRAResearch on student success inalgebra points to several ways inwhich algebra policies can berestructured to support studentsuccess more effectively. Given thatAlgebra 1 is a critical gatekeepercourse for high school graduationand post-secondary success, andthat CCSS-M has elevated thealgebra standards for all students,

we agree not just that all studentstake an Algebra 1 course (or itsIntegrated Mathematics equivalent)by ninth grade, but that the coursereflects the rigor of a true college-preparatory mathematics approachto algebra, and further, thatappropriate supports be includedto help all students succeed in sucha course. In light of the challengesthis raises for underpreparedstudents, this section offers threeevidence-based principles forimproving student success inAlgebra and beyond.

PRINCIPLE ONE: STUDENTSNEED EARLY, SYSTEMATICEXPOSURE TO ALGEBRA

In a traditional view of teachingalgebra, algebra content is notaddressed until a first formalAlgebra course in eighth or ninthgrade. This view is based onperceptions that algebra cannot betaught until particular prerequisiteskills (e.g., percentages, decimals,fractions) have been mastered. Fordecades, however, the NationalCouncil of Teachers of Mathematics(NCTM)23—and more recentlyCCSS-M—have promoted a vision ofalgebra teaching and learning thatbegins in pre-kindergarten andprogressively expands in coverageand sophistication across theelementary and middle grades. Suchearly exposure to algebra is criticalfor student success in formal algebracourses in later grades.

Research indicates that earlyexposure to algebra has been linkedto higher algebra performance.24

Key algebraic ideas to be developedthrough grades K-7 include themeaning and use of variables, themeaning of the equal sign as a“balance point”, generalizingarithmetic, generalizing patternsand rules for functional situations,and the equivalence of expressions.Given the importance of earlyalgebra, if students areencountering algebra content forfirst time in significant ways ineighth or ninth grade, the challengeand likelihood of failure increase. Inaddition, topics in the Numberstrand—proportional reasoning inparticular—have been shown to bea gateway to the modes ofabstraction prevalent in algebra.25

An evidence-based approach toimproving success in Algebra wouldtherefore start with ensuring asound curriculum in K-8mathematics, in alignment with theCCSS-M, and implemented withquality instruction, particularly innumber and algebraic reasoning.

PRINCIPLE TWO:UNDERPREPAREDSTUDENTS NEEDTARGETED, STRUCTUREDSUPPORT IN ALGEBRA 1

In order for underpreparedstudents to succeed at Algebra ineighth or ninth grade, they must beprovided with targeted, structured

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Algebra and the Underprepared Learner 7

22 Illinois will use assessments developed by the Partnership for Assessment of Readiness of College and Careers (PARCC). PARCC is a 22-stateconsortium working to developing K-12 assessments in English and mathematics.

23 National Council of Teachers of Mathematics, Principles and Standards for School Mathematics (Reston, VA: National Council of Teachers ofMathematics, 2000).

24 Barbara Brizuela, The Impact of Early Algebra on Later Algebra Learning, NSF-REESE Award No. 0633915, Year 3 Findings Report (Medford, MA:Tufts University, 2010); Scott A. Strother, “Algebra Knowledge in Early Elementary School Supporting Later Mathematics Ability” (PhD diss.,University of Louisville, 2011).

25 See, for example, Richard Lesh, Thomas Post, and Merlyn Behr, “Proportional Reasoning,” in Number Concepts and Operations in the MiddleGrades, ed. James Hiebert and Merlyn Behr (Reston, VA: National Council of Teachers of Mathematics, 1988), 93-118.

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policyBRIEF

Completion of Algebra 1 in middle school createsopportunities for students to take more advancedmathematics courses in high school, includingAdvanced Placement courses in calculus andstatistics. The number of students—includingstudents of color and economically disadvantagedstudents—taking Algebra in 8th grade hasincreased dramatically over the past severaldecades. Enrollments vary by state, but nationally8th graders today take Algebra more than any othermathematics course.1 This trend is supported inurban districts by efforts like the Chicago AlgebraInitiative, which has helped open mathematicsopportunities for algebra-ready middle schoolstudents to take a rigorous Algebra 1 course taughtby a qualified teacher. Since 2003, the initiative hasresulted in 225 credentialed teachers currentlyoffering 8th grade algebra in 205 K-8 schools inChicago.2

For students who are well prepared to succeed andwho take the equivalent of a full, college-preparatory Algebra I course, placement in thecourse in 8th grade serves those students well.3

But districts and schools must carefully considerissues related to accelerating students into algebrain 8th grade. In cases where students are notacademically prepared to succeed and/or the rigorof the courses is not strong, the consequences oftaking the course too early are detrimental, andfailure in the course sets students further behind

rather than ahead.4 In 2002-03, for example,Charlotte-Mecklenburg schools dramaticallyincreased the percentage of moderately-performingstudents enrolled in 8th grade Algebra, from lessthan half to nearly 90%. These underpreparedstudents scored significantly lower on end-of-course Algebra I tests, and were either no morelikely or significantly less likely to pass subsequentmath courses.5

Students who are not prepared to take Algebra 1 in8th grade are better served by a rich, demandingmiddle-school course in mathematics, one alignedto CCSS-M Grade-8 standards. In one study, low-achieving students (those with initial scores at orbelow the 20th percentile) attained higher tenthgrade test scores if they took Algebra in high school,rather than in 8th grade.6

The percentage of students enrolled in 8th gradealgebra is sometimes used as a metric to measuredistrict or school achievement. The Illinois StateBoard of Education has recently added this metricto the State of Illinois school report cards. Given thefindings related to success in 8th grade algebrabeing linked to students’ level of preparation,policies like this should be reconsidered. A possibleconsequence of such a policy is that schools mightbe influenced to enroll underprepared 8th-gradersin the course in an attempt to display morefavorable data.

CONSIDERATIONS FOR ALGEBRA IN 8TH GRADE

1 Brown Center on Education Policy, Tom Loveless, and Brookings Institution. The Brown Center report on American education [2013]: How well areAmerican students learning? (Washington, D.C.: Brown Center on Education Policy, The Brookings Institution, 2013).

2 David Jabon, Lynn Narasimhan, John Boller, Paul Sally, John Baldwin, and Regeta Slaughter, “The Chicago Algebra Initiative,” Notices of theAmerican Mathematical Society, 57, no. 7, (2010): 865-867. Retrieved from www.ams.org/notices/201007/rtx100700865p.pdf

3 Matthew Rosin, Heather Barondess, and Julian Leichty, Algebra Policy in California Great Expectations and Serious Challenges (Mountain View, CA:EdSource, 2009); Jill Walston and Jill Carlivati McCarroll, Eighth-grade Algebra: Findings from the Eighth-grade Round of the Early ChildhoodLongitudinal Study, Kindergarten Class of 1998-99 (ECLS-K)(Washington, DC: National Center for Education Statistics, Institute of EducationSciences, 2010).

4 Loveless, Brown Center Report.5 Charles Clotfelter, Helen Ladd, & Jacob Vigdor, “The aftermath of accelerating algebra: Evidence from a district policy initiative,” NBER Working

Paper Series, Working Paper 18161 (Cambridge, MA: National Bureau of Economic Research, 2012).6 Adam Gamoran and Eileen Hannigan, “Algebra for everyone? Benefits of college preparatory mathematics for students with diverse abilities in

early secondary school,” Educational Evaluation and Policy Analysis, 22, No. 3, (2000), 241-254.

policyBRIEF

Algebra and the Underprepared Learner 9

support. There is promisingevidence that coupling a policy ofrequiring algebra for all students inninth grade with the provision ofadditional instructional time cansignificantly benefit underpreparedlearners.26 In its less intensiveforms, extra instruction may occurin the context of after-schoolprograms that involve tutoring,additional practice, technologyintegration, algebra-relatedenrichment activities, or summertransition programs for enteringninth-graders. Examples of thelatter include Portland SchoolsFoundation’s Ninth Grade Counts,which was found to have a clear,positive effect on high school creditattainment,27 and CPS’ summerintervention Step Up to High Schoolprogram, which showed promise inimproving students’ adjustment toninth-grade Algebra.28

A more intensive intervention,which is becoming increasinglyprevalent in school districtsnationwide, is to provideunderprepared students (typicallyidentified through use ofassessment data, grades, teacher

recommendations, or acombination thereof) with asecond daily period of Algebra 1instruction.29 Providing extra dailyalgebra instruction has resulted insome promising outcomes thus far.A study on the effects of one suchpolicy enacted in CPS in 2003, forexample, showed thatunderprepared students—in thiscase, those who scored in the lower50th percentile on the eighth-gradeIllinois Standard Achievement Test(ISAT) mathematics test—benefitted from the additionalperiod of algebra instruction onvarious long-term metrics,including their ACT mathematicsscores and reading scores, highschool graduation rates, andcollege entrance rates.30 Otherimplementations of double-periodalgebra have resulted in substantialincreases in overall algebra passrates.31 A key aspect in each of theseimplementations was a soundprocess for identifying whichstudents receive the additionalinstruction. Issues of availableresources, need, potential benefit,and available data all factored intothe criteria.

Extra time alone, however, isinsufficient for meeting theexpectations of policy makers,parents, and teachers for studentlearning—as well as those ofstudents themselves. For manystudents, learning algebra involvesovercoming a history of struggle inprevious mathematics courses,which has left them multiple gradelevels behind academically anddiscouraged emotionally. With somuch additional ground to coverwithin a single year of instruction, acomprehensive, coherent system ofsupports is needed to exact thegreatest benefit from the additionalinstruction. Drawing from researchliterature, a number of instructionalapproaches show promise forproviding cognitive and socio-emotional supports for studentswho struggle with algebra. Whencoupled with the necessary extratime to implement them, theseapproaches can create an“architecture of support” thatattends to the varied and significantinstructional needs of students.32

An appropriate architecture ofsupport should include several

26 Extra instructional time in the form of spreading Algebra I over two years was previously noted as a strategy to avoid, since it delays students’completion of Algebra I and puts students at higher risk of not completing the required high school mathematics sequence. While therecommendation of implementing a double period of algebra also requires more time and resources and separates students according to level ofpreparation, we see this strategy as “a tracking to un-track” strategy. In many contexts, a double-period algebra intervention constitutes the lastfeasible point in K-12 education to systematically catch up underprepared mathematics learners. After completing a double-period algebracourse, the goal is for students to be on par with their peers in subsequent mathematics courses.

27 Portland Schools Foundation, Ninth Grade Counts Student Data Report Summer 2009 and Participation for Summer 2010 (Portland, OR:Northwest Evaluation Association, 2011).

28 Bret Feranchak, Student Reactions to Step Up: Reflections from Students in ninth Grade. (Chicago, IL: Chicago Public Schools Department ofProgram Evaluation, 2007); Office of Research, Evaluation, and Accountability, Evaluation of the 2003 Step Up Program, Department of Evaluationand Data Analysis (Chicago, IL: Chicago Public Schools, 2004).

29 The additional period has been implemented using a variety of configurations, such as a true double block with a single instructor teaching thesame group of students for two continuous class periods, or else as a supplemental period that acts as an entirely separate class with a differentteacher, group of students, and curriculum. At this point, there is little evidence on which model is most effective. However, when consideringissues of instructional coherence, the model of the same teacher and students in a single block (i.e., back-to-back periods) seems most promising.

30 Kalena Cortes, Joshua Goodman, and Takako Nomi, “A Double Dose of Algebra: Intensive Math Instruction Has Long-term Benefits,” EducationNext, 13, no. 1, (2013): 70-76.

31 Robert Balfanz, Nettie Legters, and Vaughan Byrnes, What the Challenge of Algebra for All Has to Say about Implementing the Common Core: AStatistical Portrait of Algebra I in Thirteen Large Urban Districts (Center for Social Organization of Schools, Johns Hopkins University, 2012).

32 Agile Mind, Charles A. Dana Center at the University of Texas at Austin, Learning Sciences Research Institute at the University of Illinois at Chicago,Intensified Algebra I: Program and Research Update (San Francisco, CA: Agile Mind, 2012).

elements. First, it should includecurriculum and instruction aimed atreasoning, problem-solving,mathematical discourse, proceduralfluency, sense-making, andapplication of concepts. Oncethought appropriate only forselected high-achieving students, anapproach that integrates higher-order mathematical practices hasproved more effective than roteteaching of procedures for studentsacross a wide spectrum of initialachievement levels, family incomelevels, and cultural and linguisticbackgrounds.33 In addition, aneffective architecture of supportshould involve an approach toalgebra that helps students makesense of concepts and develop waysof thinking algebraically. In afunctions-based approach, forexample, the “function is the centralconcept around which schoolalgebra curriculum is meaningfullyorganized.”34 A functions-basedapproach can help students accessalgebra more readily by buildingfrom students’ pre-existing numbersense and abilities to recognizepatterns. Another possible curricular

approach is one that helps studentsunderstand algebra as generalizedarithmetic. Also, a framework ofsupport should incorporatedistributed practice, or spacingpractice problems in small dosesover a long span of time.35 Finally,instruction that confronts andsystematically exposes commonmathematical misconceptions anderrors—rather than avoids them—has been found to provideunderprepared students with anefficient means of reviewing andrepairing necessary prerequisiteunderstandings for learningalgebra.36

PRINCIPLE THREE:INCREASING STUDENTS’SUCCESS IN ALGEBRAREQUIRES ENHANCEDTEACHING CAPACITY

Teachers with more years ofexperience are generally moreeffective in helping students learn.37

However, administrators oftenassign the least-experiencedinstructors to teach Algebra 1,especially to sections of

10 UIC Research on Urban Education Policy Initiative

policyBRIEF

Teachers with more

years of experience

are generally more

effective in helping

students learn.

33 Jomills Henry Braddock and James M. McPartland, “Education of Early Adolescents,” Review ofResearch in Education, 19, (1993): 135-170; Eugene E Garcia, “Language, Culture, andEducation,” Review of Research in Education, 19, (1993): 51-98; Michael S. Knapp, “AcademicChallenge in High-Poverty Classrooms,” Phi Delta Kappan, 76, no. 10, (1995): 770-776.

34 Michal Yerushalmy, “Problem Solving Strategies and Mathematical Resources: A LongitudinalView on Problem Solving in a Function Based Approach to Algebra,” Educational Studies inMathematics, 43, no. 2, (2000): 125-147.

35 Harold Pashler, Patrice M. Bain, Brian A. Bottge, Arthur C. Graesser, Kenneth Koedinger, MarkMcDaniel, and Janet Metcalfe, Organizing Instruction and Study to Improve Student Learning,NCER 2007-2004 (Washington, DC: National Center for Education Research, Institute ofEducation Sciences, U.S. Department of Education, 2007).

36 Mike Askew and Dylan Wiliam, Recent Research in Mathematics Education (London: HMSO,1995), 5-15.

37 Douglas N. Harris and Tim R. Sass, “Teacher Training, Teacher Quality and StudentAchievement,” Journal of Public Economics, 95, no. 7, (2011): 798-812; Dan D. Goldhaber andDominic J. Brewer, “Does Teacher Certification Matter? High School Teacher Certification Statusand Student Achievement,” Educational Evaluation and Policy Analysis, 22, no. 2, (2000): 129-145; Jennifer Rice, The Impact of Teacher Experience: Examining the Evidence and PolicyImplications, CALDER Policy Brief 11 (Washington, DC: The Urban Institute, 2010).

38 Charles T. Clotfelter, Helen F. Ladd, and Jacob L. Vigdor, The Aftermath of Accelerating Algebra:Evidence from a District Policy Initiative, NBER Working Paper 18161 (Cambridge, MA: NationalBureau of Economic Research, 2012); Balfanz et al, What the Challenge of Algebra for All Has toSay about Implementing the Common Core.

policyBRIEF

Algebra and the Underprepared Learner 11

39 Linda Darling-Hammond, “Teacher Quality and Student Achievement: A Review of State Policy Evidence,” Educational Policy Analysis Archives, 8,no. 1, (2000), http://epaa.asu.edu/ojs/article/view/392/515; Eric A. Hanushek, John F. Kain, Daniel O’Brien, and Steven G. Rivkin, The Market forTeacher Quality, NBER Working Paper 11154 (Cambridge, MA: National Bureau of Economic Research, 2005).

40 Joshua Aronson (Ed.). Improving Academic Achievement: Impact of Psychological Factors on Education (San Diego, CA: Academic Press, 2002); LisaS. Blackwell, Kali H. Trzesniewski, and Carol Sorich Dweck, “Implicit Theories of Intelligence Predict Achievement Across an Adolescent Transition:A Longitudinal Study and an Intervention,” Child Development, 78, no. 1, (2007): 246-263.

41 John Easton, Stephen Ponisciak, and Sturat Luppescu, From High School to the Future: The Pathway to 20 (Chicago: Consortium on ChicagoSchool Research, 2008).

42 Deborah Loewenberg Ball and Francesca Forzani, “The Work of Teaching and the Challenge for Teacher Education,” Journal of Teacher Education,60, no. 5, (2009): 497-511.

underprepared learners,38 despitethe well-established research aboutthe critical role of algebra forstudents’ academic success, andthe fact that teaching qualitytrumps virtually all other influenceson student achievement.39 Withregard to the teaching of algebra, akey to enhancing teacher quality isa commitment among bothleadership and teaching corps todevelop content knowledge andpedagogical skills that helpstruggling learners make sense ofalgebra. These capacities includedeep understanding of algebraicreasoning, effective questioningstrategies, implementation of richmathematical tasks, establishmentof an environment of mathematicalexploration and discourse, analysisof student work, and usingassessment to support studentlearning.

Teachers’ ability to address thesocial and emotional factorsassociated with learningmathematics is also related tostruggling learners’ success inalgebra. A characteristic of manyschools and classrooms that aresuccessful with helpingunderprepared learners is the useof an asset-based approach thatbuilds on students’ strengths andhelps them develop academic skillsand identities. Students who havenot experienced academic successoften do not understand how“academics are played.” Teachers

can explicitly teach skills that helpstudents conceive of themselves ascapable learners.40 In addition,fostering positive teacher-studentrelationships has been found tohave a strong impact onattendance, pass rates, and gradesfor ninth-grade students in coreacademic classes.41

In the same way that mathematicalability is not a fixed trait instudents, these professionalteaching capacities are not inherentabilities that some teachers possessand others do not. Rather, they canbe developed through teacherpreparation and ongoingprofessional learning.42 Enhancingteacher capacity in support ofstudents’ success in Algebrarequires consideration of policydevelopment around two equallyimportant aspects: (1) developingthese capacities in teachersthrough teacher preparation,professional development, andevaluation; and (2) prioritizingAlgebra 1 by assigning teacherswho possess the capacitiesdiscussed above.

RECOMMENDATIONSSeveral research-informedapproaches can be implemented toimprove current algebra policies.This section contains sixrecommendations that the State,local boards of education anddistrict leaders, local school

administrators and teaching corps,and leaders in teacher preparationprograms, should consider.

RECOMMENDATION ONE:PROVIDE ALL STUDENTSWITH A TRUE COLLEGE-PREPARATORY ALGEBRACOURSE BY THE END OFNINTH GRADE

Replacing ninth-grade Algebra withremedial alternatives such as Pre-Algebra, basic math, algebrastretched over two years in gradesnine and ten, etc., or else wateringdown content in courses named“Algebra 1” does not help studentswho are behind to catch up. Rather,it puts them further behind andmakes it more difficult for studentsenrolled in these courses to meettheir mathematics graduationrequirements, and nearlyimpossible to go on to theadvanced mathematics and sciencecourses that pave the way to morepromising post-secondaryopportunities. Moreover, minoritystudents and economicallydisadvantaged students aretypically disproportionately placedinto these less rigorous courses,thus amplifying the inequitablestructures that persistently obstructtheir opportunities in mathematics.Similarly, the programming andnomenclature of differentiatedtracks of Algebra (e.g., Honors,Regular, Basic, etc.) perpetuatefixed beliefs among adults and

12 UIC Research on Urban Education Policy Initiative

children regarding what students areable to do and what opportunitiesthey should be afforded. As such,placement policies should bedesigned to limit or reverse thenegative consequences of inflexibletracking practices.

In order to ensure that such anAlgebra course meets the increasedexpectations of CCSS-M, the contentshould be strong in intellectual rigorand provide appropriate sense-making opportunities for students.43

Content should reflect powerfulalgebraic ideas, which should not bedelayed until students have“mastered the basics.” The CSSS-Mdevelopers discuss rigor aspromoting with equal intensity threeaspects of learning: conceptualunderstanding, procedural skill andfluency, and application/modeling.To support rigor in all Algebracourses, a careful selection processfor the instructional materialsshould be adopted. The curriculumshould include a coherent sequenceof algebra concepts that aligns withthe Algebra 1 expectations in theCCSS-M model courses; curriculumselection processes, however, shouldextend beyond a “checklist”approach of standards addressed toalso include criteria that address thedegree to which the materialsaddress the CCSS-M Standards forMathematical Practice.

RECOMMENDATION TWO:ENACT A K-8 MATHEMATICSCURRICULUM THATPREPARES STUDENTS TOSUCCEED IN A HIGH-SCHOOL LEVEL ALGEBRACOURSE BY NINTH GRADE

School mathematics programsshould carefully addressmathematics ideas that research hasshown are foundational for buildingalgebraic understanding as they arearticulated in the NCTM Principlesand Standards for SchoolMathematics, and more recently, inCCSS-M. Students should begin todevelop understanding about pre-formal algebraic ideas in earlyelementary grades and build uptheir algebraic knowledge and skillsthroughout the middle grades.44

Important algebraic underpinningsinclude proportional reasoning; themeaning and use of variables; themeaning of the equal sign as a“balance point”; generalizingarithmetic; generalizing patternsand rules for functional situationsand the equivalence of expressions.Indeed, algebra should be conceivedas a content strand that is developedacross all grade levels. Moreover,math educators must be familiarwith the standards across all grades,with a deep understanding of howalgebraic concepts are developed inprevious and subsequent grades.

policyBRIEF

Content should

reflect powerful

algebraic ideas,

which should not be

delayed until

students have

“mastered the

basics.”

43 Iris R. Weiss, Joan D. Pasley, P. Sean Smith, and Eric R. Banilower, Looking Inside the Classroom: AStudy of K-12 Mathematics and Science Education in the United States (Chapel Hill, NC: HorizonResearch, Inc., 2003).

44 For decades, NCTM principles and standards had advanced the development of algebraicconcepts and skills throughout the K-8 mathematics curriculum. As states used the NCTMstandards to develop their own mathematics standards, however, wide variation came tocharacterize what should be expected at each grade level, K-8, in the sub-strands of algebra (seeBarbara Reys and Glenda Lappan, “Consensus or Confusion? The Intended Math Curriculum inState-Level Standards,” Phi Delta Kappan, 88, no. 9, (2007): 676-680). Through a cleararticulation of algebra learning expectations in grades K-8, CCSS-M presents a means fordistricts and schools to build mathematics programs that better prepare students for Algebra 1.The PARCC assessments, in assessing foundational algebraic understandings via formativeassessments in grades K-2 and via summative assessments in grades 3-8, will serve to focusattention on the need for a strong K-8 algebra strand.

Algebra and the Underprepared Learner 13

RECOMMENDATION THREE:CAREFULLY ESTABLISHCRITERIA TO DETERMINEWHICH STUDENTS NEEDEXTRA SUPPORT TO BESUCCESSFUL IN ALGEBRA

Careful criteria should be used toidentify which students shouldreceive targeted, structuredsupport. In cases where nosystematic, multi-faceted process isin place to identify these students,an identification system should bebuilt. This system should involvemultiple sources of evidence, suchas seventh- and eighth-grademathematics grades; mathematicsassessment data (e.g. ISAT scalescores and performance-leveldescriptions); algebra readinesstests; teacher recommendations;and student self-assessments.

The process should be flexibleenough to involve some degree ofstudent and parent choice, and itshould be well-documented,openly communicated, andfrequently reviewed and adjusted toincrease its effectiveness. Theprocess should also avoid over-tracking and overly-rigid placementcriteria by allowing motivated andresilient students, perhaps withparent consent, to opt out of asuggested placement if there isindication from previouscoursework or teacherrecommendation that they cansucceed.

RECOMMENDATION FOUR:PROVIDE TARGETED,STRUCTURED SUPPORT TOUNDERPREPAREDSTUDENTS

Underprepared students should beprovided with additionalinstructional time to help themsucceed in Algebra 1. Double-period algebra classes can providenecessary, structured support withthe explicit goal of helpingunderprepared students, over thecourse of a year, catch up to theirpeers so that they can succeed infuture on-level mathematics andscience courses.45 Summertransition programs (eighth gradeto ninth grade) and after-schoolprograms offer additionalopportunities for support.

Given that more time is importantbut not enough, the extra timeshould be used well. A coherent setof instructional materials andinstructional practices shouldincorporate the following keyaspects to provide appropriateinstructional supports forunderprepared students: (1) Use ofcurricular approaches that helpstudents make sense of algebraicconcepts and ways of thinking (e.g.,a functions-based approach,algebra as generalized arithmetic,conceptual development throughuse of rich problems); (2) emphasisof the CCSS-M Standards forMathematical Practice; and (3) use

of routines and structures thatsupport students’ learning andretention of algebraic ideas andskills (e.g., worked examples,spaced practice, tasks and activitiesthat help students build on priorknowledge and repair existingmisconceptions).

RECOMMENDATION FIVE:ASSIGN NINTH-GRADEALGEBRA COURSES TOTEACHERS MOSTQUALIFIED TO TEACH THECOURSE—PARTICULARLYWHERE UNDERPREPAREDLEARNERS ARE ENROLLED

Because Algebra 1 is such a high-stakes course, schooladministrators should make it a toppriority in making teacherassignments. Teachers who aremost qualified to teach the courseshould be assigned to teach Algebra1. Experience, math background,teaching abilities, and teacherdispositions should all beconsidered in this process. Indeed,high student-to-teacher ratios inAlgebra 1 compared with othermathematics courses are typical inmost districts and schools. Becauseof the critical importance ofAlgebra 1 and its implications forkeeping students on track tograduate, district and schooldecision makers should look toreverse this situation to allocateresources where they are most

policyBRIEF

45 We make this recommendation acknowledging that extended-time algebra classes place demands on district, school, and student resources.However, we advance this recommendation based on recognition of the critical importance of students’ succeeding in Algebra 1 and the negativeconsequences of high failure rates in Algebra 1, which include the associated costs of remediating students who fail the course.

14 UIC Research on Urban Education Policy Initiative

needed. Assigning the most-qualified teachers to teach Algebra1 may involve confronting anestablished merit system, wheremore experienced teachers “earnthe right” to teach the advancedand/or upper-level courses.

RECOMMENDATION SIX:ENHANCE TEACHERS’CAPACITIES TO PROVIDEHIGH-QUALITYMATHEMATICSINSTRUCTION ANDSUPPORT THE NEEDS OFUNDERPREPAREDSTUDENTS IN ALGEBRA

A program of professional learningshould support algebra teachers’domain-specific content knowledge(e.g., the different meanings anduses of variables; varied methodsfor solving algebraic problems;distinct properties of numbersystems) and pedagogical contentknowledge (e.g., ways to addresscommon algebraic misconceptions,connect mathematical ideastogether, decide whichinstructional strategies are mosteffective for particular concepts,and assess particular algebraicunderstandings). Enhancing thesecapacities becomes particularlyimportant in light of the changes incourse content and emphasis onmathematical practices broughtabout by CCSS-M.

For teacher professionaldevelopment and secondarymathematics teacher preparationprograms to support therecommendations listed above,they should also include an explicit

focus on teaching underpreparedstudents in algebra, who often lackkey proficiencies as a result ofprevious struggles in mathematics.For example, becauseunderprepared students in Algebra1 often struggle with middle-gradesmathematics concepts, high schoolmathematics teachers and teachercandidates would benefit from aprogram of professionaldevelopment (or pre-servicecourse) that develops theirpedagogical content knowledgerelated to middle-schoolmathematics topics, and providesexploration of ways that common,algebra-related misconceptions canbe addressed. Relatedly, elementaryand middle-level teachers couldbenefit from professional learningwith a focus on understanding howalgebra concepts are developedthrough the elementary grades andhigh school.

Preservice and inserviceprofessional learning should alsoinclude an aspect to help teachersbuild their capacity to positivelyenhance students’ academicidentities and dispositions towardlearning. Social-motivationalsupports and ideas from socialpsychology can be incorporatedinto the fabric of an Algebra 1course, especially in courses with ahigh percentage of students whohave traditionally not succeeded inmathematics. Moreover, the explicitteaching of the role of effectiveeffort and the theory of malleableintelligence (i.e., that one’sintelligence is not fixed) has beenlinked to increases in student’spersistence, willingness to take

academic risks, and academicperformance.46

CONCLUSIONSuccessful completion of Algebra 1continues to be a key benchmarktoward attaining a high schooldiploma and preparing students totake more advanced mathematicscourses. Enacting Algebra for Allpolicies and aligning algebracontent to CCSS-M both serve thepurpose of raising expectations forall students with regard to meetingthis benchmark. However, for thesepolicies to be meaningful withregard to students’ actual academictrajectories, completion of Algebra1 must be timely, the content of thecourse must be rigorous, andsupports for underpreparedstudents must be sufficient toprovide them with a pathwaytoward success. This requires acarefully planned, systemicapproach that considers thepotential impact of the existing K-8mathematics curriculum, extrainstructional time with targetedsupports in grade nine, and theteaching capacity required toprovide high-quality instruction inAlgebra 1.

policyBRIEF

46 Catherine Good and Carol S. Dweck, “A Motivational Approach to Reasoning, Resilience, and Responsibility,” in Optimizing Student Success inSchool Reasoning, Resilience, and Responsibility with the Other Three R’s, ed. Robert J. Stemberg and Rena Faye Subotnick (Charlotte, NC:Information Age Publishing, 2005), 39-56.

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

• Education policies should directly engage with what happens in schools and classrooms

• Education policies should account for local context

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.

Learn more at www.education.uic.edu/ruepi

policyBRIEF

Algebra and the Underprepared Learner 15

This brief, Algebra and the Underprepared Learner, was developed in cooperation with the Chicago STEM EducationConsortium (C-STEMEC). C-STEMEC comprises four STEM-related university centers: the Center for ElementaryMathematics and Science Education at the University of Chicago, the Loyola Center for Science and MathematicsEducation at Loyola University, the Learning Sciences Research Institute at the University of Illinois at Chicago, and theSTEM Center at DePaul University. Support for C-STEMEC comes from the Searle Funds at The Chicago CommunityTrust.

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