Ed Source Report 0609

7/27/2019 Ed Source Report 0609

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R E P O R T

M A Y 2 0 0 9

Most Caliornia policymakers and educators would likely agree that al

students need to take and master algebraand that they need to do so

as early as possible in their school careers.

HigHligHts

n Caliornia has used its academic

content standards and accountability

policies to push or earlier student

participation and success in algebra ...... 2

n The state has seen large increases

in 8th grade algebra participationand profciency ......................................5

n Test scores, repeater data, and

the NAEP all provide evidence that

math perormance alls well short

o the states expectations or

many students ......................................6

n Critics are raising hard questions

about the states algebra policies

and pushing or clarifcation about

what to teach and when ......................11

n The debate sheds light on shortcomings

in Caliornias teacher credentialing

policies and a lack o support or

proessional development ...................14

EdSource is a not-for-profit 501(c)(3) or ganization established in California in 1977.

Independent and impartial, EdSource strives to advance the common good by developing and widely distributing trustworthy, usef ul

information that clarifies complex K12 education issues and promotes thoughtful decisions about C alifornias public school system.

Aebra Pocy n Caorna

Great Expectations and Serious Challenges

Ag reemen on h is goa l represens

imporan progress in a sae whereless

han 10 years agohe noion o algebra

as a high school graduaion requiremen

seemed like a radical idea. ha said, he

same Caliornians are much more divided

regarding when exacly sudens should

ake algebra and how o assure hem a

reasonable chance or success. ha divi-

sion was releced in srong reacions o a

Sae Board o Educaion decision made

las Julyblocked by a Caliornia cour

ruling ha is currenly under appeal

ha would have increased pressure or all

sudens o ake Algebra I by 8h grade.

Since he lae 1990s, sae ocials haveused assessmen and accounabiliy poli-

cies as powerul levers o encourage schools

o enroll more 8h and 9h grade sudens

in Algebra I courses. In he process, schools

have raised expecaions and a orded greaer

opporuniy o housands o previously

underserved sudens. Nearly 45,000 more

Caliornia 8h graders scored procien

or advanced on he saes Algebra I es in

2008 han in 2003. Nearly 26,000 more low

income 8h graders did so. However, oo

many Caliornia sudens sill sruggle o

ge hrough he Algebra I gaeway leading o

more rigorous mah and science courses in

high school.Paricipaion or all clearly doesno ranslae auomaically ino success or all

Many call or srenghening mah

insrucion, paricularly in he lae elemen

ary and middle grades, as he crucial nex

sep in moving Caliornia oward is goals

Some also say his is an opporune momen

or Caliornia o consider is mahemaic

policies more broadly, including is academic

conen sandards and annual assessmensAny o hese would require invesmens o

ime and unding. W ha combinaion o sae

policies and school pracices would be mos

eecive o help sudens succeed? Wha

invesmens in educaor capaciy would be

mos sraegic? Tese are complex bu i mpor

an issues or Caliornia o explore, and

hey are he ocus o his EdSource repor

EdSource thanks the Noyce Foundaon for

underwriting the research, development, and

dissemination of this publication.


2/20

E d S O u R c E R E P O R T

n Al ge bra Pol icy in C al ifor nia n May 2009 Copyright 2009 by EdSource, Inc.

Caorna connue o reach oward earer uden ucce n aebra

When Caliornia adopted academic content standards in mathematics in 1997, no one assumed that

large-scale changes in math achievement and course-takingincluding in algebra success in grade 8

would happen overnight. Early decisions by Caliornia policymakers establishing the content standards

in math and the 2004 requirement that students complete Algebra I to graduate rom high school let

many debates or the uture.

A bre hory o he sae Board o Educaon aebra decon

In July 2008, the California State Board of Education

(SBE) passed a motionnow blocked by a state

courtthat called for the states Algebra I test

to become the sole test of record in grade 8

mathematics for federal accountability purposes.

California and federal education policies make

different assumptions about testing in grade 8 math.

n California policy assumes that the California

Standards Test (CST) an 8th grader takes in

math is connected to the math course she or he

takes. Most commonly, 8th graders enrolled in

Algebra I take the Algebra I CST and 8th graders

not yet enrolled in an algebra course take the

General Mathematics CST.

n In contrast, the federal No Child Left Behind

law (NCLB) assumes that math testing in

grade 8 is based on a states content standards

for that grade.

On Feb. 6, 2008, the U.S. Department of Education

(ED) notified California that its General Math CST does

not comply with federal requirements because it tests

8th graders on content defined by Californias math

standards as intended for grades 6 and 7. Failure to

enter an agreement with the ED to align Californias

assessment system with federal expectations wouldresult in $1 million in Title I Part A administrative

funds being withheld from the state and provided

instead to Californias local education agencies. (At

the time of this writing, California and ED officials

were discussing a settlement of this matter.)

One option for complying with federal expectations

was to have all 8th graders take the Algebra I CST. With

SBE approval, the California Department of Education

(CDE) also explored a second option: the development

of a blueprint for a new grade 8 math test. This test, if

approved by SBE and accepted by the U.S. Department

of Education, would replace the General Math CST

and be taken by students not yet enrolled in algebra.

It would be based on a subset of the states Algebra I

standards, excluding more rigorous content such as

factoring and quadratic equations.

This new CST blueprint sparked some intense

disagreement:

n Someincluding CDE, the California School

Boards Association (CSBA) , and the Association

of California School Administrators (ACSA)

supported the blueprint as an improvement on

the General Math CST that would allow local

educators to make judgments about proper

student placements.

n Other state leaders saw the blueprint as lowering

the states academic standards for what counts

as grade-level math in grade 8. Three former state

secretaries of education and four former SBE

presidents signed a letter arguing that anything

less than Algebra I should not be considered

grade-level proficient at eighth grade.

One day before the state board was to consider

the new blueprint further, in July 2008, Gov. Arnold

Schwarzenegger also went public with his opposition

to it. He sent a letter encouraging the state board to

pursue the Algebra I CST as the sole test of record

in grade 8 math for federal accountability purposes.

By a vote of 8-1, the board passed a motion to

this effect.

The boards motion directed state education officials

to negotiate with the ED for:

nAn agreement to make the Algebra I CST the soletest of record in California for grade 8 math;

nA transition period for building the states

capacity to ensure all 8th graders can succeed

on the test; and

n In the long term, better accommodation of

Californias education policies under federal law.

In September 2008, CSBA and ACSA filed a lawsuit

later joined by the California Teachers Association

(CTA) and State Superintendent of Public Instruction

Jack OConnellto block the state boards decision.They claimed that SBE (1) violated the Bagley-Keene

Open Meeting Act by not providing adequate public

notice of the action it took that day; and (2) exceeded

its legal authority by implicitly changing Californias

academic content standards to require Algebra I in

grade 8, despite the fact that the math standards

for grades 812 are organized by discipline rather

than grade level.

In January 2009, the Sacramento County Superior

Court ruled in favor of the plaintiffs on both grounds

and issued a preliminary injunction preventing

the state board from taking any further steps to

implement its algebra decision. SBE is appealing

the courts ruling that the board exceeded its legal

authority but is not disputing the ruling pertaining to

the Bagley-Keene Act.


3/20


May 2009 n Al geb ra Policy in C al ifor ni a n Copyright 2009 by EdSource, Inc.

A July 2008 decision by he Sae Board o

Educaion (SBE) has raised issues no re-

solved 10 years ago. Tis decisionblocked

by a Sacrameno Couny cour rul ing ha is

currenly under appealdireced he sae

o ener an agreemen wih he U.S. Depar-

men o Educaion (ED) o make he Algebra ICaliornia Sandards es (CS) he sole

es o record in grade 8 mah or ederal

accounabiliy purposes. Depending on he

kind o agreemen reached, his expecaion

would have gone ino eec in hree or our

years . (For more inor maion on wha

promped he SBEs decision, see he box on

page 2: A brie hisory o he Sae Board o

Educaions algebra decision.)

Te SBEs acion would have se Calior-

nia apar rom virually all oher saes in

eecively maki ng Algebra I he deaul mahcourse in grade 8. Caliornias prospecive

company in his expecaion is Minnesoa,

which se a slower imeable or implemen-

aion. In 2006, Minnesoa leaders decided

ha, beginning wih he class o 2015, su-

dens mus complee Algebra I by he end o

8h grade and complee Algebra II o gradu-

ae rom high school.

Te SBEs decision sirred vigorous

debae among Caliornia educaion leaders

abou wheher esing al l 8h grade sudens

in Algebra I, even i phased in over several

years, is a sound policy. Schools and dis -

rics would have been held accounable or

he exen o which all 8h graders can suc-

ceed on he saes Algebra I es. Currenly,

43% o 8h graders ake he General Mah

CS, which assesses suden achievemen

on Caliornias mah sandards or grades

6 and 7.

A his momen, a preliminar y injunc ion

prevens he board rom aking any urher

seps o implemen is algebra decision. Buhe imporan issues raised by he decision

remain, and disrics are sruggling o gure

ou wha he boards decision means or heir

suden placemen policies, insrucional

capaciy, and insrucional maerials. Te

res o his repor explores some o hese

issues, describes where Caliornia currenly

nds isel wih regard o K8 mah achieve-

men, and discusses where i migh go nex.

Californias math content standards left thestates Algebra I expectations ambiguousTe Sae Board o Educaion adoped

Caliornias academic conen sandards in

mahemaics in December 1997. Tese san-

dards, in conjuncion wih sae esing and

accounabiliy policy, have pushed schools o

enroll sudens in algebra earlier, opimally in

8h grade. Te sae did no require 8h grad-ers o ake algebra, however. So ar, he only

ocial expecaion has been ha sudens in

he class o 2004 and laer mus pass a course

ha mees or exceeds he sandards or Alge-

bra I o graduae rom high school .

Tree conceps help explain how algebra

s ino he saes mah conen sandards

and how hose sandards relae o wha is

augh in schools.

Californias math content standards are organized

differently for grades K7 than for grades 812

In grades K7, Caliornias mah conen

sandards are se or each grade level. each-

ers are expeced o help sudens developincreasingly sophisicaed compuaional

and procedural skills, concepual under-

sanding, and problem solving along ve

inerrelaed srands ha exend across

grades K7. (See Figure 1.)

In grades 812, however, Caliornias

mah conen sandards are organized ino

nine specialized disciplines raher han bygrade level, beginning wih Algebra I. (See

Figure 1.) As noed in he box on page 2, hisCaliornia pracice diverges rom ederal as

sumpions under he No Child Le Behind

law (NCLB), which groups grades K8

ogeher and reas grades 912 separaely.

Te annual Caliornia Sandards ess

(CSs) in mahemaics refec he saes

approach. Sudens in grades 26 all ake a

single CS or each grade. A g rade-level CS

is also adminisered in grade 7, bu a smal

percenage o 7h graders enrolled in algebra

ake he Algebra I CS insead.

Sudens in grades 811 ake dieren mah

CSs depending on wha courses hey ake

Tose 8h and 9h graders who are no ye

ready or algebra ake he General Mahemaics

CS, which is aligned wih he mah conen

sandards or grades 6 and 7. Te saes accoun

abiliy sysem provides schools wih incenives

o enroll sudens in Algebra I by grade 8

however. (See he discussion on page 4.)

Algebra as a content standard is different from

algebra as a course or part of a curriculumEvery Caliornia high school mus provide

courses ha ulll he minimum crieria or

eligibiliy o he Universiy o Caliornia

(UC) and he Caliornia Sae Universiy

(CSU). Bu Caliornias mah conen san

dards do no call or any discipline-specic

course o be augh in any paricular grade

beween 8 and 12. Insead, he sandards

acknowledge ha disrics migh adop

in rade K7, he mahemac conen

andard were eabhed or each rade eve,

un fve common rand:

in rade 812, he mahemac conen

andard were eabhed or nne pecazed

mah dcpne:

n Number sensenAlgebra and functions

n Measurement and geometry

n Statistics, data analysis, and probability

n Mathematical reasoning

nAlgebra In Geometry

nAlgebra II

n Probability and Statistics

nTrigonometry

n Linear Algebra

n Mathematical Analysis

nAdvanced Placement Probability and Statis tics

n Calculus

Source:Mahe mai cs Con en S andard s for Cali forni a Public Sc hools: K inde rgar en Troug h Grade welve EdSource 5/

fgure 1 How Caorna academc conen andard n mahemac are oranzed n

rade K7 veru rade 812


4/20



dieren philosophies and approaches

oward heir mah curricula.

Disrics migh pursue a radiional

curriculum ha begins wih Algebra I and

coninues wih Geomery, ollowed by Alge-

bra II. Disr ics migh also oer hese courses

in a dieren sequence, such as placing su-dens in Geomery only aer hey have com-

pleed boh Algebra I and II. Disrics migh

also adop an inegraed mah curriculum

ha weaves ogeher opics rom hese disci-

plines during several years, hough his has

become ar less com mon in Cal iornia.

Ta said, algebra is sill he minimum san-

dard or he conen he sae hopes a growing

number o sudens will learn beginning in

grade 8. Tis sandard is he same regardless o

wha curricular approach a disric akes. Tis

disincion beween algebra as a conen san-dard and as a course was a key poin o conen-

ion in he lawsui brough agains he sae

board. (See he box on page 2.)

Mandatory testing and accountability policies push

schools to meet standards and increase participation

in higher math

Te Caliornia Educaion Code esablishes

ha he academic conen sandards are

inended as models. Te mah conen san-

dards noe, excep or he saues, regula-

ions, and cour decisions ha are reerenced

herein, he documen [seting ou he mah

sandards] is exemplary, and compliance

wih i is no mandaor y. Tis lang uage

relieves he sae rom any obligaion o

reimburse disrics nancially or mandaes

relaed o he conen sandards hemselves.

Oher regulaions, however, underscore he

expecaion ha disrics sandards will be

a leas as rigorous as he saes.

For example, sae unds or insrucional

maerials can be used only or maerials al igned

wih he conen sandards. In addiion, schools

are required o oer he annual CSs in grades

211. Te CSs provide a srong incenive or

local educaors o align insrucion wih con-

en sandards because he ess are used orepor publicly on he academic progress o

schools and disrics, and o ideniy hose

considered in need o improvemen.

Federal educaion policy uses school

accounabiliy o encourage suden parici-

paion in such esing. Te No Child Le

Behind Ac o 2001 requires 95% o all su-

dens in a disric or school o paricipae in

relevan sae ess or he insiu ion o make

adequae yearly progress (AYP). In mahe-

maics in Caliornia, his includes grade-level

and end-o-course mah CSs and, or highschools, he mah secion o he Caliornia

High School Exi Exam (CAHSEE) in grade

10, which includes an Algebra I componen.

Failure o mee his ederal requiremen or

any subgroup o sudens (based on eh niciy,

disabiliy, or English learner saus) or wo

years in a row leads o a school or disric

being placed in Program Improvemen . In

par, NCLB emphasizes paricipaion o dis-

courage schools rom excluding sruggling

sudens. (Caliorn ia law requires disrics o

exemp sudens rom esing i parens

reques i, however.)

In addiion, Caliornia accounabiliy

policy explicily encourages paricipaion in

higher mah courses, such as Algebra I.

Rules adoped by SBE or he calculaion o

he Academic Perormance Index (API)

which summarizes suden achievemen

or a disric or school and or is suden

subgroups or accounabiliy purposes

provide schools wih wo incenives o move

sudens ino higher mah courses.

Firs, because he General Mah CS

assesses mah conen ha is below he saes

expecaions or grades 8 and 9, schools

receive less credi on he API or h igh suden

scores on he General Mah CS in hesegrades. Sudens may achieve one o ve per

ormance levels on a CS: advanced, pro

cien, basic, below basic, or ar below basic.

n Te scores o 8h graders who ake he

General Mah CS are lowered by one

perormance level or he purposes o cal

culaing a schools API. For example, i

an 8h grader scores procien on his

CS, a school only ges credi or a score

o basic.

n Te scores o 9h graders who ake he

General Mah CS are lowered by woperormance levels or he purposes o

calculaing a schools API. For example

i a 9h grader scores procien on his

CS, a school only ges credi or a score

o below basic. (Te sae does no

penalize high schools or 9h graders

who ake he Algebra I CS.)

Second, schools are penalized on he

Base API or any suden no acively aking

mahemaics courses in he upper grades. Al

sudens in grades 811 who do no ake an

end-o-course CS in mahemaics are auo

maically assigned a score o 200or ar

below basicor he purposes o calcula

ing a schools Base API. Tis penaly also

oers schools an opporuniy because

increases in suden enrollmen in higher

mah courses rom one year o he nex can

conribue o gains in a schools Growh API

Tis Assignmen o 200 rule also applies or

high school science courses.


5/20



Noably, his growh in paricipaion has

been accompan ied by a higher success rae

on he Algebra I CS, wih greaer numbers

o sudens scoring advanced or procien.

However, a grea many sudens are no suc-

ceeding in he course, and large numbers

repea i once or more. Furhermore, some

say ha daa rom he Naional Assessmen

o Educaional Progress (NAEP) pain a

sobering picure o 8h grade mah achieve-

men in Caliornia compared wih ohersaes. CS daa rom grades 27 sugges

ha hese problems become clear in he lae

elemenary and early middle grades.

Many more students now take algebraTere are wo ways o measure he success

o Caliornias policy decisions regarding

algebra. Te rs is suden paricipaion inhigher mah courses; he second is sudensuccess in hose courses. Tis repor ocuses

primarily on 8h graders who ake he Alge-

bra I CS, how well hey do, and how his

has changed over ime. Considered ogeher,

hese wo measures show ha Calior-

nia schools have changed heir collecive

approach o when sudens ake Algebra I.

o he exen ha SBE policy has been

moivaed by concern ha schools were no

being held o sucienly high expeca ions

or suden achievemen in grade 8 mah,

here have clearly been imporan changes inhe sae. Early suden paricipaion in Alge-

bra I has increased grea ly in recen years .

(See Figure 2A.)

In 1999, he rs year Caliornia adminis-

ered course-specic mah ess in grade 8,

only 16% o 8h graders ook he es or

Algebra I. By 2003, his percenage had in-

creased o 32%. In 2008, 51% o 8h graders

ook he Algebra I CS. Some 7h graders

5% in 2008now ake he es as well.

Paricipaion in he Algebra I CS has

increased among 8h graders o all racial and

ehnic backgrounds. (See Figure 2B.) Te

percenage o Arican American 8h graders

aking he es nearly doubled beween 2003

and 2008, rom 24% o 47%. Te same is al so

rue or Laino 8h graders (26% o 48%).

Te number o sudens aking he Algebra I

CS in grade 9 has also increased. Many o

hese sudens are repeaing he course, how

ever, as will be explored in more deph laer.Suden paricipaion in Algebra Ihe

beginning o he ypical high school mah

sequenceis jus one measure o paricipa

ion in higher mah. Mah CSs in laer grades

also provide a rough measure o how many

sudens successully pursue a sequence o

higher mahemaics courses beyond Algebra I

For example, CS daa show ha 25% o 10h

graders and 45% o 11h graders had compleed

or were enrolled in Algebra II in 2008.

lare ncreae n aebra parcpaon n rade 8 nce 2003 havebrouh encouran reu and ome worre

Since the initial adoption o Caliornias math content standards in 1997, growing numbers o students

have been taking Algebra I, and taking it earlier. This section ocuses on changes since 2003.

Numbero

fstudentstakingAlgebraICST

190,179

224,291230,284

239,240247,810

187,396

222,333

248,498261,699

271,300 274,334

113,421

135,614 136,319143,144 140,317

132,813

53,352

66,22172,816 72,158 72,218 66,945

151,714

0

50,000

100,000

150,000

200,000

250,000

300,000

2003 2004 2005 2006 2007 2008

Grade 8

Grade 9

Grade 10

Grade 11

Data: Califor nia Departme nt of Education, STAR, CBEDS. Accessed 1/. EdSource 5/

fgure A More Caorna uden are akn Aebra i and are akn earer

0%

10%

20%

30%

40%

50%

60%

70%

2003 2004 2005 2006 2007 2008

Perce

ntof8thGraders

African American

Native American/Alaska Native

Asian

Filipino

Hispanic/Latino

Pacific Islander

White

fgure B Emaed parcpaon rae n Aebra i have ncreaed amon

8h rader o a raca/ehnc roup nce 2003

Notes: Figure 2A : In 2007, 21,739 7th graders took the Algebra I C ST. The number increased to 25,635 in 2008. ( 2007 was the first year that qualified 7th graders could t ake the Algebra I CST.) Figure 2B

These rates are calculated by dividing the number of Algebra I CST-t akers for a st udent group in grade 8 (der ived from STAR data ) by that groups tot al grade 8 enro llment (de rived fr om CBEDS da ta) . STAR data

do not include a count of total enrollments by subgroup in each grade at the time of S TAR testing. CBEDS enrollment data, which are based on student counts at the beginning of the academic year, are used

to estimate participation rates for subgroups.


6/20



Mixed results show the positive andnegative consequences of increasedalgebra participation to dateAlgebra I CS daa provide evidence or

severala imes conficingsories abou

Caliornia sudens algebra achievemen in

grade 8 since 2003. Some nd evidence hahe saes schools and 8h graders are mee-

ing high expecaions in mahemaics, while

ohers poin o resuls ha sugges growing

numbers o sudens are being placed in

algebra courses or which hey are no pre-

pared. Consider some examples. (Addiional

chars showing 8h grade Algebra I CS

oucomes among dieren suden groups

are available rom he EdSource websie a:

ww w.edsource.org)

8th grade performance on Algebra I CST overall

Firs, consider all 8h graders who ook he

Algebra I CS in 2003 and 2008. (See Figure

3A.) In general, here was a sligh improve-

men in he proporion o sudens scoring

procien or advanced, even given a large

increase in paricipaion. In addiion, he

percenage scoring in he lowes achieve-

men caegory (ar below basic) decreased

slighly, rom 9% o 7%.

Te scale o change since 2003 is paricu-

larly noable:

n 1.8 imes as many 8h gradersabou104,100scored procien or advanced on

he Algebra I CS in 2008 as in 2003.

n A he same ime, 1.5 imes as many 8hgradersabou 76,800scored below or ar

below basic on he es in 2008 as in 2003.

Tese overall saisics obscure imporan

dierences in 8h grade Algebra I achievemen

among various suden groups, however.

8th grade performance on Algebra I CST by economic

backgroundChanges in algebra achievemen or socio-

economically disadvanaged (SED) 8h

graders conras wih hose or nonsocio-

economically disadvanaged (non-SED) 8h

graders. Sudens are caegorized as SED i

(a) hey paricipae in a ree or reduced-price

meal program, or (b) he educaion level o

heir parens is coded as no high school

graduae.

For non-SED 8h graders, Caliornias

push oward expanded algebra success in

grade 8 has been comparaively successul.

(See Figure 3B on page 7.) Only abou 4,100

more non-SED sudens scored basic or

below on he A lgebra I CS i n 2008 han in

2003, compared wih abou 21,200 more

who scored procien or advanced.

For SED sudens, he sory is more

complex. (See Figure 3C.) Te percenage

o SED 8h graders scoring procien or

advanced on he Algebra I CS increased

by 8 percenage poins beween 2003 and

2008. In ac, 3.2 imes as many SED 8hgradersabou 37,600did so in 2008.

Tis shows ha many SED sudens who

migh no previously have had access o analgebra course in grade 8 are no only

aking he course, bu also rising o he

challenge.

A he same ime, however, roughly he

same number o SED 8h graders now scores

below or ar below basic on he Algebra I CS

as ook he es a all in 2003. Tis means hamore SED 8h graders53,900 in 2008are

a risk o ailing a nd repeaing Algebra I.

8th grade performance on Algebra I CST by ethnicity

Te Algebra I sory is also complex or 8h

graders o dieren racial and ehnic back-

grounds. Consider Caliornias Arican

Amer ican and Laino 8h graders. For boh

groups, 8h grader paricipaion in he Alge-

bra I CS increased subsania lly beween

2003 and 2008.

n 2.6 imes as many Arican American 8hgraders scored procien or advanced on

he Algebra I CS in 2008 as in 2003, and

he percenage scoring below or ar be

low basic decreased. On he oher hand

nearly as many Arican American 8h

graders (abou 9,000) now score below or

ar below basic as ook he es a all in

2003 (abou 9,900). (See Figure 3D.)n 3.2 imes as many Laino 8h grader

scored procien or advanced on he

Algebra I CS in 2 008 as in 2003, and he

percenage scoring below or ar below

basic decreased. On he oher hand, abou

47,900 Laino 8h graders now score

below or ar below basic, or nearly as

many as ook he es a all in 2003

(abou 51,200). (See Figure 3E.)

50,066

76,821

42,480

66,90959,168

104,080

0

50,000

100,000

150,000

200,000

250,000

300,000

2003 2008

NumberofStudents

Proficient or Advanced

Basic

Below Basic orFar Below Basic

(33%)

(27%)(39%)

(42%)

(31%)

(28%)

Data: Califor nia Departmen t of Education, STAR. Accessed 1/. EdSource 5/

Note: The counts of 8th gr aders shown here are based on the numbers teste d on the Algebra I CST, rather than the preferable number

students with valid scores. This is because the latter data are not published for 2003 as they are for 2008. These counts are estimate

derived from state reports of per formance and may not match the number of students tested due to rounding.

Perormance o a 8h rader akn he Aebra i Cstfgure A


7/20



Tese daa ell wo sories. One is a sory

abou Arican American and Laino sudens

succeeding when provided access o Alge-bra I in grade 8, whereas in prior years hey

may no have had such access. Anoher sory

is abou uninended consequences and he

subsanial cohors o Arican American and

Laino 8h graders who migh have been

placed in Algebra I wihou adequae prepa-

raion and/or suppor and migh need o

repea he course. Abou hree in our Laino

and hree in ve Arican American 8h

graders who ook he es in 2008 were

socioeconomically disadvanaged.

Tis sands in sark conras o Asian andwhie 8 h graders. For bo h groups, he num-

ber o 8h graders scori ng procien or

advanced on he Algebra I CS has grown

subsanially more since 2003 han has he

number scoring basic or below. Alhough

abou 1,100 more Asian 8h graders scored

basic or below in 2008 han did so in 2003,

abou 5,800 more now score procien or

advanced. Te comparable increases among

whie 8h grader s were abou 3,600 and

10,200 sudens, respecively.

8th grade performance on Algebra I CST of English

learners and students with disabilities

Algebra I CS achievemen daa or 8h grad-

ers who are designaed as English learners or

as sudens wih disabiliies warran paricu

lar consideraion. Sudens are placed in hese

wo caegories because hey have been ideni

ed as needing addiional suppor o be suc

cessul in Caliornias public schools. English


Basic


5,332

9,004

4,682

4,322

2,765

1,679

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

16,000

18,000

20,000

2003 2008

Num

bero

f8thGra

ders

Ta

king

Alge

bra

ICST

(54%)

(28%)

(17%)

(24%)

(26%)

(50%)

26,101

47,916

33,085

33,085

14,842

10,236

0

20,000

40,000

60,000

80,000

100,000

120,000

2003 2008

Numb

ero

f8thGra

ders

Ta

king

Alge

bra

ICST

(51%)

(29%)

(29%)

(29%)

(20%)

(42%)


Basic



Basic


23,562 24,504

27,48930,630

46,142

67,387

0

20,000

40,000

60,000

80,000

100,000

120,000

140,000

2003 2008

Num

bero

f8thGra

ders

Ta

king

Alge

bra

ICST

(24%)

(28%)

(47%)

(20%)

(25%)

(55%)


Basic


26,660

53,919

35,110

37,618

15,463

11,730

0

20,000

40,000

60,000

80,000

100,000

120,000

140,000

2003 2008

Num

bero

f8thGra

ders

Ta

king

Alge

bra

ICST

(50%)

(22%)

(29%)(43%)

(30%)

(28%)

Data: Californ ia Departme nt of Education, STAR. Accessed 1/. EdSource 5/

Note: The counts of 8th graders shown here are based on the numbers tested on the Algebra I CST, rather than the preferable number of students with valid scores. This is because the latter data are not

published for 2003 as they are for 2008. These counts are estimates derived from state report s of performance and may not match the number of students tested due to rounding.

Perormance o nonocoeconomcay dadvanaed 8h raderfgure B Perormance o ocoeconomcay dadvanaed 8h raderfgure C

Perormance o Arcan Amercan 8h raderfgure D Perormance o lano 8h raderfgure E


8/20



learners (ELs) and sudens wih disabiliies

were abou 13% and 4% respecively o 8h

graders who ook he Algebra I CS in 2008.

Algebra I CS paricipaion increased

subsanially or boh groups o 8h graders

beween 2003 and 2008. (See Figures 3F and

3G.) Tis is especially rue or 8h graders

wih d isabi liies . Nearly2.5 imes as many 8hgraders wih disabiliiesabou 10,400 in

allook he es in 2008 versus 2003.

Even wih his growh in paricipaion,

he percenages o hese 8h graders scoring

a dieren achievemen levels on he Alge-

bra I CS in 2008 was roughly he same as in

2003, wih small decreases i n he percenages

scoring ar below basic. One resul is ha

greaer numbers o 8h graders in boh

groups now score procien or advanced.

Abou 1.7 imes as many EL 8h graders didso compared wih 2003, as did abou2.3 imesas many 8h g raders wih disabiliies.

However, anoher upsho is ha abouwo-hirds o 8h graders in boh groups sill

score below or ar below basic on he Alge-

bra I CS. As a resul, many more o hese

sudens may need o repea Algebra I. Abou

1.2 imes as many EL 8h graders and 1.7 imesas many 8h graders wih disabiliies scored

below or ar below basic on he Algebra I

CS in 2008 as ook he es a all in 2 003. o

he exen ha Algebra I becomes a deaul

course-aking expecaion or grade 8, par-

icular atenion regarding how o suppor

he mah achievemen o EL sudens and

sudens wih disabiliies mos eecively is

clearly warraned.

General Math CST

Suden oucomes are also mi xed among 8h

graders who do no ake he Algebra I CS.

In 2008, 43% o he saes 8h graders ook

he General Mah CS because hey were

eiher no enrolled in algebra or enrolled in

he rs year o a wo-year algebra course.

Pre-algebra success among 8h graders

no ye aking he Algebra I CS is improv-

ing bu remains a concern. O hese 8h grad-

ers, less ha n one-hird (31%) scored procien

or advanced on he es, and 4 1% scored below

or ar below basic. In 2003, when 60% o 8h

graders ook he General Mah CS, only

24% scored procien or advanced.

Many students repeat Algebra ICaliornia mah educaors and policymakers

inerpre he Algebra I CS daa presened

so ar in diering ways. Bu mos agree ha

oo many sudens are repeaing he course,

someimes muliple imes.

Caliornia is now able o quaniy his

problem more precisely using suden-level

daa. Tese daa show ha 38% o 9h graders

who ook he Algebra I CS in 2008 had

aken he es in a prior year. More han hal

o 10h and 11h graders who ook he CS

were repeai ng i as well . (See Figure 4 on

page 9.) Repeaing Algebra I in grade 10 or

laer is o paricular concern because i can

preven sudens rom compleing college

prep courses in science ha have algebra as

a prerequisie.

Tese daa also raise larger quesions

abou curren sudens preparaion o ake

advanage o earlier access o algebra. Many

sudens who repea he Algebra I CS may

have sruggled in mah in earlier grades as

well . Some worr y ha coninuous lack o

success in mah can have he pernicious

eec o convincing some sudens hey are

unable o undersand and use mahemaics

A he ex reme, some say repeaed algebra

course ailure causes some sudens o disen

gage rom school enirely and drop ou.

Te Caliornia Deparmen o Educaion(CDE) cauions ha some uncerainy sur

rounds hese repeaer daa:

n Some sudens in he sae ake Algebra I

as a wo-year course. CDE inends or

sudens in he rs year o such a course

o ake he General Mah CS. Only su

dens compleing Algebra I are expeced

o ake he Algebra I CS. However

wheher a ll disrics ad miniser he CS

11,099

20,704

7,230

3,700

4,929

2,819

0

5,000

10,000

15,000

20,000

25,000

30,000

35,000

2003 2008

Num

bero

f8thGra

ders

Ta

king

Alg

ebra

ICST

(63%)

(21%)

(16%)

(22%)

(63%)

(15%)


Basic



Basic


2,908

7,076

1,769

674

1,561

674

0

2,000

4,000

6,000

8,000

10,000

12,000

2003 2008

Num

bero

f8thGra

ders

Ta

king

Alge

bra

ICST

(69%)

(16%)

(16%)(68%)

(17%)

(15%)

Note: The counts of 8th graders shown here are based on the numbers tested on the Algebra I CST, rather than the preferable number of students with valid scores. This is because the latter data are not

published for 2003 as they are for 2008. These counts are estimates derived from state report s of performance and may not match the number of students tested due to rounding.

Data: Californ ia Departmen t of Education, STAR. Accessed 1/. EdSource 5/

Perormance o Enh earner 8h raderfgure F Perormance o 8h rader wh dabefgure G


9/20



in his way is unclear. Some sudens in

wo-year algebra courses migh ake he

Algebra I CS wice, even hough hey

did no acually repea he course.

n In addiion, some sudens who pass

Algebra I in grade 8 migh be placed in

he course again by high schools hacriicize he qualiy o 8h grade courses.

California compares poorly in grade 8 mathon a national assessmentTe CSs are no he only available meas-

ures o Caliornia sudens mah achieve-

men in grade 8. Te Naional Assessmen

o Educaional Progress (NAEP), which is

adminisered o a sample o Caliornia su-

dens, provides a way o compare Calior-

nias grade 8 mah achievemen wih oher

saes. Some say NAEP provides an objec-ive and valuable measure o Caliornias

overall mahemaics curriculum.

Daa rom he 2007 NAEP (see Figure

5A) show ha:

n Caliornia 8h graders generally score

below he naiona l average and below he

oher our larges saes (Florida, Illinois,

New York, and exas).

n exas in paricular ouscores Caliornia

across all suden groups.

n Caliornias average NAEP scores in

grade 8 mah generally are also below hose

or Massachusets and Minnesoa. Tese

wo saes are paricularly noable in con-

necion wih ye anoher assessmen: he

rends in Inernaional Mahemaics and

Science Sudy (IMSS). Massachusets

and Minnesoa are he only wo saes

whose sudens scores on he IMSS are

benchmarked separaely agains sudens

rom oher naionswih greaer average

success in mah han sudens in he

Unied Saes as a whole.Some in Caliornia insis ha NAEP

resuls in general should be inerpreed wih

cauion. Te NAEP in grade 8 mah is no

specically aligned wih Caliornias conen

sandards, nor is i an Algebra I es. In addi-

ion, Caliornias scores (1) or all sudens

and (2) or Laino sudens are complicaed

by he ac ha Caliorn ia excludes a much

lower proporion o is English learner

sudens rom paricipaion in he NAEP

compared wih he naion and he oher six

saes discussed here. (See Figure 5B.)

However, ohers see hese resuls as com-

pelling evidence ha whaever progress su-

dens may have made relaive o he saes

own sandards and assessmens, Caliornia

sudens are no receiving a bala nced mahe

maics educaion in grades K8 compared

wih heir peers in oher saes . For some

hese daa heighen heir concern ha Cali

ornias sudensand he public schoo

suden group CA Fl il MA MN NY tX Naon

African American 253 259 * 264 * * 271 259

Asian/Pacific Islander 293 * * 315 * 302 309 296

Latino 256 270 265 270 269 264 277 264

White 287 * * 305 297 * 300 290

English Learner 241 * 257 * 258 * 252 245

Not English Learner 278 * * 299 293 282 288 282

All Students 270 277 280 298 292 280 286 280

* Difference with comparable California score is not statistically significant.

fgure A 2007 NAEP 8h rade mahemac averae cae core

grade suden n grade

takn he Aebra i Cst

n 2008

Aebra i

Cst-aker Who Are

Fr-me Examnee

Aebra i Cst-aker

Who Are Repean he

Aemen

7 25,573 25,573 (100%) 0 (0%)

8 246,587 242,062 (98%) 4,525 (2%)

9 272,353 167,819 (62%) 104,534 (38%)

10 131,415 62,834 (48%) 68,581 (52%)

11 66,108 31,901 (48%) 34,207 (52%)

Data: California Department of Education, 00 Sandardized esing and Reporing (SAR) EdSource 5/Program S ummar y of Resu ls , August 8.

fgure Many uden n he hh choo rade have aken he Aebra i Cst more han once

# Rounds to zero.

suden group CA Fl il MA MN NY tX Naon

Percentage of 8th

Graders Identified as EL

22% 6% 4% 3% 5% 5% 8% 7%

Percentage of 8th

Graders Excluded Due

to EL Status

1% 1% 1% 1% # 1% 2% 1%

Percentage of 8th

Grade EL Students

Excluded

5% 17% 25% 33% # 20% 25% 14%

Data: National Center for Education Statistics (NCES). EdSource 5/

fgure B 2007 NAEP 8h rade mahemac Enh earner excuon


10/20


10 n Al ge bra Pol icy in C al ifor nia n May 2009 Copyright 2009 by EdSource, Inc.

sysem in generalare no prepared o

make Algebra I in grade 8 a deaul curric-

ulum and ha he uninended conse-

quences could be quie serious.

Math achievement problems begin in grade 5Mos Caliornia mah expers, including

policymakers and educaors, agree ha

Caliornia sudens mah prociency when

hey arrive in grade 8, on average, does no

mee he saes aspiraions. Te key daa

relae o sudens mah achievemen in

grades 57.

Te good news is ha he percenage o

sudens scoring procien or advanced on

mah CSs increased in each o grades 2

hrough 7 beween 2003 a nd 2008. (See Fig

ure 6A.) In addiion, 5% o 7h graders now

ake he Algebra I CS, wih our ou o v

o hese sudens scoring procien o

advanced.

However, some analyss cauion ha

some o he improvemen in grades 27 ilikely a consequence o increased amil iariy

wih he ess. Fur her, Cal iornia observer

are roubled by a decline in mah achieve

men across grades, beginning in grade 5 and

persising in he early middle grades. Large

percenages o sudens in hese grades scor

below or ar below basic on mah CSs

Nearly hree in 10 sudens in grades 6 and 7

scored in hese lowes wo caegories in

2008, compared wih jus 16% o 4h graders

(See Figure 6B.)

For many in he sae, hese daa indicaa roo cause behind Caliornias challenge

in grade 8 mahemaics, including laer alge

bra repei ion: sudens mah prepara ion

in earlier grades is inadequae and suer

beginni ng in grade 5. Te mah achievemen

gaps among dieren suden groups noed

earlier wih respec o grade 8 Algebra I also

appear across grades 2 7.

How NAEP and Cst der

The National Assessment of Educational Progress (NAEP) and the California Standards Tests (CSTs) in

grade 8 mathematics are very different tests.

nThe NAEP includes both multiple-choice and open-ended, constructed-response items. In contrast, the

math CSTs that California 8th graders take are entirely multiple-choice questions.

n No student takes the entire NAEP exam, in contrast with the CSTs. The NAEP follows a matrix design:

individual students take only two sections of the test, and the results for many sampled students are

combined.

n In grade 8, the NAEP in mathematics assesses content pertaining to number properties and operations,

measurement, geometry, data analysis and probability, and algebra at varying levels of mathematical

complexity. In contrast, California 8th graders take different CSTs that assess different content

depending on the math courses in which they are enrolled.

For more extensive discuss ion of NAEP and CSTs, see EdSources May 2008 report, NAEP and the California

Standards Tests: A Case of Apples and Oranges.

* Includes both 7th graders taking the Grade 7 Mathematics CST and those taking the Algebra I CST in 2008.

Note: The counts of students in Figure 6B are based on the numbers tested on the relevant CSTs, in order to remain consistent with Figures 3AG. These counts are estimates derived from state reports of

performance and may not match the number of s tudents tested due to rounding.

2003

2008

6A. suden scorn Procen or Advanced on Mahemac Cst,* 2003 and 2008

53%

46% 45%

35% 34%

30%

59%61% 61%

51%

44% 43%

0%

10%

20%

30%

40%

50%

60%

70%

Grade 2 Grade 3 Grade 4 Grade 5 Grade 6 Grade 7

%ofSt

udentsProficient/Advanced

Data: Califor nia Departme nt of Education, STAR. Accessed 1/. EdSource 5/

fgure Ahouh more uden n rade 27 are corn hhy on mah Cst, uden achevemen decne bennn n rade 5

6B. suden Perormance on Mahemac Cst* n 2008

88,165 76,256 71,774

113,126131,638 134,776

94,198 103,175

108,601

136,339 132,383

273,624 273,639230,777

206,860 202,581

97,446

273,776

0

50,000

100,000

150,000

200,000

250,000

300,000

350,000

400,000

450,000

500,000

Grade 2 Grade 3 Grade 4 Grade 5 Grade 6 Grade 7

NumberofStudents

59%

17% 16%

25%28% 29%

21%21% 23%

29% 28%

24%

61% 61%

51%

44% 43%

19%

Proficient or Advanced Basic Below Basic or Far Below Basic


11/20


May 2009 n Al geb ra Poli cy i n Ca lifornia n 11 Copyright 2009 by EdSource, Inc.

Different perspectives on the timing ofalgebra highlight the importance of supportand the risk of unintended consequences

A decade ago, he big quesion i n Ca liornia

was wheher all sudens should be expec ed

o ake a year o algebra beore hey gradu-

aed rom high school. Sae lawmakers

responded yes o his quesion in 2000. Su-

dens in he class o 2004 were he rs o berequired o pass Algebra I o earn a diploma.

Bu he ransiion was no easy. EducaionWeek repored in May 2004 ha nearly halo Caliornia disrics applied or waiv-

ers rom he requiremen ha year. oday,

his requiremen appears o be ully imple-

mened as a minimum sandard or high

school graduaion.

In conras, Caliornias Mahemaics

Framework saes ha one o is goals is o

prepare all sudens o sudy algebra by he

eighh grade. Tis aspiraion is consisen

wih ndi ngs rom IMSS, repored by

Wil liam Schmid and ohers, ha high-

achieving naions in mahemaics end

o begin insrucion in algebra by grade 8.

Tese ndings uel worr ies ha oher naions

expec more rom heir sudens han do

mos saes, wih roubling implicaions or

Amer ican economic compe iiveness.

In addiion, such naions requenly ake

a dieren approach o heir mah curricula

han Caliornia. For example, conen per-aining o inroducory algebra and geom-

ery migh be augh o all sudens over

he course o grades 79, raher han hrough

wo separae courses in jus wo years. High-

perorming naions also end o ocus on

ewer imporan mah opics in greaer

deph in he grades leading up o algebra.

Tere is broad agreemen in Caliornia

ha earlier success in a lgebra would be good

or sudens and or he sae generally. Tere

is also general agreemen ha every Calior-

nia suden deserves o be challenged aca-

demically, augh and suppored by aduls

who believe srong ly in his or her poenia l,

and provided a air chance o achieve aca-

demic success. Bu some Caliornia mah

educaors and policymakers dier regard-

ing how sae policy migh bes supporhese ideals.

Consider he debae ha surrounded he

Sae Board o Educaions response o ed-

eral demands ha Caliornia bring is grade 8

assessmens ino compliance wih NCLB.

(See he box on page 2.) In he absence o a

waiver al lowi ng Caliornia o pursue is own

approach o grade 8 mah, he sae board

ocused on wo opions:

n Pursue he Algebra I CS or all 8h

graders, which would clearly mee ed-

eral demands and coninue he saes

emphasis on geting more sudens ino

he course.

n Pursue, i acceped by he U.S. Depar-

men o Educaion, a new grade 8 CS

based on Algebra I bu exclud ing such

conen as acoring and quadraic

equaions.

Some saw he proposed blueprin or a

new grade 8 CS as undercui ng he inen

o he saes conen sandards o ensure

high expecaions or all sudens. he pro-posed es would have assess ed less conen

han he Algebra I CS, bu i would have

been designaed gr ade-level or ed era l

accounabiliy purposes. Criics argued

his would coner grade-level saus on

lower expecaions or some sudens. For

hem, he sae board made a deensible

decision when i insised ha all schools

should be held accounable or universally

high expecaions hrough he Algebra I

CS in grade 8.

Ohers saw he proposed blueprin as an

improvemen on he General Mah CS ha

would provide less prepared sudens wih

iniial exposure o algebra and leave room

or local educaors o use heir bes judg

men in making suden placemen decisions

For hem, Caliornia policy should ocus onacceleraing early success in algebra only as

appropriae or individual sudenssuch

as by grade 8 or 9raher han use he es

ing sysem o insis on algebra in a paricula

grade. Tey worry ha requiring he Alge

bra I CS or al l 8h graders could se up

many sudens or course ailure and expand

he already large number o sudens who

repea he course.

Recen sudies have underscored con

cern ha a grade 8 algebra or all policy

could have uninended repercussions o

sudens. Te mos recen is a 2009 sudy by

wo researchers rom he Consorium on Chi

cago School Research, Elaine M. Allensworh

and akako Nomi. Te sudy explored he

oucomes o a 1997 Chicago Public Schools

policy o require Algebra I or all sudens by

grade 9 as par o an eor o broaden suden

access o college-prep curricula. Allensworh

and Nomi looked a course daa or 11 cohors

o rs-ime Chicago 9h graders beween

1994 and 2004. Te Chicago researchersound ha more sudens enrolled in Alge

bra I, as inended under he policy. Howeve

mah course ailure and abseneeism in

creased among hose sudens who sared wih

low and average levels o mah achievemen.

A 2008 repor by om Loveless o he

Brookings Insiuion, Te Misplaced MahSuden, repored on he exen o whichsome early algebra placemens migh be

the aebra debae rae hard queon abou Caorna expecaonor mah achevemen

The relationship between a states academic content standards and actual classroom practice is

highly complex. But Caliornias algebra debate raises a question that goes to the heart o the states

standards-based reorms. Does Caliornia have the right expectations when it comes to algebra?


12/20



inappropriae. Loveless looked a mah ou-

comes or he lowes-achieving 10% o 8h

graders on NAEP. He ound ha, whereas

only 8% o hese lower-achieving sudens

were enrolled in Algebra I or higher in 2000,

almos 29% were enrolled in such courses

in 2005. However, hese sudens were re-quenly unable o correcly answer es iems

ha assessed such basic mah conceps as

rounding a decimal o he neares whole num-

ber. Loveless concludes ha policies aimed

a more equiable access o rigorous mah

curricula had he uninended consequence

o puting less-prepared eachers in algebra

classrooms wih sudens o widely diering

levels o preparaion. He argues urher ha

his burden ell disproporionaely on minor-

iy sudens in urban, low-income schools.

A recen UCLA analysis o CS scoresa 112 randomly seleced middle schools in

he Los Angeles area raises similar concerns,

suggesing ha lower-perorming middle

schools are more likely o enroll 8h graders

who scored below or ar below basic on he

grade 7 mah CS in an Algebra I course.

(Alhough he grade 7 mah CS is no a

diagnosic es and resuls are generally no

available in ime o in orm grade 8 placemen

decisions, he UCLA sudy used he grade 7

CS o judge he resriciveness o school

placemen policies.)

Some worry ha minoriy sudens in

hard-o-sa, urban schools who excel in

mah and wish o pursue he mos challeng-

ing courses could, under an algebra or al l in

8h grade policy, nd hemselves enrolled

in algebra courses ha are insucienly

challenging. Tis could eecively place

hese sudens on a less compeiive mah

rajecory. A he same ime, however, some

research suggess ha acceleraed mah

course-aking in he middle grades can work,provided sudens receive adequae suppor

o be successul. For example, a recen longi-

udinal sudy in Long Island, NY, by Carol

Corbet Burris and colleagues, cies such

pracices as workshops or sudens needing

addiional help, common preparaion ime

or eachers, and assigning mah eachers

o work in boh acceleraed regular class-

rooms and suppor workshops.

Tese sudies highligh he challenge o

achieving broader access o rigorous mah cur-

ricula while assuring qualiy insrucion and

successul oucomes or sudens. Alhough

he Chicago and Brookings sudies are oen

inerpreed as cauionary ales, hese sudies

do no necessarily mean he goal o getingmos 8h graders ino Algebra I is no worh

pursuing. Anoher inerpreaion is hese

sudies highligh he imporance o suppor

or local capaciy and insrucional qualiy.

For example, Lovelesss nding ha some

algebra sudens canno round decimals o

he neares whole number raises he quesion

o why hese sudens were no prepared ade-

quaely in prior years. In his sense, suden

paricipaion and success in a rigorous mah

curriculum, and he high expecaions ha

accompany i, begin in elemenary school.Universal Algebra I in grade 8 may also

have some imporan implicaions or high

schools and possecondary insiuions. One

reason oen given or algebra in grade 8 is

o ensure he broades and earlies possible

access o a rigorous high school curriculum

ha will prepare sudens or smooh ransi-

ions o some orm o possecondary sudy.

Wihou quesion, prepara ion in mahema-

ics is very imporan o colleges and univer-

siies. Many Caliornia sudens enroll in

communiy college needing basic skills mah

courses beore hey can succeed in degree-

applicable ones, or example.

Earlier paricipaion and success in algebra

could reduce he need or remediaion among

recen high school graduaes, provided su-

dens ake mah courses every year during high

school as Caliornias public universiies rec-

ommend. I could also increase he demand or

courses in higher mah in high schools. Very di-

eren consequences are also possible, however.

Widespread Algebra I in grade 8 could increasehe numbers o sudens who, having com-

pleed he mah course requiremen or eligi-

biliy o UC or CSU by he end o grade 10,

decide o noake mah courses during heirjunior and senior years. Tis ime away rom

he sudy o mah could resul in more high

school graduaes perorming poorly on college

placemen exams and needing remediaion in

mah. Ta said, sudens who have compleed

or enroll in Algebra II by grade 11 could sil

receive early eedback abou heir college

readiness in mah by paricipaing in he

Early Assessmen Program. (Trough his pro

gram, high school juniors can ake expanded

CSs o deermine college readiness or he

Caliornia Sae Universiy sysem.)

Does the algebra debate raise deeperquestions about Californias standards-based reforms?Caliornias curren mah conen sandards

were he produc o a conenious adop

ion process oen reerred o as he mah

wars . Te debae posiioned suppor ers o a

sronger saewide emphasis on basic

operaional skills and mahemaical preci

sion agains hose who sressed concepual

undersanding and he pracical relevanceo mahemaics (as in he model sandards

o he Naional Council o eachers o

Mahemaics, or example).

Mah educaors and policymakers under

sand ha hese muliple aspecs o mah pro

ciency are closely inerrelaed and essenia

or sudens o learn. A he same ime, mos

acknowledge ha a back o basics approach

o he sandards won he day in Caliornia

Te philosophical ensions ha spurred his

debae coninue o linger. Tere is sill dis

agreemen among knowledgeable people in

he sae abou wheher he oundaion pro

vided by Caliornias mah conen sa ndards

and he assessmens o suden achievemen

provided by he mah CSs, oer sudens

and educaors a world-class or a narrow

vision o mah proc iency.

For supporers o he choices Caliornia

made, he curren mah sandards are a he

core o he saes insrucional capaciy o

expand algebra success by grade 8. Tey poin

o suden achievemen gains on he CSsas evidence ha sudens can succeed when

held o high expecaions and given a air

chance o mee hem. Supporers also poin

o posiive raings o he saes mah san

dards by such organizaions as he Fordham

Foundaion and he American Federaion o

eachers. Furher, he Naional Mahemaics

Advisor y Panel, creaed in Apri l 2006 by hen

Presiden George W. Bush, ound in 2008 ha


13/20


May 2009 n Al geb ra Poli cy i n Ca lifornia n 1 Copyright 2009 by EdSource, Inc.

he K8 mah sandards o six saesinclud-

ing Caliornia and Massachusetson he

whole, provide an emphasis on ewer impor-

an opics per year han mos saes.

However, he panel added ha his more

coheren ocus sill alls shor o wha is

done in high-perorming naions, such asSingapore. Panel members also cauioned

ha sandards mus be accompanied by

meaningul assessmens, curricula, and

eecive eacher preparaion and proes-

sional developmenin eec, he oher

elemens necessary o suppor coninuous

improvemen in eaching and suden

achievemen. Tese observaions bolser he

argumen o hose who say ha Caliorn ias

lackluser perormance on NAEP compared

wi h oher saes shows ha Cal iornias

policy choices have no provided sudens

an adequae oundaion or well-roundedmah prociency. From heir perspecive,

Caliornia should be open o learning rom

oher saes abou how o more eecively

prepare all s udens or algebra. Some poin

o exas, which ouscores Caliornia on

NAEP, and Massachusets and Minnesoa,

which are bench marked independen ly

agains oher naions on IMSS.

Massachusets, or example, is reviewing

is Mahemaics Curriculum Framework,whichincludes he saes mah sandards, o ideniy

possible revisions. Te revision panels progress

repor, discussed by he Massachusets Boardo Elemenary and Secondary Educaion in

March 2009, considers he sreamlining, prior

izing, and verical alignmen o he saes mah

sandards hrough grade 7. Te goal is o sup

por increased, successul paricipaion in alge

bra in grade 8 while sill allowing sudens who

Caorna are mah andard or aebra readne

Californias current Mathematics Framework sets out the states expectations for algebra readiness instructional materials, to be used with 8th graders not yet

ready for algebra. These materials build on key math standards from grades 26, with the goal of achieving 16 target standards from grade 7 and Algebra I thatprepare students for a full algebra course.

13 areed mah andard rom rade 7Number sene rand:

nAdd, subtract, multiply, and divide rational numbers (integers, fractions,

and terminating decimals) and take positive rational numbers to whole-

number powers.

n Convert fractions to decimals and percents and use these representations

in estimations, computations, and applications.

n Know that every rational number is either a terminating or repeating deci-

mal and be able to convert terminating decimals into reduced fractions.

n Understand negative whole-number exponents. Multiply and divide ex-

pressions involving exponents with a common base.

Aebra and Funcon rand:

n Use variables and appropriate operations to write an expression, an equation,

an inequality, or a system of equations or inequalities that represents a

verbal description (e.g., three less than a number, half as large as area A).

n Simplify numerical expressions by applying properties of rational numbers

(e.g., identity, inverse, distributive, associative, commutative) and justify

the process used.

n Interpret positive whole-number powers as repeated multiplication and

negative whole-number powers as repeated division or multiplication bythe multiplicative inverse. Simplify and evaluate expressions that include

exponents.

n Graph linear functions, noting that the vertical change (change in y-value)

per unit of horizontal change (change in x-value) is always the same and

know that the ratio (rise over run) is called the slope of a graph.

n Plot the values of quantities whose ratios are always the same (e.g., cost

to the number of an item, feet to inches, circumference to diameter of

a circle). Fit a line to the plot and understand that the slope of the line

equals the ratio of the quantities.

n Solve two-step linear equations and inequalities in one variable over the

rational numbers, interpret the solution or solutions in the context from

which they arose, and verify the reasonableness of the results.

n Solve multistep problems involving rate, average speed, distance, and

time or direct variation.

Meauremen and geomery rand:n Use measures expressed as rates (e.g., speed, density) and measures

expressed as products (e.g., person-days) to solve problems; check

the units of the solutions; and use dimensional analysis to check the

reasonableness of the answer.

n Know and understand the Pythagorean theorem and its converse and

use it to find the length of the missing side of a right triangle and the

lengths of other line segments and, in some situations, empirically verify

the Pythagorean theorem by direct measurement.

three areed mah andard rom Aebra i

n Students understand and use such operations as taking the opposite,

finding the reciprocal, taking a root, and raising to a fractional power. Theyunderstand and use the rules of exponents [excluding fractional powers].

n Students simplify expressions before solving linear equations and

inequalities in one variable, such as 3(2x 5) + 4(x 20) = 12 [excluding

inequalities].

n Students solve multistep problems, including word problems, involving

linear equations and linear inequalities in one variable and provide

justification for each step [excluding inequalities].

Source:Mahe mai cs Frame work for Cal iforni a Public S chools , Kinde rgar en Troug h Grade welve , Appendix E


14/20



the aebra debae pu eacher capacy n he poh

Beyond instructional materials and other resources, public education is ultimately about people.

need an exra year o underake an algebra read-

iness opion. Te panel is also considering new

high school course opions. One would suppor

suden readiness or Algebra II in high school.

Te oher would provide mah insrucion

beyond Algebra II or sudens hoping o pur-

sue college majors or careers ha are no mah-inensive. A rs dra o he revised mah

ramework will be submited o he Massachu-

sets board in all 2009.

What is the fate of Californias algebrareadiness instructional materials?

Alhough Calior nia currenly has no pro-

cess or periodically revising is mah conen

sandards, he sae does updae is Mahe-

maics Framework every six years o refec

changes in research and pracice. Te rame-

work provides guidance o local educaorsand exbook publishers on how o use Cali-

ornias mahemaics sandards o inorm

curriculum developmen and classroom in-

srucion. Uncerainy abou he saes alge-

bra policies has complicaed saewide and

local eors o make decisions abou middle

grades mah insrucional maerials, however.

Caliornias curren mah ramework was

adoped in March 2005. Based on is goals, he

Sae Board o Educaion adoped new algebra

readiness insrucional maerials in November

2007, inended or 8h graders who are no ye

ready or algebra. Tese maerials are designed

o srenghen sudens oundaional skil ls and

concepual undersanding in mah. o do his,

algebra readiness maerials build on key mah

sandards rom grades 26, wih he ulimaegoal o achieving 16 arge sandards: 13 san-

dards rom grade 7 and hree rom Algebra I.

(See he Caliornias arge Mah Sandards

or Algebra Readiness box on page 13.) Ideally,

hese maerials should help local educaors

deermine heir sudens insrucional needs

and help sudens recognize heir own capac-

iies o learn and undersand mahemaics.

In January 2009, he sae board approved

a imeline or anoher updae o he saes

Mahemaics Framework. I is unclear how

he updae will address algebra readiness,however. CDE has recommended ha he

board revisi he saes algebra and algebra

readiness insrucional programs o bring

he nex ramework ino alignmen wih

SBE policy on saewide assessmens.

A his wriing, sae educaion leaders

have no resolved his issue. As a resul, here

is a grea deal o uncerainy among disrics

as hey pilo and make decisions abou which

sae-adoped K8 mahemaics programs o

purchase or heir sudens. On he one hand

mos agree ha algebra readiness maerials

could be o grea value. Furher, a new Alge

bra I policysuch as he one conained in SBEs

suspended July 2008 moionwould sill pro

vide disrics wih several years during which

hey could enroll 8h graders in mah coursesbelow algebra , while working o prepare su

dens in earlier grades or he Algebra I CS

On he oher hand, disrics ha have

already invesed ime in piloing algebra

readiness maerials are in an ambiguous

posiion. Te new sae budge allows dis

rics o delay he purchase o insrucional

maerials in mahemaics uni l July 1, 2010, a

which ime hey a re ex peced o have maeri

als rom he mos recen sae-approved lis

in place in boh mah and English language

ars. Disrics mus consider wheher algebra readiness maeria ls could soon be obso

lee or some insrucional purposes and

wheher more exensive inves men in Alge

bra I maerials is warra ned. I disric s inves

exbook unds in algebra readiness mae

rials now, hey will no have hese unds

available o purchase addiional Algebra

maerials laer.

As Caliornia look s o help more sudens

succeed in algebra earlier, no resource is more

imporan han qual ied eachers who have a

deep and coninuously growing undersand-ing o mah conen and pedagogy.

Tis secion provides an inroducion o key

consideraions in wo areas o sae eacher pol-

icy: credenialing and proessional developmen.

Te preparaion o muliple-subjec eachers or

mah insrucion in he elemenary and middle

grades is o paricular concern as Caliornia

looks ahead, as is improving he proessional

capaciy o he saes exising eacher workorce

o each mah well. Tese underlying challenges

pre-dae Caliornias curren policy debae abou

grade 8 mah and will coninue o be pressing

regardless o how his debae is resolved.

Teacher credentialing for math in grades K8is an ongoing topic of policy discussionCredenialing or mah insrucion in

grades K8 is a cenral quesion as Cali-

ornia works o enable more sudens o

succeed in algebra early. In Ocober 2008,

he Caliornia Commission on eacher

Credenialing (CC), which grans eaching

credenials in he sae, began reviewing

he saes mah auhorizaions. An adv isory

panel recenly convened by he CC has

begun o rev iew he saes uure credenialing needs or mah insrucion.

Californias supply and distribution of prepared

middle grades algebra teachers is a concern

Even wihou a change in sae policy regard

ing grade 8 mah, eacher qualicaions are an

issue in Caliornia. According o he Cener o

he Fuure o eaching and Learning (CFL)

abou one-hird o middle grades Algebra I


15/20


May 2009 n Al geb ra Policy i n Ca liforni a n 1 Copyright 2009 by EdSource, Inc.

eachers may no be adequaely prepared o

each he course eecively. (See Figure 7.)

Alogeher 8% o middle grades Algebra I

eachers had no received a preliminary or

clear eaching credenial, and 23% held eiher a

single-subjec credenial in anoher subjec or a

muliple-subjec credenial wihou a subjec-mater auhorizaion in mah. Moreover, CFL

noes, alhough sudens who are sruggling o

reach prociency on he Algebra I CS are in

paricular need o eachers who are especially

skilled a remediaion, sudens in lower-

perorming schools are less likely o be augh

by ea chers wi h a s rong m ah backgrou nd.

Teachers with varied backgrounds can teach Algebra I

In general, middle grades eachers in Cali-

ornia earn eiher:

n A single-subjec credenial, similar o highschool eachers; or

n A muliple-subjec credenial, similar o

elemenary school eachers.

Currenly, Caliornia acceps several

opions regarding which educaors are

auhorized o each Algebra I in he middle

grades. Tis fexibiliy enables schools serv-

ing he middle grades o pursue an array o

approaches o organ izing heir classrooms:

n eachers may each algebra in a depar-

menalized seting wih a single-subjeccredenial in mahemaics.

n Middle grades eachers may also each

Algebra I wih a muliple-subjec credeniali hey do so in (1) a sel-conained class-

room in which all subjecs are augh; or

(2) a core classroom in which wo or

more subjecs, such as science and mah,

are augh o he same group o sudens.

n eachers wih a muliple-subjec or single-

subjec credenial in anoher subjec may

also secure a subjec-mater auhorizaion

in mahemaics. Tis add-on auhorizesmah insrucion in courses covering mahconen or grades 9 and lower in a depar-

menalized classroom. Te auhorizaion

requires a degree equivalen 32 semes-

er unis o course work, including cerain

minimum course-aking requiremens.

n In 2003, he CC esablished he single-subjec credenial in foundaional mahe-maics. Te oundaional mah credenial

auhorizes a eacher o provide insrucion

in such areas as algebra, geomery, and

probabiliy and saisics, bu i excludes

calculus and mah analysis. Te credenial

can sand alone or eachers wishing o

each only hose courses, or i can be added

o a credenial in anoher subjec area.

CFL atribues much o he recen rise in

he number o mah credenials graned sae-

wide o he inroducion o he oundaional

mah credenial. Tey expec his rend o con-

inue among eachers who wish o each Alge-

bra I bu need more background and rain ing.

n In 200203, beore he oundaional mah

credenial was oered, CC issued 1,005

new single-subjec mah credenials.

n Four years laer, in 200607, CC issued

1,804 new single-subjec mah credenials,

wih almos 40% o hese in oundaionalmahemaics.

Policymakers are concerned about the preparation of

multiple-subject teachers for math instruction

Algebra ins rucion by muliple-subjec

eachers has become a key opic o concern or

CC. A school acing a shorage o mah

eachers can assign a eacher wih a muliple-

subjec credenial o each Algebra I in a

sel-conained or core classroom. Bu he exam

inaion requiremens or he muliple-subjec

credenial are aligned o he K7 academic

conen sandards in mahemaics, as CC

noes in is January 2009 meeing agenda. In

ligh o his, CC is considering how o addres

he misalignmen beween wha he Muliple

Subjec credenial holder is auhorized o each

wih respec o Mahemaics and he conen

preparaion required or he credenial.

Te capaciy o muliple-subjec each

ers o each mahemaics eecively in he

elemenary grades is also a opic o concernor CC, given he decline in CS achieve

men ha begins in grade 5. Quesions raised

by he commission in Ocober 2008 include

wheher preparaion programs or muliple

subjec eachers are adequae as hey relae

o mah insrucion and wheher he examinaion aken by muliple-subjec candidaes

assesses heir undersanding o mahe

maical conen sucienly.

Te adequacy o elemenary mah in

srucion is also a opic o naional conversa

ion. For example, he 2008 repor by he

Naional Mahemaics Advisory Panel drew

naional atenion by recommending ha

schools devoe ample ime o hree criica

One-hrd o mdde rade Aebra i eacher may no be prepared o each he ubjec

Credena sau o Fu-tme, Mdde grade Aebra teacher, 200708

8%

66%

3%

23%

Underprepared (i.e., without apreliminary or clear credential)

Fully credentialedwithout a math authorization

More than one credential type

Fully credentialed with a math authorization

fgure

Data: Center for the Futur e of Teaching and Lear ning (CFTL), 8 EdSource 5/


16/20



oundaions o algebra. Tese include

srenghening sudens fuency in working

wih (1) whole numbers , (2) racions, and (3)

paricular aspecs o geomery and measure-

men. Te panel suggesed ha fuency wih

racions in paricular is inadequaely devel-

oped in he naions schools and called oneacher educaion programs o make under-

sanding o he hree oundaions a ocus o

eacher preparaion or elemenary and mid-

dle grades mahemaics.

In addiion, a 2008 repor by he Naional

Council on eacher Qualiy ound litle con-

sensus among elemenary eacher prepara-

ion programs a 77 insiuions naionally

o which hree were in Caliornia, includ-

ing wo Caliornia Sae Universiy (CSU)

campusesregarding he mah conen ha

muliple-subjec, elemenary eachers areexpeced o learn. Te sudy did noe one

unorunae area o agreemen among mos

insiuions in he sample, howeverwide-

spread inatenion o algebra.

CTC is considering a math specialist credential

One opic on he agenda o he new CC

advisory panel is wheher Caliornia should

revive a mahemaics specialis credenial

originally adoped in 1985. Alhough his

credenial has no been used much in Cali-

ornia, a similar auhorizaion or reading

specialiss has been popular and could serve

as a model or mahemaics.

Mah specialiss could ulll hree roles:

n Work in small groups wih sudens who

are having serious diculy wih mah.

n Help eachers improve heir subjec-area

and pedagogical knowledge.

n Lead he developmen o mah programs

in heir school, disric, or couny oce.

CC noed in is December 2008 agenda

ha mah specialiss could suppor muliple-subjec eachers in he elemenary and middle

grades in paricular. Mah specialiss migh

provide proessional developmen, demon-

sraion lessons and observaions in he mul-

iple subjec eachers classroom ocusing on

mahemaics, possibly wih a ocus on he

elemenary and middle school years. Tis

migh provide a new rung on he career lad-

der or veeran eachers.

Reviving he mah specialis credenial

would require CC acion. Te oudaed

sandards or he credenial would need o be

aligned wih Caliornias curren academic

conen sandards in mahemaics, and CC

would need o approve preparaion programs.

The states current professional developmentapproach in mathematics falls short of whatis needed to meet goals

Along wih addressing he qualicaions oeachers o mahemaics, Caliornia also needs

o consider is approach o he proessional

growh o he saes exising eachers. Tis

is paricularly he case in he elemenary and

middle grades as eachers work o mee escala-

ing academic expecaions in mah. Currenly,

eachers in Caliornia receive proessional de-

velopmen in mah hrough a variey o sources,

such as conerences held by proessional

organizaions like he Caliornia Mahemaics

Council or hrough couny oces o educaion

Tis secion ocuses on wo sae-unded pro

grams: he Mahemaics and Reading Proes

sional Developmen Program (MRPDP) and

he Caliornia Mahemaics Projec.

MRPDP focuses on training for locally adopted curricula

Te 2007 Criical Pah Analysis by he Caliornia Council on Science and echnology

(CCS) and CFL calls he sae-undedMRPDP he predominan mahemaics

proessional developmen currenly organized

and oered by sae or local ocials. Te

program was esablished in 2001 hrough

Assembly Bil l (A B) 466 and reauhor ized in

2006 hrough Senae Bill (SB) 472.

Te MRPDP provides disrics wih

incenive unding or raining in mahema

ics and reading conneced o each disrics

Caorna eor o recru and rean mah eacher

A 2007 study es timated that California needs about 3,300 new middle grades and high school math and

science teachers annually during the next 10 years. Californias public universities are working to increase

the number of math and science teachers they send into the teaching workforce:

nThe California State Universit ys Mahemac and scence teacher inave intends to double (from

750 to 1,500) the number of new math and science teachers that CSU prepares by 2010. For more

information, see: www.calstate.edu/teacherED/MSTI/index.shtml

nThe Universit y of Californias Caorna teach program aims to place 1,000 new math and science

teachers into California classrooms annuallya fourfold increase from the 250 who previously graduated

from UC each year. See: www.universityofcalifornia.edu/academics/1000teachers

Retaining Californias current mathematics teaching force is also important. Recent efforts to recruit and

retain knowledgeable math teachers, particularly in low-performing schools, include the following:

n senae B 1660 authorizes school districts to use professional development funds to compensate

new and existing math, science, and Special Education teachers in schools in the lowest 30% of the

Academic Performance Index (API) .

nAumpon Proram o loan or Educaon (APlE ), run by the California Student Aid Commission,

pays a portion of students loans (up to $11,000) for every year they teach in hard-to-staff schools or

subjects, such as middle and high school math and science.

n Caorna Mahemac Projec supporn teacher o increae Reenon (CMP stiR) program

provides induction and support for mathematics teachers in grades 612, particularly in schools with

high need or which are in Program Improvement under the federal No Child Left Behind (NCLB) law.

CMP STIR is currently in the second year of a five-year grant through the California Postsecondary

Education Commissions Improving Teacher Quality Grant program.


17/20


May 2009 n Al geb ra Poli cy i n Ca lifor nia n 1 Copyright 2009 by EdSource, Inc.

adoped insrucional maerials. In K8,

hese insrucional maerials mus be rom

he SBE-adoped lis. Fory hours o iniial

raining hrough an SBE-approved provider

and 80 hours o ollow-up are a he

MRPDPs core. SB 472 also provides unds

or SBE-approved ollow-up raining oreachers o English learners, which eachers

may pursue as par o he 80-hour ollow-up

or in addiion o i. Disrics receive $1,250

or each program componen a paricipaing

eacher complees, o which up o $500 per re-

imbursemen may be used or a eacher sipend.

Recen disagreemens beween CDE and

he Bureau o Sae Audis over he MRPDPs

success o dae sugges i has no been uilized

o he exen policymakers had iniially hoped.

School disrics surveyed by he bureau or a

2006 repor mos oen cied lack o eacherineres as a reason or low MRPDP paricipa-

ion. Some eachers see he raining as eiher

oo long or oo closely ied o exbooks, as

opposed o a broader ocus on undersand-

ing sae sandards, according o he repor.

CDE also cied lack o eacher ineres in is

response o he bureaus ndings, as well as

compeing demands on eachers ime.

According o CFL , a recen legislaive

updae o he MRPDP during he 200708

legislaive sessionAB 2391is inended o

make ollow-up raining under he program

more relevan, and hereore more appeal-

ing o eachers. AB 2391 allows eachers o

devoe up o 40 hours o he 80-hour ollow-

up o proessional developmen in such areas

as daa analysis, he use o daa o improve

suden achievemen, and he use o dieren-

iaed insrucion and suden grouping.

In he iniial 200809 budge, he Legisla-

ure allocaed abou $57 million or MRPDP

caegorical unding. However, MRPDP was

among abou 40 caegorical programs hawere subsequenly cu by 15%, wih dis rics

given ull fexibiliy in heir use o hese

unds. A h is wriing, i was no ye clear how

his would a ec he programs operaion.

California Subject Matter Project offers discipline-

focused, standards-based professional development

Te Caliornia Subjec Mater Projec,

adminisered by he Universiy o Caliornia

Oce o he Presiden, provides eachers

wih sandard s-al igned proessional develop-

men o srenghen heir conen area and

pedagogical experise, especially in low-

perorming disrics. Tis work is organized

ino nine disciplines, including he Calior-

nia Mahemaics Projec (CMP). Te projecsprovide hese services hrough abou 100

sies on college campuses across he sae.

Originally launched in 1988, he Subjec

Mater Projec was revised o refec Calior-

nias sandards-based approach o public educa-

ion in 1998 hrough AB 1734. Te law empha-

sized helping eachers develop and enhance

he conen knowledge and pedagogical skills

necessary o mee he saes academic conen

sandards and improve suden learning.

Despie general praise or he projecs,

nancial suppor has been uneven. Saeunding peaked in 200001 and 200102 a

$35 million bu hen decreased dramaically.

Al hough ederal unds have been used o

ose some o he reducion, unding since

200304 has been only abou $10 million

annually or he projecs as a whole.

CMP has received sae and ederal

ile II unds oaling beween $1.2 million

and $1.4 million annually during he pas

several years and currenly oers proessional

developmen hrough 19 sies. CMP sies

and heir parnering disrics secure grans

hrough many sources, including:

n Te ederally unded Caliornia Mahe

maics & Science Parnership, adminis

ered by CDE;

n Te ederally unded Improving eacher

Qualiy Grans, adminisered by he

Caliornia Possecondary Educaion

Commission (CPEC);n Naional Science Foundaion grans;

n Philanhropic grans; and

n Conracs wih schools and disrics.

CMP programs include monhly work

shops; inensi

Documents

Ed Source Report 0609