Improving Mathematics Teacher Preparation Policy in IL

Improving Mathematics Teacher PreparationPolicy in IllinoisBy Benjamin Michael Superfine and Alison Castro Superfine

EXECUTIVE SUMMARYEducation policies around the U.S.have focused intensely onreforming teacher preparationprograms. Illinois has engaged insuch efforts by restructuringrequirements governing thecurriculum of teacher preparationprograms and testingrequirements for teachercertification in mathematics andother disciplines. The recentmoves to improve mathematicsteacher preparation in particularare driven largely by the belief thatwell-prepared teachers are criticalfor ensuring that students receivestrong mathematics educations.However, policy efforts to increasethe quality of mathematics teacherpreparation programs are oftendisconnected from each other andfail to work coherently andstrategically toward developingmathematics teacher knowledgeand skills. These policy effortsaccordingly can be improved inseveral ways. First, these efforts

should explicitly articulate astrong vision of the skills andknowledge mathematics teachersshould have. Such skills andknowledge should be grounded insubject matter knowledge andpedagogical content knowledge –an understanding of the priorconceptions and knowledge thatstudents of different ages andbackgrounds bring with them intothe classroom and ways ofrepresenting and communicatingmathematics in ways that make itcomprehensible by students.Second, policy efforts shouldensure that all elements ofmathematics teacher preparationprograms – ranging fromassessments and curriculum tomathematics teacher educatortraining – are aligned with such avision. Third, these policy effortsshould not be subject to constantrevision and should be coherentwith other major education policyreform efforts in Illinois.

education.uic.edu/ruepi

ABOUT THE AUTHORS

Benjamin MichaelSuperfine is anAssociate Professor of Educational PolicyStudies in the Collegeof Education at theUniversity of Illinois

at Chicago. He is also the Directorof the Research on UrbanEducation Policy Initiative.

Alison CastroSuperfine is anAssociate Professorof MathematicsEducation andLearning Sciences

at the University of Illinois atChicago. She is also the Directorof the Office of MathematicsEducation at UIC.

policyBRIEFUIC Research on Urban Education Policy Initiative

June 2013

Vol. 2, Book 1

2 UIC Research on Urban Education Policy Initiative

INTRODUCTIONEducation policies around the U.S.have focused intensely onreforming teacher preparationprograms. Illinois recently hasengaged in such efforts byrestructuring requirementsgoverning the curriculum ofteacher preparation programs andtesting requirements for teachercertification in mathematics andother disciplines. These policies arepart of a broader effort, bothnationally and in Illinois, toimprove the quality andeffectiveness of teachers. Like manyother states, Illinois has enactedpolicies focused on evaluatingteachers based on theirperformance, especially on thebasis of their students’ achievementgrowth on standardized tests.Although the policy efforts toevaluate practicing teachers havegarnered substantial politicalattention, policymakers have begunto view teacher preparationprograms as an essential element ofincreasing teacher qualityeffectiveness as well. Such recentmoves to improve mathematicsteacher preparation are drivenlargely by the belief that wellprepared teachers are critical forensuring that students receivestrong mathematics educations.Indeed, modifying policiesgoverning teacher preparationprograms holds the promise ofenhancing the quality of newteachers as they embark upon theirteaching careers.

However, policy efforts to increasethe quality of teacher preparationprograms in mathematics can beimproved in several ways. First,these efforts should explicitlyarticulate a strong vision of theskills and knowledge that

mathematics teachers should have.To be sure, many recommendationsfor improving mathematics teacherpreparation programs have focusedon the number of mathematicscourses students should take tograduate or whether students havea degree in mathematics. However,these recommendations are largelybased on the assumption thatteachers will be more effective withsimple increases in their levels ofmathematical knowledge. Therecommendations contained in thisbrief are based on a more complexand research-based vision of themathematics teachers should knowin order to be effective instructors –mathematical knowledge forteaching. Such a vision ofmathematics is groundedparticularly in subject matterknowledge and pedagogicalcontent knowledge – anunderstanding of the priorconceptions and knowledge thatstudents of different ages andbackgrounds bring with them intothe classroom and ways ofrepresenting and communicatingmathematics in ways that make itcomprehensible by students.

Second, grounded in a stronglyarticulated vision of mathematicalknowledge for teaching, policyefforts should ensure that allelements of mathematics teacherpreparation programs are alignedwith this vision. These elementsrange from assessments andcurriculum to mathematics teachereducator training. Third, thesepolicy efforts should not be subjectto constant revision and should becoherent with other majoreducation policy reform efforts inIllinois, such as recently enactedpolicies focused on teacherevaluation and accountability.

There are several other approachesthat could be taken to improve thequality of mathematics teachersentering the teacher workforce.Reforms could focus on teacherpreparation programs’ selection ofcandidates, preparation programs’graduation requirements, difficultyof licensure tests, or alternativeroutes to certification. Severalrecent policies have concentratedprecisely on such approaches, andthese efforts deserve thoroughconsideration and examination.However, what mathematicsteachers should know and teacherpreparation programs’ role inhelping teachers acquire thisknowledge have received far toolittle attention from policymakers,despite the leverage such anapproach potentially has forimproving the quality of futureteachers.

This brief accordingly examinesrecent policy efforts aimed atimproving mathematics teacherpreparation policies in the U.S. andparticularly Illinois. First, the policylandscape governing mathematicsteacher preparation programs isexamined. Second, relevantresearch on mathematicalknowledge for teaching isexamined, in addition to promisingstrategies for helping teachers learnthese knowledge and skills. Thisbrief concludes by analyzing theprospects for teacher preparationpolicies in Illinois and offeringrecommendations for makingmathematics teacher preparationpolicies more effective.

policyBRIEF

THE TEACHERPREPARATION POLICYLANDSCAPEEducation policies in the U.S., andIllinois in particular, haveincreasingly focused on enhancingthe quality of future mathematicsteachers through the reform ofteacher preparation programs.Teacher preparation programscurrently play a central role in theU.S. public education system byrecruiting, selecting, and preparingabout 200,000 future teachers eachyear.1 The U.S. contains 1,434colleges approved by states to trainelementary and secondary teachers,2

and Illinois contains 59 approvedteacher education institutions ofhigher education.3 Statestraditionally have served as theprimary regulators of the quality ofteacher preparation programs andhave employed two primary levers todo so.4 First, state educationalagencies review teacher preparationprograms to ensure that they meetvarious state law and regulationsabout program content, such asthose governing specific courserequirements, and they approveprograms on the bases of thesereviews. Second, states set therequirements for teachercertification, which generallyinclude completion of an approved

program and the passage of certaincontent and pedagogical tests. Manystates also require or encourageteacher preparation programs to beaccredited by independent agencieslike the National Council for theAccreditation of Teacher Educationor the Teacher EducationAccreditation Council, which reviewprograms under their ownstandards.5

Despite the presence of these qualitycontrol mechanisms, teacherpreparation programs have beencriticized harshly in recent years.This criticism has been especiallyintense in mathematics, which isoften viewed as crucial for theeconomic competitiveness of statesand the U.S. as a whole. Forexample, the National Council onTeacher Quality (NCTQ) found in a2008 report that teacher preparationprograms for elementarymathematics teachers are notrigorous, use inadequate textbooks,have low standards for admissionand graduation, and employ teachereducators who are not professionallyequipped to teach mathematics.6 Ina review of 111 undergraduate andgraduate teacher preparationprograms in 53 education schools inIllinois, NCTQ found that teacherpreparation programs areinconsistent, fail to equip future

1 U.S. Department of Education,Our Future, Our Teachers: The Obama Administration’s Plan forTeacher Education Reform and Improvement (Washington, D.C.: U.S. Deparment of Education,2011).

2 Chad Alderman, Kevin Carey, Eric Dillon, Ben Miller, and Elena Silva, A Measured Approach toImproving Teacher Preparation (Washington, D.C.: Education Sector, 2011).

3 Illinois State Board of Education,Directory of Approved Programs for the Preparation ofEducational Personnel in Illinois Institutions of Higher Education (Springfield, IL: Illinois StateBoard of Education, 2012).

4 Jane G. Coggshall, Lauren Bivona, and Daniel J. Reschly, Evaluating the Effectiveness of TeacherPreparation Programs for Support and Accountability (Washington, D.C.: NationalComprehensive Center for Teacher Quality, 2012).

5 Coggshall, Bivona, and Reschly, Evaluating the Effectiveness of Teacher Preparation Programs forSupport and Accountability.

6 National Council on Teacher Quality,No Common Denominator: The Preparation of ElementaryTeachers in Mathematics by America’s Education Schools (Washington, D.C.: National Council onTeacher Quality, 2008).

Improving Mathematics Teacher Preparation Policy in Illinois 3

policyBRIEF

In a comprehensive

review of the

effectiveness of

teacher preparation

accountability and

support policies,

the National

Comprehensive

Center for Teacher

Quality found that

teacher preparation

programs generally

fail to be based on

evidence about

their effectiveness.

teachers with strategies for effectiveteaching, discount the importanceof selecting the most academicallycapable teacher candidates, andassign faculty members to teacherout of their areas of expertise.7 As aresult, NCTQ gave only oneprogram a grade of A-, while itgraded 43 programs asunacceptably weak and 16 asfailing. In a comprehensive reviewof the effectiveness of teacherpreparation accountability andsupport policies, the NationalComprehensive Center for TeacherQuality (NCCTQ) found thatteacher preparation programsgenerally fail to be based onevidence about their effectiveness.8

Such attacks have emerged fromthe political sphere as well. U.S.Secretary of Education ArneDuncan publicly stated, “By almostany standard, many if not most ofthe nation’s 1,450 schools, colleges,and departments of education aredoing a mediocre job of preparingteachers for the realities of the 21stcentury classroom,” and, “America’suniversity-based teacherpreparation programs needrevolutionary change—notevolutionary tinkering.”9 In a planfor improving teacher preparationprograms, the U.S. Department ofEducation (ED) further argued thatonly 23% of all teachers and 14% ofteachers in high-poverty schoolscome from the top third of college

graduates, that 90% of high-minority districts have difficultyattracting highly qualifiedmathematics and science teachers,and too many teacher preparationprograms fail to provide teacherswith rigorous experiences thatprepare them for actual teaching.10

Given such criticism, policymakershave begun to enact reformsfocused on teacher preparation atboth federal and state levels. In1998, the federal Higher EducationAct was modified to require statesto provide ED with data aboutteacher preparation, such as thepass rates of teacher candidates onstate certification tests, informationon teacher preparation programs,and statewide certificationrequirements.11 States currentlymust report 440 different types ofsuch data annually.12 However, EDhas argued that such data are not“meaningful indicators” of programeffectiveness, largely because suchdata do not reveal how effectivelyprogram graduates teach.13 Giventhis position, a federal rule-makingpanel under the Obamaadministration engaged indiscussions in mid-2012 tooverhaul federal reportingregulations to place a greateremphasis on outcome measures ofteacher preparation programs, suchas the job placement of teachersfrom these programs and theachievement growth of students

served by teachers from theseprograms.14 However, the rule-making process ultimately stalleddue to the controversy aboutwhether teacher educationprograms should be evaluated onthe basis of their graduates’ jobplacement rates, employers’satisfaction with graduates theyhired, and students’ performanceon standardized tests. While EDrepresentatives felt that teacherpreparation programs were noteffective and insufficientlyaccountable for the performance oftheir graduates, opponents claimedthat such use of test scores hadlittle scientific basis.

Significant changes also haveemerged at the state level. Asreported by NCCTQ, at least sixstates have enacted significantchanges to their policies governingteacher preparation programs inrecent years.15 Louisiana has begunto use the same value-addedmeasure of student performanceon achievement tests to evaluateboth in-service teachers andteacher preparation programs, inaddition to modifying itscertification requirements andusing a web-based performanceassessment system to evaluateteacher candidates. Texas alsoemploys value-added measures ofstudent performance, surveysprincipals about the quality ofteachers, and examines the pass

7 National Council on Teacher Quality, Ed School Essentials: A Review of Illinois Teacher Preparation (Washington, D.C.: National Council on TeacherQuality, 2011).

8 Coggshall, Bivona, and Reschly, Evaluating the Effectiveness of Teacher Preparation Programs for Support and Accountability.9 Jennifer Medina, “Teacher Training Termed Mediocre,”New York Times, October 22, 2009. Retrieved on April 1, 2013 from www.lexisnexis.com.10 U.S. Department of Education,Our Future, Our Teachers: The Obama Administration’s Plan for Teacher Education Reform and Improvement.11 Higher Education Act, 20 U.S.C. 1001 et seq. (1998).12 U.S. Department of Education,Our Future, Our Teachers: The Obama Administration’s Plan for Teacher Education Reform and Improvement.13 U.S. Department of Education,Our Future, Our Teachers: The Obama Administration’s Plan for Teacher Education Reform and Improvement, 914 Libby Nelson, “Going It Alone,” Inside Higher Education, April 13, 2012. Retrieved April 1, 2013 from

www.insidehighered.com/news/2012/04/13/rule-making-teacher-preparation-programs-fails-reach-consensus.15 Coggshall, Bivona, and Reschly, Evaluating the Effectiveness of Teacher Preparation Programs for Support and Accountability.

policyBRIEF



policyBRIEFrates of teacher candidates oncertification exams to evaluateteacher preparation programs.Florida, North Carolina, Ohio, andTennessee have begun to move inbroadly similar directions. At least13 states and the District ofColumbia have planned to reportvalue-added information on theirteacher preparation programs inthe coming years.16 The evaluationof outcome measures of suchprograms is accordingly becomingone of the most important tools forassessing and regulating teacherpreparation program quality.

Such changes reflect a broad-basedpolicy push to improve teacherquality and effectiveness. With itspassage in early 2002, No Child LeftBehind (NCLB) required states toensure that a “highly qualifiedteacher” (HQT) is present in everypublic school classroom. While thedefinition of HQT varies fordifferent types of teachers, NCLBgenerally required teachers to befully certified and to havedemonstrated their knowledge andskills by taking sufficient academiccoursework in their field, passing astate test, or successfullycompleting a rigorous stateevaluation.17 The Race to the TopFund (RTT), a $4.35 billioncompetitive grant fund that waspart of the federal “Stimulus,”provided money to states to enactparticular types of education

reforms that notably included theevaluation of teachers on the basisof increases in the performance oftheir students on tests.18 Each of the14 states that won RTT grantspromised to use studentacheivement data as a signficantpart of teacher evaluation andteacher evaluation data to makepersonnel decisions.19 Moreover,RTT pushed many states to adoptthe Common Core State Standards(CCSS), written specifications of theskills and knowledge studentsshould learn in mathematics andlanguage arts that are beingdeveloped by a collaboration ofstates. In addition to states thatactually won RTT grants, manyother states instituted such reformsin anticipation of submitting RTTapplications (e.g. Colorado,Indiana, and Louisiana). Illinois,which also has begun to restructureits teacher preparation policies, hasinstituted such reforms as well.

TEACHER PREPARATIONPOLICY IN ILLINOISAlthough teacher preparationpolicies in Illinois have not changedas dramatically as in states likeLouisiana or Texas, they have begunto shift in ways that reflect thebroader political and policylandscape. Illinois currently has inplace a patchwork of policyrequirements for teacher

preparation. First, the state requiresteachers to be certified by theIllinois State Board of Education(ISBE) in at least one of five areas:Early Childhood (birth to grade 3),Elementary (grades Kindergarten to9), Secondary (grades 6 to 12), aparticular subject (gradesKindergarten to 12), and SpecialEducation (grades Kindergarten to12 or preschool to age 21).20

However, there are exceptions forcertain types of teachers, such asthose in charter schools or whohold alternative certificates.

In order to be certified, teachercandidates must pass certaintests.21 They must pass the Test ofAcademic Proficiency (TAP), whichassesses candidates’ basic skills inreading comprehension, languagearts, mathematics, and writing.22

Teacher candidates also must passa test on the Illinois ProfessionalTeaching Standards, the CommonCore Language Arts Standards, andthe Common Core TechnologyStandards. Such standards requirethat a teacher possesses certaincontent area and pedagogicalknowledge to be certified. Forexample, teachers shouldunderstand “major concepts,assumptions, debates, andprinciples; processes of inquiry;and theories that are central to thedisciplines”, “the cognitiveprocesses associated with variouskinds of learning (e.g., critical and

16 Stephen Sawchuck, “‘Value Added’ Concept Proves Beneficial to Teacher Colleges,” Education Week, February 22, 2012. Retrieved April 1, 2013from www.edweek.org.

17 No Child Left Behind Act, 20 U.S.C.S. 6319(a)(2) (2002).18 American Recovery and Reinvestment Act, 123 Stat. 115, 284 (2009).19 Benjamin M. Superfine, Jessica J. Gottlieb, and Mark A Smylie, “The Expanding Federal Role in Teacher Workforce Policy,” Educational Policy 20,

no. 1 (2012): 58-78.20 23 Illinois Administrative Code 25.11 (2012), 105 ILCS 5/21 (2012).21 23 Illinois Administrative Code 25.11 (2012).22 In 2012, Illinois adopted emergency rules allowing students to substitute an ACT composite score of at least 22 or an SAT score of at least 1030 for

passage of the TAP. Illinois State Board of Education, Illinois Licensure Testing System. Retrieved on April 1, 2013 from www.isbe.net/certification/html/testing.htm.

creative thinking, problem-structuring and problem-solving,invention, memorization, andrecall)”, “the relationship ofknowledge within the disciplines toother content areas and to lifeapplications”, and “how diversestudent characteristics and abilitiesaffect processes of inquiry andinfluence patterns of learning”.23

Teacher candidates also must pass asubject matter area test. While thecontent of this test differs by type ofcertification, the frameworks for thecontent tested are fairly broad. Forexample, the mathematicsknowledge assessed by the contentarea test for Elementary certificationincludes whether future teachers“understand concepts and skillsrelated to numbers, number sense,and numeration (includingfractions, decimals, ratios, andpercents) to support the learning ofmathematics”, “understand andapply concepts and methods relatedto algebra and geometry to supportthe learning of mathematics”, and“understand and apply principles,concepts, and procedures related tomeasurement, statistics, andprobability to support the learningof mathematics”.24 Beginning in2015, teachers also must pass theTeacher Performance Assessment(TPA) to be certified. Thisassessment was developed atStanford University and “requires

planning, teaching, assessing, andproviding extended commentary ona three to five day lesson that isvideotaped”.25 This assessment willfocus on elements such as teachers’abilities to plan focused, sequencedinstruction; use knowledge ofstudents to inform instruction;engage students in learning; deepenstudent learning during instruction;analyze student work; useassessment to inform instruction;and monitor student progress andadjust instruction. Notably, the TPAincorporates many elements fromthe Framework for Teaching (arubric used in many districts andschools to evaluate practicingteachers) and the National Board forProfessional Teaching Standards(used to evaluate “master” teachersfor National Board certification).26

Illinois also requires teacherpreparation programs to beapproved by the Illinois State Boardof Education (ISBE). In order to beapproved, teacher preparationprograms must include certainelements, such as specific courserequirements (which differ bycertificate type) and a pre-studentteaching field experience (which isusually a 12-16 week classexperience under a classroomteacher and higher education facultymember). Moreover, the course ofstudy taken by future teachercandidates must meet the Illinois


policyBRIEF

When teacher

candidates

graduate from

approved and

accredited teacher

preparation

programs, become

certified, and enter

the teacher

workforce in Illinois,

they become

subject to policies

that mirror those

currently being

implemented

around much of the

U.S.

23 23 Illinois Administrative Code 24.130(b)(1)(B)-(E) (2012).24 Illinois Certification Testing System, Field 110: Elementary/Middle Grades Test Framework

(Amherst, MA: Pearson Education, Inc., 2003): 007-009.25 Cynthia Shanahan and Carole Mitchener, Teacher Performance Assessment (Chicago, IL:

University of Illinois at Chicago). Retrieved on April 1, 2013 from www.qc.cuny.edu/Academics/Degrees/Education/Documents/Teachers%20Performance%20Assessment%20CUNY[2].pdf.

26 The Framework for Teaching, created by Charlotte Danielson, is a set of components ofinstruction aligned to the Interstate Teacher Assessment and Support Consortium Model CoreTeaching Standards. This Framework can act as a rubric for evaluating teachers in four domainsof teaching: (1) Planning and Preparation, (2) Classroom Environment, (3) Instruction, and (4)Professional Responsibilities. Charlotte Danielson, Framework for Teaching EvaluationInstrument (Princeton, NJ: The Danielson Group, 2013).

Professional Teaching Standardsand the applicable Content AreaStandards. Teacher preparationprograms must be accredited.

Notably, these requirements forteacher preparation programs inIllinois have been enacted recentlyand are only the most recentiteration of a constantly changingpolicy landscape. Although ISBElong has overseen teacherpreparation programs in the state,it has shifted programrequirements repeatedly. Forexample, the state recently requiredteachers to be certified in one offour areas (Early Childhood,Elementary, Secondary, or Special(K-12)). Given this certificationstructure, the state used theAssessment of ProfessionalTeaching (APT) to assess teachercandidates on the IllinoisProfessional Teaching Standards,and language arts and technologystandards.27 Similarly, the statepreviously required teachercandidates to pass the Basic Skillstest, which has been phased out infavor of the TAP. Indeed, instabilityhas long been a central feature ofpolicy requirements governingteacher preparation programs.

When teacher candidates graduatefrom approved and accreditedteacher preparation programs,become certified, and enter theteacher workforce in Illinois, theybecome subject to policies thatmirror those currently beingimplemented around much of theU.S. Illinois is currently phasing inthe CCSS. As such, the Illinois

Standards Achievement Test (ISAT),an assessment annually given tostudents in the state beginning ingrade 3, is increasinglyincorporating content from theCCSS.28 Beginning in 2014, the ISATwill be replaced by an assessmentaligned with the CCSS anddeveloped by the Partnership forAssessment of Readiness forCollege and Careers (PARCC), a 23-state consortium. Illinois teachersaccordingly will be responsible forteaching the content of the CCSS totheir students.

Heightening the stakes of theseassessments, Illinois adopted thePerformance Evaluation Reform Act(PERA) in 2010.29 Under this law, allschool districts must evaluate non-tenured teachers at least once eachyear and tenured teachers at leastonce every two years. Suchevaluations must incorporate theuse of data and indicators ofstudent growth as a significantfactor in rating teacherperformance. As implemented inChicago, these evaluations mustincorporate teacher evaluation datagathered through the Frameworkfor Teaching (which is partiallyintegrated into the TPA). Whendistricts perform evaluations, theymust rate teachers as excellent,proficient, needs improvement, orunsatisfactory. In 2011, Illinoisfurther enacted SB7, which tiesteacher tenure and certificationdecisions to teachers’ evaluationsunder PERA, and includes aprocedure for revoking teachingcertificates with multiple

unsatisfactory ratings.30 The lawalso ensures that performanceevaluation plays an important rolein decisions about teacher layoffsand teaching assignment, andstreamlines the dismissal processfor teachers with tenure. Inparticular, SB7 allows the StateSuperintendent of Education tosuspend, revoke, or limit a tenuredteacher’s certificate forincompetency, which is defined asreceiving an unsatisfactoryperformance evaluation in two ormore school terms in a seven-yearperiod. So, the process forremaining a teacher withcertification and in good standinghas recently become more difficultand driven by outcome data.

RESEARCH ONMATHEMATICALKNOWLEDGE FORTEACHINGWhile many teacher preparationpolicy documents in Illinois offergeneral descriptions of theknowledge and skills teachercandidates are required to have,there is a growing body of evidenceabout the specific knowledge andskills teachers should have to beeffective in the classroom. Giventhe current ambiguity of theserequirements and how they haveconstantly shifted, this sectiondiscusses research onmathematical knowledge forteaching—a type of mathematicalunderstanding that is specificallytailored for teaching students

policyBRIEF


27 Illinois State Board of Education, Certification and Professional Preparation (Springfield, IL: Illinois State Board of Education, 2005).28 Illinois State Board of Education, Roadmap for the 2013 Illinois Standards Achievement Test Mathematics (Springfield, IL: Illinois State Board of

Education). Retrieved on April 1, 2013 from, www.isbe.net/assessment/pdfs/2013/isat/roadmap-math-13.pdf.29 Performance Education Reform Act, 105 ILCS 5/24 (2012).30 SB 7, ILCS 5/10-22.4 (2012).

mathematical knowledge and skills.This vision of the mathematicalknowledge that teachers shouldknow can serve as a robust basis forpolicy requirements governingmathematics teacher preparationprograms moving forward.

Mathematics education researchersincreasingly have emphasized theneed for teacher candidates todevelop mathematical knowledgefor teaching. This type of knowledgefor teaching includes two differenttypes of knowledge: (1) pedagogicalcontent knowledge and (2) subjectmatter knowledge.31 Drawing fromearly research on teacherknowledge,32 pedagogical contentknowledge includes knowledge ofthe interrelated aspects of contentand students (e.g. deciding which ofseveral errors students are likely tomake based on where they are in thedevelopment of their mathematicalunderstanding), content andteaching (e.g. knowinginstructionally viable models forplace value and how to teach themeffectively), and content andcurriculum (e.g. understandingwhere division with whole numbersfits within the elementary schoolcurriculum in relation to students’developmental trajectories).33 Takenas a whole, pedagogical contentknowledge is an understanding ofthe prior conceptions andknowledge that students of different

ages and backgrounds bring withthem into the classroom and ways ofrepresenting and communicatingmathematics in ways that make itcomprehensible, and thus learnable,by students.

Subject matter knowledge, on theother hand, includes two separatedomains of knowledge: commoncontent knowledge and specializedcontent knowledge.34 Commoncontent knowledge is thesubstantive type of mathematicalknowledge that is used by bothteachers and those in otherprofessions. For example, commoncontent knowledge includesunderstanding how to usepercentages to compute amounts ofdiscounts. Specialized contentknowledge is the type of substantiveknowledge required exclusively forteaching. For example, suchknowledge includes understandinghow to evaluate the validity of themathematics in solution methods.35

Indeed, researchers have found thatboth common and specializedcontent knowledge are related toincreased student achievement.36 Assuch, it is not enough for teachers tojust know mathematics. Rather,teachers should know mathematicsin the ways that are neededspecifically for teaching students.


policyBRIEF

Researchers have

found that both

common and

specialized content

knowledge are

related to increased

student

achievement. As

such, it is not

enough for teachers

to just know

mathematics.

Rather, teachers

should know

mathematics in the

ways that are

needed specifically

for teaching

students.31 Deborah L. Ball, Mark H. Thames and Geoffrey Phelps. “Content Knowledge for Teaching: What

Makes It Special?” Journal of Teacher Education, 59, no. 5 (2008): 389-407.32 Lee Shulman. “Those Who Understand: Knowing Growth in Teaching.” Educational Researcher,

15, no. 2 (1986): 4-14.33 Ball, Thames, and Phelps, “Content Knowledge for Teaching: What Makes It Special?”34 Ball, Thames, and Phelps, “Content Knowledge for Teaching: What Makes It Special?”35 Deborah L. Ball and Hyman Bass, “Interweaving Content and Pedagogy in Teaching and

Learning to Teach: Knowing and Using Mathematics.” In Jo Boaler (Ed.),Multiple Perspectives onthe Teaching and Learning of Mathematics (Westport, CT: Ablex, 2000): 83-104.

36 Heather Hill, Brian Rowan, & Deborah L. Ball, “Effects of Teachers’ Mathematical Knowledge forTeaching on Student Achievement.” American Educational Research Journal, 42, no. 2 (2005):371-406.

policyBRIEF


APPROACHES FOREVALUATINGMATHEMATICALKNOWLEDGE FOR TEACHING

Given the growing consensus thatteachers need to understandmathematics in ways needed forteaching to be effective in theclassroom, researchers have begunto identify approaches particularlysuited for evaluating teachers’mathematical knowledge forteaching and helping them apply itin the classroom. Researchers havelargely focused on the developmentof assessments and the reform ofteacher preparation programs.Because mathematical knowledgefor teaching is a highly integratedconstruct of pedagogical and subjectmatter content knowledge,traditional assessments of teacherknowledge are inappropriate forassessing it. As part of the LearningMathematics for Teaching (LMT)Project, researchers at the Universityof Michigan accordingly havedeveloped a suite of assessmentsthat measures elementary teachers’mathematical knowledge forteaching in different areas ofmathematics. These areas includenumber and operations, algebra,and patterns and functions. Itemson these assessments not onlycapture whether teachers cananswer the problems they use withstudents, but also how teacherssolve the special mathematical tasksthat arise during teaching. Forexample, items on the LMTassessment include the followingquestions: (1) Is the number 0 evenor odd? (2) Can two differenttriangles have the same area? (3)Given three different multiplicationstrategies, which method can beused to multiply any two numbers?Although few teacher education

programs currently report using theLMT assessments, they areincreasingly being used in variousprofessional development settingsaround the U.S, such as district- andschool-level professionaldevelopment programs. However,the use of such assessments inteacher preparation programsshould be integral for evaluating theeffectiveness of programs that focuson the development ofmathematical knowledge forteaching.

REFORMING TEACHERPREPARATION PROGRAMSAND MATHEMATICALKNOWLEDGE FOR TEACHING

In addition to employing specificassessments for evaluating anddeveloping mathematical knowledgefor teaching in teacher candidates,researchers have recommendedparticular strategies for reformingteacher preparation programs. Thereis a growing consensus that teachereducation programs should be morepractice-based. A practice-basedapproach in teacher educationfocuses teacher candidates’ learningon actual teaching practice, thusproviding opportunities for them toenact and rehearse practices that arecentral to mathematics teaching. Forexample, teacher candidates maylearn about leading a whole classdiscussion, and then haveopportunities to rehearse thispractice in a classroom setting,receive feedback on the rehearsal,and enact this practice again. Suchan approach is particularly suited forthe development of mathematicalknowledge for teaching in teachercandidates and their ability to applyit effectively in the classroom. Incontrast to common content

Given the growing

consensus that

teachers need to

understand

mathematics in

ways needed for

teaching to be

effective in the

classroom,

researchers have

begun to identify

approaches

particularly suited

for evaluating

teachers’

mathematical

knowledge for

teaching and

helping them apply

it in the classroom.

knowledge, mathematicalknowledge for teaching involvesmore than simply knowledge aboutmathematics; it involves theapplication of this knowledge in thereal-world settings of classroomswith a range of students who cometo the classroom with their ownstrengths and weaknesses.37 Becausemathematical knowledge forteaching is inherently practice-oriented, teacher preparationprograms should be more practice-oriented as well.

Reforming teacher preparationprograms to be more practice-basedparticularly would help teachercandidates develop their skills atenacting high leverage instructionalpractices in mathematics.38 High-leverage practices are instructionalpractices that occur frequently inteaching, preserve the complexity ofteaching, are research-based, andhave the strong potential to improvestudent achievement. For example,high-leverage practices inmathematics might include leadinga mathematical discussion thatinvolves probing student ideas,evaluating the mathematical validityof students’ ideas and explanations,and connecting students’ ideas byarticulating the common conceptsunderlying them. Indeed,mathematical knowledge forteaching undergirds many of thesepractices because many of theminvolve a complex blend of subjectmatter knowledge and pedagogicalcontent knowledge. If teacherpreparation programs are groundedin such a vision of mathematical

knowledge, teacher candidates willenter the classroom with anefficacious foundation for effectiveteaching. Moreover, if acommitment is made to such avision, this commitment can serveas a stable policy anchor for theconstantly shifting teacherpreparation program requirements.

POLICY COHERENCE ANDMATHEMATICALKNOWLEDGE FORTEACHINGNotably, none of these reforms toteacher preparation programsshould be designed andimplemented in isolation. Asdemonstrated in the K-12 setting,attempting to import andimplement several programs andservices can generate seriouschallenges in schools. For example,early research on the individual andaggregate effects of multiple federalcategorical programs on school anddistrict operations found that policyincoherence was associated withsubstantial program “interference”and “cross-subsidy” whichcompromised the implementationand effects of these programs.39

These programs not only interferedwith each other, they interfered withbasic school-level operations andinstructional programs. Moreover,schools and districts found that theyhad to reallocate resources fromcategorical programs and fromgeneral operating funds to meetimplementation demands. Morerecently, research has found that


policyBRIEF

Reforming teacher

preparation

programs to be

more practice-

based particularly

would help teacher

candidates develop

their skills at

enacting high

leverage

instructional

practices in

mathematics.

37 Ball, Thames and Phelps, “Content Knowledge for Teaching: What Makes It Special?”38 Pam Grossman, Karen Hammerness and Morva McDonald, “Redefining Teaching, Re-imagining

Teacher Education. Teachers and Teaching: Theory and Practice, 15, no. 2 (2009): 273-289.39 Jackie Kimbrough and Paul T. Hill, The Aggregate Effects of Federal Education Programs (Santa

Monica, CA: RAND, 1981).

policyBRIEF


40 Fred M. Newmann, BetsAnn Smith, Elaine Allensworth and Anthony S. Bryk. “Instructional Program Coherence: What It Is and Why It ShouldGuide school Improvement Policy.” Educational Evaluation and Policy Analysis, 23, no. 4 (2001): 297-321.

41 Benjamin M. Superfine, Mark A. Smylie, Marlon I. Cummings and Steven Tozer. “The Challenging Road to Coherence in Illinois Education Policy,”in The Illinois Report 2012 (Urbana: IL: Institute for Government and Public Affairs, 2012).

42 Michael S. Knapp, Jerry D. Bamburg, Michele C. Ferguson and Paul T. Hill. “Converging Reforms and the Working Lives of Frontline Professionalsin Schools.” Educational Policy, 12, no. 4 (1998): 397-418.

43 Anthony S. Bryk, Peter B. Sebring, Elaine Allensworth, Stuart Luppescu and John Q. Easton.Organizing Schools for Improvement: Lessons fromChicago (Chicago, IL: University of Chicago Press, 2006).

44 Linda Darling-Hammond. “Teacher Quality and Student Achievement.” Education Policy Analysis Archives, 9 (2000). Retrieved April 1, 2013 fromhttp://epaa.asu.edu/ojs/article/ view/392; Laura Goe, The Link between Teacher Quality and Student Outcomes: A Research Synthesis (Washington,D.C.: National Center for Teacher Quality, 2007). Retrieved April 1, 2013 from ww.tqsource.org/publications/LinkBetweenTQandStudentOutcomes.pdf.

“cluttered and contradictory”federal, state, and district policyinitiatives are associated withfragmentation and compromiseimprovement at the school level.40

Instead, reforms focused on thedevelopment of mathematicalknowledge for teaching and teachercandidates’ abilities to apply itshould be coherent.41 In particular,these reforms should bestrategically designed together sothat they converge around similargoals, strategies, and resourcedemands.42 In this way, thesereforms would complement eachother and thus be mutuallyreinforcing. As elaborated in severalempirical studies, the logic ofinstructional program coherencethat lies behind them is consistentwith research on learning andcognition—that students are morelikely to learn and perform wellwhen their experiences connectwith and build on each other.43 Inshort, mathematics teacherpreparation programs should bereformed with the development ofmathematical knowledge forteaching as a central goal. If suchreform is undertaken, it shouldinvolve not only the modification ofcourse content but also thereconstruction of programs,practices, and ultimately policiesfrom the ground up. Thisreconstruction would involve the

selection of assessments andincreased integration of practice-based experiences for teachercandidates. It would further requireattention to alignment withmathematical knowledge forteaching as new reforms areconsidered and enacted as well.

THE PROSPECTS FORMATHEMATICS TEACHERPREPARATION POLICIES INILLINOISGiven the research on theknowledge needed for teachingmathematics and approaches fordeveloping this knowledge, whatare the prospects for mathematicsteacher preparation policies inIllinois? On a very broad level,Illinois appears to be moving in apositive direction. The recentlyenacted changes to teachereducation programs in the state aregenerally intended to improve theknowledge and skills of futureteachers, including futuremathematics teachers. Thesereforms also reflect a broadermovement in Illinois and the U.S.to improve the quality andeffectiveness of teachers, whichseveral researchers have argued isone of the most important factorsdriving student learning.44 Indeed,by giving teacher preparation sucha prominent position on the reform

agenda, Illinois has altered thegeneral politics surrounding thisarea by creating emphasis anddefining the rules of engagement.Some elements of Illinois’ approachare also likely to align with reformselsewhere in the state. Many recentstate and federal laws, includingRTT, PERA, and SB7, weregenerated in a policy environmentthat generally includes theimprovement and evaluation ofteachers. To this end, the TPAalready includes many elements ofthe Framework for Teaching, whichis also used to evaluate practicingteachers in Chicago under PERAand SB7. Such broad alignment inevaluation policy makes Illinoiseducation policy more coherent.

However, a careful look at teacherpreparation programs in Illinoisreveals that the new requirementsfor mathematics teacherpreparation in particular raisesignificant concerns. The standardsspecifying what teachers shouldknow and be able to do, as reflectedin policy instruments like the TAP,are very broad. For example, asdiscussed above, such standardssimply require that teachers shouldunderstand major concepts,assumptions, debates, andprinciples. As a result, there is verylittle guidance to mathematicsteacher preparation programsabout the curriculum and learning


opportunities they should have inplace for students. Subject mattertests for different types ofcertification are more specific. Yet,the content frameworks for thesetests are fairly broad as well. Whilethere is rightfully a certain amountof discretion accorded tomathematics teacher preparationprograms about exactly whichcontent and skills should be taught,the lack of specificity also leavesmuch room for sometimesundesirable variation amongprograms—while some programsmay draw on the expertise of facultyin these programs to create stronglearning experiences for students,not all programs will necessarilyrespond in such a fashion.

The mathematical contentframeworks are even more vagueabout the relationship betweensubject matter and pedagogicalcontent knowledge. While it isunderstandable that the frameworksdo not use these particular terms, theframeworks’ treatment of thedifferences between these types ofmathematical knowledge is cursoryat best. For example, many of theframeworks simply state thatteachers must know certainmathematical content “to supportthe learning of mathematics.” Such astatement is far too broad to offermeaningful guidance about the typesof mathematics teacher candidatesshould know. Moreover, assessmentsof content knowledge andpedagogical knowledge are largelydivorced from each other inapplicable standards and contentframeworks. Indeed, every futureteacher, no matter what grade level orsubject, must take the same test ofthe Illinois Professional TeachingStandards. Such an approach followsthe line of thinking that permeates

much of the current reform agenda –that bare mathematical contentknowledge is one of the mostimportant drivers of effectivemathematics teaching. However, thisapproach does not square withmodern research on mathematicalknowledge for teaching and its utilityfor helping teachers implement highleverage teaching practices.

Illinois mathematics teacherpreparation policies also face severalpotential problems involvingincoherence. Policy efforts toincrease the quality of mathematicsteacher preparation program inIllinois have been largelydisconnected from each other. Theserequirements have constantlyshifted, creating an environment ofincoherence and instability for theseprograms. Given these rapidlychanging demands, teacherpreparation programs have had verylittle opportunity to work outappropriate and effectiveimplementation practices before newrequirements are enacted. Indeed,these programs have never reflecteda coherent vision of mathematicalknowledge teachers should have.

Given that such a vision has failed toform a foundation for Illinoiseducation policies more broadly,teacher education programs remainlargely unaligned with these policiesas well. For example, PERA and SB7are generally grouped aroundincreasing teacher quality andeffectiveness through evaluation. Butthe types of evaluation emphasizedin these policies are tied to statestandards, particular assessmentsgiven to students, certain evaluationrubrics, and consequences flowingfrom the results of evaluations. Someother states (e.g. Louisiana and Texas)are modifying their teacher

policyBRIEF

However, a careful

look at teacher

preparation

programs in Illinois

reveals that the new

requirements for

mathematics

teacher programs in

particular raise

significant

concerns.


preparation programs in ways thatare more closely aligned with statestandards and teacher evaluationsystems. Illinois has begun to movein this direction by using the TPA,which includes elements of theFramework for Teaching. However,the Framework for Teaching can begenerally used to evaluate anyteacher, regardless of the contentbeing taught. Because it is nottailored specifically for the highleverage instructional practices thatare salient in mathematics, thisevaluation is not sufficientlyconnected to a robust vision ofmathematics teacher knowledge aswell. Moreover, the suite of reformsbesides the TPA that are aimed atimproving the effectiveness ofpracticing teachers mathematics arelargely separate from the frameworkscontained in certification tests.Similarly, teacher preparationpolicies are largely divorced at thistime from the CCSS, which willconstitute the dominant studentlearning standards in Illinois in thecoming years.

In short, Illinois policies make fewdirect links between how teachers areprepared and how teachers aremanaged once they formally enter theteacher workforce. The entire teacherworkforce system, includingpreparation, recruitment, hiring,evaluation, development, and firingshould be aligned to a strong andconcrete vision of what a teachershould know and be able to do. As itcurrently stands, this vision is vagueat best and does not account for theways that mathematical knowledge ofteaching should be integrated intopolicy to support teachers’ enactmentof high leverage teaching practices.

RECOMMENDATIONSThere are several possible ways toimprove mathematics teacherpreparation policies in Illinois. Inthis section, three principles arediscussed for reforming currentmathematics teacher preparationpolicies. First and most importantly,mathematics teacher preparationprograms should be grounded in astrong conception of whatmathematics teachers should knowand be able to do. This vision shouldbe guided by the best availableresearch and encompass more thansimply teachers’ bare knowledge ofmathematics. Instead, this visionshould draw on research focused onthe development of mathematicalknowledge for teaching. Whileteachers should be very well trainedin common content knowledge—thetype of knowledge that those invarious professions and fieldsshould know—teachers should alsoknow mathematics in ways that areparticularly suited for teaching.

Given the centrality in currentpolicies of improving pre-serviceand practicing teachers, this visionof mathematical knowledge forteaching should be explicitlyarticulated. In order to articulate thisvision, Illinois should convenerepresentatives from majorstakeholders in mathematics teacherpreparation, including teachers,school administrators,policymakers, university personnel,and researchers. In doing so, thestate would not only lay thegroundwork for all othermathematics teacher preparationpolicies but would become aninnovator among states in this fieldas well. To be sure, ISBE has alreadymade some efforts to reach out todifferent education stakeholdersinvested in changing teacher

policyBRIEF

Policy efforts to

increase the quality

of mathematics

teacher preparation

program in Illinois

have been largely

disconnected from

each other. These

requirements have

constantly shifted,

creating an

environment of

incoherence and

instability for these

programs.


certification requirements.However, these efforts should beenhanced and ongoing as aresearch-based vision ofmathematical knowledge forteaching is more explicitlydeveloped and articulated.

Second, state policies should beenacted to ensure that the propersorts of instruments andexperiences are put in place inteacher preparation programs todevelop mathematical knowledgefor teaching in future mathematicsteachers. The state currently relieson a suite of assessments as agatekeeper for teachers and, in thisway, effectively drives the contentof teacher education programs.However, as discussed above, theseassessments are not necessarilyaligned to each other and a strongand consistent vision of whatmathematics teachers should knowand be able to do. While someassessments such as the TPA maybe a step in the right direction, stateassessment systems formathematics teacher candidatesshould be more closely aligned withmathematical knowledge forteaching. The LMT assessmentcould be a useful starting point forbuilding such assessment systems,however it is possible that the statecould design its own assessments inlight of its own vision ofmathematical knowledge. Given therange of practice-based dataincorporated into the TPA, thisassessment could be preserved asthe core of such a system as well.

In addition to modifying itsassessment policy, the state shouldenact laws or regulations to ensurethat practice-based learning plays amore central role in mathematics

teacher preparation. Practice-basedlearning is particularly critical forgrounding teacher preparationprograms in mathematicalknowledge for teaching and helpingfuture teachers learn how toimplement high leverage teachingpractices. Indeed, there needs to beknowledgeable university facultyinstructors who can model effectiveand high leverage practices forfuture mathematics teachers.Moreover, state policy should ensurethat a range of other elements ofteacher preparation programs alignswith its vision of mathematicalknowledge for teaching, includingcurriculum, the training ofmathematics teacher educators, andstandards for admission to teacherpreparation programs.

Finally, mathematics teacherpreparation policies should bealigned with other major educationpolicies in the state. In this respect,it is critical that a consistent visionof mathematical knowledge forteaching underlies all suchmathematics policies. For example,the vision of teachers’mathematical knowledgeunderlying evaluation andaccountability reforms like PERAand SB7 should be aligned with thatunderlying mathematics teacherpreparation programs. Similarly,this vision should align with whatstudents should know and be ableto do under the CCSS. As it stands,there are already some areas ofoverlap across the differentreforms. However, many gapsremain. Given that policycoherence is crucial for makingsure that policies work together andare mutually reinforcing, suchalignment is critical no matter whatthe underlying vision is.

CONCLUSIONMathematics teacher preparationpolicies are quickly changing inIllinois. Such attention toenhancing mathematics teacherquality and effectiveness ispromising. However, these currentpolicies can be improved in severalways. Grounding these policies in astrong and explicit vision ofmathematical knowledge forteaching will ensure that thesepolicies are better aligned withcurrent knowledge about the kindof mathematical understandingteachers need to teach effectively.Aligning all elements ofmathematics teacher preparationprograms to this vision, rangingfrom assessments and curriculumto mathematics teacher educatortraining, will help develop suchknowledge in future teachers.Finally, aligning mathematicsteacher preparation policies withother major education policies inIllinois will make the state’s policiesmore coherent, stable, andultimately effective. By undertakingsuch policy reforms, Illinois canultimately increase the odds that itssignificant efforts in educationreform have not been undertakenin vain and that its students receivethe mathematical learningopportunities that they deserve.

policyBRIEF

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


CONTACT US

[email protected]/ruepi

facebook.com/ruepi

FOLLOW US

policyBRIEFUIC Research on Urban Education Policy Initiative

1040 West Harrison StreetChicago, Illinois 60607