Organization by Design: Supply- and Demand-side Models of ... · tic models of educational career systems and to validate them via comparisons to observed reality. COURSE-TAKING LITERATURE

Organization by DesignSupply- and Demand-side Models of

Mathematics Course Taking

Daniel A McFarlandStanford University

Simon RodanSan Jose State University

Prior work has proposed different theoretical mechanisms to explain studentsrsquo course-taking

patterns in schools On the one hand there are oversocialized accounts that claim that rules

social background factors and supply-side factors shape observed career patterns On the

other hand there are undersocialized accounts that claim that the decisions of strategic agents

and demand-side dynamics shape course-taking careers In this article the authors use simu-

lations to illustrate how these theoretical mechanisms can generate course-taking patterns

Grounding the simulations in empirical data on the mathematics course taking of students in

two high schools they assess the relative merits of these competing theories by testing how

closely observed and predicted career patterns align The results reveal that the characteristics

of students and the organizational rules and requirements of course-taking career systems ren-

der certain allocation mechanisms more salient than others In particular highly competitive

and structurally constrained systems are shaped by supply dynamics while less regulated sys-

tems of diverse populations are shaped by agent-based decision making

Sociology of Education 2009 Vol 82 (October) 315ndash343 315

Scholars have long offered supply- anddemand-side depictions of studentsrsquocourse taking On the one hand sociolo-

gists have described course-taking careers ascomposed of oversocialized actors who are sel-dom given an active role in deciding whichcourses to take (Garet and Delany 1988Kerckhoff 1993 Riehl Pallas and Natriello1999150) Course-taking careers are describedas structurally determined by institutional rules(Oakes Gamoran and Page 1992 Riehl et al1999 Stevenson Schiller and Schneider1993) administrative processes (DeLany 1991Rosenbaum 1978) parents (Kilgore 1991Useem 1991) ascribed traits (Lucas 1999) cul-tural backgrounds (Oakes and Guiton 1995)

and vacancies (Chase 1991 Soslashrenson 1987)This is a long-held well-established view insociology in which a world of institutions andnorms render behavior almost completelydeterministic

On the other hand economists havedescribed course-taking careers as generatedby undersocialized actors with heroic capaci-ties for information gathering and interpreta-tion who are mostly unfettered by structuraldeterminants (Eckstein and Wolpin 1999Gambetta 1987 Keane and Wolpin 1997Manski 1993a 1993b March 1994) Here is aworld of individual decision makers with near-perfect information with known traits andequations to represent their behavior who

Delivered by Ingenta to Stanford University

Fri 18 Dec 2009 181626

then interact (often in a market) in a way thatleads to the evolution or emergence of a larg-er system

By contrast in this article we take a middleroad On the one hand we recognize thatyouths enter built environments in whichrules and procedures define situations forthem as well as how they and others are tointerpret attributes that are conferred uponthem as markers for selection and promotion(Salancik and Pfeffer 1978) Moreover wenote that they are often influenced by priorexperiences and attitudes as well as by inter-actions among peers whose decisions influ-ence one another (Macy and Willer 2002March 1994) Hence social structures pastsand peers all play a role in course-takingcareers

On the other hand even within these con-straints we believe that youths still have roomfor decisions and the capacity to make themGranted these capacities are limited (Simon1945) and few persons are able to acquireand make sense of the vast array of informa-tion that is salient to a career decision includ-ing features of course content the likely work-load its relevance to a variety of future out-comes the degree to which prior knowledgematters and so on Instead persons usuallyapply economizing cognitive heuristics toreach a decision (Gigerenzer Todd and theABC Research Group 1999 March and Simon1958) Toward this end we model two class-es of decision-making heuristics that avoid theneed to make as Macy and Flache (20027230) put it ldquoheroic assumptions about theknowledge and calculating abilities of theplayersrdquo

Therefore distinct from prior work weargue that the world of course taking may beseen as one that is composed of socializedinteracting individuals who apply satisficingheuristics to decide among limited optionsand to enter situations that are already great-ly defined for them (Gigerenzer and Goldstein1996 Simon 1945) In this view a mixture oftop-down rules and bottom-up adaptationscharacterizes educational course-takingcareers

Context also matters Most social scientistswould agree that organizational contexts con-sist of rules that organize experience andaction (Giddens 1986 Mead 1934 Sewell1992 2005chap 4) When it comes to

schools and curricula these rules are oftenwritten and ostensive and they define the setof potential curricular moves that are availableto a student (Cyert and March 1963 Hallinan1996 March and Simon 1958 Riehl et al1999) For example all curricula have if-thenrules or standard operating procedures thatdefine how actors in certain locations andwith certain properties (like grades) mustmove or at least narrow the set of coursesthat are available to them (eg rules oncourse prerequisites graduation and failure)

Within this context of rules and the oppor-tunity sets they define there operate differenthypothetical processes by which studentsmove between courses It is within the con-text of these constraints that the different allo-cation processes supply- and demand-sidemodels (Padgett 1990) play out We describeand analyze three allocation processes vacan-cy competition in which course vacanciesdrive studentsrsquo mobility patterns (Chase1991 Geerlings and Van Veen 2001Soslashrenson 1987 White 1970) retrospectiveadaptation in which actors alter their trajec-tory when current experiences diverge frompast ones and those of their peers (Bidwelland Friedkin 1988 Macy 1990 Macy andFlache 2002 Roth and Erev 1995) andprospective emulation in which actors altercourse when on the basis of the experiencesof older role models they anticipate that aparticular course may prove too demandingor insufficiently challenging (Cyert and March1963 Manski 1993a 1993b)

Our general aim is to integrate a bottom-up depiction of individual decision makersand their interaction into a top-down rule-driven system and we do so using simulationmodels Our depiction of decision makinguses agent-based modeling Studentsrsquo deci-sions are both influenced by the context andat the same time change the context Agent-based models differ from microsimulation(Macy and Willer 2002145) in that actors domore than follow rules they interact andadapt to one another Hence our actors fol-low simple rules make individual decisionsare adaptiveprospective looking and areinterdependent

With this perspective of course-taking deci-sions in mind we model studentsrsquo education-al course-taking careers as reflected in theirsequence of mathematics course taking and

316 McFarland and Rodan


Fri 18 Dec 2009 181626

achievement patterns in two high schools Werender course-taking patterns as the hypo-thetical outcome of three different allocationprocesses working within the confines oforganizational rules and procedures that arederived from empirical observations tounderstand which generates the most accu-rate depiction of observed educational careersunder realistic assumptions We comparethese competing theories by first contrastingthem rhetorically and then implementingeach in a simulation to assess their fit with ourpredictions We anchor our simulations inempirical data so as to construct more realis-tic models of educational career systems andto validate them via comparisons to observedreality

COURSE-TAKING LITERATURE

The more courses that students take and themore advanced curricular materials that theymaster the more they know This is especiallytrue for mathematics in which course takingis by far the greatest predictor of mathemat-ics achievement (Jones et al 1986 Lee et al1998 Stevenson et al 1993) Students withthe same course-taking histories regardless ofdifferences in social background have indis-tinguishable levels of achievement (HofferRaskinski and Moore 1995) Hence it is im-portant to understand how students end upin particular courses especially mathematicscourses because doing so allows us to identi-fy means of extending math course-takingcareers and achieving greater returns to learn-ing

There is a large body of research on coursetaking that spans disciplines Research by edu-cational sociologists has primarily identifiedinstitutional rules that determine studentsrsquocourse-taking patterns (Riehl et al 1999)Scholars have cited access rules such asgrade-level requirements and course prereq-uisites that lead students to take courses inordered sequences (Hallinan 1996 Stevensonet al 1993) Others have described howlabels for courses and programs guide stu-dents to take courses within stratified tracks(Garet and DeLany 1988 Oakes et al1992575ndash77) In addition there are a varietyof rules concerning grade requirements fail-

ure retaking courses graduation collegeentry class size and so forth In most casesthese organizational rules are so common andfamiliar that we take them for grantedHowever prior research has done an invalu-able service by recognizing them as key fac-tors that lead students to take certain coursesover others

If fixed rules and operating procedures tellonly part of the story and there are instancesin which rules do not resolve possible choicesthen we still need to explain how students areallocated across their remaining courseoptions To do so we turn to factors that acti-vate conditional ldquoif-thenrdquo rules and identifyprocesses that lead students to select amongthe remaining course options in a systematicfashion Fortunately educational sociologistshave identified various factors that activaterules and guide selections among the remain-ing options Some scholars have argued thatcounselors teachers (Rosenbaum 1978) andparents (Kilgore 1991 Useem 1991) pressurestudents to take certain courses over othersSchool officials typically pressure students tofollow rules and meet formal and informalstandards of tracks and course requirements(often dictated by achieved grades) Parentson the other hand exert pressures that aremore consistent with social background(Lareau and Horvat 1999) The effects ofsocial background also extend to individualstudents (Lucas 1999 Oakes and Guiton1995) sometimes biasing the informationand values they associate with various course-taking career paths In the case of social back-ground scholars claim not only that thesetraits guide decisions by biasing individualsrsquoorientations and perceptions but that thesetraits bias othersrsquo perceptions of those whohave such ascribed characteristics

Like research on organizational rulesresearch on social pressures and social back-ground has been invaluable in identifying fac-tors that are associated with course selectionsUnfortunately most of this work has beenderived from interviews with subjects thathave been used to assess relations and moti-vations and we are never sure if these rela-tions actually bear on decisive moments con-cerning course taking We are not even sure ifyearly attitudinal assessments accuratelyreflect what the actors intended to do or whatthey actually did when it came to taking a

Organization by Design 317


Fri 18 Dec 2009 181626

course Since most of this research has reliedon responses to questionnaires it can identifyonly associations between ldquoindependentrdquovariables and infer how generative mecha-nisms work Remiss in all this work is adescription and empirical assessment of howrules orientations and relations work togeth-er to constrain action and guide it down cer-tain paths Also remiss is a direct depiction ofhow people enter these built environments asagents and engage in decisions

While many sociologists have presentedarguably oversocialized depictions of actorseconomists have tended to provide underso-cialized depictions of a particular type of deci-sion maker (Granovetter 1985 although anotable exception is Akerlof and Kranton2002) Most educational economists haveassumed that the particular courses thatyouths take depend on their making choicesThese choices depend on a studentrsquos prefer-ences and capacities and the predicted utilityof various course selections As such educa-tional economists presuppose that actorshave heroic capacities for gathering and inter-preting information (Macy and Flache 2002)and are mostly unfettered by structural deter-minants (Gambetta 1987 March 1994) Tobe fair some discuss structural constraints andpeer effects on choice (Eckstein and Wolpin1999 Keane and Wolpin 1997 Manski1993a 1993b) but they fail to describe deci-sion-making processes that differ fromprospective forms of utility maximization Inaddition they often fail to take into accountbiases of perception and how they interactwith such decisions (March 1994)

Some sociologists have developed modelsof decision making (Macy 1990) and havepresented nuanced theoretical accounts ofhow course-taking decisions arise (Bidwelland Friedkin 1988) These views depart fromutility maximization and portray actors asstructurally embedded agents who react totheir situational experiences Hence withinthe constraints of rules relations and back-ground orientations there remains an oppor-tunity set of courses to which a studentapplies a decision-making process that isbased on adaptive learning Unfortunatelythese more nuanced and elaborate theories ofcourse taking are difficult to assess using cur-rent empirical data and inferential statisticalmethods Few scholars have access to all the

data that are necessary to account for thesemechanisms and even if they did inferentialstatistics would test only independent effectsand interactions between two or maybe threefactorsmdashwhich fall quite short of depicting asocial systemrsquos generative mechanisms

That said prior studies have provided morenuanced accounts of course taking than theirempirical analyses suggest To depict thesetheories accurately scholars need to illustratecomplex interactions not only among multi-ple organizational rules and procedures(which set the context of social action) butamong multiple actors who have certain traitsand dispositions and engage in complex mul-tipart decisionsmdashall of which rely on massiveamounts of data It is difficult to analyze suchtheories using traditional methodsFortunately simulations allowed us to teaseout theoretical implications by modelingthese complex processes (Cohen March andOlsen 1972) Moreover by empiricallygrounding simulation models scholars havethe capacity to wed theoretical clarity withempirical validity In short agent-based socialsimulation is an important way to address thegaps in prior work on course taking by direct-ly conveying how motives decision process-es and applications of rules work together inan immediate systemic fashion It is thismethod and approach that we used to extendtheoretical understandings of course takingHence we modeled a rule-based frameworkfor course taking that greatly narrows theavailable range of course-taking moves Thento characterize selection among the remain-ing alternatives we modeled allocationprocesses that reflect the structural ldquopullrdquo ofvacancy competition and the demand ldquopushrdquoof cognitive decision-making heuristics likeretrospective learning and prospective emula-tion (Gambetta 1987)

EMPIRICAL SETTING AND DATA

As an empirical frame of reference we drewon data from mathematics course taking andachievement in two actual high schools Welimited the scope to two cases in mathemat-ics1 because our aim was first to model rela-tively simple well-known particulars beforewe conducted more general simulated exper-



Fri 18 Dec 2009 181626

iments of other subjects types of curriculaand populations Moreover we were interest-ed in designing and developing models ofindividual schools (Coleman 1993) Startingwith two distinct cases we developed modelsof educational course-taking careers that canlater be applied to a wide variety of educa-tional systems

The first school Rural High (all names arepseudonyms) was a rural community school(1600 students in Grades 9ndash12) in whichmany of the teachers had been studentsthemselves The school had healthy vocation-al and honorsAdvanced Placement (AP) pro-grams and its student population was diversein terms of family income and career orienta-tions Upon entry to mathematics in the 9thgrade Rural High students were sorted intoone of five courses according to test scoresprior grades and teachersrsquo recommenda-tions The courses reflected ability groupingsof special education lower-basic upper-basicregular and accelerated mathematics curricu-la Each ability level retained consistent courseofferings over at least two years of schooling(McFarland 2006) In addition students wererequired to complete only two full years ofmath to graduate but some (~15) tookupward of three years before they graduatedbecause they aspired to enter the local statecolleges2 Thus educational motivations werediverse and requirements were relativelymodest leaving a good deal of course-takingchoice to students and their aspirations Theobserved transitions for Rural High mathe-matics are presented in Table 1

Table 1 illustrates the observed frequenciesof moving from an origin state to a destina-tion state Transitions with higher frequenciesreveal paths and extended chains revealcourse-taking trajectories Following thesetransitions across courses one readily seesrecognizable trajectories with a substantialamount of career exits and track changes Theaim of this article is to model individual tran-sitions across these courses particularly thosethat cross tracks and the grades that studentsachieve within them

The second school Magnet High was anarts and science magnet school (900 studentsin Grades 8ndash12) for college-bound students inan urban school district Magnet Highrsquos gen-eral goal was to prepare students for collegeThis mission was frequently stated by the fac-

ulty posted in the main office and written inthe curriculum guide

Our curriculum fosters a wide scope of skillsand interests through which students can pur-sue their common goals Our regular classesemphasize the basic skills necessary for successat the college level Our advanced programscourses (International Baccalaureate andAdvanced Placement) further challenge stu-dents to extend and expand these skills and tomore fully prepare for a smooth transition tocollegeuniversity study These courses providethe opportunity for concurrent college enroll-ment while providing the background for life-time learning

All the courses that the school offered weregeared toward college attendance In factthe lowest ability-level course that was offeredwas equivalent to honors-level course work inthe local district high schools More demand-ing courses prepared the students for college-credit courses like AP and InternationalBaccalaureate (IB) courses

Magnet Highrsquos students were selected fortheir high motivation and ability to learn Theentry requirements were stringent High-per-forming seventh graders had to fill out anelaborate application take a standardized testand attain the necessary test score and behighly recommended by their teachers Tostay at Magnet High students had to main-tain a minimum average grade of C- follow astrict attendance policy and complete at leastfour years of mathematics and science

Upon entry to Magnet High in the eighthgrade all students took the same mathcourse Thereafter they were required to takethree more math classes but were given theoption of taking increasingly more challeng-ing sequences of mathematics coursesStopping was not an option Given the stu-dentsrsquo motivation and the stringent gradua-tion requirements it is no surprise that flowsof participants across courses resemble a treestructure with branches extending upwardinto increasingly demanding and higher-sta-tus tracks Actual transitions for Magnet Highmathematics are depicted in Table 2

In sum Magnet High was the opposite ofRural High in many respects Whereas RuralHigh was homogeneous in race and class andheterogeneous in ability and motivationMagnet High was heterogeneous in race andclass and homogeneous in ability and motiva-



Fri 18 Dec 2009 181626

Tab

le1

Rur

alH

igh

Mat

hem

atic

smdashTr

ansi

tion

Prob

abili

tyM

atri

xfo

rSt

uden

tM

oves

Des

tinat

ion

Stat

es

Tran

sien

tSt

ates

Poin

tsof

Exit

8th

Gra

dea

06

06

19

4

30

51

20

8

0

4

376

Tran

sfer

02

0

50

2

14

24

17

0

20

21

0

21

42

Out

side

Mat

h0

1

01

02

02

01

00

00

03

44

46

248

Spec

ialE

dM

ath

1

46

10

05

34

05

41

Spec

ialE

dM

ath

2

07

07

0

7

14

43

21

14

Basi

cM

ath

17

46

0

5

2

21

0

41A

lgeb

raA

01

15

64

0

1

12

09

12

9A

lgeb

raB

12

3

8

10

28

12

82

Alg

ebra

1

01

01

05

72

0

5

12

02

01

205

Geo

met

ry

0

94

7

09

06

22

08

283

Alg

ebra

2

11

17

0

1

03

38

31

178

Pre-

Cal

culu

s

07

03

20

70

60

Acc

Alg

ebra

1a

1

5

78

18

02

02

04

55A

ccG

eom

etry

a

0

21

6

0

16

31

1

09

02

88

Acc

Alg

ebra

IITr

ig

0

2

06

7

7

06

06

03

100

Acc

Pre-

Cal

culu

s

0

1

0

1

40

0

65

180

Acc

Cal

culu

s

1

0038

Mov

esw

ithin

atr

ack

are

show

nin

the

bloc

kson

the

lead

ing

diag

onal

(ligh

tsh

adin

g)D

arke

rsh

adin

gin

dica

tes

repe

atin

gth

esa

me

cour

se

All

valu

esre

flect

the

ratio

ofst

uden

tsm

ovin

gfr

omth

eor

igin

stat

eto

the

dest

inat

ion

stat

eVa

lues

grea

ter

than

10

are

inbo

ldfo

nt

aRo

wsu

ms

exce

ed1

sinc

eso

me

stud

ents

from

this

loca

tion

take

mor

eth

anon

eco

urse

atth

ene

xtst

age


Special Ed Math 1

Special Ed Math 2

Basic Math

Algebra A

Algebra B

Algebra 1

Geometry

Algebra 2

Pre-Calculus

AccAlgebra 1

Acc Geometry

Acc AlgTrig

Acc Pre-Calculus

Acc Calculus

Leave School

Outside Math

Graduate

Students

Entrypoints Transient states

Origin State (1997)


Fri 18 Dec 2009 181626

Organization by Design 321Ta

ble

2M

agn

etH

igh

Mat

hem

atic

smdashTr

ansi

tion

Prob

abili

tyM

atri

xof

Stud

ent

Mov

es

Des

tinat

ion

Stat

es

Tran

sien

tSt

ates

Exit

Stat

es

7th

Gra

de9

7

0

3

17

2Tr

ansf

er2

70

90

9

1

81

8

0

9

0

9

11O

utsi

deM

ath

0

2

02

9

7

66

Alg

ebra

IHon

ors

02

39

4

2

18

177

Geo

met

ryH

onor

s

5

8

22

20

55A

lgeb

raIi

Hon

ors

6

3

04

0

20

42

794

Func

tions

52

27

18

04

83D

iscr

ete

Mat

h

new

cour

se98

rsquoN

A

Geo

met

ryPr

e-Ib

09

8

2

1

011

5A

lgIi

ampTr

igPr

e-Ib

01

21

3

5

15

1

9

09

105

Func

tions

Sta

tsT

rigIb

75

02

0

21

40

744

Prec

alc

ampD

isc

Mat

hIb

1

00

23

Prec

alcu

lus

Ibs

03

8

2

15

34

Cal

culu

sIb

s

100

16

Prec

alc

ampTr

igIb

h

0

7

89

0

4

27A

dvC

alc

Ibh

1

00

18

Mov

esw

ithin

atr

ack

are

show

nin

the

bloc

kson

the

lead

ing

diag

onal

(ligh

tsh

adin

g)D

arke

rsh

adin

gin

dica

tes

repe

atin

gth

esa

me

cour

se

All

valu

esre

flect

the

ratio

ofst

uden

tsm

ovin

gfr

omth

eor

igin

stat

eto

the

dest

inat

ion

stat

eVa

lues

grea

ter

than

10

are

inbo

ldfo

nt

Algebra I Hon

Geometry Hon

Algebra Ii Hon

Functions

Discrete Math

Geometry Pre-Ib

Alg Ii amp Trig Pre-Ib

FunctionsStatsTrig Ib

Precalc amp Disc Math Ib

Precalculus Ibs

Calculus Ibs

Precalc amp Trig Ibh

Adv Calc Ibh

Graduate

Outside Math

Leave School

Students


Origin State (1997)


Fri 18 Dec 2009 181626

tion Rural High students faced few require-ments demanded little and faced a trackedmath curriculum Magnet High studentsfaced heavy requirements demanded muchand faced an increasingly differentiated anddemanding set of curricular offerings in mathThe strong divergence in these well-under-stood cases affords a useful starting pointfrom which to model and assess how differenttheoretical mechanisms form studentsrsquocourse-taking careers

METHODS

In contrast with empirical approaches thatinfer the presence of particular social mecha-nisms from a set of associations betweenobserved variables we start with theoreticalcharacterizations of social mechanisms Theallocation process described in each theory isrepresented by a set of algorithms and if-thenrules that are then executed as a sequentialprogram or simulation with a realistic set ofinitial conditions We then assess how closelyeach simulated process generates course-tak-ing and achievement patterns to thoseobserved in reality In particular the modelswe present are based on descriptions ofhuman behavior in the literature on coursetaking and decision making and are ground-ed in a detailed field study of mathematicscourse-taking patterns at two high schools(Rural and Magnet) We use empirical data toinform the parameters of each model and toassess the accuracy with which each simulat-ed mechanism captures observed reality

Through this exercise we demonstrate theusefulness of simulation techniques for study-ing key organizing processes in educationalsystems such as course-taking patterns andachievement (Gilbert and Troitzsch 1999) Weshow how simulation research can provideprecisely defined descriptions of socialprocesses and the complex ways in whichtheir component features interrelate under avariety of conditions3 By representing hypo-thetical social processes through simpleheuristics we adopt a different approach todeducing how a system may function in real-ity

DESCRIPTION OF THESIMULATION

Each of the two schools Rural High andMagnet High was simulated independentlybut the logic of the simulation is the same(see Figure 1)4 Students entering the simulat-ed school are assigned to courses in the sameproportions as those entering the schoolsfrom which the empirical data were collectedThis initial assignment is simple at Magnetsince students begin in a single course but atRural the students are divided among multi-ple courses on the basis of test scores Weassigned every student an intrinsic abilityscore drawn from a standard normal distribu-tion5 From this score we generated anachievement score a based on intrinsic abili-ty and a random component ε6 The achieve-ment score for an incoming student is givenin Equation 17 The notion here is thatachievement is not a perfect measure of abili-ty Hence while there is a correlation betweenachievement and ability it is less than 1

aict = 0 = Abilityi 06 + ε 04 (1)

On the basis of their achievement studentsare ranked and then assigned to freshman-year courses in the same proportions as at thereal schools being modeled

Next all students are graded as they wouldbe at the end of each school year For stu-dents finishing their first year of math a meas-ure of achievement (aict) for student i incourse c at time t = 1 is again generatedusing a combination of ability and a randomcomponent (Equation 1 again) For thosewith more than one year of school behindthem achievement depends not only on abil-ity but on what they have learned duringtheir high school course-taking career to dateIt is a linear combination of their ability theiraverage past achievement B (andashict-1) and arandom component (ε)

aict = Abilityi abwt + (1ndash abwt)andashict-1)06+ ε 04 (2)

The model parameter abwt determines thedegree to which achievement depends onraw ability relative to learning in earlier class-es8 The contribution from the testing error



Fri 18 Dec 2009 181626


Figure 1 Simulation Logic


Fri 18 Dec 2009 181626

(ε) is again weighted so as to mimic theempirical data Achievement is then mappedinto grades (gict) through the mapping func-tion G that translates rank order into gradesusing the empirically observed grade distribu-tions for each course in the particular schoolbeing simulated

gict = G(aicitrsquoabullict) (3)

This mapping is designed to ensure thatthe number of simulated students getting aparticular grade for example a B- inGeometry at Rural High is the same as thecorresponding number in the real school

ldquoHardrdquo and ldquoSoftrdquo InstitutionalRules

The next step is to define the structural con-straints on movement as defined by eachschoolrsquos course-taking rules Each school has asimilar set of ldquoif-thenrdquo rules that define how astudent can move from year to year (Marchand Simon 1958) Some of these if-then rulesare ldquohardrdquo in that if certain conditions exist astudent has no option but to adopt a singlemove Such hard rules pertain to graduatingretaking courses and leaving school Otherrules are ldquosoftrdquo in that once a student fulfillscertain requirements his or her career optionsopen further One such soft rule pertains towhen a student has the option to stop takingmathematics courses (Hallinan 1996)

Rule 1mdashGraduate Rural If you completefour years of school and pass at least twoyears of math then you will graduateMagnet If you complete five years of schooland pass at least four years of math then youwill graduate9

Rule 2mdashRepeat a Course Rural If you havenot completed two years of math and you faila math class then you will retake the mathclass Magnet No one is allowed to repeat amath class at Magnet see Rule 3

Rule 3mdashLeave School Rural If you fail twomath classes in a row before you completethe math requirements or if you have com-pleted four years of school and have not com-pleted the math requirements then you willleave10 Magnet If you fail a math class or

acquire a GPA less than C- then you willleave

Rule 4mdashStop Math Rural If you pass twomath classes then you may stop math in the11th grade Magnet If you pass four mathclasses then you may stop math in the 12thgrade

We ascertained if any students met theseconditions and applied the appropriate ruleOnly some students find themselves in situa-tions where they must graduate retake acourse or leave school Those who are notallocated to particular destination states bythe hard rules encounter ldquosoftrdquo organization-al rules that define the opportunity set of cur-ricular moves given their history and courselocation From most origin courses theopportunity set is relatively constrainedaffording only a few options For examplemathematics courses have a rule of progres-sion in which persons go backward only totake Algebra 1 after they have completedTrigonometry in exceptional cases and weclassified these rare moves as disallowed tran-sitions In addition there are prerequisiterules preventing persons in Algebra 1 fromjumping over other courses into AdvancedCalculus We identified this set of allowablecourse-to-course transitions through curricu-lar handbooks and discussions with depart-ment heads and counselors at each school11

Allocation Processes

Thus far we have described the circumstancesin which certain hard and soft organizationalrules apply thereby determining when singu-lar moves must be adopted and what range ofmoves is open to students in each curricularlocation As such we have defined structuralconstraints on the allocation processes thatwe analyzed (Keane and Wolpin 1997) Nextwe describe the hypothetical allocationprocesses that guide studentsrsquo course takingwithin the range of available moves

We focus our discussion on three allocationprocesses that we hypothesized shape curric-ular flows and achievements We assumedthat students select from among a variety ofoptions in a nonrandom fashion and that atheoretically viable allocation mechanismwould provide a more accurate assessment ofcurricular moves and achievements than



Fri 18 Dec 2009 181626

would a random allocation process Hencewe used random allocation of students toallowed courses as a baseline comparison forall models However beyond the comparisonto a baseline case we were particularly inter-ested in the relative strengths of each alloca-tion mechanism and compared them to eachother

The first allocation process that weexplored is vacancy competition (Hallinan andSoslashrenson 1986) Theories of vacancy compe-tition argue that supply-side mechanics guidestudentsrsquo patterns of movement across curric-ula (Chase 1991 Padgett 1990 White 1970)The second and third allocation processesconcern individual decision making particu-larly prospective and retrospective forms of itWe elaborate these processes next and pres-ent them in Table 3

Vacancy Competition One theory arguesthat it is the vacancies in courses ahead thatpull students onward in their careers(Geerlings and Van Veen 2001 Padgett 1990Soslashrenson 1987) To model this vacancyprocess we needed to know the number ofvacancies in courses into which students maymove For a course curriculum the number ofvacancies depends on the number of coursesections that are offered and the size of eachclass Studies on course scheduling (DeLany1991 Oakes and Guiton 1995 Riehl et al1999) have found that schools seek to re-cre-ate the number of course sections (teachingassignments to particular rooms and periods)to retain a cap on class sizes and to spreadstudents evenly so as not to overburden anyparticular teacher unfairly We therefore keptthe number of sections constant and applied


Table 3 Summary of Allocation Processes and Implementation

Location in Simulation

Allocation Mechanism Heuristics of Implementation Flow Diagram

Random allocation Students are assigned randomly to one of the (baseline) courses to which they are eligible to move

given the hard and soft rules that define the schoolrsquos structural constraints (1)

Vacancy-competition Students are rank-ordered by grades Starting with the highest track courses students are drawn from the pool of those eligible to move to this course in descending order of grade (2)

Retrospective adaptation Students compare their current course experience to their past experience to acquire a reward-tolerance index If they score below the RT down threshold they will move to a course in a lower track next year If their experience surpasses the RT up threshold they will choose a course in a higher track for the following year (3)

Prospective emulation Students compare their current course experience with that of persons who have completed the same course-grade history and are a year ahead in schooling This is their RT index If they score below the RT down threshold they will move to a course in a lower track next year If their experience surpasses the RT up threshold they will choose a course in a higher track for the following year (4)


Fri 18 Dec 2009 181626

a single class size to all classes in the simula-tion We took the number of course sectionsfrom the empirical data and then multiplied itby a parameter for class size which we variedbetween experiments We then subtractedthe number of students who were retakingthe course (see Hard Rule 2) to give the esti-mated number of vacancies in coursesahead12

The next step was to identify students whowere eligible to move into these slots To doso we looked at the feeder courses for acourse destination (see eg Table 2 RuralHigh Destination Accelerated GeometryFeeders Accelerated Algebra 1 and Algebra1) We rank-ordered all the students in thefeeder courses who are eligible to moveonward (ie those who did not fit Hard Rules1ndash3) by achieved grades and allocated themsequentially until the vacancies in the destina-tion course were filled (Soslashrenson 1987) Oncethe destination course is filled the remainingstudents in the feeder courses have to waituntil slots in the next lower track course intowhich they are allowed to move are allocated(eg Geometry and after that stoppingmath) When allocations are decided for thenext course eligible students in all feedercourses are again ranked by performance Forexample a Rural High student in AcceleratedAlgebra 1 who failed to get into AcceleratedGeometry must now compete for a place inGeometry with other students who are mov-ing down track from Accelerated Algebrawith those moving onward from Algebra 1and with those from Algebra B who are mov-ing up track Depending on the value of theparameter for class size some students maynot find a place in the courses they are eligi-ble to take Students for whom a place cannotbe found because of the lack of space are notejected from the model but are placed onetrack below their prior track

Decision Processes In contrast to thevacancy allocation mechanism in which stu-dents respond mechanically to their circum-stances our second and third mechanismsinvolve agency Within the constraints oforganizational rules students may be activelyselecting courses by certain decision process-es

If course-taking decisions are based on ret-rospective adaptation then students will

reflect on their current and past academic sit-uations in an effort to assess whether theiracademic career has been satisfactorilyrewarding or if they would prefer a more- (orless-) challenging educational experience(Bidwell and Friedkin 1988 Macy 1990) Tomodel this process we first needed to calcu-late a reward and tolerance index (Equation 4)The index (rt) reflects the studentrsquos education-al experience Students with good andimproving grades will feel positively abouttheir educational experience reflected in apositive rt value poor and declining gradeswill render a negative experience and rt valueStudentsrsquo decisions to take on more- or less-challenging course work are predicated onthe value of their rt index at the end of eachschool year

rtit = perfit (1ndashadwt) + adaptit adwt (4)

The rt index consists of two components(see Appendix Table A1) the studentrsquos relativeperformance (perfit Equation 5) and successin adapting to prior standards (adaptitEquation 6) The adwt term in Equation 4 is aparameter that allowed us to vary the contri-bution of the adaptation term

Relative performance captures the degreeto which a studentrsquos current academic per-formance measures up to the standard shehas set for herself given her past performanceand her current performance relative to thatof her peers (Bidwell and Friedkin 1988)

perfit = (gictndashgndashibullt) (1ndashpe) +(gictndashgndashct)pe (5)

In Equation 5 gict is student irsquos grade13 incourse c for the current period t and gndashibullt isstudent irsquos average grade to date excludingthe current period The term gndashct is the aver-age performance of the studentrsquos peers in thecurrent course and pe denotes the strengthof the peer effect relative to a comparisonwith onersquos own past A high value of the peparameter makes perceived performancelargely a function of peer comparisons whilea small value means performance is largely amatter of self-reflection

The second component of the reward-tol-erance index concerns the studentrsquos capacityto adapt to educational situationsAdaptability (adaptit) simply refers to the



Fri 18 Dec 2009 181626

degree to which student i has become hard-ened by time t to the demands of an increas-ingly tough set of courses or converselybecome more sensitive to punishment as hisor her load lightens Adaptability provides asecond-order dampening effect

adaptit = perfit ndash perfit-1 (6)

A linear combination of these two compo-nentsmdashperformance and adaptabilitymdashisused to form rt (Equation 4) the reward-toler-ance index (Bidwell and Friedkin 1988)

The second step is to define how studentsinterpret and react to their rt value If studentsoutperform their peers and improve on theirprior yearrsquos performance they have a height-ened sense of reward that enables them totolerate harder courses and materials Thesestudents will select more difficult course workthat matches their augmented sense of capac-ity Conversely a student whose grades arelower than expected and lower than his or herpeers will have a very low sense of reward anda low tolerance for the educational demandsbeing placed upon him or her Studentswhose performance remains constant relativeto their prior work (in other words has mettheir expectations) and relative to their peerswill have a neutral experience and an rt valueof 0

Once a studentrsquos reward-tolerance index iscalculated a satisficing heuristic is used todetermine whether the level of reward andtolerance (or punishment and intolerance) issufficient to warrant various rank-ordered cur-ricular moves (Gigerenzer and Goldstein1996 Simon 1945)

The thresholds for upward (rt_up) anddownward (rt_down) moves are modelparameters set exogenously If the studentrsquosfeeling of reward-tolerance (rt) is higher thanthe upward threshold there is an allowedcourse in a higher track and Hard Rules 1ndash3do not apply then the student will move upConversely if the studentrsquos feeling of punish-ment (ldquonegativerdquo reward) falls below thedownward threshold and a lower-track courseis offered the student will choose that lower-track course However if the studentrsquos senseof reward and tolerance falls between thert_down threshold and the rt_up thresholdthen the student will simply move on in his orher current track

Whereas retrospective adaptation relies onpast experience prospective emulation is adecision process that relies on role modelswho are more advanced in their course-takingcareers (Manski 1993a 1993b) The decidingstudent (call the student ldquoegordquo) considers allstudents who have completed the samesequence of courses and have achieved thesame grades (ie they share the same course-grade history) but are one year aheadStudents who match ego in courses andgrades over egorsquos entire course-taking historyform a role-model set Beginning with thenext course in the same track ego assessesthe reward-tolerance values of students in hisor her role-model set who took that coursenext in their careers and this becomes egorsquosexpected rt index14 The expected rt is the aver-age actual rt index of all those in the focal stu-dentrsquos role-model set It is the aggregation ofstructurally equivalent studentsmdashin course-taking termsmdashwho have actually taken thecourses and thus had the experiences that thefocal student is considering This expected rtindex is then used in a similar fashion to theretrospective case If the expected rt value liesbetween the two thresholds the studentaccepts this course as an appropriate nextstep If the studentrsquos role modelsrsquo expected rt isbelow the rt_down threshold the student willconsider a course in a lower track To do sothe student returns to her or his role-modelset this time picking those who have takenthis lower-track class and calculates asbefore their average rt experience to gener-ate her or his expected rt If this expected rt lieswithin acceptable bounds (ie between the rtthresholds) this course is chosen If not theprocess is repeated for lower tracks and if nolower tracks are considered acceptable thenthe student will attempt to leave math Theprocess works symmetrically for upwardmoves with higher-track courses being con-sidered and discarded if they are too reward-ing until a course in a track that generates anexpected rt value within bounds is found

Because the modeled decisions entail satis-ficing rather than optimizing processes(March and Simon 1958 Simon 1969) theremay be a range of satisfactory course selec-tions According to satisficing theory studentswill select the first course they identify as sat-isfactory even if there are others that are alsosatisfactory and perhaps optimal Thus the



Fri 18 Dec 2009 181626

initial course the student considers each timehe or she makes a decision may matter In thedecision-making models the initial courseassignment is the highest course within thestudentrsquos current track15

Model Fitness We estimated the fitness ofthe three allocation processes by comparingthe simulated pattern of curricular moves andachieved grades to that recorded in mathe-matics at Rural High and Magnet High overtwo years This sample consisted of 1242 stu-dents at Rural High and 754 students atMagnet High We calculated a fitness measureby comparing the occupancy along fivedimensions of simulated outcomes to the fivedimensional occupancy counts for students inthe empirical data set The five dimensions onwhich the simulation and the empirical datawere compared were the studentrsquos origincourse achieved grade in the origin coursedestination course achieved grade in the des-tination course and grade level We usedsuch a detailed comparison to address thepotential problem that even though simulat-ed outputs may correspond to observed real-ities at the level of course-to-course movesthey may do so by a process that is quite dif-ferent from that being modeled (ie a poten-tial ecological fallacy) Although assessingpredictions for both grades and courses forevery student is not a definitive answer to thisissue increasing the points of contactbetween the simulated and empirical dataimproves the level of confidence that themechanisms in the model reflect those thatare believed to be at work in reality

Our fitness measures are based on a com-parison of two vectors one representing thereal data and the other representing the sim-ulated data16 Each vector is a linearization ofa five-dimensional array representing the fivedimensions just described Each cell in thearray is a count of the number of students atthat point in this five-dimensional space Theunit of analysis is the course-grade transitionat a given grade level a cell in this space rep-resents the number of course moves for givenchanges in grade at a particular grade levelFor example at Rural High cell (9 8 4 3 2)contains the number of students in the ninthgrade who after completing Algebra 1(course 8) with an A grade (ie a grade pointof 4) then moved to Accelerated Geometry

(course 3) where they managed only a C(ie a grade point of 2) In the linearized vec-tor this cell would be in position 1207717

The pattern of occupancy in the simulateddata vector is compared to the empirical pat-tern by correlating the two vectors18 Thiscorrelation between the empirical pattern ofcourse-grade transitions at a particular gradelevel and the simulated pattern of transitionsis our measure of fitness

Because studentsrsquo ability and grades have arandom component each simulation that isrun produces slightly different outcomeswhich in turn leads to a better or worse fitbetween the empirical and simulated dataFor a given run this variation in fitness is nor-mally distributed allowing us to use straight-forward statistical tests in comparing one setof simulation runs (an experiment) to anoth-er To test for significant differences betweenallocation processes we conducted 10000experiments with a randomly selected alloca-tion mechanism (random vacancy competi-tion retrospective adaptation and prospec-tive emulation) In each experiment the othermodel parameters (rt_up rt_down class sizeadaptation weight ability weight and peerpressure) were also randomly selected thus intesting the accuracy of one model over anoth-er our results are not contingent on a partic-ular choice of parameters

To assess the influence of each mechanismmultivariate regressions were run for eachschool with dummy variables for vacancycompetition retrospective adaptation andprospective emulation Random allocationwas the omitted category and representedthe baseline against which other mechanismswere compared T-tests were also conductedto assess not only whether each mechanismproduced a significantly better (or worse) fitthan the random model but whether the pre-dictive power of one mechanism was betterthan another

Empirically Informed Model ParametersSimulated outputs are meaningful only in sofar as they hold to intuitive parameter settingsor realistic assumptions For the vacancy-com-petition model a realistic assumption is thatclass size varies in the region of the class sizesfound in the two schools From schoolrecords we know the average class sizesMagnet = 1825 (SD = 484) and Rural =



Fri 18 Dec 2009 181626

2155 (SD = 722) If vacancy competition isan accurate theory then predicted outcomeson realistic parameter settings will closelyalign with those observed in reality We con-servatively defined realistic parameter settingsas being within a standard deviation ofobserved average class sizes In this mannerwe explored whether the vacancy modelworks well for Rural High and Magnet Highacross a range of reasonable parameters

Parameter values for the two rt thresholdsrt_down and rt_down were derived from dataon studentsrsquo grades We lacked the threeyears of data necessary to estimate empiricalrt thresholds so we used current GPAs as aproxy for grade histories in the first compo-nent of the performance equation (5)19 Thesecond component of peer comparison how-ever is readily calculated by comparing eachstudentrsquos math grade with the average for stu-dents in the same course We next dividedstudents into three categories those whomoved up those who moved down andthose who stayed in the same track We thencalculated the averages and standard devia-tions for the empirical rt values of those mov-ing up and those moving down and usedthem to generate our experimental parameterranges For example students moving down atrack at Magnet High had a mean rt value of-0315 with a standard deviation of 0185 ineach simulation run rt parameter values weredrawn randomly from within a range of onestandard deviation either side of the mean

Parameter values for the four other modelparameters (abwt in Equation 2 adwt inEquation 4 and pe in Equation 5) were drawnfrom a uniform distribution in the range[0109] By exploring a broad range ofparameter settings we investigated whichallocation process best fits the observed reali-ty under a wide variety of assumptionsregarding the relative strengths of the variouselements of the theorized processes

Hypotheses Comparing AllocationMechanisms

In general we believe that our models foreach allocation mechanism will bear someresemblance to observed grades and course-taking patterns and that evidence of thisbelief will afford some validation of each the-ory However we believe that certain alloca-

tion models will be more accurate than othersbecause of the school contexts Reflecting onour two cases again we can posit certainhypotheses

We expect that Magnet students will fol-low a vacancy-competition process for severalreasons First Magnet High has many courserequirements for graduation so students typ-ically take math for five years (Grades 8ndash12)without fail Second Magnet students areachievement sorted by a barrage of standard-ized tests from the entry examination to stan-dardized tests like the PSAT ACT and SAT aswell as IB and AP examinations in most sub-jects Third the students are homogeneous inability and ambition seeming to take onwhatever challenges the school sends theirway As the head counselor excitedly said inan interview ldquoWe just keep giving them moreand more and they keep doing itrdquo All thissupports a vacancy-competition characteriza-tion or at least suggests that decision makingwith a low threshold for upward movesshould be indistinguishable from the vacancycompetition Therefore while limited choicesmay exist for Magnet students it is likely thatthe supply of seats in the highest-track cours-es will pull students upward and onward

By contrast we expect Rural students tofollow a retrospective decision process Thereare at least two reasons to believe that choiceis important at Rural High First counselorsclaim that there is an open assignment policyAs the head counselor said in an interviewldquoEvery student at Rural High has the opportu-nity to take an accelerated course should theyso wishrdquo Hence students can select anothercourse if they prefer it which suggests the pri-macy of decision making over a competition-based allocation process Second Rural Highrsquoslow math requirements mean that studentshave broadening opportunity sets and canstop taking math relatively early in theircareers And third Rural students are not onlyless homogeneous in goal orientation thanare Magnet students but are less inclined topush upward into harder tracks whenever theopportunity presents itself In many regardsRural students are far less interested in long-term educational careers than are Magnetstudents and therefore are less prospectivelyoriented20 Thus we anticipate that a reason-able proportion of Rural students will spendrelatively little time thinking about and plan-



Fri 18 Dec 2009 181626

ning for their future classes and that a retro-spective model represents a better characteri-zation of their approach to decision makingthan does prospective emulation Thus weexpect the retrospective decision model toafford the most accurate description of Ruralstudentsrsquo behaviors

We also hypothesize that certain allocationprocesses will become more salient acrosstracks and ranges of available choices We sus-pect that increasingly higher-status tracks willentail less random movement and clearer evi-dence for our hypothesized allocationprocesses This is likely the case because thecareer moves in higher tracks are more consis-tent and less prone to rule exceptions andinfluences from life circumstance outside theschool (eg divorce or a change of resi-dence) In contrast we believe that increasingthe opportunity set of available coursesdiminishes the effects of structural logics andincreases the salience of decisions

RESULTS

The results are presented in Tables 4ndash6 andFigures 2ndash5 Depending on the choice ofparameters the simulation generates fitnessscores ranging from -051 to 094 Such highcorrelation values show that particular param-eters can generate patterns of moves andgrades that closely mirror the empirical dataHowever we are less interested in the choiceof particular parameters than in understand-ing the usefulness of one theoretical alloca-tion process over another in accuratelydescribing studentsrsquo course-taking careers Todemonstrate the explanatory efficacy of onemodel over another we consider not just afew best-fitting models but a large number ofmodels over a wide range of parametersmdashapproximately 10000 individual experi-ments each with a unique combination ofmodel parameters (class size and decisionthresholds) We then take these data andcompare the fit of each simulated allocationprocess in multivariate regressions

Table 4 presents regression results thatshow the predictive power of the differentallocation models In each model thedependent variable was a fitness measure thecorrelation between the two vectors that rep-

resent the occupancy of each cell in the five-dimensional space described earlier Althoughthe dependent variable is bounded between 0and 1 the distribution of values is fairly closeto normal hence we relied on the ordinaryleast-squares estimation procedure

The model estimated was as follows

yi = a + b1 x1i + b2x2i + b3x3i + ε

where the xrsquos are dummy variables for thethree purposive mechanisms the omitted cat-egory being random allocation The regres-sion intercept coefficient a is the fit achievedby the random allocation process It repre-sents the average fitness (the correlationbetween empirical and simulated allocationpatterns) that a random allocation processachieves within the constraints of hard andsoft rules Coefficient b1 captures the improve-ment in fit achieved relative to the randomcase by vacancy competition b2 the improve-ment relative to random allocation achievedusing retrospective adaptation and b3 theimprovement generated by prospective emu-lation For example a coefficient of 01 forretrospective adaptation (b3) would indicatethat this mechanism produces an increase of01 in the correlation between the simulatedand empirical allocations patterns relative tothe random allocation process21

The two models in Table 4 reveal for eachschool the accuracy of the predictions gener-ated by each allocation mechanism relative tothe random allocation baseline At MagnetHigh the vacancy-allocation model affordsthe most additional fit with the observeddata improving the correlation by 163Taken together the intercept a and theimprovement term b1 show that vacancy-competition experiments across all parametersettings produce an average correlationbetween the simulated and empirical datavectors of 03222 Adaptive decisions alsoafford some further fit but at half the magni-tude of vacancy (089) In contrast Rural Highdecision models generally seem to provide amore accurate representation than the ran-dom baseline Adaptive decisions affordslightly greater improvement (080) overprospective decision models but not signifi-cantly so The main finding is that our alloca-tion modelsmdashvacancy at Magnet High anddecisions at Rural Highmdashafford a significantly



Fri 18 Dec 2009 181626

better fit with the observed data (on fivedimensions) than the random case even whenwe used a wide range of parameter values(ie a conservative test)

Table 5 and Figures 2 and 3 present regres-sion results that look more specifically at howthe allocation models align with differentpopulations of students and programmaticexpectations The models present the resultsfor regressions within each curricular track

At Magnet High vacancy-allocation mod-els hold regardless of the track but they getincreasingly more predictive as we get intomore selective tracks and students By con-trast a pattern of decreasing relevance is seenfor decisions particularly adaptive decisionsThe salience of random allocation declinessteadily as we increase selectivity At RuralHigh random allocation is strong and dimin-ishes as the students enter more selectivetracks Vacancy and decisions really apply onlyto students in the general and honors tracks(the vast bulk of the curriculum) and growmost salient for the honors track

Taken together these results suggest thatthe allocation mechanisms used in this articleare less applicable to lower-track students andmore reflective of general and high-achievingstudents who make up the bulk of each cur-riculum Lower-track students may have theircareer dynamics influenced by factors otherthan grades and perceptions of them Forexample many of these youths tend to comefrom disadvantaged backgrounds and a vari-

ety of factors that are associated with theseconditions could complicate and undermineany structural or rational decision-makingapparatus (eg divorce moving devianceand social network pressures)

Table 6 and Figures 4 and 5 present regres-sion results that reveal how allocation modelsgrow and diminish in salience with the num-ber of move options At Magnet High thetrend from two to four move options seems tosuggest that increased choice diminishes thesalience of random movement and increasesthe salience of vacancy competition andadaptive decision making However the raresituation in which five move options are avail-able seems to counter this trend Five moveoptions at Magnet occur only for one courselocation Algebra IITrigonometry Pre-IB It isunclear if this shift is a course effect teachereffect both or something else Nonethelessthe evidence suggests that greater choice ren-ders random allocation less accurate and thatsome decisionstructural logic applies In thecase of Magnet this is primarily a structurallogic of vacancy-competition that sorts stu-dents into observed patterns

At Rural High a similar trend occursRandom allocation diminishes with choicewhile decision models grow in salienceVacancy competition however never seemsto take hold Prospective emulation outper-forms adaptation when fewer choices areavailable and the reverse holds true whengreater choice is afforded Although the result


Table 4 Multiple Regression Predicting Accuracy (correlation of simulated withobserved) of Allocation Mechanisms

Magnet Rural

Intercept (random) 155 296(0008) (0012)

Vacancy 163 -098(0012) (0017)

Decision adapt 089 080(0012) (0017)

Decision prospective 016 067(0012) (0017)

Adj R Sq 211 150

N observations = 806 Magnet 773 Rural df = 4 p lt 001 p lt 01 p lt 05 dagger lt 10Note Adaptive and Prospective decisions are statistically indistinguishable at Rural


Fri 18 Dec 2009 181626

is minor it suggests that prospective decisionsare more readily carried out for constrainedchoice sets and retrospective decisions aremore readily carried out for broader choicesets (and therefore more boundedly rational)

For both schools greater choice rendersrandom allocation processes less accurateand our hypothesized allocation mechanismsgain explanatory power In particular vacan-cy-competition best models math careers atMagnet and decisions (adaptive has an edge)best model math careers at Rural Finally thewider the choice set the fewer decisions aremade prospectively and the more they arebased on reflection and adaptation

We believe that the retrospective decision

model has a slight edge over prospectiveemulation because it represents a lesser cog-nitive burden for students When thinking ret-rospectively students look to their own pastexperience and that of their immediate peersin a course By contrast when thinkingprospectively they consider how someonesimilar to them performs in the cohort aheadso there is an added degree of conjecture andsocial distance that makes the process slightlyless realistic

That said some readers may believe thatboth decision processes entail a heroic capac-ity for knowing all other studentsrsquo gradesHowever this is not the case Our model doesnot require knowing every studentrsquos grade


Table 5 Multiple Regression Predicting Accuracy (correlation with observed) ofAllocation Mechanisms by Track

Magnet

Honors IB IBS IBH

Intercept (random) 181 077 -095 -256(0007) (0016) (0019) (0022)

Vacancy 159 296 685 1029(0011) (0023) (0027) (0033)

Decision adapt 078 099 143 404(001) (0022) (0026) (0031)

Decision prospective 007 -018 -030 109(001) (0022) (0026) (0031)

Adj R Sq 262 221 520 592

Rural

SpecEd Basic General Honors

Intercept (random) 291 338 308 205(0006) (0008) (0013) (0014)

Vacancy -184 -200 -128 068(0009) (0012) (0019) (002)

Decision adapt 007 -103 082 195(0009) (0011) (0018) (0019)

Decision prospective 006 -029 056 159(0009) (0011) (0018) (0019)

Adj R Sq 454 319 163 139

N observations = 806 Magnet 773 Rural df = 4 p lt 001 p lt 01 p lt 05 dagger lt 10Note Adaptive and Prospective decisions are statistically indistinguishable in general and

honors tracks at Rural


Fri 18 Dec 2009 181626

only knowing the central tendency or aver-age grade in a course (~ how ldquohardrdquo thecourse is) We think this is a fair assumptionsince students get a sense of othersrsquo gradesthrough peer networks that are couchedwithin their courses In fact prior work byMcFarland (1999) and by Frank et al (2008)found that course-taking patterns form clus-ters or social milieus from which friendshipnetworks and many types of social compari-son arise Hence there is direct evidence thatcourse memberships are loci of associationand sense making

CONCLUSION

This article has presented several importantfindings First multiple allocation processescan predict the observed patterns of coursetaking and achievement at both schools Thisfinding is surprising given that we used onlya small set of simple rules to simulate course-taking careers and grade histories The accu-racy of Magnet Highrsquos vacancy models seemgreatly driven by course-taking requirementsand the motivational biases of students whoare quite ambitious and skilled For Magnet


Figure 2 Fitness of Allocation Models by Track Magnet High

Figure 3 Fitness of Allocation Models by Track Rural High Note The error bars represent a95 confidence interval Because the nonrandom allocation mechanismsrsquo coefficients in theregression represent gains (losses) relative to the random allocation baseline the baseline coef-ficient has been added to each to show the total effect for each mechanism


Fri 18 Dec 2009 181626

students the only acceptable choice is ldquouprdquoin a sense rendering decision making mootSimilarly the accuracy of Rural Highrsquos decisionmodels seems strongly influenced by the lessdemanding course requirements and hetero-geneous motivations of students

Our findings suggest that the motivationalcomposition of students and the organizationalrules (course opportunities) at each school alterthe dynamics of educational careers We alsobelieve that these results show that most stu-dentsrsquo course-taking careers are negotiated tra-jectories where adaptive learning and rule fol-lowing guides students in their choices It ispossible that a utility model on educationalinvestment in post-high school destinations willexplain more about studentsrsquo decisions atMagnet and Rural (Manski and Wise 1983) AtMagnet every student could go to a regular

school in the district and be an honors studentcomplete much less work and still attend thesame state schools At Rural many studentsmay be adjusting their career patterns accord-ing to the chances they believe they have forreaching a particular post-high school statesuch as a job the military or a two- or four-yearcollege That decision making plays a greaterrole in less structured settings like Rural Highsuggests the possibility that decision makingwill also represent a more appropriate descrip-tion in other fields for example course takingin the humanities in which fewer formal rulesgovern the prerequisites for and sequencing ofcourses Future work will explore such utilitymodels

The more general effort of this article hasbeen to model both supply- and demand-sideallocation processes as embedded in organi-


Table 6 Multiple Regression Predicting Accuracy (correlation with observed) ofAllocation Mechanisms by Number of Move Options

Magnet

Honors IB IBS IBH

Intercept (random) -133 -041 -322 019(0012) (0015) (0017) (0016)

Vacancy 433 633 917 351(0017) (0022) (0026) (0023)

Decision adapt 168 252 322 132(0016) (0021) (0025) (0022)

Decision prospective 065 069 055 103(0016) (002) (0024) (0022)

Adj R Sq 478 559 663 228

Rural

2 Options 3 Options 4 Options NA

Intercept (random) 312 255 151(0013) (0013) (0011)

Vacancy -105 -019 -032(0018) (0018) (0016)

Decision adapt 037 133 306(0018) (0018) (0016)

Decision prospective 080 101 241(0018) (0018) (0016)

Adj R Sq 130 118 478

N observations = 806 Magnet 773 Rural df = 4 p lt 001 p lt 01 p lt 05 dagger lt 10Note Adaptation is slightly more predictive than prospectvie at Rural when it comes to 3

options (p lt 10)


Fri 18 Dec 2009 181626

zational rules As such our effort was tomodel actual course-taking career systemsthat could be subject to design Through sim-ulations we rendered explicit those theoreti-cal arguments for how career systems work inschools

Distinct from a great deal of other simulationresearch (Macy 1990 March 1999 Mark 19982002) the work presented here was empirical-ly grounded In particular we focused on thecareer dynamics in two high school mathemat-ics curricula In so doing we analyzed two well-understood contexts and sought to develop

accurate models of this reality Such an effort isdeemed preferable for initial simulation worksince it makes certain that the mechanisms arewell grounded before generalizations and awide array of experiments across a variety ofhypothetical conditions (eg cohort sizes pop-ulation characteristics number of tracks andgrading distributions) are attemptedFurthermore we preferred to use individualschools because our ultimate interest is inschool design (Coleman 1993) Modeling par-ticular individual curricula will enable futureresearch to propose a variety of career struc-


Figure 4 Fitness of Allocation Models by Move Options Magnet High

Figure 5 Fitness of Allocation Models by Move Options Rural High Note The error bars rep-resent a 95 confidence interval Because the nonrandom allocation mechanismsrsquo coefficientsin the regression represent gains (losses) relative to the random allocation baseline the base-line coefficient has been added to each to show the total effect for each mechanism


Fri 18 Dec 2009 181626

tures and predict how various conditions andpopulations will react to them By continuallycomparing such models with observed realitieswe will develop a better understanding of edu-cational systems and the social processes thatreside within them

The work presented here used designmethods to gain a better understanding ofthe social processes and dynamics that areinherent in organizations (Coleman 1993Soslashrenson 1970 1987 1998) Looking backon this effort we believe there are severalroutes by which future simulation researchwill best advance understanding of course-taking career systems in schools First futuresimulation models need to focus on othersubjects and a wider array of schools andorganizations so as to understand how thesesocial processes are affected by each organi-zational context Second future researchwould benefit from a more programmatictheoretical enterprise that varied the modelsby certain structural features and populationcompositions Structures could vary by theirdegree of selectivity (number of tracks) andelectivity (requirements) and compositionscould vary by the range of population aspira-tions or social backgrounds (heterogeneity)Such research would answer important ques-tions For example how would the same cur-riculum work if a different array of studentsentered it How would the same set of stu-dents react in a different curricular programLast future work would benefit from selectinga dependent variable and identifying whetherchanges in the mobility structure alter out-comes One outcome of value is educationaland occupational attainment By identifying acontinuous dependent variable the simula-tion research presented here can be moredirectly related to analytic methods and issuesof school design We could ask what effectincreasing the size of the honors track wouldhave on studentsrsquo educational attainment ateach school and other similar questions It istoward these questions that we hope futurework turns

NOTES

1 Mathematics is the most hierarchicallyand sequentially organized subject in high

schools (Stevenson et al 1993) Hence thenumber of organizational rules is kept to aminimum Other subjects entail further com-plications but we believe that they can befeasibly designed after simpler examples (likemath) are established

2 The local small colleges (eg NorthernState) require the completion of geometryand the larger state universities require thecompletion of Algebra 2 More elite schoolsrequest the completion of precalculus andorcalculus

3 This is not to say that simulation is a sub-stitute for analytic methods Analytic tech-niques have certain advantages over simula-tion they can derive more generalizableresults and can establish individual causal rela-tions (equifinality) That said simulation isperhaps more useful for issues of design andmodeling social systems and complexprocesses like career decisions Simulationbrings the features of social processes intofocus and models how the identified featuresof each process would need to operate togenerate the empirically observed outcomessuch as observed mobility patterns

4 The simulation was written in C++ Thesource code is available from us on request

5 The particular shape of the distributionsused is actually immaterial since grades arebased on rank order The ordering of grades isthe same whether students are bunchedtoward the center in a normal distribution orspread evenly across the range in a uniformdistribution

6 We empirically derived the degree oferror by regressing prior grades on currentgrades At both schools about 40 percent ofthe variance in achieved grades is notexplained by prior achievement The errorterm ε is drawn from a standard normal distri-bution

7 For entering students c and t are irrele-vant and set arbitrarily to 0

8 We use the term parameter to designatemodel variables that are set exogenouslyThese variables differ from one set of experi-ment to another but remain constant for anygiven set of experimental runs All other vari-ables are endogenous to the model

9 At Magnet High students start in theeighth rather than the ninth grade

10 Although this is not a written formalrule at Rural High it is an informal rule relat-



Fri 18 Dec 2009 181626

ed by counselors Students who failed thesame required class twice in a row invariablydropped out and at best attended nightschool (which is not included as an courseoption in these records)

11 The allowable intracurricular moveswere rendered in ldquopermitted transition matri-cesrdquo that are available from us on request

12 In both schools the first authorobserved principals creating their teachingschedules and saw that across five years ofteaching assignments little variationoccurred In both instances the principalsrelied on the prior yearrsquos schedule as a tem-plate and duplicated those teaching assign-ments almost exactly The prior schedule wasmerely tweaked depending on whether cer-tain teachers retired or left (thereby allowingteachers to move through courses) and ifclasses became too large (thereby makinganother section necessary) or too small(thereby merging sections) However thischange seldom arose in core subjects likemath and was more common in electivecourses In addition we found that bothschools and districts had written rules regard-ing the maximum class size (~ 35 students)However these district rules were altered bylocal principals and teachers often toward alower maximum value that reflected theteachersrsquo preferences for smaller classes

13 We did not measure grades on a 4-point scale but varied them between 0 and 1Hence A = 1 B = 75 C =50 and so forth

14 In the event that there are no studentswith the exact same grade-course history thestudent repeats the search looking only for amatch in course histories Should no otherstudent be found with the exact same set ofcourses the student selects a course at ran-dom from those allowed by the soft rules Thefailure to find a role-model happens in about17 percent of the cases at Rural High and 6percent at Magnet High

15 We tried three other approaches toselecting the default course random selectionfrom the studentrsquos choice set the highestcourses in the choice set and the lowestcourses in the choice set All performed lesswell than using the next course in the stu-dentrsquos current track as the default option

16 The simulated vector is the generatedoutput from models that have reached a sta-ble dynamic equilibrium By stable dynamic

equilibrium we mean models whose courseto course transition matrix for a given yearcorrelates with the prior yearrsquos course tocourse transition matrix with a value exceed-ing 99 This situation typically arises afternine cycles although in rare cases (fewer than1 in 1000) the model does not settle into astable state and these experiments are dis-carded

17 12077 = (Grade level ndash 8)185185+Origin course5185+Destination course185+Origin grade5+destination grade =11 8 5 1 8 5 + 8 5 1 8 5 + 4 1 8 5 +35+2 Magnet students start in Grade 8 so 8is subtracted from the top dimension forgrade level The total length of the linearizedarray is 40500 (5 grade levels 18 originstates 5 origin state grade possibilities 18destination states and 5 destination stategrade possibilities)

18 We also tested a segregation measure(Theil and Finezza 1971) as a means of assess-ing the similarity of the two vectors The seg-regation-based measure produced identicalresults in terms of the models rank-order fit-ness so we opted to use the more common-ly understood similarity measure of correla-tion

19 Yearly GPAs at both schools were stableover time which suggests that GPA is adecent proxy for grade histories and suitablein our model

20 In surveys the Rural students reportedsignificantly less interest in and a sense ofimportance about their course work than didthe Magnet students (McFarland 1999) Inaddition upon graduating about 31 percentof the Rural students said that they planned toattend local state colleges or more prestigiousfour-year colleges 29 percent said that theyplanned to attend a local junior college andabout 10 percent said that they planned towork or go into the military The remaining 30percent are uncertain of their plans eventhough they responded to such questions aweek before graduation Of course the statusof each destination is mildly correlated withtracks but it is common enough for honorsstudents to attend local junior colleges andfor regular-track students to attend goodstate colleges so the range of aspirationsremains relatively broad (and low in compari-son to Magnet High) even within curricularpositions



Fri 18 Dec 2009 181626


21 Since the coefficients are the dummyvariables for each of the mechanisms they aremutually exclusive and fully independent andtherefore they do not need to be introducedsequentially

22 Although the best-fitting models

achieved correlations of 98 percent and high-er in the data created for the regressionanalysis each experiment was a single simula-tion run thus one cannot tell to what extentthese outcomes were a result of suitableparameter choices rather than chance


Fri 18 Dec 2009 181626

Organization by Design 339A

PP

END

IX

Tab

leA

1D

efin

itio

ns

ofVa

riab

les

and

Para

met

ers

Des

crip

tion

Rela

tions

hip

toO

ther

Mod

elVa

riabl

esEq

nN

o

Abi

lity

Ab

ility

Inv

aria

ntpr

oper

tyof

each

stud

ent

Stan

dard

norm

alFi

xed

mod

elva

riabl

edi

strib

utio

nse

ta

stud

entrsquos

ldquocre

atio

nrdquo(i

ee

ntry

into

the

syst

em)

AA

chie

vem

ent

isre

late

dto

abili

tyM

ore

able

stud

ents

gene

rally

For

inco

min

gst

uden

tsan

dst

uden

tsin

thei

rfir

stye

ar

1ac

hiev

em

ore

inac

adem

icte

rms

Ther

eis

also

ara

ndom

com

pone

nt

a ic

t=1

=Ab

ility

i0

6+

ε

04

(ε~

N(0

1))

to

achi

evem

ent

Ach

ieve

men

tde

pend

sno

ton

lyon

abili

ty

but

onw

hat

the

stud

ents

have

lear

ned

over

the

cour

seof

thei

rhi

ghIn

subs

eque

ntye

ars

scho

oled

ucat

iona

lcar

eers

toth

atpo

int

a ic

t=

Abili

tyi

abw

t+

(1ndasha

bwt)

andash ict

-10

6+

ε

04

2

GG

rad

esar

em

appe

dfr

omth

eem

piric

algr

ade

dist

ribut

ions

for

each

g ic

t=

G(a

icit

rsquoabulli

ct)

3co

urse

inth

etw

osc

hool

sst

udie

don

the

basi

sof

the

rank

orde

rof

achi

evem

ent

Gis

am

appi

ngfu

nctio

nth

atre

turn

sth

eap

prop

riate

grad

efo

rth

est

uden

trsquospo

sitio

nin

the

rank

orde

r(b

yac

hiev

emen

t)fo

ra

give

nco

urse

ina

give

nsc

hool

RtR

ewar

dto

lera

nce

depe

nds

onpr

ior

perf

orm

ance

and

stud

entrsquos

succ

ess

rtit

=pe

rfit

(1

ndashadw

t)+

adap

t it

adw

t4

inad

aptin

gto

chan

ges

inst

anda

rds

resu

lting

from

upw

ard

ordo

wnw

ard

trac

km

oves

(ada

ptab

ility

)

Perf

Rel

ativ

ep

erfo

rman

ceca

ptur

esth

ede

gree

tow

hich

the

stud

ents

perf

it=

(gic

tndashgndash ibull

t)

(1ndashp

e)+

(gic

tndashgndash c

t)pe

5ex

ceed

ed(o

rno

t)th

eir

prio

rpe

rfor

man

cean

dth

eir

perf

orm

ance

rela

tive

toth

eir

cour

seco

hort

adap

tA

dap

tab

ility

The

degr

eeto

whi

chth

est

uden

trsquospe

rfor

man

cech

ange

sad

apt i

t=

perf

itndash

perf

it-1

6fr

omon

epe

riod

toth

ene

xtA

dow

nwar

dm

ove

shou

ldca

use

are

duct

ion

inpe

rfor

man

ceb

utth

em

ore

adap

tabl

est

uden

tw

illsu

ffer

alo

wer

drop

than

will

ale

ssad

apta

ble

one

Con

vers

ely

anad

apta

ble

stud

ent

will

not

doas

wel

lin

alo

wer

trac

kas

one

who

refu

ses

toch

ange

his

orhe

rst

anda

rds

just

beca

use

heor

she

has

mov

eddo

wn

atr

ackDelivered by Ingenta to

Stanford UniversityFri 18 Dec 2009 181626

340 McFarland and RodanA

PP

END

IX

Tab

leA

1C

onti

nue

d

Des

crip

tion

Mod

elPa

ram

eter

s(E

quat

ions

24

and

5)

RT[a

b]

Rew

ard

tole

ran

ceth

resh

old

sA

nex

ogen

ous

para

met

erth

atse

tsth

ebo

unds

ofac

cept

able

educ

atio

nale

xper

ienc

eVa

lues

outs

ide

this

rang

etr

igge

rtr

ack

chan

ges

ais

the

valu

eof

rtdo

wn

bth

atof

rtup

Edu

catio

nale

xper

ienc

eva

lues

low

erth

anrt

dow

ntr

igge

ra

mov

eto

alo

wer

-tra

ckco

urse

Val

ues

high

erth

anrt

uptr

igge

ra

mov

eto

ahi

gher

-tra

ckco

urse

abw

tA

bili

tyw

eig

ht

Am

odel

para

met

erth

atad

just

sth

ede

gree

tow

hich

achi

evem

ent

isa

func

tion

ofra

wab

ility

and

how

muc

ha

func

tion

ofpr

ior

lear

ning

(ach

ieve

men

t)

adw

tA

dap

tati

onw

eig

ht

Am

odel

para

met

erad

just

ing

the

degr

eeto

whi

chad

apta

tion

mod

erat

esth

eim

pact

ofpe

rfor

man

ceco

mpa

rison

s(r

elat

ive

tose

lfan

dre

lativ

eto

peer

s)on

the

way

the

educ

atio

nale

xper

ienc

eis

perc

eive

dby

the

stud

ent

pePe

eref

fect

wei

gh

tA

mod

elpa

ram

eter

adju

stin

gth

eex

tent

tow

hich

perf

orm

ance

isju

dged

rela

tive

toa

stud

entrsquos

prio

rpe

rfor

man

ceas

oppo

sed

toa

stud

entrsquos

perf

orm

ance

rela

tive

tohe

ror

his

peer

s


Fri 18 Dec 2009 181626


REFERENCES

Akerlof George A and Rachael E Kranton 2002ldquoIdentity and Schooling Some Lessons for theEconomics of Educationrdquo Journal of EconomicLiterature 40 1167ndash1201

Bidwell Charles and Noah Friedkin 1988 ldquoTheSociology of Educationrdquo Pp 449ndash71 inHandbook of Sociology edited by Neil JSmelser Beverly Hills CA Sage

Chase Ivan 1991 ldquoVacancy Chainsrdquo AnnualReview of Sociology 17133ndash54

Cohen Michael D James G March and Johan POlsen 1972 ldquoA Garbage Can Model ofOrganizational Choicerdquo Administrative ScienceQuarterly 171ndash25

Coleman James S 1993 ldquoThe Design ofOrganizations and the Right to ActrdquoSociological Forum 8527ndash46

Cyert Richard and James G March 1963Behavioral Theory of the Firm Oxford EnglandBlackwell

DeLany Brian 1991 ldquoAllocation Choice andStratification within High Schools How theSorting Machine Copesrdquo American Journal ofEducation 99181ndash207

Eckstein Zvi and Kenneth I Wolpin 1999rdquoWhyYouths Drop Out of High School The Impactof Preferences Opportunities and AbilitiesrdquoEconometrica 671295ndash1339

Frank Kenneth A Chandra Muller Kathryn SSchiller Catherine Riegle-Crumb AnnaStrassmann Mueller Robert Crosnoe andJennifer Pearson 2008 ldquoThe Social Dynamicsof Mathematics Course-taking in HighSchoolrdquo American Journal of Sociology1131645ndash96

Gambetta Diego 1987 Were They Pushed or Didthey Jump Cambridge England CambridgeUniversity Press

Garet Michael S and Brian DeLany 1988ldquoStudents Courses and StratificationrdquoSociology of Education 6161ndash77

Geerlings W S J and K Van Veen 2001ldquoSimulating Patterns of OrganizationalCareersrdquo Computational and MathematicalOrganization Theory 7287ndash310

Giddens Anthony 1986 The Constitution ofSociety Outline of the Theory of StructurationBerkeley University of California Press

Gigerenzer Gerd and Daniel Goldstein 1996ldquoReasoning the Fast and Frugal Way Modelsof Bounded Rationalityrdquo Psychological Review103650ndash69

Gigerenzer Gerd Peter M Todd and the ABCResearch Group 1999 Simple Heuristics ThatMake Us Smart Oxford England OxfordUniversity Press

Gilbert Nigel and Klaus G Troitzsch 1999

Simulation for the Social Scientist PhiladelphiaOpen University Press

Granovetter Mark 1985 ldquoEconomic Action andSocial Structure The Problem ofEmbeddednessrdquo American Journal of Sociology91481ndash510

Hallinan Maureen 1996 ldquoTrack Mobility inSecondary Schoolrdquo Social Forces74983ndash1002

Hallinan Maureen and Aage Soslashrenson 1986ldquoStudent Characteristics and Assignment toAbility Groups Two ConceptualFormulationsrdquo Sociological Quarterly 271ndash13

Hoffer Thomas Kenneth Rasinski and WhitneyMoore 1995 ldquoSocial Background Differencesin High School Mathematics and ScienceCourse-taking and Achievement (NCESWorking Paper No 95-206) Washington DCUS Department of Education Office ofEducational Research and Improvement

Jones Lyle Ernest Davenport Aloha Bryson TanjaBekhuis and Rebecca Zwick 1986ldquoMathematics and Science Test Scores asRelated to Courses Taken in High School andOther Factorsrdquo Journal of EducationalMeasurement 23197ndash208

Keane Michael P and Kenneth I Wolpin 1997ldquoThe Career Decisions of Young Menrdquo Journalof Political Economy 105473ndash522

Kerckhoff Alan C 1993 Diverging Pathways SocialStructure and Career Deflections CambridgeEngland Cambridge University Press

Kilgore Sally 1991 ldquoThe Organizational Contextof Tracking in Schoolsrdquo American SociologicalReview 56189ndash203

Lareau Annette and Erin Horvat 1999 ldquoMomentsof Social Inclusion and Exclusion Race Classand Cultural Capital in Family-SchoolRelationshipsrdquo Sociology of Education7237ndash53

Lee Valerie David Burkam Todd Chow-Hoy BeckySmerdon and Douglas Geverdt 1998 ldquoHighSchool Curriculum Structure Effects onCourse-taking and Achievement inMathematics for High School Graduatesrdquo(NCES Working Paper No 98-09)Washington DC US Department ofEducation Office of Educational Research andImprovement

Lucas Samuel R 1999 Tracking InequalityStratification and Mobility in American HighSchools New York Teachers College Press

Macy Michael W 1990 ldquoChains of CooperationThreshold Effects in Collective ActionrdquoAmerican Sociological Review 56730ndash47

Macy Michael W and Andreas Flache 2002ldquoLearning Dynamics in Social DilemmasrdquoProceedings of the National Academy of Sciences997229ndash30


Fri 18 Dec 2009 181626


Macy Michael W and Robb Willer 2002 ldquoFromFactors to Actors Computational Sociologyand Agent-Based Modelingrdquo Annual Review ofSociology 28143ndash66

Manski Charles F 1993a ldquoAdolescentEconometricians How Do Youth Infer theReturns to Schoolingrdquo Pp 43ndash60 in Studies ofSupply and Demand in Higher Education editedby Charles Clotfelter and Michael RothschildChicago University of Chicago Press

mdash- 1993b ldquoDynamic Choice in Social SettingsLearning from the Experiences of OthersrdquoJournal of Econometrics 58121ndash36

Manski Charles F and David A Wise 1983College Choice in America Cambridge MAHarvard University Press

March James G 1994 A Primer on Decision MakingHow Decisions Happen New York Free Press

mdash- 1999 The Pursuit of Organizational IntelligenceMalden MA Blackwell

March James G and Herbert A Simon 1958Organizations New York Wiley

Mark Noah P 1998 ldquoBeyond IndividualDifferences Social Differentiation from FirstPrinciplesrdquo American Sociological Review63309ndash31

mdash- 2002 ldquoCultural Transmission DisproportionatePrior Exposure and the Evolution ofCooperationrdquo American Sociological Review67323ndash45

McFarland Daniel A 1999 ldquoOrganized Behavior inSocial Systems A Study of Student Engagementand Resistance in High Schoolsrdquo UnpublishedPhD dissertation University of Chicago

mdash- 2006 ldquoCurricular Flows Trajectories TurningPoints and Assignment Criteria in High SchoolMath Careersrdquo Sociology of Education79177ndash205

Mead George Herbert 1934 George Herbert Meadon Social Psychology Edited by Anselm StraussChicago University of Chicago Press

Oakes Jeannie Adam Gamoran and Reba N Page1992 ldquoCurriculum DifferentiationOpportunities Consequences and MeaningrdquoPp 570ndash608 in Handbook of Research onCurriculum edited by Philip W Jackson NewYork Macmillan

Oakes Jeannie and G Guiton 1995ldquoMatchmaking The Dynamics of High SchoolTracking Decisionrdquo American EducationalResearch Journal 323ndash33

Padgett John F 1990 ldquoMobility as ControlCongressmen Through Committeesrdquo Pp27ndash58 in Social Mobility and Social Structureedited by Ronald L Breiger CambridgeEngland Cambridge University Press

Riehl Carolyn Aaron Pallas and Gary Natriello1999 ldquoRites and Wrongs InstitutionalExplanations for Student Course-Scheduling

Process in Urban High Schoolsrdquo AmericanJournal of Education 107116ndash54

Rosenbaum James E 1978 ldquoThe Structure ofOpportunity in Schoolrdquo Social Forces57236ndash56

Roth Alvin E and Ido Erev 1995 ldquoLearning inExtensive Form Games Experimental Data andSimple Dynamic Models in the IntermediateTermrdquo Games and Economics Behavior8164ndash212

Salancik Gerald R and Jeffrey Pfeffer 1978 ldquoASocial Information Processing Approach to JobAttitudes and Task Designrdquo AdministrativeScience Quarterly 23224ndash53

Sewell William H Jr 1992 ldquoA Theory of StructureDuality Agency and TransformationrdquoAmerican Journal of Sociology 981ndash29

mdash- 2005 Logics of History Social Theory and SocialTransformations Chicago University ofChicago Press

Simon Herbert A 1945 Administrative Behavior AStudy of Decision-Making Processes inAdministrative Organization (1st ed) NewYork Macmillan

mdash- 1969 The Sciences of the Artificial (2nd ed)Cambridge MA MIT Press

Soslashrenson Aage B 1970 ldquoOrganizationalDifferentiation of Students and EducationalOpportunityrdquo Sociology of Education43355ndash76

mdash- 1987 ldquoThe Organizational Differentiation ofStudents in Schools as an OpportunityStructurerdquo Pp 103ndash29 in The SocialOrganization of Schools NewConceptualizations of the Learning Process edit-ed by Maureen T Hallinan New York Plenum

mdash- 1998 ldquoTheoretical Mechanisms and theEmpirical Study of Social Processesrdquo Pp238ndash66 in Social Mechanisms An AnalyticalApproach to Social Theory edited by PeterHedstroumlm and Richard Swedberg CambridgeEngland Cambridge University Press

Stevenson David Katherine Schiller and BarbaraSchneider 1993 ldquoSequences of Opportunitiesfor Learningrdquo Sociology of Education67184ndash98

Theil Henri and Anthony J Finezza 1971 ldquoA Noteon the Measurement of Racial Integration ofSchools by Means of Informational ConceptsrdquoJournal of Mathematical Sociology 1187ndash94

Useem Elizabeth L 1991 ldquoStudent Selection intoCourse Sequences in Mathematics TheImpact of Parental Involvement and SchoolPoliciesrdquo Journal of Research on Adolescence1231ndash50

White Harrison C 1970 Chains of OpportunitySystem Models of Mobility in OrganizationsCambridge MA Harvard University Press


Fri 18 Dec 2009 181626


Daniel A McFarland PhD is Associate Professor of Education (by courtesy) and AssociateProfessor of Sociology and Organizational Behavior School of Education Stanford University Hismain fields of interest are social networks social interaction the creation of knowledge sociology ofeducation and organizations Dr McFarland is currently conducting two National ScienceFoundation projects one on the dynamics of youthsrsquo social networks and one on the effects of inter-disciplinary collaboration on scientific innovation He is also conducting a wide assortment of proj-ects that apply computional linguistics and the study of communication to understanding the evo-lution of social networks

Simon Rodan PhD is Associate Professor of Strategy and Organization Theory Department ofOrganization and Management College of Business San Jose State University His main fields ofinterest are organizational learning social networks and simulation His current work is on the col-lective-level effects of individual-level structural holes

We thank James Moody and James G March for their helpful comments on earlier drafts of this arti-cle Address correspondence to Daniel A McFarland School of Education Stanford University 520Galvez Mall Stanford CA 94305 e-mail dmcfarlastanfordedu


Fri 18 Dec 2009 181626

then interact (often in a market) in a way thatleads to the evolution or emergence of a larg-er system

By contrast in this article we take a middleroad On the one hand we recognize thatyouths enter built environments in whichrules and procedures define situations forthem as well as how they and others are tointerpret attributes that are conferred uponthem as markers for selection and promotion(Salancik and Pfeffer 1978) Moreover wenote that they are often influenced by priorexperiences and attitudes as well as by inter-actions among peers whose decisions influ-ence one another (Macy and Willer 2002March 1994) Hence social structures pastsand peers all play a role in course-takingcareers

On the other hand even within these con-straints we believe that youths still have roomfor decisions and the capacity to make themGranted these capacities are limited (Simon1945) and few persons are able to acquireand make sense of the vast array of informa-tion that is salient to a career decision includ-ing features of course content the likely work-load its relevance to a variety of future out-comes the degree to which prior knowledgematters and so on Instead persons usuallyapply economizing cognitive heuristics toreach a decision (Gigerenzer Todd and theABC Research Group 1999 March and Simon1958) Toward this end we model two class-es of decision-making heuristics that avoid theneed to make as Macy and Flache (20027230) put it ldquoheroic assumptions about theknowledge and calculating abilities of theplayersrdquo

Therefore distinct from prior work weargue that the world of course taking may beseen as one that is composed of socializedinteracting individuals who apply satisficingheuristics to decide among limited optionsand to enter situations that are already great-ly defined for them (Gigerenzer and Goldstein1996 Simon 1945) In this view a mixture oftop-down rules and bottom-up adaptationscharacterizes educational course-takingcareers

Context also matters Most social scientistswould agree that organizational contexts con-sist of rules that organize experience andaction (Giddens 1986 Mead 1934 Sewell1992 2005chap 4) When it comes to

schools and curricula these rules are oftenwritten and ostensive and they define the setof potential curricular moves that are availableto a student (Cyert and March 1963 Hallinan1996 March and Simon 1958 Riehl et al1999) For example all curricula have if-thenrules or standard operating procedures thatdefine how actors in certain locations andwith certain properties (like grades) mustmove or at least narrow the set of coursesthat are available to them (eg rules oncourse prerequisites graduation and failure)

Within this context of rules and the oppor-tunity sets they define there operate differenthypothetical processes by which studentsmove between courses It is within the con-text of these constraints that the different allo-cation processes supply- and demand-sidemodels (Padgett 1990) play out We describeand analyze three allocation processes vacan-cy competition in which course vacanciesdrive studentsrsquo mobility patterns (Chase1991 Geerlings and Van Veen 2001Soslashrenson 1987 White 1970) retrospectiveadaptation in which actors alter their trajec-tory when current experiences diverge frompast ones and those of their peers (Bidwelland Friedkin 1988 Macy 1990 Macy andFlache 2002 Roth and Erev 1995) andprospective emulation in which actors altercourse when on the basis of the experiencesof older role models they anticipate that aparticular course may prove too demandingor insufficiently challenging (Cyert and March1963 Manski 1993a 1993b)

Our general aim is to integrate a bottom-up depiction of individual decision makersand their interaction into a top-down rule-driven system and we do so using simulationmodels Our depiction of decision makinguses agent-based modeling Studentsrsquo deci-sions are both influenced by the context andat the same time change the context Agent-based models differ from microsimulation(Macy and Willer 2002145) in that actors domore than follow rules they interact andadapt to one another Hence our actors fol-low simple rules make individual decisionsare adaptiveprospective looking and areinterdependent

With this perspective of course-taking deci-sions in mind we model studentsrsquo education-al course-taking careers as reflected in theirsequence of mathematics course taking and



Fri 18 Dec 2009 181626










Fri 18 Dec 2009 181626










Fri 18 Dec 2009 181626













Fri 18 Dec 2009 181626

Tab

le1

Rur

alH

igh

Mat

hem

atic

smdashTr

ansi

tion

Prob

abili

tyM

atri

xfo

rSt

uden

tM

oves

Des

tinat

ion

Stat

es

Tran

sien

tSt

ates

Poin

tsof

Exit

8th

Gra

dea

06

06

19

4

30

51

20

8

0

4

376

Tran

sfer

02

0

50

2

14

24

17

0

20

21

0

21

42

Out

side

Mat

h0

1

01

02

02

01

00

00

03

44

46

248

Spec

ialE

dM

ath

1

46

10

05

34

05

41

Spec

ialE

dM

ath

2

07

07

0

7

14

43

21

14

Basi

cM

ath

17

46

0

5

2

21

0

41A

lgeb

raA

01

15

64

0

1

12

09

12

9A

lgeb

raB

12

3

8

10

28

12

82

Alg

ebra

1

01

01

05

72

0

5

12

02

01

205

Geo

met

ry

0

94

7

09

06

22

08

283

Alg

ebra

2

11

17

0

1

03

38

31

178

Pre-

Cal

culu

s

07

03

20

70

60

Acc

Alg

ebra

1a

1

5

78

18

02

02

04

55A

ccG

eom

etry

a

0

21

6

0

16

31

1

09

02

88

Acc

Alg

ebra

IITr

ig

0

2

06

7

7

06

06

03

100

Acc

Pre-

Cal

culu

s

0

1

0

1

40

0

65

180

Acc

Cal

culu

s

1

0038

Mov

esw

ithin

atr

ack

are

show

nin

the

bloc

kson

the

lead

ing

diag

onal

(ligh

tsh

adin

g)D

arke

rsh

adin

gin

dica

tes

repe

atin

gth

esa

me

cour

se

All

valu

esre

flect

the

ratio

ofst

uden

tsm

ovin

gfr

omth

eor

igin

stat

eto

the

dest

inat

ion

stat

eVa

lues

grea

ter

than

10

are

inbo

ldfo

nt

aRo

wsu

ms

exce

ed1

sinc

eso

me

stud

ents

from

this

loca

tion

take

mor

eth

anon

eco

urse

atth

ene

xtst

age


Special Ed Math 1

Special Ed Math 2

Basic Math

Algebra A

Algebra B

Algebra 1

Geometry

Algebra 2

Pre-Calculus

AccAlgebra 1

Acc Geometry

Acc AlgTrig

Acc Pre-Calculus

Acc Calculus

Leave School

Outside Math

Graduate

Students


Origin State (1997)


Fri 18 Dec 2009 181626


ble

2M

agn

etH

igh

Mat

hem

atic

smdashTr

ansi

tion

Prob

abili

tyM

atri

xof

Stud

ent

Mov

es

Des

tinat

ion

Stat

es

Tran

sien

tSt

ates

Exit

Stat

es

7th

Gra

de9

7

0

3

17

2Tr

ansf

er2

70

90

9

1

81

8

0

9

0

9

11O

utsi

deM

ath

0

2

02

9

7

66

Alg

ebra

IHon

ors

02

39

4

2

18

177

Geo

met

ryH

onor

s

5

8

22

20

55A

lgeb

raIi

Hon

ors

6

3

04

0

20

42

794

Func

tions

52

27

18

04

83D

iscr

ete

Mat

h

new

cour

se98

rsquoN

A

Geo

met

ryPr

e-Ib

09

8

2

1

011

5A

lgIi

ampTr

igPr

e-Ib

01

21

3

5

15

1

9

09

105

Func

tions

Sta

tsT

rigIb

75

02

0

21

40

744

Prec

alc

ampD

isc

Mat

hIb

1

00

23

Prec

alcu

lus

Ibs

03

8

2

15

34

Cal

culu

sIb

s

100

16

Prec

alc

ampTr

igIb

h

0

7

89

0

4

27A

dvC

alc

Ibh

1

00

18

Mov

esw

ithin

atr

ack

are

show

nin

the

bloc

kson

the

lead

ing

diag

onal

(ligh

tsh

adin

g)D

arke

rsh

adin

gin

dica

tes

repe

atin

gth

esa

me

cour

se

All

valu

esre

flect

the

ratio

ofst

uden

tsm

ovin

gfr

omth

eor

igin

stat

eto

the

dest

inat

ion

stat

eVa

lues

grea

ter

than

10

are

inbo

ldfo

nt

Algebra I Hon

Geometry Hon

Algebra Ii Hon

Functions

Discrete Math

Geometry Pre-Ib




Precalculus Ibs

Calculus Ibs


Adv Calc Ibh

Graduate

Outside Math

Leave School

Students


Origin State (1997)


Fri 18 Dec 2009 181626


METHODS





aict = 0 = Abilityi 06 + ε 04 (1)







Fri 18 Dec 2009 181626




Fri 18 Dec 2009 181626

















Fri 18 Dec 2009 181626














Fri 18 Dec 2009 181626














Fri 18 Dec 2009 181626











Fri 18 Dec 2009 181626











Fri 18 Dec 2009 181626











Fri 18 Dec 2009 181626



RESULTS





yi = a + b1 x1i + b2x2i + b3x3i + ε





Fri 18 Dec 2009 181626










Magnet Rural


Vacancy 163 -098(0012) (0017)

Decision adapt 089 080(0012) (0017)


Adj R Sq 211 150



Fri 18 Dec 2009 181626








Magnet

Honors IB IBS IBH


Vacancy 159 296 685 1029(0011) (0023) (0027) (0033)

Decision adapt 078 099 143 404(001) (0022) (0026) (0031)


Adj R Sq 262 221 520 592

Rural



Vacancy -184 -200 -128 068(0009) (0012) (0019) (002)

Decision adapt 007 -103 082 195(0009) (0011) (0018) (0019)


Adj R Sq 454 319 163 139




Fri 18 Dec 2009 181626


CONCLUSION






Fri 18 Dec 2009 181626







Magnet

Honors IB IBS IBH


Vacancy 433 633 917 351(0017) (0022) (0026) (0023)

Decision adapt 168 252 322 132(0016) (0021) (0025) (0022)


Adj R Sq 478 559 663 228

Rural



Vacancy -105 -019 -032(0018) (0018) (0016)

Decision adapt 037 133 306(0018) (0018) (0016)


Adj R Sq 130 118 478


options (p lt 10)


Fri 18 Dec 2009 181626








Fri 18 Dec 2009 181626



NOTES














Fri 18 Dec 2009 181626















Fri 18 Dec 2009 181626






Fri 18 Dec 2009 181626


PP

END

IX

Tab

leA

1D

efin

itio

ns

ofVa

riab

les

and

Para

met

ers

Des

crip

tion

Rela

tions

hip

toO

ther

Mod

elVa

riabl

esEq

nN

o

Abi

lity

Ab

ility

Inv

aria

ntpr

oper

tyof

each

stud

ent

Stan

dard

norm

alFi

xed

mod

elva

riabl

edi

strib

utio

nse

ta

stud

entrsquos

ldquocre

atio

nrdquo(i

ee

ntry

into

the

syst

em)

AA

chie

vem

ent

isre

late

dto

abili

tyM

ore

able

stud

ents

gene

rally

For

inco

min

gst

uden

tsan

dst

uden

tsin

thei

rfir

stye

ar

1ac

hiev

em

ore

inac

adem

icte

rms

Ther

eis

also

ara

ndom

com

pone

nt

a ic

t=1

=Ab

ility

i0

6+

ε

04

(ε~

N(0

1))

to

achi

evem

ent

Ach

ieve

men

tde

pend

sno

ton

lyon

abili

ty

but

onw

hat

the

stud

ents

have

lear

ned

over

the

cour

seof

thei

rhi

ghIn

subs

eque

ntye

ars

scho

oled

ucat

iona

lcar

eers

toth

atpo

int

a ic

t=

Abili

tyi

abw

t+

(1ndasha

bwt)

andash ict

-10

6+

ε

04

2

GG

rad

esar

em

appe

dfr

omth

eem

piric

algr

ade

dist

ribut

ions

for

each

g ic

t=

G(a

icit

rsquoabulli

ct)

3co

urse

inth

etw

osc

hool

sst

udie

don

the

basi

sof

the

rank

orde

rof

achi

evem

ent

Gis

am

appi

ngfu

nctio

nth

atre

turn

sth

eap

prop

riate

grad

efo

rth

est

uden

trsquospo

sitio

nin

the

rank

orde

r(b

yac

hiev

emen

t)fo

ra

give

nco

urse

ina

give

nsc

hool

RtR

ewar

dto

lera

nce

depe

nds

onpr

ior

perf

orm

ance

and

stud

entrsquos

succ

ess

rtit

=pe

rfit

(1

ndashadw

t)+

adap

t it

adw

t4

inad

aptin

gto

chan

ges

inst

anda

rds

resu

lting

from

upw

ard

ordo

wnw

ard

trac

km

oves

(ada

ptab

ility

)

Perf

Rel

ativ

ep

erfo

rman

ceca

ptur

esth

ede

gree

tow

hich

the

stud

ents

perf

it=

(gic

tndashgndash ibull

t)

(1ndashp

e)+

(gic

tndashgndash c

t)pe

5ex

ceed

ed(o

rno

t)th

eir

prio

rpe

rfor

man

cean

dth

eir

perf

orm

ance

rela

tive

toth

eir

cour

seco

hort

adap

tA

dap

tab

ility

The

degr

eeto

whi

chth

est

uden

trsquospe

rfor

man

cech

ange

sad

apt i

t=

perf

itndash

perf

it-1

6fr

omon

epe

riod

toth

ene

xtA

dow

nwar

dm

ove

shou

ldca

use

are

duct

ion

inpe

rfor

man

ceb

utth

em

ore

adap

tabl

est

uden

tw

illsu

ffer

alo

wer

drop

than

will

ale

ssad

apta

ble

one

Con

vers

ely

anad

apta

ble

stud

ent

will

not

doas

wel

lin

alo

wer

trac

kas

one

who

refu

ses

toch

ange

his

orhe

rst

anda

rds

just

beca

use

heor

she

has

mov

eddo

wn

atr




PP

END

IX

Tab

leA

1C

onti

nue

d

Des

crip

tion

Mod

elPa

ram

eter

s(E

quat

ions

24

and

5)

RT[a

b]

Rew

ard

tole

ran

ceth

resh

old

sA

nex

ogen

ous

para

met

erth

atse

tsth

ebo

unds

ofac

cept

able

educ

atio

nale

xper

ienc

eVa

lues

outs

ide

this

rang

etr

igge

rtr

ack

chan

ges

ais

the

valu

eof

rtdo

wn

bth

atof

rtup

Edu

catio

nale

xper

ienc

eva

lues

low

erth

anrt

dow

ntr

igge

ra

mov

eto

alo

wer

-tra

ckco

urse

Val

ues

high

erth

anrt

uptr

igge

ra

mov

eto

ahi

gher

-tra

ckco

urse

abw

tA

bili

tyw

eig

ht

Am

odel

para

met

erth

atad

just

sth

ede

gree

tow

hich

achi

evem

ent

isa

func

tion

ofra

wab

ility

and

how

muc

ha

func

tion

ofpr

ior

lear

ning

(ach

ieve

men

t)

adw

tA

dap

tati

onw

eig

ht

Am

odel

para

met

erad

just

ing

the

degr

eeto

whi

chad

apta

tion

mod

erat

esth

eim

pact

ofpe

rfor

man

ceco

mpa

rison

s(r

elat

ive

tose

lfan

dre

lativ

eto

peer

s)on

the

way

the

educ

atio

nale

xper

ienc

eis

perc

eive

dby

the

stud

ent

pePe

eref

fect

wei

gh

tA

mod

elpa

ram

eter

adju

stin

gth

eex

tent

tow

hich

perf

orm

ance

isju

dged

rela

tive

toa

stud

entrsquos

prio

rpe

rfor

man

ceas

oppo

sed

toa

stud

entrsquos

perf

orm

ance

rela

tive

tohe

ror

his

peer

s


Fri 18 Dec 2009 181626


REFERENCES
































Fri 18 Dec 2009 181626


































Fri 18 Dec 2009 181626






Fri 18 Dec 2009 181626










Fri 18 Dec 2009 181626










Fri 18 Dec 2009 181626













Fri 18 Dec 2009 181626

Tab

le1

Rur

alH

igh

Mat

hem

atic

smdashTr

ansi

tion

Prob

abili

tyM

atri

xfo

rSt

uden

tM

oves

Des

tinat

ion

Stat

es

Tran

sien

tSt

ates

Poin

tsof

Exit

8th

Gra

dea

06

06

19

4

30

51

20

8

0

4

376

Tran

sfer

02

0

50

2

14

24

17

0

20

21

0

21

42

Out

side

Mat

h0

1

01

02

02

01

00

00

03

44

46

248

Spec

ialE

dM

ath

1

46

10

05

34

05

41

Spec

ialE

dM

ath

2

07

07

0

7

14

43

21

14

Basi

cM

ath

17

46

0

5

2

21

0

41A

lgeb

raA

01

15

64

0

1

12

09

12

9A

lgeb

raB

12

3

8

10

28

12

82

Alg

ebra

1

01

01

05

72

0

5

12

02

01

205

Geo

met

ry

0

94

7

09

06

22

08

283

Alg

ebra

2

11

17

0

1

03

38

31

178

Pre-

Cal

culu

s

07

03

20

70

60

Acc

Alg

ebra

1a

1

5

78

18

02

02

04

55A

ccG

eom

etry

a

0

21

6

0

16

31

1

09

02

88

Acc

Alg

ebra

IITr

ig

0

2

06

7

7

06

06

03

100

Acc

Pre-

Cal

culu

s

0

1

0

1

40

0

65

180

Acc

Cal

culu

s

1

0038

Mov

esw

ithin

atr

ack

are

show

nin

the

bloc

kson

the

lead

ing

diag

onal

(ligh

tsh

adin

g)D

arke

rsh

adin

gin

dica

tes

repe

atin

gth

esa

me

cour

se

All

valu

esre

flect

the

ratio

ofst

uden

tsm

ovin

gfr

omth

eor

igin

stat

eto

the

dest

inat

ion

stat

eVa

lues

grea

ter

than

10

are

inbo

ldfo

nt

aRo

wsu

ms

exce

ed1

sinc

eso

me

stud

ents

from

this

loca

tion

take

mor

eth

anon

eco

urse

atth

ene

xtst

age


Special Ed Math 1

Special Ed Math 2

Basic Math

Algebra A

Algebra B

Algebra 1

Geometry

Algebra 2

Pre-Calculus

AccAlgebra 1

Acc Geometry

Acc AlgTrig

Acc Pre-Calculus

Acc Calculus

Leave School

Outside Math

Graduate

Students


Origin State (1997)


Fri 18 Dec 2009 181626


ble

2M

agn

etH

igh

Mat

hem

atic

smdashTr

ansi

tion

Prob

abili

tyM

atri

xof

Stud

ent

Mov

es

Des

tinat

ion

Stat

es

Tran

sien

tSt

ates

Exit

Stat

es

7th

Gra

de9

7

0

3

17

2Tr

ansf

er2

70

90

9

1

81

8

0

9

0

9

11O

utsi

deM

ath

0

2

02

9

7

66

Alg

ebra

IHon

ors

02

39

4

2

18

177

Geo

met

ryH

onor

s

5

8

22

20

55A

lgeb

raIi

Hon

ors

6

3

04

0

20

42

794

Func

tions

52

27

18

04

83D

iscr

ete

Mat

h

new

cour

se98

rsquoN

A

Geo

met

ryPr

e-Ib

09

8

2

1

011

5A

lgIi

ampTr

igPr

e-Ib

01

21

3

5

15

1

9

09

105

Func

tions

Sta

tsT

rigIb

75

02

0

21

40

744

Prec

alc

ampD

isc

Mat

hIb

1

00

23

Prec

alcu

lus

Ibs

03

8

2

15

34

Cal

culu

sIb

s

100

16

Prec

alc

ampTr

igIb

h

0

7

89

0

4

27A

dvC

alc

Ibh

1

00

18

Mov

esw

ithin

atr

ack

are

show

nin

the

bloc

kson

the

lead

ing

diag

onal

(ligh

tsh

adin

g)D

arke

rsh

adin

gin

dica

tes

repe

atin

gth

esa

me

cour

se

All

valu

esre

flect

the

ratio

ofst

uden

tsm

ovin

gfr

omth

eor

igin

stat

eto

the

dest

inat

ion

stat

eVa

lues

grea

ter

than

10

are

inbo

ldfo

nt

Algebra I Hon

Geometry Hon

Algebra Ii Hon

Functions

Discrete Math

Geometry Pre-Ib




Precalculus Ibs

Calculus Ibs


Adv Calc Ibh

Graduate

Outside Math

Leave School

Students


Origin State (1997)


Fri 18 Dec 2009 181626


METHODS





aict = 0 = Abilityi 06 + ε 04 (1)







Fri 18 Dec 2009 181626




Fri 18 Dec 2009 181626

















Fri 18 Dec 2009 181626














Fri 18 Dec 2009 181626














Fri 18 Dec 2009 181626











Fri 18 Dec 2009 181626











Fri 18 Dec 2009 181626











Fri 18 Dec 2009 181626



RESULTS





yi = a + b1 x1i + b2x2i + b3x3i + ε





Fri 18 Dec 2009 181626










Magnet Rural


Vacancy 163 -098(0012) (0017)

Decision adapt 089 080(0012) (0017)


Adj R Sq 211 150



Fri 18 Dec 2009 181626








Magnet

Honors IB IBS IBH


Vacancy 159 296 685 1029(0011) (0023) (0027) (0033)

Decision adapt 078 099 143 404(001) (0022) (0026) (0031)


Adj R Sq 262 221 520 592

Rural



Vacancy -184 -200 -128 068(0009) (0012) (0019) (002)

Decision adapt 007 -103 082 195(0009) (0011) (0018) (0019)


Adj R Sq 454 319 163 139




Fri 18 Dec 2009 181626


CONCLUSION






Fri 18 Dec 2009 181626







Magnet

Honors IB IBS IBH


Vacancy 433 633 917 351(0017) (0022) (0026) (0023)

Decision adapt 168 252 322 132(0016) (0021) (0025) (0022)


Adj R Sq 478 559 663 228

Rural



Vacancy -105 -019 -032(0018) (0018) (0016)

Decision adapt 037 133 306(0018) (0018) (0016)


Adj R Sq 130 118 478


options (p lt 10)


Fri 18 Dec 2009 181626








Fri 18 Dec 2009 181626



NOTES














Fri 18 Dec 2009 181626















Fri 18 Dec 2009 181626






Fri 18 Dec 2009 181626


PP

END

IX

Tab

leA

1D

efin

itio

ns

ofVa

riab

les

and

Para

met

ers

Des

crip

tion

Rela

tions

hip

toO

ther

Mod

elVa

riabl

esEq

nN

o

Abi

lity

Ab

ility

Inv

aria

ntpr

oper

tyof

each

stud

ent

Stan

dard

norm

alFi

xed

mod

elva

riabl

edi

strib

utio

nse

ta

stud

entrsquos

ldquocre

atio

nrdquo(i

ee

ntry

into

the

syst

em)

AA

chie

vem

ent

isre

late

dto

abili

tyM

ore

able

stud

ents

gene

rally

For

inco

min

gst

uden

tsan

dst

uden

tsin

thei

rfir

stye

ar

1ac

hiev

em

ore

inac

adem

icte

rms

Ther

eis

also

ara

ndom

com

pone

nt

a ic

t=1

=Ab

ility

i0

6+

ε

04

(ε~

N(0

1))

to

achi

evem

ent

Ach

ieve

men

tde

pend

sno

ton

lyon

abili

ty

but

onw

hat

the

stud

ents

have

lear

ned

over

the

cour

seof

thei

rhi

ghIn

subs

eque

ntye

ars

scho

oled

ucat

iona

lcar

eers

toth

atpo

int

a ic

t=

Abili

tyi

abw

t+

(1ndasha

bwt)

andash ict

-10

6+

ε

04

2

GG

rad

esar

em

appe

dfr

omth

eem

piric

algr

ade

dist

ribut

ions

for

each

g ic

t=

G(a

icit

rsquoabulli

ct)

3co

urse

inth

etw

osc

hool

sst

udie

don

the

basi

sof

the

rank

orde

rof

achi

evem

ent

Gis

am

appi

ngfu

nctio

nth

atre

turn

sth

eap

prop

riate

grad

efo

rth

est

uden

trsquospo

sitio

nin

the

rank

orde

r(b

yac

hiev

emen

t)fo

ra

give

nco

urse

ina

give

nsc

hool

RtR

ewar

dto

lera

nce

depe

nds

onpr

ior

perf

orm

ance

and

stud

entrsquos

succ

ess

rtit

=pe

rfit

(1

ndashadw

t)+

adap

t it

adw

t4

inad

aptin

gto

chan

ges

inst

anda

rds

resu

lting

from

upw

ard

ordo

wnw

ard

trac

km

oves

(ada

ptab

ility

)

Perf

Rel

ativ

ep

erfo

rman

ceca

ptur

esth

ede

gree

tow

hich

the

stud

ents

perf

it=

(gic

tndashgndash ibull

t)

(1ndashp

e)+

(gic

tndashgndash c

t)pe

5ex

ceed

ed(o

rno

t)th

eir

prio

rpe

rfor

man

cean

dth

eir

perf

orm

ance

rela

tive

toth

eir

cour

seco

hort

adap

tA

dap

tab

ility

The

degr

eeto

whi

chth

est

uden

trsquospe

rfor

man

cech

ange

sad

apt i

t=

perf

itndash

perf

it-1

6fr

omon

epe

riod

toth

ene

xtA

dow

nwar

dm

ove

shou

ldca

use

are

duct

ion

inpe

rfor

man

ceb

utth

em

ore

adap

tabl

est

uden

tw

illsu

ffer

alo

wer

drop

than

will

ale

ssad

apta

ble

one

Con

vers

ely

anad

apta

ble

stud

ent

will

not

doas

wel

lin

alo

wer

trac

kas

one

who

refu

ses

toch

ange

his

orhe

rst

anda

rds

just

beca

use

heor

she

has

mov

eddo

wn

atr




PP

END

IX

Tab

leA

1C

onti

nue

d

Des

crip

tion

Mod

elPa

ram

eter

s(E

quat

ions

24

and

5)

RT[a

b]

Rew

ard

tole

ran

ceth

resh

old

sA

nex

ogen

ous

para

met

erth

atse

tsth

ebo

unds

ofac

cept

able

educ

atio

nale

xper

ienc

eVa

lues

outs

ide

this

rang

etr

igge

rtr

ack

chan

ges

ais

the

valu

eof

rtdo

wn

bth

atof

rtup

Edu

catio

nale

xper

ienc

eva

lues

low

erth

anrt

dow

ntr

igge

ra

mov

eto

alo

wer

-tra

ckco

urse

Val

ues

high

erth

anrt

uptr

igge

ra

mov

eto

ahi

gher

-tra

ckco

urse

abw

tA

bili

tyw

eig

ht

Am

odel

para

met

erth

atad

just

sth

ede

gree

tow

hich

achi

evem

ent

isa

func

tion

ofra

wab

ility

and

how

muc

ha

func

tion

ofpr

ior

lear

ning

(ach

ieve

men

t)

adw

tA

dap

tati

onw

eig

ht

Am

odel

para

met

erad

just

ing

the

degr

eeto

whi

chad

apta

tion

mod

erat

esth

eim

pact

ofpe

rfor

man

ceco

mpa

rison

s(r

elat

ive

tose

lfan

dre

lativ

eto

peer

s)on

the

way

the

educ

atio

nale

xper

ienc

eis

perc

eive

dby

the

stud

ent

pePe

eref

fect

wei

gh

tA

mod

elpa

ram

eter

adju

stin

gth

eex

tent

tow

hich

perf

orm

ance

isju

dged

rela

tive

toa

stud

entrsquos

prio

rpe

rfor

man

ceas

oppo

sed

toa

stud

entrsquos

perf

orm

ance

rela

tive

tohe

ror

his

peer

s


Fri 18 Dec 2009 181626


REFERENCES
































Fri 18 Dec 2009 181626


































Fri 18 Dec 2009 181626






Fri 18 Dec 2009 181626










Fri 18 Dec 2009 181626













Fri 18 Dec 2009 181626

Tab

le1

Rur

alH

igh

Mat

hem

atic

smdashTr

ansi

tion

Prob

abili

tyM

atri

xfo

rSt

uden

tM

oves

Des

tinat

ion

Stat

es

Tran

sien

tSt

ates

Poin

tsof

Exit

8th

Gra

dea

06

06

19

4

30

51

20

8

0

4

376

Tran

sfer

02

0

50

2

14

24

17

0

20

21

0

21

42

Out

side

Mat

h0

1

01

02

02

01

00

00

03

44

46

248

Spec

ialE

dM

ath

1

46

10

05

34

05

41

Spec

ialE

dM

ath

2

07

07

0

7

14

43

21

14

Basi

cM

ath

17

46

0

5

2

21

0

41A

lgeb

raA

01

15

64

0

1

12

09

12

9A

lgeb

raB

12

3

8

10

28

12

82

Alg

ebra

1

01

01

05

72

0

5

12

02

01

205

Geo

met

ry

0

94

7

09

06

22

08

283

Alg

ebra

2

11

17

0

1

03

38

31

178

Pre-

Cal

culu

s

07

03

20

70

60

Acc

Alg

ebra

1a

1

5

78

18

02

02

04

55A

ccG

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etry

a

0

21

6

0

16

31

1

09

02

88

Acc

Alg

ebra

IITr

ig

0

2

06

7

7

06

06

03

100

Acc

Pre-

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culu

s

0

1

0

1

40

0

65

180

Acc

Cal

culu

s

1

0038

Mov

esw

ithin

atr

ack

are

show

nin

the

bloc

kson

the

lead

ing

diag

onal

(ligh

tsh

adin

g)D

arke

rsh

adin

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dica

tes

repe

atin

gth

esa

me

cour

se

All

valu

esre

flect

the

ratio

ofst

uden

tsm

ovin

gfr

omth

eor

igin

stat

eto

the

dest

inat

ion

stat

eVa

lues

grea

ter

than

10

are

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ldfo

nt

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wsu

ms

exce

ed1

sinc

eso

me

stud

ents

from

this

loca

tion

take

mor

eth

anon

eco

urse

atth

ene

xtst

age


Special Ed Math 1

Special Ed Math 2

Basic Math

Algebra A

Algebra B

Algebra 1

Geometry

Algebra 2

Pre-Calculus

AccAlgebra 1

Acc Geometry

Acc AlgTrig

Acc Pre-Calculus

Acc Calculus

Leave School

Outside Math

Graduate

Students


Origin State (1997)


Fri 18 Dec 2009 181626


ble

2M

agn

etH

igh

Mat

hem

atic

smdashTr

ansi

tion

Prob

abili

tyM

atri

xof

Stud

ent

Mov

es

Des

tinat

ion

Stat

es

Tran

sien

tSt

ates

Exit

Stat

es

7th

Gra

de9

7

0

3

17

2Tr

ansf

er2

70

90

9

1

81

8

0

9

0

9

11O

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deM

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0

2

02

9

7

66

Alg

ebra

IHon

ors

02

39

4

2

18

177

Geo

met

ryH

onor

s

5

8

22

20

55A

lgeb

raIi

Hon

ors

6

3

04

0

20

42

794

Func

tions

52

27

18

04

83D

iscr

ete

Mat

h

new

cour

se98

rsquoN

A

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met

ryPr

e-Ib

09

8

2

1

011

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ampTr

igPr

e-Ib

01

21

3

5

15

1

9

09

105

Func

tions

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tsT

rigIb

75

02

0

21

40

744

Prec

alc

ampD

isc

Mat

hIb

1

00

23

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alcu

lus

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03

8

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15

34

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culu

sIb

s

100

16

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alc

ampTr

igIb

h

0

7

89

0

4

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dvC

alc

Ibh

1

00

18

Mov

esw

ithin

atr

ack

are

show

nin

the

bloc

kson

the

lead

ing

diag

onal

(ligh

tsh

adin

g)D

arke

rsh

adin

gin

dica

tes

repe

atin

gth

esa

me

cour

se

All

valu

esre

flect

the

ratio

ofst

uden

tsm

ovin

gfr

omth

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igin

stat

eto

the

dest

inat

ion

stat

eVa

lues

grea

ter

than

10

are

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ldfo

nt

Algebra I Hon

Geometry Hon

Algebra Ii Hon

Functions

Discrete Math

Geometry Pre-Ib




Precalculus Ibs

Calculus Ibs


Adv Calc Ibh

Graduate

Outside Math

Leave School

Students


Origin State (1997)


Fri 18 Dec 2009 181626


METHODS





aict = 0 = Abilityi 06 + ε 04 (1)







Fri 18 Dec 2009 181626




Fri 18 Dec 2009 181626

















Fri 18 Dec 2009 181626














Fri 18 Dec 2009 181626














Fri 18 Dec 2009 181626











Fri 18 Dec 2009 181626











Fri 18 Dec 2009 181626











Fri 18 Dec 2009 181626



RESULTS





yi = a + b1 x1i + b2x2i + b3x3i + ε





Fri 18 Dec 2009 181626










Magnet Rural


Vacancy 163 -098(0012) (0017)

Decision adapt 089 080(0012) (0017)


Adj R Sq 211 150



Fri 18 Dec 2009 181626








Magnet

Honors IB IBS IBH


Vacancy 159 296 685 1029(0011) (0023) (0027) (0033)

Decision adapt 078 099 143 404(001) (0022) (0026) (0031)


Adj R Sq 262 221 520 592

Rural



Vacancy -184 -200 -128 068(0009) (0012) (0019) (002)

Decision adapt 007 -103 082 195(0009) (0011) (0018) (0019)


Adj R Sq 454 319 163 139




Fri 18 Dec 2009 181626


CONCLUSION






Fri 18 Dec 2009 181626







Magnet

Honors IB IBS IBH


Vacancy 433 633 917 351(0017) (0022) (0026) (0023)

Decision adapt 168 252 322 132(0016) (0021) (0025) (0022)


Adj R Sq 478 559 663 228

Rural



Vacancy -105 -019 -032(0018) (0018) (0016)

Decision adapt 037 133 306(0018) (0018) (0016)


Adj R Sq 130 118 478


options (p lt 10)


Fri 18 Dec 2009 181626








Fri 18 Dec 2009 181626



NOTES














Fri 18 Dec 2009 181626















Fri 18 Dec 2009 181626






Fri 18 Dec 2009 181626


PP

END

IX

Tab

leA

1D

efin

itio

ns

ofVa

riab

les

and

Para

met

ers

Des

crip

tion

Rela

tions

hip

toO

ther

Mod

elVa

riabl

esEq

nN

o

Abi

lity

Ab

ility

Inv

aria

ntpr

oper

tyof

each

stud

ent

Stan

dard

norm

alFi

xed

mod

elva

riabl

edi

strib

utio

nse

ta

stud

entrsquos

ldquocre

atio

nrdquo(i

ee

ntry

into

the

syst

em)

AA

chie

vem

ent

isre

late

dto

abili

tyM

ore

able

stud

ents

gene

rally

For

inco

min

gst

uden

tsan

dst

uden

tsin

thei

rfir

stye

ar

1ac

hiev

em

ore

inac

adem

icte

rms

Ther

eis

also

ara

ndom

com

pone

nt

a ic

t=1

=Ab

ility

i0

6+

ε

04

(ε~

N(0

1))

to

achi

evem

ent

Ach

ieve

men

tde

pend

sno

ton

lyon

abili

ty

but

onw

hat

the

stud

ents

have

lear

ned

over

the

cour

seof

thei

rhi

ghIn

subs

eque

ntye

ars

scho

oled

ucat

iona

lcar

eers

toth

atpo

int

a ic

t=

Abili

tyi

abw

t+

(1ndasha

bwt)

andash ict

-10

6+

ε

04

2

GG

rad

esar

em

appe

dfr

omth

eem

piric

algr

ade

dist

ribut

ions

for

each

g ic

t=

G(a

icit

rsquoabulli

ct)

3co

urse

inth

etw

osc

hool

sst

udie

don

the

basi

sof

the

rank

orde

rof

achi

evem

ent

Gis

am

appi

ngfu

nctio

nth

atre

turn

sth

eap

prop

riate

grad

efo

rth

est

uden

trsquospo

sitio

nin

the

rank

orde

r(b

yac

hiev

emen

t)fo

ra

give

nco

urse

ina

give

nsc

hool

RtR

ewar

dto

lera

nce

depe

nds

onpr

ior

perf

orm

ance

and

stud

entrsquos

succ

ess

rtit

=pe

rfit

(1

ndashadw

t)+

adap

t it

adw

t4

inad

aptin

gto

chan

ges

inst

anda

rds

resu

lting

from

upw

ard

ordo

wnw

ard

trac

km

oves

(ada

ptab

ility

)

Perf

Rel

ativ

ep

erfo

rman

ceca

ptur

esth

ede

gree

tow

hich

the

stud

ents

perf

it=

(gic

tndashgndash ibull

t)

(1ndashp

e)+

(gic

tndashgndash c

t)pe

5ex

ceed

ed(o

rno

t)th

eir

prio

rpe

rfor

man

cean

dth

eir

perf

orm

ance

rela

tive

toth

eir

cour

seco

hort

adap

tA

dap

tab

ility

The

degr

eeto

whi

chth

est

uden

trsquospe

rfor

man

cech

ange

sad

apt i

t=

perf

itndash

perf

it-1

6fr

omon

epe

riod

toth

ene

xtA

dow

nwar

dm

ove

shou

ldca

use

are

duct

ion

inpe

rfor

man

ceb

utth

em

ore

adap

tabl

est

uden

tw

illsu

ffer

alo

wer

drop

than

will

ale

ssad

apta

ble

one

Con

vers

ely

anad

apta

ble

stud

ent

will

not

doas

wel

lin

alo

wer

trac

kas

one

who

refu

ses

toch

ange

his

orhe

rst

anda

rds

just

beca

use

heor

she

has

mov

eddo

wn

atr




PP

END

IX

Tab

leA

1C

onti

nue

d

Des

crip

tion

Mod

elPa

ram

eter

s(E

quat

ions

24

and

5)

RT[a

b]

Rew

ard

tole

ran

ceth

resh

old

sA

nex

ogen

ous

para

met

erth

atse

tsth

ebo

unds

ofac

cept

able

educ

atio

nale

xper

ienc

eVa

lues

outs

ide

this

rang

etr

igge

rtr

ack

chan

ges

ais

the

valu

eof

rtdo

wn

bth

atof

rtup

Edu

catio

nale

xper

ienc

eva

lues

low

erth

anrt

dow

ntr

igge

ra

mov

eto

alo

wer

-tra

ckco

urse

Val

ues

high

erth

anrt

uptr

igge

ra

mov

eto

ahi

gher

-tra

ckco

urse

abw

tA

bili

tyw

eig

ht

Am

odel

para

met

erth

atad

just

sth

ede

gree

tow

hich

achi

evem

ent

isa

func

tion

ofra

wab

ility

and

how

muc

ha

func

tion

ofpr

ior

lear

ning

(ach

ieve

men

t)

adw

tA

dap

tati

onw

eig

ht

Am

odel

para

met

erad

just

ing

the

degr

eeto

whi

chad

apta

tion

mod

erat

esth

eim

pact

ofpe

rfor

man

ceco

mpa

rison

s(r

elat

ive

tose

lfan

dre

lativ

eto

peer

s)on

the

way

the

educ

atio

nale

xper

ienc

eis

perc

eive

dby

the

stud

ent

pePe

eref

fect

wei

gh

tA

mod

elpa

ram

eter

adju

stin

gth

eex

tent

tow

hich

perf

orm

ance

isju

dged

rela

tive

toa

stud

entrsquos

prio

rpe

rfor

man

ceas

oppo

sed

toa

stud

entrsquos

perf

orm

ance

rela

tive

tohe

ror

his

peer

s


Fri 18 Dec 2009 181626


REFERENCES
































Fri 18 Dec 2009 181626


































Fri 18 Dec 2009 181626






Fri 18 Dec 2009 181626













Fri 18 Dec 2009 181626

Tab

le1

Rur

alH

igh

Mat

hem

atic

smdashTr

ansi

tion

Prob

abili

tyM

atri

xfo

rSt

uden

tM

oves

Des

tinat

ion

Stat

es

Tran

sien

tSt

ates

Poin

tsof

Exit

8th

Gra

dea

06

06

19

4

30

51

20

8

0

4

376

Tran

sfer

02

0

50

2

14

24

17

0

20

21

0

21

42

Out

side

Mat

h0

1

01

02

02

01

00

00

03

44

46

248

Spec

ialE

dM

ath

1

46

10

05

34

05

41

Spec

ialE

dM

ath

2

07

07

0

7

14

43

21

14

Basi

cM

ath

17

46

0

5

2

21

0

41A

lgeb

raA

01

15

64

0

1

12

09

12

9A

lgeb

raB

12

3

8

10

28

12

82

Alg

ebra

1

01

01

05

72

0

5

12

02

01

205

Geo

met

ry

0

94

7

09

06

22

08

283

Alg

ebra

2

11

17

0

1

03

38

31

178

Pre-

Cal

culu

s

07

03

20

70

60

Acc

Alg

ebra

1a

1

5

78

18

02

02

04

55A

ccG

eom

etry

a

0

21

6

0

16

31

1

09

02

88

Acc

Alg

ebra

IITr

ig

0

2

06

7

7

06

06

03

100

Acc

Pre-

Cal

culu

s

0

1

0

1

40

0

65

180

Acc

Cal

culu

s

1

0038

Mov

esw

ithin

atr

ack

are

show

nin

the

bloc

kson

the

lead

ing

diag

onal

(ligh

tsh

adin

g)D

arke

rsh

adin

gin

dica

tes

repe

atin

gth

esa

me

cour

se

All

valu

esre

flect

the

ratio

ofst

uden

tsm

ovin

gfr

omth

eor

igin

stat

eto

the

dest

inat

ion

stat

eVa

lues

grea

ter

than

10

are

inbo

ldfo

nt

aRo

wsu

ms

exce

ed1

sinc

eso

me

stud

ents

from

this

loca

tion

take

mor

eth

anon

eco

urse

atth

ene

xtst

age


Special Ed Math 1

Special Ed Math 2

Basic Math

Algebra A

Algebra B

Algebra 1

Geometry

Algebra 2

Pre-Calculus

AccAlgebra 1

Acc Geometry

Acc AlgTrig

Acc Pre-Calculus

Acc Calculus

Leave School

Outside Math

Graduate

Students


Origin State (1997)


Fri 18 Dec 2009 181626


ble

2M

agn

etH

igh

Mat

hem

atic

smdashTr

ansi

tion

Prob

abili

tyM

atri

xof

Stud

ent

Mov

es

Des

tinat

ion

Stat

es

Tran

sien

tSt

ates

Exit

Stat

es

7th

Gra

de9

7

0

3

17

2Tr

ansf

er2

70

90

9

1

81

8

0

9

0

9

11O

utsi

deM

ath

0

2

02

9

7

66

Alg

ebra

IHon

ors

02

39

4

2

18

177

Geo

met

ryH

onor

s

5

8

22

20

55A

lgeb

raIi

Hon

ors

6

3

04

0

20

42

794

Func

tions

52

27

18

04

83D

iscr

ete

Mat

h

new

cour

se98

rsquoN

A

Geo

met

ryPr

e-Ib

09

8

2

1

011

5A

lgIi

ampTr

igPr

e-Ib

01

21

3

5

15

1

9

09

105

Func

tions

Sta

tsT

rigIb

75

02

0

21

40

744

Prec

alc

ampD

isc

Mat

hIb

1

00

23

Prec

alcu

lus

Ibs

03

8

2

15

34

Cal

culu

sIb

s

100

16

Prec

alc

ampTr

igIb

h

0

7

89

0

4

27A

dvC

alc

Ibh

1

00

18

Mov

esw

ithin

atr

ack

are

show

nin

the

bloc

kson

the

lead

ing

diag

onal

(ligh

tsh

adin

g)D

arke

rsh

adin

gin

dica

tes

repe

atin

gth

esa

me

cour

se

All

valu

esre

flect

the

ratio

ofst

uden

tsm

ovin

gfr

omth

eor

igin

stat

eto

the

dest

inat

ion

stat

eVa

lues

grea

ter

than

10

are

inbo

ldfo

nt

Algebra I Hon

Geometry Hon

Algebra Ii Hon

Functions

Discrete Math

Geometry Pre-Ib




Precalculus Ibs

Calculus Ibs


Adv Calc Ibh

Graduate

Outside Math

Leave School

Students


Origin State (1997)


Fri 18 Dec 2009 181626


METHODS





aict = 0 = Abilityi 06 + ε 04 (1)







Fri 18 Dec 2009 181626




Fri 18 Dec 2009 181626

















Fri 18 Dec 2009 181626














Fri 18 Dec 2009 181626














Fri 18 Dec 2009 181626











Fri 18 Dec 2009 181626











Fri 18 Dec 2009 181626











Fri 18 Dec 2009 181626



RESULTS





yi = a + b1 x1i + b2x2i + b3x3i + ε





Fri 18 Dec 2009 181626










Magnet Rural


Vacancy 163 -098(0012) (0017)

Decision adapt 089 080(0012) (0017)


Adj R Sq 211 150



Fri 18 Dec 2009 181626








Magnet

Honors IB IBS IBH


Vacancy 159 296 685 1029(0011) (0023) (0027) (0033)

Decision adapt 078 099 143 404(001) (0022) (0026) (0031)


Adj R Sq 262 221 520 592

Rural



Vacancy -184 -200 -128 068(0009) (0012) (0019) (002)

Decision adapt 007 -103 082 195(0009) (0011) (0018) (0019)


Adj R Sq 454 319 163 139




Fri 18 Dec 2009 181626


CONCLUSION






Fri 18 Dec 2009 181626







Magnet

Honors IB IBS IBH


Vacancy 433 633 917 351(0017) (0022) (0026) (0023)

Decision adapt 168 252 322 132(0016) (0021) (0025) (0022)


Adj R Sq 478 559 663 228

Rural



Vacancy -105 -019 -032(0018) (0018) (0016)

Decision adapt 037 133 306(0018) (0018) (0016)


Adj R Sq 130 118 478


options (p lt 10)


Fri 18 Dec 2009 181626








Fri 18 Dec 2009 181626



NOTES














Fri 18 Dec 2009 181626















Fri 18 Dec 2009 181626






Fri 18 Dec 2009 181626


PP

END

IX

Tab

leA

1D

efin

itio

ns

ofVa

riab

les

and

Para

met

ers

Des

crip

tion

Rela

tions

hip

toO

ther

Mod

elVa

riabl

esEq

nN

o

Abi

lity

Ab

ility

Inv

aria

ntpr

oper

tyof

each

stud

ent

Stan

dard

norm

alFi

xed

mod

elva

riabl

edi

strib

utio

nse

ta

stud

entrsquos

ldquocre

atio

nrdquo(i

ee

ntry

into

the

syst

em)

AA

chie

vem

ent

isre

late

dto

abili

tyM

ore

able

stud

ents

gene

rally

For

inco

min

gst

uden

tsan

dst

uden

tsin

thei

rfir

stye

ar

1ac

hiev

em

ore

inac

adem

icte

rms

Ther

eis

also

ara

ndom

com

pone

nt

a ic

t=1

=Ab

ility

i0

6+

ε

04

(ε~

N(0

1))

to

achi

evem

ent

Ach

ieve

men

tde

pend

sno

ton

lyon

abili

ty

but

onw

hat

the

stud

ents

have

lear

ned

over

the

cour

seof

thei

rhi

ghIn

subs

eque

ntye

ars

scho

oled

ucat

iona

lcar

eers

toth

atpo

int

a ic

t=

Abili

tyi

abw

t+

(1ndasha

bwt)

andash ict

-10

6+

ε

04

2

GG

rad

esar

em

appe

dfr

omth

eem

piric

algr

ade

dist

ribut

ions

for

each

g ic

t=

G(a

icit

rsquoabulli

ct)

3co

urse

inth

etw

osc

hool

sst

udie

don

the

basi

sof

the

rank

orde

rof

achi

evem

ent

Gis

am

appi

ngfu

nctio

nth

atre

turn

sth

eap

prop

riate

grad

efo

rth

est

uden

trsquospo

sitio

nin

the

rank

orde

r(b

yac

hiev

emen

t)fo

ra

give

nco

urse

ina

give

nsc

hool

RtR

ewar

dto

lera

nce

depe

nds

onpr

ior

perf

orm

ance

and

stud

entrsquos

succ

ess

rtit

=pe

rfit

(1

ndashadw

t)+

adap

t it

adw

t4

inad

aptin

gto

chan

ges

inst

anda

rds

resu

lting

from

upw

ard

ordo

wnw

ard

trac

km

oves

(ada

ptab

ility

)

Perf

Rel

ativ

ep

erfo

rman

ceca

ptur

esth

ede

gree

tow

hich

the

stud

ents

perf

it=

(gic

tndashgndash ibull

t)

(1ndashp

e)+

(gic

tndashgndash c

t)pe

5ex

ceed

ed(o

rno

t)th

eir

prio

rpe

rfor

man

cean

dth

eir

perf

orm

ance

rela

tive

toth

eir

cour

seco

hort

adap

tA

dap

tab

ility

The

degr

eeto

whi

chth

est

uden

trsquospe

rfor

man

cech

ange

sad

apt i

t=

perf

itndash

perf

it-1

6fr

omon

epe

riod

toth

ene

xtA

dow

nwar

dm

ove

shou

ldca

use

are

duct

ion

inpe

rfor

man

ceb

utth

em

ore

adap

tabl

est

uden

tw

illsu

ffer

alo

wer

drop

than

will

ale

ssad

apta

ble

one

Con

vers

ely

anad

apta

ble

stud

ent

will

not

doas

wel

lin

alo

wer

trac

kas

one

who

refu

ses

toch

ange

his

orhe

rst

anda

rds

just

beca

use

heor

she

has

mov

eddo

wn

atr




PP

END

IX

Tab

leA

1C

onti

nue

d

Des

crip

tion

Mod

elPa

ram

eter

s(E

quat

ions

24

and

5)

RT[a

b]

Rew

ard

tole

ran

ceth

resh

old

sA

nex

ogen

ous

para

met

erth

atse

tsth

ebo

unds

ofac

cept

able

educ

atio

nale

xper

ienc

eVa

lues

outs

ide

this

rang

etr

igge

rtr

ack

chan

ges

ais

the

valu

eof

rtdo

wn

bth

atof

rtup

Edu

catio

nale

xper

ienc

eva

lues

low

erth

anrt

dow

ntr

igge

ra

mov

eto

alo

wer

-tra

ckco

urse

Val

ues

high

erth

anrt

uptr

igge

ra

mov

eto

ahi

gher

-tra

ckco

urse

abw

tA

bili

tyw

eig

ht

Am

odel

para

met

erth

atad

just

sth

ede

gree

tow

hich

achi

evem

ent

isa

func

tion

ofra

wab

ility

and

how

muc

ha

func

tion

ofpr

ior

lear

ning

(ach

ieve

men

t)

adw

tA

dap

tati

onw

eig

ht

Am

odel

para

met

erad

just

ing

the

degr

eeto

whi

chad

apta

tion

mod

erat

esth

eim

pact

ofpe

rfor

man

ceco

mpa

rison

s(r

elat

ive

tose

lfan

dre

lativ

eto

peer

s)on

the

way

the

educ

atio

nale

xper

ienc

eis

perc

eive

dby

the

stud

ent

pePe

eref

fect

wei

gh

tA

mod

elpa

ram

eter

adju

stin

gth

eex

tent

tow

hich

perf

orm

ance

isju

dged

rela

tive

toa

stud

entrsquos

prio

rpe

rfor

man

ceas

oppo

sed

toa

stud

entrsquos

perf

orm

ance

rela

tive

tohe

ror

his

peer

s


Fri 18 Dec 2009 181626


REFERENCES
































Fri 18 Dec 2009 181626


































Fri 18 Dec 2009 181626






Fri 18 Dec 2009 181626

Tab

le1

Rur

alH

igh

Mat

hem

atic

smdashTr

ansi

tion

Prob

abili

tyM

atri

xfo

rSt

uden

tM

oves

Des

tinat

ion

Stat

es

Tran

sien

tSt

ates

Poin

tsof

Exit

8th

Gra

dea

06

06

19

4

30

51

20

8

0

4

376

Tran

sfer

02

0

50

2

14

24

17

0

20

21

0

21

42

Out

side

Mat

h0

1

01

02

02

01

00

00

03

44

46

248

Spec

ialE

dM

ath

1

46

10

05

34

05

41

Spec

ialE

dM

ath

2

07

07

0

7

14

43

21

14

Basi

cM

ath

17

46

0

5

2

21

0

41A

lgeb

raA

01

15

64

0

1

12

09

12

9A

lgeb

raB

12

3

8

10

28

12

82

Alg

ebra

1

01

01

05

72

0

5

12

02

01

205

Geo

met

ry

0

94

7

09

06

22

08

283

Alg

ebra

2

11

17

0

1

03

38

31

178

Pre-

Cal

culu

s

07

03

20

70

60

Acc

Alg

ebra

1a

1

5

78

18

02

02

04

55A

ccG

eom

etry

a

0

21

6

0

16

31

1

09

02

88

Acc

Alg

ebra

IITr

ig

0

2

06

7

7

06

06

03

100

Acc

Pre-

Cal

culu

s

0

1

0

1

40

0

65

180

Acc

Cal

culu

s

1

0038

Mov

esw

ithin

atr

ack

are

show

nin

the

bloc

kson

the

lead

ing

diag

onal

(ligh

tsh

adin

g)D

arke

rsh

adin

gin

dica

tes

repe

atin

gth

esa

me

cour

se

All

valu

esre

flect

the

ratio

ofst

uden

tsm

ovin

gfr

omth

eor

igin

stat

eto

the

dest

inat

ion

stat

eVa

lues

grea

ter

than

10

are

inbo

ldfo

nt

aRo

wsu

ms

exce

ed1

sinc

eso

me

stud

ents

from

this

loca

tion

take

mor

eth

anon

eco

urse

atth

ene

xtst

age


Special Ed Math 1

Special Ed Math 2

Basic Math

Algebra A

Algebra B

Algebra 1

Geometry

Algebra 2

Pre-Calculus

AccAlgebra 1

Acc Geometry

Acc AlgTrig

Acc Pre-Calculus

Acc Calculus

Leave School

Outside Math

Graduate

Students


Origin State (1997)


Fri 18 Dec 2009 181626


ble

2M

agn

etH

igh

Mat

hem

atic

smdashTr

ansi

tion

Prob

abili

tyM

atri

xof

Stud

ent

Mov

es

Des

tinat

ion

Stat

es

Tran

sien

tSt

ates

Exit

Stat

es

7th

Gra

de9

7

0

3

17

2Tr

ansf

er2

70

90

9

1

81

8

0

9

0

9

11O

utsi

deM

ath

0

2

02

9

7

66

Alg

ebra

IHon

ors

02

39

4

2

18

177

Geo

met

ryH

onor

s

5

8

22

20

55A

lgeb

raIi

Hon

ors

6

3

04

0

20

42

794

Func

tions

52

27

18

04

83D

iscr

ete

Mat

h

new

cour

se98

rsquoN

A

Geo

met

ryPr

e-Ib

09

8

2

1

011

5A

lgIi

ampTr

igPr

e-Ib

01

21

3

5

15

1

9

09

105

Func

tions

Sta

tsT

rigIb

75

02

0

21

40

744

Prec

alc

ampD

isc

Mat

hIb

1

00

23

Prec

alcu

lus

Ibs

03

8

2

15

34

Cal

culu

sIb

s

100

16

Prec

alc

ampTr

igIb

h

0

7

89

0

4

27A

dvC

alc

Ibh

1

00

18

Mov

esw

ithin

atr

ack

are

show

nin

the

bloc

kson

the

lead

ing

diag

onal

(ligh

tsh

adin

g)D

arke

rsh

adin

gin

dica

tes

repe

atin

gth

esa

me

cour

se

All

valu

esre

flect

the

ratio

ofst

uden

tsm

ovin

gfr

omth

eor

igin

stat

eto

the

dest

inat

ion

stat

eVa

lues

grea

ter

than

10

are

inbo

ldfo

nt

Algebra I Hon

Geometry Hon

Algebra Ii Hon

Functions

Discrete Math

Geometry Pre-Ib




Precalculus Ibs

Calculus Ibs


Adv Calc Ibh

Graduate

Outside Math

Leave School

Students


Origin State (1997)


Fri 18 Dec 2009 181626


METHODS





aict = 0 = Abilityi 06 + ε 04 (1)







Fri 18 Dec 2009 181626




Fri 18 Dec 2009 181626

















Fri 18 Dec 2009 181626














Fri 18 Dec 2009 181626














Fri 18 Dec 2009 181626











Fri 18 Dec 2009 181626











Fri 18 Dec 2009 181626











Fri 18 Dec 2009 181626



RESULTS





yi = a + b1 x1i + b2x2i + b3x3i + ε





Fri 18 Dec 2009 181626










Magnet Rural


Vacancy 163 -098(0012) (0017)

Decision adapt 089 080(0012) (0017)


Adj R Sq 211 150



Fri 18 Dec 2009 181626








Magnet

Honors IB IBS IBH


Vacancy 159 296 685 1029(0011) (0023) (0027) (0033)

Decision adapt 078 099 143 404(001) (0022) (0026) (0031)


Adj R Sq 262 221 520 592

Rural



Vacancy -184 -200 -128 068(0009) (0012) (0019) (002)

Decision adapt 007 -103 082 195(0009) (0011) (0018) (0019)


Adj R Sq 454 319 163 139




Fri 18 Dec 2009 181626


CONCLUSION






Fri 18 Dec 2009 181626







Magnet

Honors IB IBS IBH


Vacancy 433 633 917 351(0017) (0022) (0026) (0023)

Decision adapt 168 252 322 132(0016) (0021) (0025) (0022)


Adj R Sq 478 559 663 228

Rural



Vacancy -105 -019 -032(0018) (0018) (0016)

Decision adapt 037 133 306(0018) (0018) (0016)


Adj R Sq 130 118 478


options (p lt 10)


Fri 18 Dec 2009 181626








Fri 18 Dec 2009 181626



NOTES














Fri 18 Dec 2009 181626















Fri 18 Dec 2009 181626






Fri 18 Dec 2009 181626


PP

END

IX

Tab

leA

1D

efin

itio

ns

ofVa

riab

les

and

Para

met

ers

Des

crip

tion

Rela

tions

hip

toO

ther

Mod

elVa

riabl

esEq

nN

o

Abi

lity

Ab

ility

Inv

aria

ntpr

oper

tyof

each

stud

ent

Stan

dard

norm

alFi

xed

mod

elva

riabl

edi

strib

utio

nse

ta

stud

entrsquos

ldquocre

atio

nrdquo(i

ee

ntry

into

the

syst

em)

AA

chie

vem

ent

isre

late

dto

abili

tyM

ore

able

stud

ents

gene

rally

For

inco

min

gst

uden

tsan

dst

uden

tsin

thei

rfir

stye

ar

1ac

hiev

em

ore

inac

adem

icte

rms

Ther

eis

also

ara

ndom

com

pone

nt

a ic

t=1

=Ab

ility

i0

6+

ε

04

(ε~

N(0

1))

to

achi

evem

ent

Ach

ieve

men

tde

pend

sno

ton

lyon

abili

ty

but

onw

hat

the

stud

ents

have

lear

ned

over

the

cour

seof

thei

rhi

ghIn

subs

eque

ntye

ars

scho

oled

ucat

iona

lcar

eers

toth

atpo

int

a ic

t=

Abili

tyi

abw

t+

(1ndasha

bwt)

andash ict

-10

6+

ε

04

2

GG

rad

esar

em

appe

dfr

omth

eem

piric

algr

ade

dist

ribut

ions

for

each

g ic

t=

G(a

icit

rsquoabulli

ct)

3co

urse

inth

etw

osc

hool

sst

udie

don

the

basi

sof

the

rank

orde

rof

achi

evem

ent

Gis

am

appi

ngfu

nctio

nth

atre

turn

sth

eap

prop

riate

grad

efo

rth

est

uden

trsquospo

sitio

nin

the

rank

orde

r(b

yac

hiev

emen

t)fo

ra

give

nco

urse

ina

give

nsc

hool

RtR

ewar

dto

lera

nce

depe

nds

onpr

ior

perf

orm

ance

and

stud

entrsquos

succ

ess

rtit

=pe

rfit

(1

ndashadw

t)+

adap

t it

adw

t4

inad

aptin

gto

chan

ges

inst

anda

rds

resu

lting

from

upw

ard

ordo

wnw

ard

trac

km

oves

(ada

ptab

ility

)

Perf

Rel

ativ

ep

erfo

rman

ceca

ptur

esth

ede

gree

tow

hich

the

stud

ents

perf

it=

(gic

tndashgndash ibull

t)

(1ndashp

e)+

(gic

tndashgndash c

t)pe

5ex

ceed

ed(o

rno

t)th

eir

prio

rpe

rfor

man

cean

dth

eir

perf

orm

ance

rela

tive

toth

eir

cour

seco

hort

adap

tA

dap

tab

ility

The

degr

eeto

whi

chth

est

uden

trsquospe

rfor

man

cech

ange

sad

apt i

t=

perf

itndash

perf

it-1

6fr

omon

epe

riod

toth

ene

xtA

dow

nwar

dm

ove

shou

ldca

use

are

duct

ion

inpe

rfor

man

ceb

utth

em

ore

adap

tabl

est

uden

tw

illsu

ffer

alo

wer

drop

than

will

ale

ssad

apta

ble

one

Con

vers

ely

anad

apta

ble

stud

ent

will

not

doas

wel

lin

alo

wer

trac

kas

one

who

refu

ses

toch

ange

his

orhe

rst

anda

rds

just

beca

use

heor

she

has

mov

eddo

wn

atr




PP

END

IX

Tab

leA

1C

onti

nue

d

Des

crip

tion

Mod

elPa

ram

eter

s(E

quat

ions

24

and

5)

RT[a

b]

Rew

ard

tole

ran

ceth

resh

old

sA

nex

ogen

ous

para

met

erth

atse

tsth

ebo

unds

ofac

cept

able

educ

atio

nale

xper

ienc

eVa

lues

outs

ide

this

rang

etr

igge

rtr

ack

chan

ges

ais

the

valu

eof

rtdo

wn

bth

atof

rtup

Edu

catio

nale

xper

ienc

eva

lues

low

erth

anrt

dow

ntr

igge

ra

mov

eto

alo

wer

-tra

ckco

urse

Val

ues

high

erth

anrt

uptr

igge

ra

mov

eto

ahi

gher

-tra

ckco

urse

abw

tA

bili

tyw

eig

ht

Am

odel

para

met

erth

atad

just

sth

ede

gree

tow

hich

achi

evem

ent

isa

func

tion

ofra

wab

ility

and

how

muc

ha

func

tion

ofpr

ior

lear

ning

(ach

ieve

men

t)

adw

tA

dap

tati

onw

eig

ht

Am

odel

para

met

erad

just

ing

the

degr

eeto

whi

chad

apta

tion

mod

erat

esth

eim

pact

ofpe

rfor

man

ceco

mpa

rison

s(r

elat

ive

tose

lfan

dre

lativ

eto

peer

s)on

the

way

the

educ

atio

nale

xper

ienc

eis

perc

eive

dby

the

stud

ent

pePe

eref

fect

wei

gh

tA

mod

elpa

ram

eter

adju

stin

gth

eex

tent

tow

hich

perf

orm

ance

isju

dged

rela

tive

toa

stud

entrsquos

prio

rpe

rfor

man

ceas

oppo

sed

toa

stud

entrsquos

perf

orm

ance

rela

tive

tohe

ror

his

peer

s


Fri 18 Dec 2009 181626


REFERENCES
































Fri 18 Dec 2009 181626


































Fri 18 Dec 2009 181626






Fri 18 Dec 2009 181626


ble

2M

agn

etH

igh

Mat

hem

atic

smdashTr

ansi

tion

Prob

abili

tyM

atri

xof

Stud

ent

Mov

es

Des

tinat

ion

Stat

es

Tran

sien

tSt

ates

Exit

Stat

es

7th

Gra

de9

7

0

3

17

2Tr

ansf

er2

70

90

9

1

81

8

0

9

0

9

11O

utsi

deM

ath

0

2

02

9

7

66

Alg

ebra

IHon

ors

02

39

4

2

18

177

Geo

met

ryH

onor

s

5

8

22

20

55A

lgeb

raIi

Hon

ors

6

3

04

0

20

42

794

Func

tions

52

27

18

04

83D

iscr

ete

Mat

h

new

cour

se98

rsquoN

A

Geo

met

ryPr

e-Ib

09

8

2

1

011

5A

lgIi

ampTr

igPr

e-Ib

01

21

3

5

15

1

9

09

105

Func

tions

Sta

tsT

rigIb

75

02

0

21

40

744

Prec

alc

ampD

isc

Mat

hIb

1

00

23

Prec

alcu

lus

Ibs

03

8

2

15

34

Cal

culu

sIb

s

100

16

Prec

alc

ampTr

igIb

h

0

7

89

0

4

27A

dvC

alc

Ibh

1

00

18

Mov

esw

ithin

atr

ack

are

show

nin

the

bloc

kson

the

lead

ing

diag

onal

(ligh

tsh

adin

g)D

arke

rsh

adin

gin

dica

tes

repe

atin

gth

esa

me

cour

se

All

valu

esre

flect

the

ratio

ofst

uden

tsm

ovin

gfr

omth

eor

igin

stat

eto

the

dest

inat

ion

stat

eVa

lues

grea

ter

than

10

are

inbo

ldfo

nt

Algebra I Hon

Geometry Hon

Algebra Ii Hon

Functions

Discrete Math

Geometry Pre-Ib




Precalculus Ibs

Calculus Ibs


Adv Calc Ibh

Graduate

Outside Math

Leave School

Students


Origin State (1997)


Fri 18 Dec 2009 181626


METHODS





aict = 0 = Abilityi 06 + ε 04 (1)







Fri 18 Dec 2009 181626




Fri 18 Dec 2009 181626

















Fri 18 Dec 2009 181626














Fri 18 Dec 2009 181626














Fri 18 Dec 2009 181626











Fri 18 Dec 2009 181626











Fri 18 Dec 2009 181626











Fri 18 Dec 2009 181626



RESULTS





yi = a + b1 x1i + b2x2i + b3x3i + ε





Fri 18 Dec 2009 181626










Magnet Rural


Vacancy 163 -098(0012) (0017)

Decision adapt 089 080(0012) (0017)


Adj R Sq 211 150



Fri 18 Dec 2009 181626








Magnet

Honors IB IBS IBH


Vacancy 159 296 685 1029(0011) (0023) (0027) (0033)

Decision adapt 078 099 143 404(001) (0022) (0026) (0031)


Adj R Sq 262 221 520 592

Rural



Vacancy -184 -200 -128 068(0009) (0012) (0019) (002)

Decision adapt 007 -103 082 195(0009) (0011) (0018) (0019)


Adj R Sq 454 319 163 139




Fri 18 Dec 2009 181626


CONCLUSION






Fri 18 Dec 2009 181626







Magnet

Honors IB IBS IBH


Vacancy 433 633 917 351(0017) (0022) (0026) (0023)

Decision adapt 168 252 322 132(0016) (0021) (0025) (0022)


Adj R Sq 478 559 663 228

Rural



Vacancy -105 -019 -032(0018) (0018) (0016)

Decision adapt 037 133 306(0018) (0018) (0016)


Adj R Sq 130 118 478


options (p lt 10)


Fri 18 Dec 2009 181626








Fri 18 Dec 2009 181626



NOTES














Fri 18 Dec 2009 181626















Fri 18 Dec 2009 181626






Fri 18 Dec 2009 181626


PP

END

IX

Tab

leA

1D

efin

itio

ns

ofVa

riab

les

and

Para

met

ers

Des

crip

tion

Rela

tions

hip

toO

ther

Mod

elVa

riabl

esEq

nN

o

Abi

lity

Ab

ility

Inv

aria

ntpr

oper

tyof

each

stud

ent

Stan

dard

norm

alFi

xed

mod

elva

riabl

edi

strib

utio

nse

ta

stud

entrsquos

ldquocre

atio

nrdquo(i

ee

ntry

into

the

syst

em)

AA

chie

vem

ent

isre

late

dto

abili

tyM

ore

able

stud

ents

gene

rally

For

inco

min

gst

uden

tsan

dst

uden

tsin

thei

rfir

stye

ar

1ac

hiev

em

ore

inac

adem

icte

rms

Ther

eis

also

ara

ndom

com

pone

nt

a ic

t=1

=Ab

ility

i0

6+

ε

04

(ε~

N(0

1))

to

achi

evem

ent

Ach

ieve

men

tde

pend

sno

ton

lyon

abili

ty

but

onw

hat

the

stud

ents

have

lear

ned

over

the

cour

seof

thei

rhi

ghIn

subs

eque

ntye

ars

scho

oled

ucat

iona

lcar

eers

toth

atpo

int

a ic

t=

Abili

tyi

abw

t+

(1ndasha

bwt)

andash ict

-10

6+

ε

04

2

GG

rad

esar

em

appe

dfr

omth

eem

piric

algr

ade

dist

ribut

ions

for

each

g ic

t=

G(a

icit

rsquoabulli

ct)

3co

urse

inth

etw

osc

hool

sst

udie

don

the

basi

sof

the

rank

orde

rof

achi

evem

ent

Gis

am

appi

ngfu

nctio

nth

atre

turn

sth

eap

prop

riate

grad

efo

rth

est

uden

trsquospo

sitio

nin

the

rank

orde

r(b

yac

hiev

emen

t)fo

ra

give

nco

urse

ina

give

nsc

hool

RtR

ewar

dto

lera

nce

depe

nds

onpr

ior

perf

orm

ance

and

stud

entrsquos

succ

ess

rtit

=pe

rfit

(1

ndashadw

t)+

adap

t it

adw

t4

inad

aptin

gto

chan

ges

inst

anda

rds

resu

lting

from

upw

ard

ordo

wnw

ard

trac

km

oves

(ada

ptab

ility

)

Perf

Rel

ativ

ep

erfo

rman

ceca

ptur

esth

ede

gree

tow

hich

the

stud

ents

perf

it=

(gic

tndashgndash ibull

t)

(1ndashp

e)+

(gic

tndashgndash c

t)pe

5ex

ceed

ed(o

rno

t)th

eir

prio

rpe

rfor

man

cean

dth

eir

perf

orm

ance

rela

tive

toth

eir

cour

seco

hort

adap

tA

dap

tab

ility

The

degr

eeto

whi

chth

est

uden

trsquospe

rfor

man

cech

ange

sad

apt i

t=

perf

itndash

perf

it-1

6fr

omon

epe

riod

toth

ene

xtA

dow

nwar

dm

ove

shou

ldca

use

are

duct

ion

inpe

rfor

man

ceb

utth

em

ore

adap

tabl

est

uden

tw

illsu

ffer

alo

wer

drop

than

will

ale

ssad

apta

ble

one

Con

vers

ely

anad

apta

ble

stud

ent

will

not

doas

wel

lin

alo

wer

trac

kas

one

who

refu

ses

toch

ange

his

orhe

rst

anda

rds

just

beca

use

heor

she

has

mov

eddo

wn

atr




PP

END

IX

Tab

leA

1C

onti

nue

d

Des

crip

tion

Mod

elPa

ram

eter

s(E

quat

ions

24

and

5)

RT[a

b]

Rew

ard

tole

ran

ceth

resh

old

sA

nex

ogen

ous

para

met

erth

atse

tsth

ebo

unds

ofac

cept

able

educ

atio

nale

xper

ienc

eVa

lues

outs

ide

this

rang

etr

igge

rtr

ack

chan

ges

ais

the

valu

eof

rtdo

wn

bth

atof

rtup

Edu

catio

nale

xper

ienc

eva

lues

low

erth

anrt

dow

ntr

igge

ra

mov

eto

alo

wer

-tra

ckco

urse

Val

ues

high

erth

anrt

uptr

igge

ra

mov

eto

ahi

gher

-tra

ckco

urse

abw

tA

bili

tyw

eig

ht

Am

odel

para

met

erth

atad

just

sth

ede

gree

tow

hich

achi

evem

ent

isa

func

tion

ofra

wab

ility

and

how

muc

ha

func

tion

ofpr

ior

lear

ning

(ach

ieve

men

t)

adw

tA

dap

tati

onw

eig

ht

Am

odel

para

met

erad

just

ing

the

degr

eeto

whi

chad

apta

tion

mod

erat

esth

eim

pact

ofpe

rfor

man

ceco

mpa

rison

s(r

elat

ive

tose

lfan

dre

lativ

eto

peer

s)on

the

way

the

educ

atio

nale

xper

ienc

eis

perc

eive

dby

the

stud

ent

pePe

eref

fect

wei

gh

tA

mod

elpa

ram

eter

adju

stin

gth

eex

tent

tow

hich

perf

orm

ance

isju

dged

rela

tive

toa

stud

entrsquos

prio

rpe

rfor

man

ceas

oppo

sed

toa

stud

entrsquos

perf

orm

ance

rela

tive

tohe

ror

his

peer

s


Fri 18 Dec 2009 181626


REFERENCES
































Fri 18 Dec 2009 181626


































Fri 18 Dec 2009 181626






Fri 18 Dec 2009 181626


METHODS





aict = 0 = Abilityi 06 + ε 04 (1)







Fri 18 Dec 2009 181626




Fri 18 Dec 2009 181626

















Fri 18 Dec 2009 181626














Fri 18 Dec 2009 181626














Fri 18 Dec 2009 181626











Fri 18 Dec 2009 181626











Fri 18 Dec 2009 181626











Fri 18 Dec 2009 181626



RESULTS





yi = a + b1 x1i + b2x2i + b3x3i + ε





Fri 18 Dec 2009 181626










Magnet Rural


Vacancy 163 -098(0012) (0017)

Decision adapt 089 080(0012) (0017)


Adj R Sq 211 150



Fri 18 Dec 2009 181626








Magnet

Honors IB IBS IBH


Vacancy 159 296 685 1029(0011) (0023) (0027) (0033)

Decision adapt 078 099 143 404(001) (0022) (0026) (0031)


Adj R Sq 262 221 520 592

Rural



Vacancy -184 -200 -128 068(0009) (0012) (0019) (002)

Decision adapt 007 -103 082 195(0009) (0011) (0018) (0019)


Adj R Sq 454 319 163 139




Fri 18 Dec 2009 181626


CONCLUSION






Fri 18 Dec 2009 181626







Magnet

Honors IB IBS IBH


Vacancy 433 633 917 351(0017) (0022) (0026) (0023)

Decision adapt 168 252 322 132(0016) (0021) (0025) (0022)


Adj R Sq 478 559 663 228

Rural



Vacancy -105 -019 -032(0018) (0018) (0016)

Decision adapt 037 133 306(0018) (0018) (0016)


Adj R Sq 130 118 478


options (p lt 10)


Fri 18 Dec 2009 181626








Fri 18 Dec 2009 181626



NOTES














Fri 18 Dec 2009 181626















Fri 18 Dec 2009 181626






Fri 18 Dec 2009 181626


PP

END

IX

Tab

leA

1D

efin

itio

ns

ofVa

riab

les

and

Para

met

ers

Des

crip

tion

Rela

tions

hip

toO

ther

Mod

elVa

riabl

esEq

nN

o

Abi

lity

Ab

ility

Inv

aria

ntpr

oper

tyof

each

stud

ent

Stan

dard

norm

alFi

xed

mod

elva

riabl

edi

strib

utio

nse

ta

stud

entrsquos

ldquocre

atio

nrdquo(i

ee

ntry

into

the

syst

em)

AA

chie

vem

ent

isre

late

dto

abili

tyM

ore

able

stud

ents

gene

rally

For

inco

min

gst

uden

tsan

dst

uden

tsin

thei

rfir

stye

ar

1ac

hiev

em

ore

inac

adem

icte

rms

Ther

eis

also

ara

ndom

com

pone

nt

a ic

t=1

=Ab

ility

i0

6+

ε

04

(ε~

N(0

1))

to

achi

evem

ent

Ach

ieve

men

tde

pend

sno

ton

lyon

abili

ty

but

onw

hat

the

stud

ents

have

lear

ned

over

the

cour

seof

thei

rhi

ghIn

subs

eque

ntye

ars

scho

oled

ucat

iona

lcar

eers

toth

atpo

int

a ic

t=

Abili

tyi

abw

t+

(1ndasha

bwt)

andash ict

-10

6+

ε

04

2

GG

rad

esar

em

appe

dfr

omth

eem

piric

algr

ade

dist

ribut

ions

for

each

g ic

t=

G(a

icit

rsquoabulli

ct)

3co

urse

inth

etw

osc

hool

sst

udie

don

the

basi

sof

the

rank

orde

rof

achi

evem

ent

Gis

am

appi

ngfu

nctio

nth

atre

turn

sth

eap

prop

riate

grad

efo

rth

est

uden

trsquospo

sitio

nin

the

rank

orde

r(b

yac

hiev

emen

t)fo

ra

give

nco

urse

ina

give

nsc

hool

RtR

ewar

dto

lera

nce

depe

nds

onpr

ior

perf

orm

ance

and

stud

entrsquos

succ

ess

rtit

=pe

rfit

(1

ndashadw

t)+

adap

t it

adw

t4

inad

aptin

gto

chan

ges

inst

anda

rds

resu

lting

from

upw

ard

ordo

wnw

ard

trac

km

oves

(ada

ptab

ility

)

Perf

Rel

ativ

ep

erfo

rman

ceca

ptur

esth

ede

gree

tow

hich

the

stud

ents

perf

it=

(gic

tndashgndash ibull

t)

(1ndashp

e)+

(gic

tndashgndash c

t)pe

5ex

ceed

ed(o

rno

t)th

eir

prio

rpe

rfor

man

cean

dth

eir

perf

orm

ance

rela

tive

toth

eir

cour

seco

hort

adap

tA

dap

tab

ility

The

degr

eeto

whi

chth

est

uden

trsquospe

rfor

man

cech

ange

sad

apt i

t=

perf

itndash

perf

it-1

6fr

omon

epe

riod

toth

ene

xtA

dow

nwar

dm

ove

shou

ldca

use

are

duct

ion

inpe

rfor

man

ceb

utth

em

ore

adap

tabl

est

uden

tw

illsu

ffer

alo

wer

drop

than

will

ale

ssad

apta

ble

one

Con

vers

ely

anad

apta

ble

stud

ent

will

not

doas

wel

lin

alo

wer

trac

kas

one

who

refu

ses

toch

ange

his

orhe

rst

anda

rds

just

beca

use

heor

she

has

mov

eddo

wn

atr




PP

END

IX

Tab

leA

1C

onti

nue

d

Des

crip

tion

Mod

elPa

ram

eter

s(E

quat

ions

24

and

5)

RT[a

b]

Rew

ard

tole

ran

ceth

resh

old

sA

nex

ogen

ous

para

met

erth

atse

tsth

ebo

unds

ofac

cept

able

educ

atio

nale

xper

ienc

eVa

lues

outs

ide

this

rang

etr

igge

rtr

ack

chan

ges

ais

the

valu

eof

rtdo

wn

bth

atof

rtup

Edu

catio

nale

xper

ienc

eva

lues

low

erth

anrt

dow

ntr

igge

ra

mov

eto

alo

wer

-tra

ckco

urse

Val

ues

high

erth

anrt

uptr

igge

ra

mov

eto

ahi

gher

-tra

ckco

urse

abw

tA

bili

tyw

eig

ht

Am

odel

para

met

erth

atad

just

sth

ede

gree

tow

hich

achi

evem

ent

isa

func

tion

ofra

wab

ility

and

how

muc

ha

func

tion

ofpr

ior

lear

ning

(ach

ieve

men

t)

adw

tA

dap

tati

onw

eig

ht

Am

odel

para

met

erad

just

ing

the

degr

eeto

whi

chad

apta

tion

mod

erat

esth

eim

pact

ofpe

rfor

man

ceco

mpa

rison

s(r

elat

ive

tose

lfan

dre

lativ

eto

peer

s)on

the

way

the

educ

atio

nale

xper

ienc

eis

perc

eive

dby

the

stud

ent

pePe

eref

fect

wei

gh

tA

mod

elpa

ram

eter

adju

stin

gth

eex

tent

tow

hich

perf

orm

ance

isju

dged

rela

tive

toa

stud

entrsquos

prio

rpe

rfor

man

ceas

oppo

sed

toa

stud

entrsquos

perf

orm

ance

rela

tive

tohe

ror

his

peer

s


Fri 18 Dec 2009 181626


REFERENCES
































Fri 18 Dec 2009 181626


































Fri 18 Dec 2009 181626






Fri 18 Dec 2009 181626




Fri 18 Dec 2009 181626

















Fri 18 Dec 2009 181626














Fri 18 Dec 2009 181626














Fri 18 Dec 2009 181626











Fri 18 Dec 2009 181626











Fri 18 Dec 2009 181626











Fri 18 Dec 2009 181626



RESULTS





yi = a + b1 x1i + b2x2i + b3x3i + ε





Fri 18 Dec 2009 181626










Magnet Rural


Vacancy 163 -098(0012) (0017)

Decision adapt 089 080(0012) (0017)


Adj R Sq 211 150



Fri 18 Dec 2009 181626








Magnet

Honors IB IBS IBH


Vacancy 159 296 685 1029(0011) (0023) (0027) (0033)

Decision adapt 078 099 143 404(001) (0022) (0026) (0031)


Adj R Sq 262 221 520 592

Rural



Vacancy -184 -200 -128 068(0009) (0012) (0019) (002)

Decision adapt 007 -103 082 195(0009) (0011) (0018) (0019)


Adj R Sq 454 319 163 139




Fri 18 Dec 2009 181626


CONCLUSION






Fri 18 Dec 2009 181626







Magnet

Honors IB IBS IBH


Vacancy 433 633 917 351(0017) (0022) (0026) (0023)

Decision adapt 168 252 322 132(0016) (0021) (0025) (0022)


Adj R Sq 478 559 663 228

Rural



Vacancy -105 -019 -032(0018) (0018) (0016)

Decision adapt 037 133 306(0018) (0018) (0016)


Adj R Sq 130 118 478


options (p lt 10)


Fri 18 Dec 2009 181626








Fri 18 Dec 2009 181626



NOTES














Fri 18 Dec 2009 181626















Fri 18 Dec 2009 181626






Fri 18 Dec 2009 181626


PP

END

IX

Tab

leA

1D

efin

itio

ns

ofVa

riab

les

and

Para

met

ers

Des

crip

tion

Rela

tions

hip

toO

ther

Mod

elVa

riabl

esEq

nN

o

Abi

lity

Ab

ility

Inv

aria

ntpr

oper

tyof

each

stud

ent

Stan

dard

norm

alFi

xed

mod

elva

riabl

edi

strib

utio

nse

ta

stud

entrsquos

ldquocre

atio

nrdquo(i

ee

ntry

into

the

syst

em)

AA

chie

vem

ent

isre

late

dto

abili

tyM

ore

able

stud

ents

gene

rally

For

inco

min

gst

uden

tsan

dst

uden

tsin

thei

rfir

stye

ar

1ac

hiev

em

ore

inac

adem

icte

rms

Ther

eis

also

ara

ndom

com

pone

nt

a ic

t=1

=Ab

ility

i0

6+

ε

04

(ε~

N(0

1))

to

achi

evem

ent

Ach

ieve

men

tde

pend

sno

ton

lyon

abili

ty

but

onw

hat

the

stud

ents

have

lear

ned

over

the

cour

seof

thei

rhi

ghIn

subs

eque

ntye

ars

scho

oled

ucat

iona

lcar

eers

toth

atpo

int

a ic

t=

Abili

tyi

abw

t+

(1ndasha

bwt)

andash ict

-10

6+

ε

04

2

GG

rad

esar

em

appe

dfr

omth

eem

piric

algr

ade

dist

ribut

ions

for

each

g ic

t=

G(a

icit

rsquoabulli

ct)

3co

urse

inth

etw

osc

hool

sst

udie

don

the

basi

sof

the

rank

orde

rof

achi

evem

ent

Gis

am

appi

ngfu

nctio

nth

atre

turn

sth

eap

prop

riate

grad

efo

rth

est

uden

trsquospo

sitio

nin

the

rank

orde

r(b

yac

hiev

emen

t)fo

ra

give

nco

urse

ina

give

nsc

hool

RtR

ewar

dto

lera

nce

depe

nds

onpr

ior

perf

orm

ance

and

stud

entrsquos

succ

ess

rtit

=pe

rfit

(1

ndashadw

t)+

adap

t it

adw

t4

inad

aptin

gto

chan

ges

inst

anda

rds

resu

lting

from

upw

ard

ordo

wnw

ard

trac

km

oves

(ada

ptab

ility

)

Perf

Rel

ativ

ep

erfo

rman

ceca

ptur

esth

ede

gree

tow

hich

the

stud

ents

perf

it=

(gic

tndashgndash ibull

t)

(1ndashp

e)+

(gic

tndashgndash c

t)pe

5ex

ceed

ed(o

rno

t)th

eir

prio

rpe

rfor

man

cean

dth

eir

perf

orm

ance

rela

tive

toth

eir

cour

seco

hort

adap

tA

dap

tab

ility

The

degr

eeto

whi

chth

est

uden

trsquospe

rfor

man

cech

ange

sad

apt i

t=

perf

itndash

perf

it-1

6fr

omon

epe

riod

toth

ene

xtA

dow

nwar

dm

ove

shou

ldca

use

are

duct

ion

inpe

rfor

man

ceb

utth

em

ore

adap

tabl

est

uden

tw

illsu

ffer

alo

wer

drop

than

will

ale

ssad

apta

ble

one

Con

vers

ely

anad

apta

ble

stud

ent

will

not

doas

wel

lin

alo

wer

trac

kas

one

who

refu

ses

toch

ange

his

orhe

rst

anda

rds

just

beca

use

heor

she

has

mov

eddo

wn

atr




PP

END

IX

Tab

leA

1C

onti

nue

d

Des

crip

tion

Mod

elPa

ram

eter

s(E

quat

ions

24

and

5)

RT[a

b]

Rew

ard

tole

ran

ceth

resh

old

sA

nex

ogen

ous

para

met

erth

atse

tsth

ebo

unds

ofac

cept

able

educ

atio

nale

xper

ienc

eVa

lues

outs

ide

this

rang

etr

igge

rtr

ack

chan

ges

ais

the

valu

eof

rtdo

wn

bth

atof

rtup

Edu

catio

nale

xper

ienc

eva

lues

low

erth

anrt

dow

ntr

igge

ra

mov

eto

alo

wer

-tra

ckco

urse

Val

ues

high

erth

anrt

uptr

igge

ra

mov

eto

ahi

gher

-tra

ckco

urse

abw

tA

bili

tyw

eig

ht

Am

odel

para

met

erth

atad

just

sth

ede

gree

tow

hich

achi

evem

ent

isa

func

tion

ofra

wab

ility

and

how

muc

ha

func

tion

ofpr

ior

lear

ning

(ach

ieve

men

t)

adw

tA

dap

tati

onw

eig

ht

Am

odel

para

met

erad

just

ing

the

degr

eeto

whi

chad

apta

tion

mod

erat

esth

eim

pact

ofpe

rfor

man

ceco

mpa

rison

s(r

elat

ive

tose

lfan

dre

lativ

eto

peer

s)on

the

way

the

educ

atio

nale

xper

ienc

eis

perc

eive

dby

the

stud

ent

pePe

eref

fect

wei

gh

tA

mod

elpa

ram

eter

adju

stin

gth

eex

tent

tow

hich

perf

orm

ance

isju

dged

rela

tive

toa

stud

entrsquos

prio

rpe

rfor

man

ceas

oppo

sed

toa

stud

entrsquos

perf

orm

ance

rela

tive

tohe

ror

his

peer

s


Fri 18 Dec 2009 181626


REFERENCES
































Fri 18 Dec 2009 181626


































Fri 18 Dec 2009 181626






Fri 18 Dec 2009 181626

















Fri 18 Dec 2009 181626














Fri 18 Dec 2009 181626














Fri 18 Dec 2009 181626











Fri 18 Dec 2009 181626











Fri 18 Dec 2009 181626











Fri 18 Dec 2009 181626



RESULTS





yi = a + b1 x1i + b2x2i + b3x3i + ε





Fri 18 Dec 2009 181626










Magnet Rural


Vacancy 163 -098(0012) (0017)

Decision adapt 089 080(0012) (0017)


Adj R Sq 211 150



Fri 18 Dec 2009 181626








Magnet

Honors IB IBS IBH


Vacancy 159 296 685 1029(0011) (0023) (0027) (0033)

Decision adapt 078 099 143 404(001) (0022) (0026) (0031)


Adj R Sq 262 221 520 592

Rural



Vacancy -184 -200 -128 068(0009) (0012) (0019) (002)

Decision adapt 007 -103 082 195(0009) (0011) (0018) (0019)


Adj R Sq 454 319 163 139




Fri 18 Dec 2009 181626


CONCLUSION






Fri 18 Dec 2009 181626







Magnet

Honors IB IBS IBH


Vacancy 433 633 917 351(0017) (0022) (0026) (0023)

Decision adapt 168 252 322 132(0016) (0021) (0025) (0022)


Adj R Sq 478 559 663 228

Rural



Vacancy -105 -019 -032(0018) (0018) (0016)

Decision adapt 037 133 306(0018) (0018) (0016)


Adj R Sq 130 118 478


options (p lt 10)


Fri 18 Dec 2009 181626








Fri 18 Dec 2009 181626



NOTES














Fri 18 Dec 2009 181626















Fri 18 Dec 2009 181626






Fri 18 Dec 2009 181626


PP

END

IX

Tab

leA

1D

efin

itio

ns

ofVa

riab

les

and

Para

met

ers

Des

crip

tion

Rela

tions

hip

toO

ther

Mod

elVa

riabl

esEq

nN

o

Abi

lity

Ab

ility

Inv

aria

ntpr

oper

tyof

each

stud

ent

Stan

dard

norm

alFi

xed

mod

elva

riabl

edi

strib

utio

nse

ta

stud

entrsquos

ldquocre

atio

nrdquo(i

ee

ntry

into

the

syst

em)

AA

chie

vem

ent

isre

late

dto

abili

tyM

ore

able

stud

ents

gene

rally

For

inco

min

gst

uden

tsan

dst

uden

tsin

thei

rfir

stye

ar

1ac

hiev

em

ore

inac

adem

icte

rms

Ther

eis

also

ara

ndom

com

pone

nt

a ic

t=1

=Ab

ility

i0

6+

ε

04

(ε~

N(0

1))

to

achi

evem

ent

Ach

ieve

men

tde

pend

sno

ton

lyon

abili

ty

but

onw

hat

the

stud

ents

have

lear

ned

over

the

cour

seof

thei

rhi

ghIn

subs

eque

ntye

ars

scho

oled

ucat

iona

lcar

eers

toth

atpo

int

a ic

t=

Abili

tyi

abw

t+

(1ndasha

bwt)

andash ict

-10

6+

ε

04

2

GG

rad

esar

em

appe

dfr

omth

eem

piric

algr

ade

dist

ribut

ions

for

each

g ic

t=

G(a

icit

rsquoabulli

ct)

3co

urse

inth

etw

osc

hool

sst

udie

don

the

basi

sof

the

rank

orde

rof

achi

evem

ent

Gis

am

appi

ngfu

nctio

nth

atre

turn

sth

eap

prop

riate

grad

efo

rth

est

uden

trsquospo

sitio

nin

the

rank

orde

r(b

yac

hiev

emen

t)fo

ra

give

nco

urse

ina

give

nsc

hool

RtR

ewar

dto

lera

nce

depe

nds

onpr

ior

perf

orm

ance

and

stud

entrsquos

succ

ess

rtit

=pe

rfit

(1

ndashadw

t)+

adap

t it

adw

t4

inad

aptin

gto

chan

ges

inst

anda

rds

resu

lting

from

upw

ard

ordo

wnw

ard

trac

km

oves

(ada

ptab

ility

)

Perf

Rel

ativ

ep

erfo

rman

ceca

ptur

esth

ede

gree

tow

hich

the

stud

ents

perf

it=

(gic

tndashgndash ibull

t)

(1ndashp

e)+

(gic

tndashgndash c

t)pe

5ex

ceed

ed(o

rno

t)th

eir

prio

rpe

rfor

man

cean

dth

eir

perf

orm

ance

rela

tive

toth

eir

cour

seco

hort

adap

tA

dap

tab

ility

The

degr

eeto

whi

chth

est

uden

trsquospe

rfor

man

cech

ange

sad

apt i

t=

perf

itndash

perf

it-1

6fr

omon

epe

riod

toth

ene

xtA

dow

nwar

dm

ove

shou

ldca

use

are

duct

ion

inpe

rfor

man

ceb

utth

em

ore

adap

tabl

est

uden

tw

illsu

ffer

alo

wer

drop

than

will

ale

ssad

apta

ble

one

Con

vers

ely

anad

apta

ble

stud

ent

will

not

doas

wel

lin

alo

wer

trac

kas

one

who

refu

ses

toch

ange

his

orhe

rst

anda

rds

just

beca

use

heor

she

has

mov

eddo

wn

atr




PP

END

IX

Tab

leA

1C

onti

nue

d

Des

crip

tion

Mod

elPa

ram

eter

s(E

quat

ions

24

and

5)

RT[a

b]

Rew

ard

tole

ran

ceth

resh

old

sA

nex

ogen

ous

para

met

erth

atse

tsth

ebo

unds

ofac

cept

able

educ

atio

nale

xper

ienc

eVa

lues

outs

ide

this

rang

etr

igge

rtr

ack

chan

ges

ais

the

valu

eof

rtdo

wn

bth

atof

rtup

Edu

catio

nale

xper

ienc

eva

lues

low

erth

anrt

dow

ntr

igge

ra

mov

eto

alo

wer

-tra

ckco

urse

Val

ues

high

erth

anrt

uptr

igge

ra

mov

eto

ahi

gher

-tra

ckco

urse

abw

tA

bili

tyw

eig

ht

Am

odel

para

met

erth

atad

just

sth

ede

gree

tow

hich

achi

evem

ent

isa

func

tion

ofra

wab

ility

and

how

muc

ha

func

tion

ofpr

ior

lear

ning

(ach

ieve

men

t)

adw

tA

dap

tati

onw

eig

ht

Am

odel

para

met

erad

just

ing

the

degr

eeto

whi

chad

apta

tion

mod

erat

esth

eim

pact

ofpe

rfor

man

ceco

mpa

rison

s(r

elat

ive

tose

lfan

dre

lativ

eto

peer

s)on

the

way

the

educ

atio

nale

xper

ienc

eis

perc

eive

dby

the

stud

ent

pePe

eref

fect

wei

gh

tA

mod

elpa

ram

eter

adju

stin

gth

eex

tent

tow

hich

perf

orm

ance

isju

dged

rela

tive

toa

stud

entrsquos

prio

rpe

rfor

man

ceas

oppo

sed

toa

stud

entrsquos

perf

orm

ance

rela

tive

tohe

ror

his

peer

s


Fri 18 Dec 2009 181626


REFERENCES
































Fri 18 Dec 2009 181626


































Fri 18 Dec 2009 181626






Fri 18 Dec 2009 181626














Fri 18 Dec 2009 181626














Fri 18 Dec 2009 181626











Fri 18 Dec 2009 181626











Fri 18 Dec 2009 181626











Fri 18 Dec 2009 181626



RESULTS





yi = a + b1 x1i + b2x2i + b3x3i + ε





Fri 18 Dec 2009 181626










Magnet Rural


Vacancy 163 -098(0012) (0017)

Decision adapt 089 080(0012) (0017)


Adj R Sq 211 150



Fri 18 Dec 2009 181626








Magnet

Honors IB IBS IBH


Vacancy 159 296 685 1029(0011) (0023) (0027) (0033)

Decision adapt 078 099 143 404(001) (0022) (0026) (0031)


Adj R Sq 262 221 520 592

Rural



Vacancy -184 -200 -128 068(0009) (0012) (0019) (002)

Decision adapt 007 -103 082 195(0009) (0011) (0018) (0019)


Adj R Sq 454 319 163 139




Fri 18 Dec 2009 181626


CONCLUSION






Fri 18 Dec 2009 181626







Magnet

Honors IB IBS IBH


Vacancy 433 633 917 351(0017) (0022) (0026) (0023)

Decision adapt 168 252 322 132(0016) (0021) (0025) (0022)


Adj R Sq 478 559 663 228

Rural



Vacancy -105 -019 -032(0018) (0018) (0016)

Decision adapt 037 133 306(0018) (0018) (0016)


Adj R Sq 130 118 478


options (p lt 10)


Fri 18 Dec 2009 181626








Fri 18 Dec 2009 181626



NOTES














Fri 18 Dec 2009 181626















Fri 18 Dec 2009 181626






Fri 18 Dec 2009 181626


PP

END

IX

Tab

leA

1D

efin

itio

ns

ofVa

riab

les

and

Para

met

ers

Des

crip

tion

Rela

tions

hip

toO

ther

Mod

elVa

riabl

esEq

nN

o

Abi

lity

Ab

ility

Inv

aria

ntpr

oper

tyof

each

stud

ent

Stan

dard

norm

alFi

xed

mod

elva

riabl

edi

strib

utio

nse

ta

stud

entrsquos

ldquocre

atio

nrdquo(i

ee

ntry

into

the

syst

em)

AA

chie

vem

ent

isre

late

dto

abili

tyM

ore

able

stud

ents

gene

rally

For

inco

min

gst

uden

tsan

dst

uden

tsin

thei

rfir

stye

ar

1ac

hiev

em

ore

inac

adem

icte

rms

Ther

eis

also

ara

ndom

com

pone

nt

a ic

t=1

=Ab

ility

i0

6+

ε

04

(ε~

N(0

1))

to

achi

evem

ent

Ach

ieve

men

tde

pend

sno

ton

lyon

abili

ty

but

onw

hat

the

stud

ents

have

lear

ned

over

the

cour

seof

thei

rhi

ghIn

subs

eque

ntye

ars

scho

oled

ucat

iona

lcar

eers

toth

atpo

int

a ic

t=

Abili

tyi

abw

t+

(1ndasha

bwt)

andash ict

-10

6+

ε

04

2

GG

rad

esar

em

appe

dfr

omth

eem

piric

algr

ade

dist

ribut

ions

for

each

g ic

t=

G(a

icit

rsquoabulli

ct)

3co

urse

inth

etw

osc

hool

sst

udie

don

the

basi

sof

the

rank

orde

rof

achi

evem

ent

Gis

am

appi

ngfu

nctio

nth

atre

turn

sth

eap

prop

riate

grad

efo

rth

est

uden

trsquospo

sitio

nin

the

rank

orde

r(b

yac

hiev

emen

t)fo

ra

give

nco

urse

ina

give

nsc

hool

RtR

ewar

dto

lera

nce

depe

nds

onpr

ior

perf

orm

ance

and

stud

entrsquos

succ

ess

rtit

=pe

rfit

(1

ndashadw

t)+

adap

t it

adw

t4

inad

aptin

gto

chan

ges

inst

anda

rds

resu

lting

from

upw

ard

ordo

wnw

ard

trac

km

oves

(ada

ptab

ility

)

Perf

Rel

ativ

ep

erfo

rman

ceca

ptur

esth

ede

gree

tow

hich

the

stud

ents

perf

it=

(gic

tndashgndash ibull

t)

(1ndashp

e)+

(gic

tndashgndash c

t)pe

5ex

ceed

ed(o

rno

t)th

eir

prio

rpe

rfor

man

cean

dth

eir

perf

orm

ance

rela

tive

toth

eir

cour

seco

hort

adap

tA

dap

tab

ility

The

degr

eeto

whi

chth

est

uden

trsquospe

rfor

man

cech

ange

sad

apt i

t=

perf

itndash

perf

it-1

6fr

omon

epe

riod

toth

ene

xtA

dow

nwar

dm

ove

shou

ldca

use

are

duct

ion

inpe

rfor

man

ceb

utth

em

ore

adap

tabl

est

uden

tw

illsu

ffer

alo

wer

drop

than

will

ale

ssad

apta

ble

one

Con

vers

ely

anad

apta

ble

stud

ent

will

not

doas

wel

lin

alo

wer

trac

kas

one

who

refu

ses

toch

ange

his

orhe

rst

anda

rds

just

beca

use

heor

she

has

mov

eddo

wn

atr




PP

END

IX

Tab

leA

1C

onti

nue

d

Des

crip

tion

Mod

elPa

ram

eter

s(E

quat

ions

24

and

5)

RT[a

b]

Rew

ard

tole

ran

ceth

resh

old

sA

nex

ogen

ous

para

met

erth

atse

tsth

ebo

unds

ofac

cept

able

educ

atio

nale

xper

ienc

eVa

lues

outs

ide

this

rang

etr

igge

rtr

ack

chan

ges

ais

the

valu

eof

rtdo

wn

bth

atof

rtup

Edu

catio

nale

xper

ienc

eva

lues

low

erth

anrt

dow

ntr

igge

ra

mov

eto

alo

wer

-tra

ckco

urse

Val

ues

high

erth

anrt

uptr

igge

ra

mov

eto

ahi

gher

-tra

ckco

urse

abw

tA

bili

tyw

eig

ht

Am

odel

para

met

erth

atad

just

sth

ede

gree

tow

hich

achi

evem

ent

isa

func

tion

ofra

wab

ility

and

how

muc

ha

func

tion

ofpr

ior

lear

ning

(ach

ieve

men

t)

adw

tA

dap

tati

onw

eig

ht

Am

odel

para

met

erad

just

ing

the

degr

eeto

whi

chad

apta

tion

mod

erat

esth

eim

pact

ofpe

rfor

man

ceco

mpa

rison

s(r

elat

ive

tose

lfan

dre

lativ

eto

peer

s)on

the

way

the

educ

atio

nale

xper

ienc

eis

perc

eive

dby

the

stud

ent

pePe

eref

fect

wei

gh

tA

mod

elpa

ram

eter

adju

stin

gth

eex

tent

tow

hich

perf

orm

ance

isju

dged

rela

tive

toa

stud

entrsquos

prio

rpe

rfor

man

ceas

oppo

sed

toa

stud

entrsquos

perf

orm

ance

rela

tive

tohe

ror

his

peer

s


Fri 18 Dec 2009 181626


REFERENCES
































Fri 18 Dec 2009 181626


































Fri 18 Dec 2009 181626






Fri 18 Dec 2009 181626














Fri 18 Dec 2009 181626











Fri 18 Dec 2009 181626











Fri 18 Dec 2009 181626











Fri 18 Dec 2009 181626



RESULTS





yi = a + b1 x1i + b2x2i + b3x3i + ε





Fri 18 Dec 2009 181626










Magnet Rural


Vacancy 163 -098(0012) (0017)

Decision adapt 089 080(0012) (0017)


Adj R Sq 211 150



Fri 18 Dec 2009 181626








Magnet

Honors IB IBS IBH


Vacancy 159 296 685 1029(0011) (0023) (0027) (0033)

Decision adapt 078 099 143 404(001) (0022) (0026) (0031)


Adj R Sq 262 221 520 592

Rural



Vacancy -184 -200 -128 068(0009) (0012) (0019) (002)

Decision adapt 007 -103 082 195(0009) (0011) (0018) (0019)


Adj R Sq 454 319 163 139




Fri 18 Dec 2009 181626


CONCLUSION






Fri 18 Dec 2009 181626







Magnet

Honors IB IBS IBH


Vacancy 433 633 917 351(0017) (0022) (0026) (0023)

Decision adapt 168 252 322 132(0016) (0021) (0025) (0022)


Adj R Sq 478 559 663 228

Rural



Vacancy -105 -019 -032(0018) (0018) (0016)

Decision adapt 037 133 306(0018) (0018) (0016)


Adj R Sq 130 118 478


options (p lt 10)


Fri 18 Dec 2009 181626








Fri 18 Dec 2009 181626



NOTES














Fri 18 Dec 2009 181626















Fri 18 Dec 2009 181626






Fri 18 Dec 2009 181626


PP

END

IX

Tab

leA

1D

efin

itio

ns

ofVa

riab

les

and

Para

met

ers

Des

crip

tion

Rela

tions

hip

toO

ther

Mod

elVa

riabl

esEq

nN

o

Abi

lity

Ab

ility

Inv

aria

ntpr

oper

tyof

each

stud

ent

Stan

dard

norm

alFi

xed

mod

elva

riabl

edi

strib

utio

nse

ta

stud

entrsquos

ldquocre

atio

nrdquo(i

ee

ntry

into

the

syst

em)

AA

chie

vem

ent

isre

late

dto

abili

tyM

ore

able

stud

ents

gene

rally

For

inco

min

gst

uden

tsan

dst

uden

tsin

thei

rfir

stye

ar

1ac

hiev

em

ore

inac

adem

icte

rms

Ther

eis

also

ara

ndom

com

pone

nt

a ic

t=1

=Ab

ility

i0

6+

ε

04

(ε~

N(0

1))

to

achi

evem

ent

Ach

ieve

men

tde

pend

sno

ton

lyon

abili

ty

but

onw

hat

the

stud

ents

have

lear

ned

over

the

cour

seof

thei

rhi

ghIn

subs

eque

ntye

ars

scho

oled

ucat

iona

lcar

eers

toth

atpo

int

a ic

t=

Abili

tyi

abw

t+

(1ndasha

bwt)

andash ict

-10

6+

ε

04

2

GG

rad

esar

em

appe

dfr

omth

eem

piric

algr

ade

dist

ribut

ions

for

each

g ic

t=

G(a

icit

rsquoabulli

ct)

3co

urse

inth

etw

osc

hool

sst

udie

don

the

basi

sof

the

rank

orde

rof

achi

evem

ent

Gis

am

appi

ngfu

nctio

nth

atre

turn

sth

eap

prop

riate

grad

efo

rth

est

uden

trsquospo

sitio

nin

the

rank

orde

r(b

yac

hiev

emen

t)fo

ra

give

nco

urse

ina

give

nsc

hool

RtR

ewar

dto

lera

nce

depe

nds

onpr

ior

perf

orm

ance

and

stud

entrsquos

succ

ess

rtit

=pe

rfit

(1

ndashadw

t)+

adap

t it

adw

t4

inad

aptin

gto

chan

ges

inst

anda

rds

resu

lting

from

upw

ard

ordo

wnw

ard

trac

km

oves

(ada

ptab

ility

)

Perf

Rel

ativ

ep

erfo

rman

ceca

ptur

esth

ede

gree

tow

hich

the

stud

ents

perf

it=

(gic

tndashgndash ibull

t)

(1ndashp

e)+

(gic

tndashgndash c

t)pe

5ex

ceed

ed(o

rno

t)th

eir

prio

rpe

rfor

man

cean

dth

eir

perf

orm

ance

rela

tive

toth

eir

cour

seco

hort

adap

tA

dap

tab

ility

The

degr

eeto

whi

chth

est

uden

trsquospe

rfor

man

cech

ange

sad

apt i

t=

perf

itndash

perf

it-1

6fr

omon

epe

riod

toth

ene

xtA

dow

nwar

dm

ove

shou

ldca

use

are

duct

ion

inpe

rfor

man

ceb

utth

em

ore

adap

tabl

est

uden

tw

illsu

ffer

alo

wer

drop

than

will

ale

ssad

apta

ble

one

Con

vers

ely

anad

apta

ble

stud

ent

will

not

doas

wel

lin

alo

wer

trac

kas

one

who

refu

ses

toch

ange

his

orhe

rst

anda

rds

just

beca

use

heor

she

has

mov

eddo

wn

atr




PP

END

IX

Tab

leA

1C

onti

nue

d

Des

crip

tion

Mod

elPa

ram

eter

s(E

quat

ions

24

and

5)

RT[a

b]

Rew

ard

tole

ran

ceth

resh

old

sA

nex

ogen

ous

para

met

erth

atse

tsth

ebo

unds

ofac

cept

able

educ

atio

nale

xper

ienc

eVa

lues

outs

ide

this

rang

etr

igge

rtr

ack

chan

ges

ais

the

valu

eof

rtdo

wn

bth

atof

rtup

Edu

catio

nale

xper

ienc

eva

lues

low

erth

anrt

dow

ntr

igge

ra

mov

eto

alo

wer

-tra

ckco

urse

Val

ues

high

erth

anrt

uptr

igge

ra

mov

eto

ahi

gher

-tra

ckco

urse

abw

tA

bili

tyw

eig

ht

Am

odel

para

met

erth

atad

just

sth

ede

gree

tow

hich

achi

evem

ent

isa

func

tion

ofra

wab

ility

and

how

muc

ha

func

tion

ofpr

ior

lear

ning

(ach

ieve

men

t)

adw

tA

dap

tati

onw

eig

ht

Am

odel

para

met

erad

just

ing

the

degr

eeto

whi

chad

apta

tion

mod

erat

esth

eim

pact

ofpe

rfor

man

ceco

mpa

rison

s(r

elat

ive

tose

lfan

dre

lativ

eto

peer

s)on

the

way

the

educ

atio

nale

xper

ienc

eis

perc

eive

dby

the

stud

ent

pePe

eref

fect

wei

gh

tA

mod

elpa

ram

eter

adju

stin

gth

eex

tent

tow

hich

perf

orm

ance

isju

dged

rela

tive

toa

stud

entrsquos

prio

rpe

rfor

man

ceas

oppo

sed

toa

stud

entrsquos

perf

orm

ance

rela

tive

tohe

ror

his

peer

s


Fri 18 Dec 2009 181626


REFERENCES
































Fri 18 Dec 2009 181626


































Fri 18 Dec 2009 181626






Fri 18 Dec 2009 181626











Fri 18 Dec 2009 181626











Fri 18 Dec 2009 181626











Fri 18 Dec 2009 181626



RESULTS





yi = a + b1 x1i + b2x2i + b3x3i + ε





Fri 18 Dec 2009 181626










Magnet Rural


Vacancy 163 -098(0012) (0017)

Decision adapt 089 080(0012) (0017)


Adj R Sq 211 150



Fri 18 Dec 2009 181626








Magnet

Honors IB IBS IBH


Vacancy 159 296 685 1029(0011) (0023) (0027) (0033)

Decision adapt 078 099 143 404(001) (0022) (0026) (0031)


Adj R Sq 262 221 520 592

Rural



Vacancy -184 -200 -128 068(0009) (0012) (0019) (002)

Decision adapt 007 -103 082 195(0009) (0011) (0018) (0019)


Adj R Sq 454 319 163 139




Fri 18 Dec 2009 181626


CONCLUSION






Fri 18 Dec 2009 181626







Magnet

Honors IB IBS IBH


Vacancy 433 633 917 351(0017) (0022) (0026) (0023)

Decision adapt 168 252 322 132(0016) (0021) (0025) (0022)


Adj R Sq 478 559 663 228

Rural



Vacancy -105 -019 -032(0018) (0018) (0016)

Decision adapt 037 133 306(0018) (0018) (0016)


Adj R Sq 130 118 478


options (p lt 10)


Fri 18 Dec 2009 181626








Fri 18 Dec 2009 181626



NOTES














Fri 18 Dec 2009 181626















Fri 18 Dec 2009 181626






Fri 18 Dec 2009 181626


PP

END

IX

Tab

leA

1D

efin

itio

ns

ofVa

riab

les

and

Para

met

ers

Des

crip

tion

Rela

tions

hip

toO

ther

Mod

elVa

riabl

esEq

nN

o

Abi

lity

Ab

ility

Inv

aria

ntpr

oper

tyof

each

stud

ent

Stan

dard

norm

alFi

xed

mod

elva

riabl

edi

strib

utio

nse

ta

stud

entrsquos

ldquocre

atio

nrdquo(i

ee

ntry

into

the

syst

em)

AA

chie

vem

ent

isre

late

dto

abili

tyM

ore

able

stud

ents

gene

rally

For

inco

min

gst

uden

tsan

dst

uden

tsin

thei

rfir

stye

ar

1ac

hiev

em

ore

inac

adem

icte

rms

Ther

eis

also

ara

ndom

com

pone

nt

a ic

t=1

=Ab

ility

i0

6+

ε

04

(ε~

N(0

1))

to

achi

evem

ent

Ach

ieve

men

tde

pend

sno

ton

lyon

abili

ty

but

onw

hat

the

stud

ents

have

lear

ned

over

the

cour

seof

thei

rhi

ghIn

subs

eque

ntye

ars

scho

oled

ucat

iona

lcar

eers

toth

atpo

int

a ic

t=

Abili

tyi

abw

t+

(1ndasha

bwt)

andash ict

-10

6+

ε

04

2

GG

rad

esar

em

appe

dfr

omth

eem

piric

algr

ade

dist

ribut

ions

for

each

g ic

t=

G(a

icit

rsquoabulli

ct)

3co

urse

inth

etw

osc

hool

sst

udie

don

the

basi

sof

the

rank

orde

rof

achi

evem

ent

Gis

am

appi

ngfu

nctio

nth

atre

turn

sth

eap

prop

riate

grad

efo

rth

est

uden

trsquospo

sitio

nin

the

rank

orde

r(b

yac

hiev

emen

t)fo

ra

give

nco

urse

ina

give

nsc

hool

RtR

ewar

dto

lera

nce

depe

nds

onpr

ior

perf

orm

ance

and

stud

entrsquos

succ

ess

rtit

=pe

rfit

(1

ndashadw

t)+

adap

t it

adw

t4

inad

aptin

gto

chan

ges

inst

anda

rds

resu

lting

from

upw

ard

ordo

wnw

ard

trac

km

oves

(ada

ptab

ility

)

Perf

Rel

ativ

ep

erfo

rman

ceca

ptur

esth

ede

gree

tow

hich

the

stud

ents

perf

it=

(gic

tndashgndash ibull

t)

(1ndashp

e)+

(gic

tndashgndash c

t)pe

5ex

ceed

ed(o

rno

t)th

eir

prio

rpe

rfor

man

cean

dth

eir

perf

orm

ance

rela

tive

toth

eir

cour

seco

hort

adap

tA

dap

tab

ility

The

degr

eeto

whi

chth

est

uden

trsquospe

rfor

man

cech

ange

sad

apt i

t=

perf

itndash

perf

it-1

6fr

omon

epe

riod

toth

ene

xtA

dow

nwar

dm

ove

shou

ldca

use

are

duct

ion

inpe

rfor

man

ceb

utth

em

ore

adap

tabl

est

uden

tw

illsu

ffer

alo

wer

drop

than

will

ale

ssad

apta

ble

one

Con

vers

ely

anad

apta

ble

stud

ent

will

not

doas

wel

lin

alo

wer

trac

kas

one

who

refu

ses

toch

ange

his

orhe

rst

anda

rds

just

beca

use

heor

she

has

mov

eddo

wn

atr




PP

END

IX

Tab

leA

1C

onti

nue

d

Des

crip

tion

Mod

elPa

ram

eter

s(E

quat

ions

24

and

5)

RT[a

b]

Rew

ard

tole

ran

ceth

resh

old

sA

nex

ogen

ous

para

met

erth

atse

tsth

ebo

unds

ofac

cept

able

educ

atio

nale

xper

ienc

eVa

lues

outs

ide

this

rang

etr

igge

rtr

ack

chan

ges

ais

the

valu

eof

rtdo

wn

bth

atof

rtup

Edu

catio

nale

xper

ienc

eva

lues

low

erth

anrt

dow

ntr

igge

ra

mov

eto

alo

wer

-tra

ckco

urse

Val

ues

high

erth

anrt

uptr

igge

ra

mov

eto

ahi

gher

-tra

ckco

urse

abw

tA

bili

tyw

eig

ht

Am

odel

para

met

erth

atad

just

sth

ede

gree

tow

hich

achi

evem

ent

isa

func

tion

ofra

wab

ility

and

how

muc

ha

func

tion

ofpr

ior

lear

ning

(ach

ieve

men

t)

adw

tA

dap

tati

onw

eig

ht

Am

odel

para

met

erad

just

ing

the

degr

eeto

whi

chad

apta

tion

mod

erat

esth

eim

pact

ofpe

rfor

man

ceco

mpa

rison

s(r

elat

ive

tose

lfan

dre

lativ

eto

peer

s)on

the

way

the

educ

atio

nale

xper

ienc

eis

perc

eive

dby

the

stud

ent

pePe

eref

fect

wei

gh

tA

mod

elpa

ram

eter

adju

stin

gth

eex

tent

tow

hich

perf

orm

ance

isju

dged

rela

tive

toa

stud

entrsquos

prio

rpe

rfor

man

ceas

oppo

sed

toa

stud

entrsquos

perf

orm

ance

rela

tive

tohe

ror

his

peer

s


Fri 18 Dec 2009 181626


REFERENCES
































Fri 18 Dec 2009 181626


































Fri 18 Dec 2009 181626






Fri 18 Dec 2009 181626











Fri 18 Dec 2009 181626











Fri 18 Dec 2009 181626



RESULTS





yi = a + b1 x1i + b2x2i + b3x3i + ε





Fri 18 Dec 2009 181626










Magnet Rural


Vacancy 163 -098(0012) (0017)

Decision adapt 089 080(0012) (0017)


Adj R Sq 211 150



Fri 18 Dec 2009 181626








Magnet

Honors IB IBS IBH


Vacancy 159 296 685 1029(0011) (0023) (0027) (0033)

Decision adapt 078 099 143 404(001) (0022) (0026) (0031)


Adj R Sq 262 221 520 592

Rural



Vacancy -184 -200 -128 068(0009) (0012) (0019) (002)

Decision adapt 007 -103 082 195(0009) (0011) (0018) (0019)


Adj R Sq 454 319 163 139




Fri 18 Dec 2009 181626


CONCLUSION






Fri 18 Dec 2009 181626







Magnet

Honors IB IBS IBH


Vacancy 433 633 917 351(0017) (0022) (0026) (0023)

Decision adapt 168 252 322 132(0016) (0021) (0025) (0022)


Adj R Sq 478 559 663 228

Rural



Vacancy -105 -019 -032(0018) (0018) (0016)

Decision adapt 037 133 306(0018) (0018) (0016)


Adj R Sq 130 118 478


options (p lt 10)


Fri 18 Dec 2009 181626








Fri 18 Dec 2009 181626



NOTES














Fri 18 Dec 2009 181626















Fri 18 Dec 2009 181626






Fri 18 Dec 2009 181626


PP

END

IX

Tab

leA

1D

efin

itio

ns

ofVa

riab

les

and

Para

met

ers

Des

crip

tion

Rela

tions

hip

toO

ther

Mod

elVa

riabl

esEq

nN

o

Abi

lity

Ab

ility

Inv

aria

ntpr

oper

tyof

each

stud

ent

Stan

dard

norm

alFi

xed

mod

elva

riabl

edi

strib

utio

nse

ta

stud

entrsquos

ldquocre

atio

nrdquo(i

ee

ntry

into

the

syst

em)

AA

chie

vem

ent

isre

late

dto

abili

tyM

ore

able

stud

ents

gene

rally

For

inco

min

gst

uden

tsan

dst

uden

tsin

thei

rfir

stye

ar

1ac

hiev

em

ore

inac

adem

icte

rms

Ther

eis

also

ara

ndom

com

pone

nt

a ic

t=1

=Ab

ility

i0

6+

ε

04

(ε~

N(0

1))

to

achi

evem

ent

Ach

ieve

men

tde

pend

sno

ton

lyon

abili

ty

but

onw

hat

the

stud

ents

have

lear

ned

over

the

cour

seof

thei

rhi

ghIn

subs

eque

ntye

ars

scho

oled

ucat

iona

lcar

eers

toth

atpo

int

a ic

t=

Abili

tyi

abw

t+

(1ndasha

bwt)

andash ict

-10

6+

ε

04

2

GG

rad

esar

em

appe

dfr

omth

eem

piric

algr

ade

dist

ribut

ions

for

each

g ic

t=

G(a

icit

rsquoabulli

ct)

3co

urse

inth

etw

osc

hool

sst

udie

don

the

basi

sof

the

rank

orde

rof

achi

evem

ent

Gis

am

appi

ngfu

nctio

nth

atre

turn

sth

eap

prop

riate

grad

efo

rth

est

uden

trsquospo

sitio

nin

the

rank

orde

r(b

yac

hiev

emen

t)fo

ra

give

nco

urse

ina

give

nsc

hool

RtR

ewar

dto

lera

nce

depe

nds

onpr

ior

perf

orm

ance

and

stud

entrsquos

succ

ess

rtit

=pe

rfit

(1

ndashadw

t)+

adap

t it

adw

t4

inad

aptin

gto

chan

ges

inst

anda

rds

resu

lting

from

upw

ard

ordo

wnw

ard

trac

km

oves

(ada

ptab

ility

)

Perf

Rel

ativ

ep

erfo

rman

ceca

ptur

esth

ede

gree

tow

hich

the

stud

ents

perf

it=

(gic

tndashgndash ibull

t)

(1ndashp

e)+

(gic

tndashgndash c

t)pe

5ex

ceed

ed(o

rno

t)th

eir

prio

rpe

rfor

man

cean

dth

eir

perf

orm

ance

rela

tive

toth

eir

cour

seco

hort

adap

tA

dap

tab

ility

The

degr

eeto

whi

chth

est

uden

trsquospe

rfor

man

cech

ange

sad

apt i

t=

perf

itndash

perf

it-1

6fr

omon

epe

riod

toth

ene

xtA

dow

nwar

dm

ove

shou

ldca

use

are

duct

ion

inpe

rfor

man

ceb

utth

em

ore

adap

tabl

est

uden

tw

illsu

ffer

alo

wer

drop

than

will

ale

ssad

apta

ble

one

Con

vers

ely

anad

apta

ble

stud

ent

will

not

doas

wel

lin

alo

wer

trac

kas

one

who

refu

ses

toch

ange

his

orhe

rst

anda

rds

just

beca

use

heor

she

has

mov

eddo

wn

atr




PP

END

IX

Tab

leA

1C

onti

nue

d

Des

crip

tion

Mod

elPa

ram

eter

s(E

quat

ions

24

and

5)

RT[a

b]

Rew

ard

tole

ran

ceth

resh

old

sA

nex

ogen

ous

para

met

erth

atse

tsth

ebo

unds

ofac

cept

able

educ

atio

nale

xper

ienc

eVa

lues

outs

ide

this

rang

etr

igge

rtr

ack

chan

ges

ais

the

valu

eof

rtdo

wn

bth

atof

rtup

Edu

catio

nale

xper

ienc

eva

lues

low

erth

anrt

dow

ntr

igge

ra

mov

eto

alo

wer

-tra

ckco

urse

Val

ues

high

erth

anrt

uptr

igge

ra

mov

eto

ahi

gher

-tra

ckco

urse

abw

tA

bili

tyw

eig

ht

Am

odel

para

met

erth

atad

just

sth

ede

gree

tow

hich

achi

evem

ent

isa

func

tion

ofra

wab

ility

and

how

muc

ha

func

tion

ofpr

ior

lear

ning

(ach

ieve

men

t)

adw

tA

dap

tati

onw

eig

ht

Am

odel

para

met

erad

just

ing

the

degr

eeto

whi

chad

apta

tion

mod

erat

esth

eim

pact

ofpe

rfor

man

ceco

mpa

rison

s(r

elat

ive

tose

lfan

dre

lativ

eto

peer

s)on

the

way

the

educ

atio

nale

xper

ienc

eis

perc

eive

dby

the

stud

ent

pePe

eref

fect

wei

gh

tA

mod

elpa

ram

eter

adju

stin

gth

eex

tent

tow

hich

perf

orm

ance

isju

dged

rela

tive

toa

stud

entrsquos

prio

rpe

rfor

man

ceas

oppo

sed

toa

stud

entrsquos

perf

orm

ance

rela

tive

tohe

ror

his

peer

s


Fri 18 Dec 2009 181626


REFERENCES
































Fri 18 Dec 2009 181626


































Fri 18 Dec 2009 181626






Fri 18 Dec 2009 181626











Fri 18 Dec 2009 181626



RESULTS





yi = a + b1 x1i + b2x2i + b3x3i + ε





Fri 18 Dec 2009 181626










Magnet Rural


Vacancy 163 -098(0012) (0017)

Decision adapt 089 080(0012) (0017)


Adj R Sq 211 150



Fri 18 Dec 2009 181626








Magnet

Honors IB IBS IBH


Vacancy 159 296 685 1029(0011) (0023) (0027) (0033)

Decision adapt 078 099 143 404(001) (0022) (0026) (0031)


Adj R Sq 262 221 520 592

Rural



Vacancy -184 -200 -128 068(0009) (0012) (0019) (002)

Decision adapt 007 -103 082 195(0009) (0011) (0018) (0019)


Adj R Sq 454 319 163 139




Fri 18 Dec 2009 181626


CONCLUSION






Fri 18 Dec 2009 181626







Magnet

Honors IB IBS IBH


Vacancy 433 633 917 351(0017) (0022) (0026) (0023)

Decision adapt 168 252 322 132(0016) (0021) (0025) (0022)


Adj R Sq 478 559 663 228

Rural



Vacancy -105 -019 -032(0018) (0018) (0016)

Decision adapt 037 133 306(0018) (0018) (0016)


Adj R Sq 130 118 478


options (p lt 10)


Fri 18 Dec 2009 181626








Fri 18 Dec 2009 181626



NOTES














Fri 18 Dec 2009 181626















Fri 18 Dec 2009 181626






Fri 18 Dec 2009 181626


PP

END

IX

Tab

leA

1D

efin

itio

ns

ofVa

riab

les

and

Para

met

ers

Des

crip

tion

Rela

tions

hip

toO

ther

Mod

elVa

riabl

esEq

nN

o

Abi

lity

Ab

ility

Inv

aria

ntpr

oper

tyof

each

stud

ent

Stan

dard

norm

alFi

xed

mod

elva

riabl

edi

strib

utio

nse

ta

stud

entrsquos

ldquocre

atio

nrdquo(i

ee

ntry

into

the

syst

em)

AA

chie

vem

ent

isre

late

dto

abili

tyM

ore

able

stud

ents

gene

rally

For

inco

min

gst

uden

tsan

dst

uden

tsin

thei

rfir

stye

ar

1ac

hiev

em

ore

inac

adem

icte

rms

Ther

eis

also

ara

ndom

com

pone

nt

a ic

t=1

=Ab

ility

i0

6+

ε

04

(ε~

N(0

1))

to

achi

evem

ent

Ach

ieve

men

tde

pend

sno

ton

lyon

abili

ty

but

onw

hat

the

stud

ents

have

lear

ned

over

the

cour

seof

thei

rhi

ghIn

subs

eque

ntye

ars

scho

oled

ucat

iona

lcar

eers

toth

atpo

int

a ic

t=

Abili

tyi

abw

t+

(1ndasha

bwt)

andash ict

-10

6+

ε

04

2

GG

rad

esar

em

appe

dfr

omth

eem

piric

algr

ade

dist

ribut

ions

for

each

g ic

t=

G(a

icit

rsquoabulli

ct)

3co

urse

inth

etw

osc

hool

sst

udie

don

the

basi

sof

the

rank

orde

rof

achi

evem

ent

Gis

am

appi

ngfu

nctio

nth

atre

turn

sth

eap

prop

riate

grad

efo

rth

est

uden

trsquospo

sitio

nin

the

rank

orde

r(b

yac

hiev

emen

t)fo

ra

give

nco

urse

ina

give

nsc

hool

RtR

ewar

dto

lera

nce

depe

nds

onpr

ior

perf

orm

ance

and

stud

entrsquos

succ

ess

rtit

=pe

rfit

(1

ndashadw

t)+

adap

t it

adw

t4

inad

aptin

gto

chan

ges

inst

anda

rds

resu

lting

from

upw

ard

ordo

wnw

ard

trac

km

oves

(ada

ptab

ility

)

Perf

Rel

ativ

ep

erfo

rman

ceca

ptur

esth

ede

gree

tow

hich

the

stud

ents

perf

it=

(gic

tndashgndash ibull

t)

(1ndashp

e)+

(gic

tndashgndash c

t)pe

5ex

ceed

ed(o

rno

t)th

eir

prio

rpe

rfor

man

cean

dth

eir

perf

orm

ance

rela

tive

toth

eir

cour

seco

hort

adap

tA

dap

tab

ility

The

degr

eeto

whi

chth

est

uden

trsquospe

rfor

man

cech

ange

sad

apt i

t=

perf

itndash

perf

it-1

6fr

omon

epe

riod

toth

ene

xtA

dow

nwar

dm

ove

shou

ldca

use

are

duct

ion

inpe

rfor

man

ceb

utth

em

ore

adap

tabl

est

uden

tw

illsu

ffer

alo

wer

drop

than

will

ale

ssad

apta

ble

one

Con

vers

ely

anad

apta

ble

stud

ent

will

not

doas

wel

lin

alo

wer

trac

kas

one

who

refu

ses

toch

ange

his

orhe

rst

anda

rds

just

beca

use

heor

she

has

mov

eddo

wn

atr




PP

END

IX

Tab

leA

1C

onti

nue

d

Des

crip

tion

Mod

elPa

ram

eter

s(E

quat

ions

24

and

5)

RT[a

b]

Rew

ard

tole

ran

ceth

resh

old

sA

nex

ogen

ous

para

met

erth

atse

tsth

ebo

unds

ofac

cept

able

educ

atio

nale

xper

ienc

eVa

lues

outs

ide

this

rang

etr

igge

rtr

ack

chan

ges

ais

the

valu

eof

rtdo

wn

bth

atof

rtup

Edu

catio

nale

xper

ienc

eva

lues

low

erth

anrt

dow

ntr

igge

ra

mov

eto

alo

wer

-tra

ckco

urse

Val

ues

high

erth

anrt

uptr

igge

ra

mov

eto

ahi

gher

-tra

ckco

urse

abw

tA

bili

tyw

eig

ht

Am

odel

para

met

erth

atad

just

sth

ede

gree

tow

hich

achi

evem

ent

isa

func

tion

ofra

wab

ility

and

how

muc

ha

func

tion

ofpr

ior

lear

ning

(ach

ieve

men

t)

adw

tA

dap

tati

onw

eig

ht

Am

odel

para

met

erad

just

ing

the

degr

eeto

whi

chad

apta

tion

mod

erat

esth

eim

pact

ofpe

rfor

man

ceco

mpa

rison

s(r

elat

ive

tose

lfan

dre

lativ

eto

peer

s)on

the

way

the

educ

atio

nale

xper

ienc

eis

perc

eive

dby

the

stud

ent

pePe

eref

fect

wei

gh

tA

mod

elpa

ram

eter

adju

stin

gth

eex

tent

tow

hich

perf

orm

ance

isju

dged

rela

tive

toa

stud

entrsquos

prio

rpe

rfor

man

ceas

oppo

sed

toa

stud

entrsquos

perf

orm

ance

rela

tive

tohe

ror

his

peer

s


Fri 18 Dec 2009 181626


REFERENCES
































Fri 18 Dec 2009 181626


































Fri 18 Dec 2009 181626






Fri 18 Dec 2009 181626



RESULTS





yi = a + b1 x1i + b2x2i + b3x3i + ε





Fri 18 Dec 2009 181626










Magnet Rural


Vacancy 163 -098(0012) (0017)

Decision adapt 089 080(0012) (0017)


Adj R Sq 211 150



Fri 18 Dec 2009 181626








Magnet

Honors IB IBS IBH


Vacancy 159 296 685 1029(0011) (0023) (0027) (0033)

Decision adapt 078 099 143 404(001) (0022) (0026) (0031)


Adj R Sq 262 221 520 592

Rural



Vacancy -184 -200 -128 068(0009) (0012) (0019) (002)

Decision adapt 007 -103 082 195(0009) (0011) (0018) (0019)


Adj R Sq 454 319 163 139




Fri 18 Dec 2009 181626


CONCLUSION






Fri 18 Dec 2009 181626







Magnet

Honors IB IBS IBH


Vacancy 433 633 917 351(0017) (0022) (0026) (0023)

Decision adapt 168 252 322 132(0016) (0021) (0025) (0022)


Adj R Sq 478 559 663 228

Rural



Vacancy -105 -019 -032(0018) (0018) (0016)

Decision adapt 037 133 306(0018) (0018) (0016)


Adj R Sq 130 118 478


options (p lt 10)


Fri 18 Dec 2009 181626








Fri 18 Dec 2009 181626



NOTES














Fri 18 Dec 2009 181626















Fri 18 Dec 2009 181626






Fri 18 Dec 2009 181626


PP

END

IX

Tab

leA

1D

efin

itio

ns

ofVa

riab

les

and

Para

met

ers

Des

crip

tion

Rela

tions

hip

toO

ther

Mod

elVa

riabl

esEq

nN

o

Abi

lity

Ab

ility

Inv

aria

ntpr

oper

tyof

each

stud

ent

Stan

dard

norm

alFi

xed

mod

elva

riabl

edi

strib

utio

nse

ta

stud

entrsquos

ldquocre

atio

nrdquo(i

ee

ntry

into

the

syst

em)

AA

chie

vem

ent

isre

late

dto

abili

tyM

ore

able

stud

ents

gene

rally

For

inco

min

gst

uden

tsan

dst

uden

tsin

thei

rfir

stye

ar

1ac

hiev

em

ore

inac

adem

icte

rms

Ther

eis

also

ara

ndom

com

pone

nt

a ic

t=1

=Ab

ility

i0

6+

ε

04

(ε~

N(0

1))

to

achi

evem

ent

Ach

ieve

men

tde

pend

sno

ton

lyon

abili

ty

but

onw

hat

the

stud

ents

have

lear

ned

over

the

cour

seof

thei

rhi

ghIn

subs

eque

ntye

ars

scho

oled

ucat

iona

lcar

eers

toth

atpo

int

a ic

t=

Abili

tyi

abw

t+

(1ndasha

bwt)

andash ict

-10

6+

ε

04

2

GG

rad

esar

em

appe

dfr

omth

eem

piric

algr

ade

dist

ribut

ions

for

each

g ic

t=

G(a

icit

rsquoabulli

ct)

3co

urse

inth

etw

osc

hool

sst

udie

don

the

basi

sof

the

rank

orde

rof

achi

evem

ent

Gis

am

appi

ngfu

nctio

nth

atre

turn

sth

eap

prop

riate

grad

efo

rth

est

uden

trsquospo

sitio

nin

the

rank

orde

r(b

yac

hiev

emen

t)fo

ra

give

nco

urse

ina

give

nsc

hool

RtR

ewar

dto

lera

nce

depe

nds

onpr

ior

perf

orm

ance

and

stud

entrsquos

succ

ess

rtit

=pe

rfit

(1

ndashadw

t)+

adap

t it

adw

t4

inad

aptin

gto

chan

ges

inst

anda

rds

resu

lting

from

upw

ard

ordo

wnw

ard

trac

km

oves

(ada

ptab

ility

)

Perf

Rel

ativ

ep

erfo

rman

ceca

ptur

esth

ede

gree

tow

hich

the

stud

ents

perf

it=

(gic

tndashgndash ibull

t)

(1ndashp

e)+

(gic

tndashgndash c

t)pe

5ex

ceed

ed(o

rno

t)th

eir

prio

rpe

rfor

man

cean

dth

eir

perf

orm

ance

rela

tive

toth

eir

cour

seco

hort

adap

tA

dap

tab

ility

The

degr

eeto

whi

chth

est

uden

trsquospe

rfor

man

cech

ange

sad

apt i

t=

perf

itndash

perf

it-1

6fr

omon

epe

riod

toth

ene

xtA

dow

nwar

dm

ove

shou

ldca

use

are

duct

ion

inpe

rfor

man

ceb

utth

em

ore

adap

tabl

est

uden

tw

illsu

ffer

alo

wer

drop

than

will

ale

ssad

apta

ble

one

Con

vers

ely

anad

apta

ble

stud

ent

will

not

doas

wel

lin

alo

wer

trac

kas

one

who

refu

ses

toch

ange

his

orhe

rst

anda

rds

just

beca

use

heor

she

has

mov

eddo

wn

atr




PP

END

IX

Tab

leA

1C

onti

nue

d

Des

crip

tion

Mod

elPa

ram

eter

s(E

quat

ions

24

and

5)

RT[a

b]

Rew

ard

tole

ran

ceth

resh

old

sA

nex

ogen

ous

para

met

erth

atse

tsth

ebo

unds

ofac

cept

able

educ

atio

nale

xper

ienc

eVa

lues

outs

ide

this

rang

etr

igge

rtr

ack

chan

ges

ais

the

valu

eof

rtdo

wn

bth

atof

rtup

Edu

catio

nale

xper

ienc

eva

lues

low

erth

anrt

dow

ntr

igge

ra

mov

eto

alo

wer

-tra

ckco

urse

Val

ues

high

erth

anrt

uptr

igge

ra

mov

eto

ahi

gher

-tra

ckco

urse

abw

tA

bili

tyw

eig

ht

Am

odel

para

met

erth

atad

just

sth

ede

gree

tow

hich

achi

evem

ent

isa

func

tion

ofra

wab

ility

and

how

muc

ha

func

tion

ofpr

ior

lear

ning

(ach

ieve

men

t)

adw

tA

dap

tati

onw

eig

ht

Am

odel

para

met

erad

just

ing

the

degr

eeto

whi

chad

apta

tion

mod

erat

esth

eim

pact

ofpe

rfor

man

ceco

mpa

rison

s(r

elat

ive

tose

lfan

dre

lativ

eto

peer

s)on

the

way

the

educ

atio

nale

xper

ienc

eis

perc

eive

dby

the

stud

ent

pePe

eref

fect

wei

gh

tA

mod

elpa

ram

eter

adju

stin

gth

eex

tent

tow

hich

perf

orm

ance

isju

dged

rela

tive

toa

stud

entrsquos

prio

rpe

rfor

man

ceas

oppo

sed

toa

stud

entrsquos

perf

orm

ance

rela

tive

tohe

ror

his

peer

s


Fri 18 Dec 2009 181626


REFERENCES
































Fri 18 Dec 2009 181626


































Fri 18 Dec 2009 181626






Fri 18 Dec 2009 181626










Magnet Rural


Vacancy 163 -098(0012) (0017)

Decision adapt 089 080(0012) (0017)


Adj R Sq 211 150



Fri 18 Dec 2009 181626








Magnet

Honors IB IBS IBH


Vacancy 159 296 685 1029(0011) (0023) (0027) (0033)

Decision adapt 078 099 143 404(001) (0022) (0026) (0031)


Adj R Sq 262 221 520 592

Rural



Vacancy -184 -200 -128 068(0009) (0012) (0019) (002)

Decision adapt 007 -103 082 195(0009) (0011) (0018) (0019)


Adj R Sq 454 319 163 139




Fri 18 Dec 2009 181626


CONCLUSION






Fri 18 Dec 2009 181626







Magnet

Honors IB IBS IBH


Vacancy 433 633 917 351(0017) (0022) (0026) (0023)

Decision adapt 168 252 322 132(0016) (0021) (0025) (0022)


Adj R Sq 478 559 663 228

Rural



Vacancy -105 -019 -032(0018) (0018) (0016)

Decision adapt 037 133 306(0018) (0018) (0016)


Adj R Sq 130 118 478


options (p lt 10)


Fri 18 Dec 2009 181626








Fri 18 Dec 2009 181626



NOTES














Fri 18 Dec 2009 181626















Fri 18 Dec 2009 181626






Fri 18 Dec 2009 181626


PP

END

IX

Tab

leA

1D

efin

itio

ns

ofVa

riab

les

and

Para

met

ers

Des

crip

tion

Rela

tions

hip

toO

ther

Mod

elVa

riabl

esEq

nN

o

Abi

lity

Ab

ility

Inv

aria

ntpr

oper

tyof

each

stud

ent

Stan

dard

norm

alFi

xed

mod

elva

riabl

edi

strib

utio

nse

ta

stud

entrsquos

ldquocre

atio

nrdquo(i

ee

ntry

into

the

syst

em)

AA

chie

vem

ent

isre

late

dto

abili

tyM

ore

able

stud

ents

gene

rally

For

inco

min

gst

uden

tsan

dst

uden

tsin

thei

rfir

stye

ar

1ac

hiev

em

ore

inac

adem

icte

rms

Ther

eis

also

ara

ndom

com

pone

nt

a ic

t=1

=Ab

ility

i0

6+

ε

04

(ε~

N(0

1))

to

achi

evem

ent

Ach

ieve

men

tde

pend

sno

ton

lyon

abili

ty

but

onw

hat

the

stud

ents

have

lear

ned

over

the

cour

seof

thei

rhi

ghIn

subs

eque

ntye

ars

scho

oled

ucat

iona

lcar

eers

toth

atpo

int

a ic

t=

Abili

tyi

abw

t+

(1ndasha

bwt)

andash ict

-10

6+

ε

04

2

GG

rad

esar

em

appe

dfr

omth

eem

piric

algr

ade

dist

ribut

ions

for

each

g ic

t=

G(a

icit

rsquoabulli

ct)

3co

urse

inth

etw

osc

hool

sst

udie

don

the

basi

sof

the

rank

orde

rof

achi

evem

ent

Gis

am

appi

ngfu

nctio

nth

atre

turn

sth

eap

prop

riate

grad

efo

rth

est

uden

trsquospo

sitio

nin

the

rank

orde

r(b

yac

hiev

emen

t)fo

ra

give

nco

urse

ina

give

nsc

hool

RtR

ewar

dto

lera

nce

depe

nds

onpr

ior

perf

orm

ance

and

stud

entrsquos

succ

ess

rtit

=pe

rfit

(1

ndashadw

t)+

adap

t it

adw

t4

inad

aptin

gto

chan

ges

inst

anda

rds

resu

lting

from

upw

ard

ordo

wnw

ard

trac

km

oves

(ada

ptab

ility

)

Perf

Rel

ativ

ep

erfo

rman

ceca

ptur

esth

ede

gree

tow

hich

the

stud

ents

perf

it=

(gic

tndashgndash ibull

t)

(1ndashp

e)+

(gic

tndashgndash c

t)pe

5ex

ceed

ed(o

rno

t)th

eir

prio

rpe

rfor

man

cean

dth

eir

perf

orm

ance

rela

tive

toth

eir

cour

seco

hort

adap

tA

dap

tab

ility

The

degr

eeto

whi

chth

est

uden

trsquospe

rfor

man

cech

ange

sad

apt i

t=

perf

itndash

perf

it-1

6fr

omon

epe

riod

toth

ene

xtA

dow

nwar

dm

ove

shou

ldca

use

are

duct

ion

inpe

rfor

man

ceb

utth

em

ore

adap

tabl

est

uden

tw

illsu

ffer

alo

wer

drop

than

will

ale

ssad

apta

ble

one

Con

vers

ely

anad

apta

ble

stud

ent

will

not

doas

wel

lin

alo

wer

trac

kas

one

who

refu

ses

toch

ange

his

orhe

rst

anda

rds

just

beca

use

heor

she

has

mov

eddo

wn

atr




PP

END

IX

Tab

leA

1C

onti

nue

d

Des

crip

tion

Mod

elPa

ram

eter

s(E

quat

ions

24

and

5)

RT[a

b]

Rew

ard

tole

ran

ceth

resh

old

sA

nex

ogen

ous

para

met

erth

atse

tsth

ebo

unds

ofac

cept

able

educ

atio

nale

xper

ienc

eVa

lues

outs

ide

this

rang

etr

igge

rtr

ack

chan

ges

ais

the

valu

eof

rtdo

wn

bth

atof

rtup

Edu

catio

nale

xper

ienc

eva

lues

low

erth

anrt

dow

ntr

igge

ra

mov

eto

alo

wer

-tra

ckco

urse

Val

ues

high

erth

anrt

uptr

igge

ra

mov

eto

ahi

gher

-tra

ckco

urse

abw

tA

bili

tyw

eig

ht

Am

odel

para

met

erth

atad

just

sth

ede

gree

tow

hich

achi

evem

ent

isa

func

tion

ofra

wab

ility

and

how

muc

ha

func

tion

ofpr

ior

lear

ning

(ach

ieve

men

t)

adw

tA

dap

tati

onw

eig

ht

Am

odel

para

met

erad

just

ing

the

degr

eeto

whi

chad

apta

tion

mod

erat

esth

eim

pact

ofpe

rfor

man

ceco

mpa

rison

s(r

elat

ive

tose

lfan

dre

lativ

eto

peer

s)on

the

way

the

educ

atio

nale

xper

ienc

eis

perc

eive

dby

the

stud

ent

pePe

eref

fect

wei

gh

tA

mod

elpa

ram

eter

adju

stin

gth

eex

tent

tow

hich

perf

orm

ance

isju

dged

rela

tive

toa

stud

entrsquos

prio

rpe

rfor

man

ceas

oppo

sed

toa

stud

entrsquos

perf

orm

ance

rela

tive

tohe

ror

his

peer

s


Fri 18 Dec 2009 181626


REFERENCES
































Fri 18 Dec 2009 181626


































Fri 18 Dec 2009 181626






Fri 18 Dec 2009 181626








Magnet

Honors IB IBS IBH


Vacancy 159 296 685 1029(0011) (0023) (0027) (0033)

Decision adapt 078 099 143 404(001) (0022) (0026) (0031)


Adj R Sq 262 221 520 592

Rural



Vacancy -184 -200 -128 068(0009) (0012) (0019) (002)

Decision adapt 007 -103 082 195(0009) (0011) (0018) (0019)


Adj R Sq 454 319 163 139




Fri 18 Dec 2009 181626


CONCLUSION






Fri 18 Dec 2009 181626







Magnet

Honors IB IBS IBH


Vacancy 433 633 917 351(0017) (0022) (0026) (0023)

Decision adapt 168 252 322 132(0016) (0021) (0025) (0022)


Adj R Sq 478 559 663 228

Rural



Vacancy -105 -019 -032(0018) (0018) (0016)

Decision adapt 037 133 306(0018) (0018) (0016)


Adj R Sq 130 118 478


options (p lt 10)


Fri 18 Dec 2009 181626








Fri 18 Dec 2009 181626



NOTES














Fri 18 Dec 2009 181626















Fri 18 Dec 2009 181626






Fri 18 Dec 2009 181626


PP

END

IX

Tab

leA

1D

efin

itio

ns

ofVa

riab

les

and

Para

met

ers

Des

crip

tion

Rela

tions

hip

toO

ther

Mod

elVa

riabl

esEq

nN

o

Abi

lity

Ab

ility

Inv

aria

ntpr

oper

tyof

each

stud

ent

Stan

dard

norm

alFi

xed

mod

elva

riabl

edi

strib

utio

nse

ta

stud

entrsquos

ldquocre

atio

nrdquo(i

ee

ntry

into

the

syst

em)

AA

chie

vem

ent

isre

late

dto

abili

tyM

ore

able

stud

ents

gene

rally

For

inco

min

gst

uden

tsan

dst

uden

tsin

thei

rfir

stye

ar

1ac

hiev

em

ore

inac

adem

icte

rms

Ther

eis

also

ara

ndom

com

pone

nt

a ic

t=1

=Ab

ility

i0

6+

ε

04

(ε~

N(0

1))

to

achi

evem

ent

Ach

ieve

men

tde

pend

sno

ton

lyon

abili

ty

but

onw

hat

the

stud

ents

have

lear

ned

over

the

cour

seof

thei

rhi

ghIn

subs

eque

ntye

ars

scho

oled

ucat

iona

lcar

eers

toth

atpo

int

a ic

t=

Abili

tyi

abw

t+

(1ndasha

bwt)

andash ict

-10

6+

ε

04

2

GG

rad

esar

em

appe

dfr

omth

eem

piric

algr

ade

dist

ribut

ions

for

each

g ic

t=

G(a

icit

rsquoabulli

ct)

3co

urse

inth

etw

osc

hool

sst

udie

don

the

basi

sof

the

rank

orde

rof

achi

evem

ent

Gis

am

appi

ngfu

nctio

nth

atre

turn

sth

eap

prop

riate

grad

efo

rth

est

uden

trsquospo

sitio

nin

the

rank

orde

r(b

yac

hiev

emen

t)fo

ra

give

nco

urse

ina

give

nsc

hool

RtR

ewar

dto

lera

nce

depe

nds

onpr

ior

perf

orm

ance

and

stud

entrsquos

succ

ess

rtit

=pe

rfit

(1

ndashadw

t)+

adap

t it

adw

t4

inad

aptin

gto

chan

ges

inst

anda

rds

resu

lting

from

upw

ard

ordo

wnw

ard

trac

km

oves

(ada

ptab

ility

)

Perf

Rel

ativ

ep

erfo

rman

ceca

ptur

esth

ede

gree

tow

hich

the

stud

ents

perf

it=

(gic

tndashgndash ibull

t)

(1ndashp

e)+

(gic

tndashgndash c

t)pe

5ex

ceed

ed(o

rno

t)th

eir

prio

rpe

rfor

man

cean

dth

eir

perf

orm

ance

rela

tive

toth

eir

cour

seco

hort

adap

tA

dap

tab

ility

The

degr

eeto

whi

chth

est

uden

trsquospe

rfor

man

cech

ange

sad

apt i

t=

perf

itndash

perf

it-1

6fr

omon

epe

riod

toth

ene

xtA

dow

nwar

dm

ove

shou

ldca

use

are

duct

ion

inpe

rfor

man

ceb

utth

em

ore

adap

tabl

est

uden

tw

illsu

ffer

alo

wer

drop

than

will

ale

ssad

apta

ble

one

Con

vers

ely

anad

apta

ble

stud

ent

will

not

doas

wel

lin

alo

wer

trac

kas

one

who

refu

ses

toch

ange

his

orhe

rst

anda

rds

just

beca

use

heor

she

has

mov

eddo

wn

atr




PP

END

IX

Tab

leA

1C

onti

nue

d

Des

crip

tion

Mod

elPa

ram

eter

s(E

quat

ions

24

and

5)

RT[a

b]

Rew

ard

tole

ran

ceth

resh

old

sA

nex

ogen

ous

para

met

erth

atse

tsth

ebo

unds

ofac

cept

able

educ

atio

nale

xper

ienc

eVa

lues

outs

ide

this

rang

etr

igge

rtr

ack

chan

ges

ais

the

valu

eof

rtdo

wn

bth

atof

rtup

Edu

catio

nale

xper

ienc

eva

lues

low

erth

anrt

dow

ntr

igge

ra

mov

eto

alo

wer

-tra

ckco

urse

Val

ues

high

erth

anrt

uptr

igge

ra

mov

eto

ahi

gher

-tra

ckco

urse

abw

tA

bili

tyw

eig

ht

Am

odel

para

met

erth

atad

just

sth

ede

gree

tow

hich

achi

evem

ent

isa

func

tion

ofra

wab

ility

and

how

muc

ha

func

tion

ofpr

ior

lear

ning

(ach

ieve

men

t)

adw

tA

dap

tati

onw

eig

ht

Am

odel

para

met

erad

just

ing

the

degr

eeto

whi

chad

apta

tion

mod

erat

esth

eim

pact

ofpe

rfor

man

ceco

mpa

rison

s(r

elat

ive

tose

lfan

dre

lativ

eto

peer

s)on

the

way

the

educ

atio

nale

xper

ienc

eis

perc

eive

dby

the

stud

ent

pePe

eref

fect

wei

gh

tA

mod

elpa

ram

eter

adju

stin

gth

eex

tent

tow

hich

perf

orm

ance

isju

dged

rela

tive

toa

stud

entrsquos

prio

rpe

rfor

man

ceas

oppo

sed

toa

stud

entrsquos

perf

orm

ance

rela

tive

tohe

ror

his

peer

s


Fri 18 Dec 2009 181626


REFERENCES
































Fri 18 Dec 2009 181626


































Fri 18 Dec 2009 181626






Fri 18 Dec 2009 181626


CONCLUSION






Fri 18 Dec 2009 181626







Magnet

Honors IB IBS IBH


Vacancy 433 633 917 351(0017) (0022) (0026) (0023)

Decision adapt 168 252 322 132(0016) (0021) (0025) (0022)


Adj R Sq 478 559 663 228

Rural



Vacancy -105 -019 -032(0018) (0018) (0016)

Decision adapt 037 133 306(0018) (0018) (0016)


Adj R Sq 130 118 478


options (p lt 10)


Fri 18 Dec 2009 181626








Fri 18 Dec 2009 181626



NOTES














Fri 18 Dec 2009 181626















Fri 18 Dec 2009 181626






Fri 18 Dec 2009 181626


PP

END

IX

Tab

leA

1D

efin

itio

ns

ofVa

riab

les

and

Para

met

ers

Des

crip

tion

Rela

tions

hip

toO

ther

Mod

elVa

riabl

esEq

nN

o

Abi

lity

Ab

ility

Inv

aria

ntpr

oper

tyof

each

stud

ent

Stan

dard

norm

alFi

xed

mod

elva

riabl

edi

strib

utio

nse

ta

stud

entrsquos

ldquocre

atio

nrdquo(i

ee

ntry

into

the

syst

em)

AA

chie

vem

ent

isre

late

dto

abili

tyM

ore

able

stud

ents

gene

rally

For

inco

min

gst

uden

tsan

dst

uden

tsin

thei

rfir

stye

ar

1ac

hiev

em

ore

inac

adem

icte

rms

Ther

eis

also

ara

ndom

com

pone

nt

a ic

t=1

=Ab

ility

i0

6+

ε

04

(ε~

N(0

1))

to

achi

evem

ent

Ach

ieve

men

tde

pend

sno

ton

lyon

abili

ty

but

onw

hat

the

stud

ents

have

lear

ned

over

the

cour

seof

thei

rhi

ghIn

subs

eque

ntye

ars

scho

oled

ucat

iona

lcar

eers

toth

atpo

int

a ic

t=

Abili

tyi

abw

t+

(1ndasha

bwt)

andash ict

-10

6+

ε

04

2

GG

rad

esar

em

appe

dfr

omth

eem

piric

algr

ade

dist

ribut

ions

for

each

g ic

t=

G(a

icit

rsquoabulli

ct)

3co

urse

inth

etw

osc

hool

sst

udie

don

the

basi

sof

the

rank

orde

rof

achi

evem

ent

Gis

am

appi

ngfu

nctio

nth

atre

turn

sth

eap

prop

riate

grad

efo

rth

est

uden

trsquospo

sitio

nin

the

rank

orde

r(b

yac

hiev

emen

t)fo

ra

give

nco

urse

ina

give

nsc

hool

RtR

ewar

dto

lera

nce

depe

nds

onpr

ior

perf

orm

ance

and

stud

entrsquos

succ

ess

rtit

=pe

rfit

(1

ndashadw

t)+

adap

t it

adw

t4

inad

aptin

gto

chan

ges

inst

anda

rds

resu

lting

from

upw

ard

ordo

wnw

ard

trac

km

oves

(ada

ptab

ility

)

Perf

Rel

ativ

ep

erfo

rman

ceca

ptur

esth

ede

gree

tow

hich

the

stud

ents

perf

it=

(gic

tndashgndash ibull

t)

(1ndashp

e)+

(gic

tndashgndash c

t)pe

5ex

ceed

ed(o

rno

t)th

eir

prio

rpe

rfor

man

cean

dth

eir

perf

orm

ance

rela

tive

toth

eir

cour

seco

hort

adap

tA

dap

tab

ility

The

degr

eeto

whi

chth

est

uden

trsquospe

rfor

man

cech

ange

sad

apt i

t=

perf

itndash

perf

it-1

6fr

omon

epe

riod

toth

ene

xtA

dow

nwar

dm

ove

shou

ldca

use

are

duct

ion

inpe

rfor

man

ceb

utth

em

ore

adap

tabl

est

uden

tw

illsu

ffer

alo

wer

drop

than

will

ale

ssad

apta

ble

one

Con

vers

ely

anad

apta

ble

stud

ent

will

not

doas

wel

lin

alo

wer

trac

kas

one

who

refu

ses

toch

ange

his

orhe

rst

anda

rds

just

beca

use

heor

she

has

mov

eddo

wn

atr




PP

END

IX

Tab

leA

1C

onti

nue

d

Des

crip

tion

Mod

elPa

ram

eter

s(E

quat

ions

24

and

5)

RT[a

b]

Rew

ard

tole

ran

ceth

resh

old

sA

nex

ogen

ous

para

met

erth

atse

tsth

ebo

unds

ofac

cept

able

educ

atio

nale

xper

ienc

eVa

lues

outs

ide

this

rang

etr

igge

rtr

ack

chan

ges

ais

the

valu

eof

rtdo

wn

bth

atof

rtup

Edu

catio

nale

xper

ienc

eva

lues

low

erth

anrt

dow

ntr

igge

ra

mov

eto

alo

wer

-tra

ckco

urse

Val

ues

high

erth

anrt

uptr

igge

ra

mov

eto

ahi

gher

-tra

ckco

urse

abw

tA

bili

tyw

eig

ht

Am

odel

para

met

erth

atad

just

sth

ede

gree

tow

hich

achi

evem

ent

isa

func

tion

ofra

wab

ility

and

how

muc

ha

func

tion

ofpr

ior

lear

ning

(ach

ieve

men

t)

adw

tA

dap

tati

onw

eig

ht

Am

odel

para

met

erad

just

ing

the

degr

eeto

whi

chad

apta

tion

mod

erat

esth

eim

pact

ofpe

rfor

man

ceco

mpa

rison

s(r

elat

ive

tose

lfan

dre

lativ

eto

peer

s)on

the

way

the

educ

atio

nale

xper

ienc

eis

perc

eive

dby

the

stud

ent

pePe

eref

fect

wei

gh

tA

mod

elpa

ram

eter

adju

stin

gth

eex

tent

tow

hich

perf

orm

ance

isju

dged

rela

tive

toa

stud

entrsquos

prio

rpe

rfor

man

ceas

oppo

sed

toa

stud

entrsquos

perf

orm

ance

rela

tive

tohe

ror

his

peer

s


Fri 18 Dec 2009 181626


REFERENCES
































Fri 18 Dec 2009 181626


































Fri 18 Dec 2009 181626






Fri 18 Dec 2009 181626







Magnet

Honors IB IBS IBH


Vacancy 433 633 917 351(0017) (0022) (0026) (0023)

Decision adapt 168 252 322 132(0016) (0021) (0025) (0022)


Adj R Sq 478 559 663 228

Rural



Vacancy -105 -019 -032(0018) (0018) (0016)

Decision adapt 037 133 306(0018) (0018) (0016)


Adj R Sq 130 118 478


options (p lt 10)


Fri 18 Dec 2009 181626








Fri 18 Dec 2009 181626



NOTES














Fri 18 Dec 2009 181626















Fri 18 Dec 2009 181626






Fri 18 Dec 2009 181626


PP

END

IX

Tab

leA

1D

efin

itio

ns

ofVa

riab

les

and

Para

met

ers

Des

crip

tion

Rela

tions

hip

toO

ther

Mod

elVa

riabl

esEq

nN

o

Abi

lity

Ab

ility

Inv

aria

ntpr

oper

tyof

each

stud

ent

Stan

dard

norm

alFi

xed

mod

elva

riabl

edi

strib

utio

nse

ta

stud

entrsquos

ldquocre

atio

nrdquo(i

ee

ntry

into

the

syst

em)

AA

chie

vem

ent

isre

late

dto

abili

tyM

ore

able

stud

ents

gene

rally

For

inco

min

gst

uden

tsan

dst

uden

tsin

thei

rfir

stye

ar

1ac

hiev

em

ore

inac

adem

icte

rms

Ther

eis

also

ara

ndom

com

pone

nt

a ic

t=1

=Ab

ility

i0

6+

ε

04

(ε~

N(0

1))

to

achi

evem

ent

Ach

ieve

men

tde

pend

sno

ton

lyon

abili

ty

but

onw

hat

the

stud

ents

have

lear

ned

over

the

cour

seof

thei

rhi

ghIn

subs

eque

ntye

ars

scho

oled

ucat

iona

lcar

eers

toth

atpo

int

a ic

t=

Abili

tyi

abw

t+

(1ndasha

bwt)

andash ict

-10

6+

ε

04

2

GG

rad

esar

em

appe

dfr

omth

eem

piric

algr

ade

dist

ribut

ions

for

each

g ic

t=

G(a

icit

rsquoabulli

ct)

3co

urse

inth

etw

osc

hool

sst

udie

don

the

basi

sof

the

rank

orde

rof

achi

evem

ent

Gis

am

appi

ngfu

nctio

nth

atre

turn

sth

eap

prop

riate

grad

efo

rth

est

uden

trsquospo

sitio

nin

the

rank

orde

r(b

yac

hiev

emen

t)fo

ra

give

nco

urse

ina

give

nsc

hool

RtR

ewar

dto

lera

nce

depe

nds

onpr

ior

perf

orm

ance

and

stud

entrsquos

succ

ess

rtit

=pe

rfit

(1

ndashadw

t)+

adap

t it

adw

t4

inad

aptin

gto

chan

ges

inst

anda

rds

resu

lting

from

upw

ard

ordo

wnw

ard

trac

km

oves

(ada

ptab

ility

)

Perf

Rel

ativ

ep

erfo

rman

ceca

ptur

esth

ede

gree

tow

hich

the

stud

ents

perf

it=

(gic

tndashgndash ibull

t)

(1ndashp

e)+

(gic

tndashgndash c

t)pe

5ex

ceed

ed(o

rno

t)th

eir

prio

rpe

rfor

man

cean

dth

eir

perf

orm

ance

rela

tive

toth

eir

cour

seco

hort

adap

tA

dap

tab

ility

The

degr

eeto

whi

chth

est

uden

trsquospe

rfor

man

cech

ange

sad

apt i

t=

perf

itndash

perf

it-1

6fr

omon

epe

riod

toth

ene

xtA

dow

nwar

dm

ove

shou

ldca

use

are

duct

ion

inpe

rfor

man

ceb

utth

em

ore

adap

tabl

est

uden

tw

illsu

ffer

alo

wer

drop

than

will

ale

ssad

apta

ble

one

Con

vers

ely

anad

apta

ble

stud

ent

will

not

doas

wel

lin

alo

wer

trac

kas

one

who

refu

ses

toch

ange

his

orhe

rst

anda

rds

just

beca

use

heor

she

has

mov

eddo

wn

atr




PP

END

IX

Tab

leA

1C

onti

nue

d

Des

crip

tion

Mod

elPa

ram

eter

s(E

quat

ions

24

and

5)

RT[a

b]

Rew

ard

tole

ran

ceth

resh

old

sA

nex

ogen

ous

para

met

erth

atse

tsth

ebo

unds

ofac

cept

able

educ

atio

nale

xper

ienc

eVa

lues

outs

ide

this

rang

etr

igge

rtr

ack

chan

ges

ais

the

valu

eof

rtdo

wn

bth

atof

rtup

Edu

catio

nale

xper

ienc

eva

lues

low

erth

anrt

dow

ntr

igge

ra

mov

eto

alo

wer

-tra

ckco

urse

Val

ues

high

erth

anrt

uptr

igge

ra

mov

eto

ahi

gher

-tra

ckco

urse

abw

tA

bili

tyw

eig

ht

Am

odel

para

met

erth

atad

just

sth

ede

gree

tow

hich

achi

evem

ent

isa

func

tion

ofra

wab

ility

and

how

muc

ha

func

tion

ofpr

ior

lear

ning

(ach

ieve

men

t)

adw

tA

dap

tati

onw

eig

ht

Am

odel

para

met

erad

just

ing

the

degr

eeto

whi

chad

apta

tion

mod

erat

esth

eim

pact

ofpe

rfor

man

ceco

mpa

rison

s(r

elat

ive

tose

lfan

dre

lativ

eto

peer

s)on

the

way

the

educ

atio

nale

xper

ienc

eis

perc

eive

dby

the

stud

ent

pePe

eref

fect

wei

gh

tA

mod

elpa

ram

eter

adju

stin

gth

eex

tent

tow

hich

perf

orm

ance

isju

dged

rela

tive

toa

stud

entrsquos

prio

rpe

rfor

man

ceas

oppo

sed

toa

stud

entrsquos

perf

orm

ance

rela

tive

tohe

ror

his

peer

s


Fri 18 Dec 2009 181626


REFERENCES
































Fri 18 Dec 2009 181626


































Fri 18 Dec 2009 181626






Fri 18 Dec 2009 181626








Fri 18 Dec 2009 181626



NOTES














Fri 18 Dec 2009 181626















Fri 18 Dec 2009 181626






Fri 18 Dec 2009 181626


PP

END

IX

Tab

leA

1D

efin

itio

ns

ofVa

riab

les

and

Para

met

ers

Des

crip

tion

Rela

tions

hip

toO

ther

Mod

elVa

riabl

esEq

nN

o

Abi

lity

Ab

ility

Inv

aria

ntpr

oper

tyof

each

stud

ent

Stan

dard

norm

alFi

xed

mod

elva

riabl

edi

strib

utio

nse

ta

stud

entrsquos

ldquocre

atio

nrdquo(i

ee

ntry

into

the

syst

em)

AA

chie

vem

ent

isre

late

dto

abili

tyM

ore

able

stud

ents

gene

rally

For

inco

min

gst

uden

tsan

dst

uden

tsin

thei

rfir

stye

ar

1ac

hiev

em

ore

inac

adem

icte

rms

Ther

eis

also

ara

ndom

com

pone

nt

a ic

t=1

=Ab

ility

i0

6+

ε

04

(ε~

N(0

1))

to

achi

evem

ent

Ach

ieve

men

tde

pend

sno

ton

lyon

abili

ty

but

onw

hat

the

stud

ents

have

lear

ned

over

the

cour

seof

thei

rhi

ghIn

subs

eque

ntye

ars

scho

oled

ucat

iona

lcar

eers

toth

atpo

int

a ic

t=

Abili

tyi

abw

t+

(1ndasha

bwt)

andash ict

-10

6+

ε

04

2

GG

rad

esar

em

appe

dfr

omth

eem

piric

algr

ade

dist

ribut

ions

for

each

g ic

t=

G(a

icit

rsquoabulli

ct)

3co

urse

inth

etw

osc

hool

sst

udie

don

the

basi

sof

the

rank

orde

rof

achi

evem

ent

Gis

am

appi

ngfu

nctio

nth

atre

turn

sth

eap

prop

riate

grad

efo

rth

est

uden

trsquospo

sitio

nin

the

rank

orde

r(b

yac

hiev

emen

t)fo

ra

give

nco

urse

ina

give

nsc

hool

RtR

ewar

dto

lera

nce

depe

nds

onpr

ior

perf

orm

ance

and

stud

entrsquos

succ

ess

rtit

=pe

rfit

(1

ndashadw

t)+

adap

t it

adw

t4

inad

aptin

gto

chan

ges

inst

anda

rds

resu

lting

from

upw

ard

ordo

wnw

ard

trac

km

oves

(ada

ptab

ility

)

Perf

Rel

ativ

ep

erfo

rman

ceca

ptur

esth

ede

gree

tow

hich

the

stud

ents

perf

it=

(gic

tndashgndash ibull

t)

(1ndashp

e)+

(gic

tndashgndash c

t)pe

5ex

ceed

ed(o

rno

t)th

eir

prio

rpe

rfor

man

cean

dth

eir

perf

orm

ance

rela

tive

toth

eir

cour

seco

hort

adap

tA

dap

tab

ility

The

degr

eeto

whi

chth

est

uden

trsquospe

rfor

man

cech

ange

sad

apt i

t=

perf

itndash

perf

it-1

6fr

omon

epe

riod

toth

ene

xtA

dow

nwar

dm

ove

shou

ldca

use

are

duct

ion

inpe

rfor

man

ceb

utth

em

ore

adap

tabl

est

uden

tw

illsu

ffer

alo

wer

drop

than

will

ale

ssad

apta

ble

one

Con

vers

ely

anad

apta

ble

stud

ent

will

not

doas

wel

lin

alo

wer

trac

kas

one

who

refu

ses

toch

ange

his

orhe

rst

anda

rds

just

beca

use

heor

she

has

mov

eddo

wn

atr




PP

END

IX

Tab

leA

1C

onti

nue

d

Des

crip

tion

Mod

elPa

ram

eter

s(E

quat

ions

24

and

5)

RT[a

b]

Rew

ard

tole

ran

ceth

resh

old

sA

nex

ogen

ous

para

met

erth

atse

tsth

ebo

unds

ofac

cept

able

educ

atio

nale

xper

ienc

eVa

lues

outs

ide

this

rang

etr

igge

rtr

ack

chan

ges

ais

the

valu

eof

rtdo

wn

bth

atof

rtup

Edu

catio

nale

xper

ienc

eva

lues

low

erth

anrt

dow

ntr

igge

ra

mov

eto

alo

wer

-tra

ckco

urse

Val

ues

high

erth

anrt

uptr

igge

ra

mov

eto

ahi

gher

-tra

ckco

urse

abw

tA

bili

tyw

eig

ht

Am

odel

para

met

erth

atad

just

sth

ede

gree

tow

hich

achi

evem

ent

isa

func

tion

ofra

wab

ility

and

how

muc

ha

func

tion

ofpr

ior

lear

ning

(ach

ieve

men

t)

adw

tA

dap

tati

onw

eig

ht

Am

odel

para

met

erad

just

ing

the

degr

eeto

whi

chad

apta

tion

mod

erat

esth

eim

pact

ofpe

rfor

man

ceco

mpa

rison

s(r

elat

ive

tose

lfan

dre

lativ

eto

peer

s)on

the

way

the

educ

atio

nale

xper

ienc

eis

perc

eive

dby

the

stud

ent

pePe

eref

fect

wei

gh

tA

mod

elpa

ram

eter

adju

stin

gth

eex

tent

tow

hich

perf

orm

ance

isju

dged

rela

tive

toa

stud

entrsquos

prio

rpe

rfor

man

ceas

oppo

sed

toa

stud

entrsquos

perf

orm

ance

rela

tive

tohe

ror

his

peer

s


Fri 18 Dec 2009 181626


REFERENCES
































Fri 18 Dec 2009 181626


































Fri 18 Dec 2009 181626






Fri 18 Dec 2009 181626



NOTES














Fri 18 Dec 2009 181626















Fri 18 Dec 2009 181626






Fri 18 Dec 2009 181626


PP

END

IX

Tab

leA

1D

efin

itio

ns

ofVa

riab

les

and

Para

met

ers

Des

crip

tion

Rela

tions

hip

toO

ther

Mod

elVa

riabl

esEq

nN

o

Abi

lity

Ab

ility

Inv

aria

ntpr

oper

tyof

each

stud

ent

Stan

dard

norm

alFi

xed

mod

elva

riabl

edi

strib

utio

nse

ta

stud

entrsquos

ldquocre

atio

nrdquo(i

ee

ntry

into

the

syst

em)

AA

chie

vem

ent

isre

late

dto

abili

tyM

ore

able

stud

ents

gene

rally

For

inco

min

gst

uden

tsan

dst

uden

tsin

thei

rfir

stye

ar

1ac

hiev

em

ore

inac

adem

icte

rms

Ther

eis

also

ara

ndom

com

pone

nt

a ic

t=1

=Ab

ility

i0

6+

ε

04

(ε~

N(0

1))

to

achi

evem

ent

Ach

ieve

men

tde

pend

sno

ton

lyon

abili

ty

but

onw

hat

the

stud

ents

have

lear

ned

over

the

cour

seof

thei

rhi

ghIn

subs

eque

ntye

ars

scho

oled

ucat

iona

lcar

eers

toth

atpo

int

a ic

t=

Abili

tyi

abw

t+

(1ndasha

bwt)

andash ict

-10

6+

ε

04

2

GG

rad

esar

em

appe

dfr

omth

eem

piric

algr

ade

dist

ribut

ions

for

each

g ic

t=

G(a

icit

rsquoabulli

ct)

3co

urse

inth

etw

osc

hool

sst

udie

don

the

basi

sof

the

rank

orde

rof

achi

evem

ent

Gis

am

appi

ngfu

nctio

nth

atre

turn

sth

eap

prop

riate

grad

efo

rth

est

uden

trsquospo

sitio

nin

the

rank

orde

r(b

yac

hiev

emen

t)fo

ra

give

nco

urse

ina

give

nsc

hool

RtR

ewar

dto

lera

nce

depe

nds

onpr

ior

perf

orm

ance

and

stud

entrsquos

succ

ess

rtit

=pe

rfit

(1

ndashadw

t)+

adap

t it

adw

t4

inad

aptin

gto

chan

ges

inst

anda

rds

resu

lting

from

upw

ard

ordo

wnw

ard

trac

km

oves

(ada

ptab

ility

)

Perf

Rel

ativ

ep

erfo

rman

ceca

ptur

esth

ede

gree

tow

hich

the

stud

ents

perf

it=

(gic

tndashgndash ibull

t)

(1ndashp

e)+

(gic

tndashgndash c

t)pe

5ex

ceed

ed(o

rno

t)th

eir

prio

rpe

rfor

man

cean

dth

eir

perf

orm

ance

rela

tive

toth

eir

cour

seco

hort

adap

tA

dap

tab

ility

The

degr

eeto

whi

chth

est

uden

trsquospe

rfor

man

cech

ange

sad

apt i

t=

perf

itndash

perf

it-1

6fr

omon

epe

riod

toth

ene

xtA

dow

nwar

dm

ove

shou

ldca

use

are

duct

ion

inpe

rfor

man

ceb

utth

em

ore

adap

tabl

est

uden

tw

illsu

ffer

alo

wer

drop

than

will

ale

ssad

apta

ble

one

Con

vers

ely

anad

apta

ble

stud

ent

will

not

doas

wel

lin

alo

wer

trac

kas

one

who

refu

ses

toch

ange

his

orhe

rst

anda

rds

just

beca

use

heor

she

has

mov

eddo

wn

atr




PP

END

IX

Tab

leA

1C

onti

nue

d

Des

crip

tion

Mod

elPa

ram

eter

s(E

quat

ions

24

and

5)

RT[a

b]

Rew

ard

tole

ran

ceth

resh

old

sA

nex

ogen

ous

para

met

erth

atse

tsth

ebo

unds

ofac

cept

able

educ

atio

nale

xper

ienc

eVa

lues

outs

ide

this

rang

etr

igge

rtr

ack

chan

ges

ais

the

valu

eof

rtdo

wn

bth

atof

rtup

Edu

catio

nale

xper

ienc

eva

lues

low

erth

anrt

dow

ntr

igge

ra

mov

eto

alo

wer

-tra

ckco

urse

Val

ues

high

erth

anrt

uptr

igge

ra

mov

eto

ahi

gher

-tra

ckco

urse

abw

tA

bili

tyw

eig

ht

Am

odel

para

met

erth

atad

just

sth

ede

gree

tow

hich

achi

evem

ent

isa

func

tion

ofra

wab

ility

and

how

muc

ha

func

tion

ofpr

ior

lear

ning

(ach

ieve

men

t)

adw

tA

dap

tati

onw

eig

ht

Am

odel

para

met

erad

just

ing

the

degr

eeto

whi

chad

apta

tion

mod

erat

esth

eim

pact

ofpe

rfor

man

ceco

mpa

rison

s(r

elat

ive

tose

lfan

dre

lativ

eto

peer

s)on

the

way

the

educ

atio

nale

xper

ienc

eis

perc

eive

dby

the

stud

ent

pePe

eref

fect

wei

gh

tA

mod

elpa

ram

eter

adju

stin

gth

eex

tent

tow

hich

perf

orm

ance

isju

dged

rela

tive

toa

stud

entrsquos

prio

rpe

rfor

man

ceas

oppo

sed

toa

stud

entrsquos

perf

orm

ance

rela

tive

tohe

ror

his

peer

s


Fri 18 Dec 2009 181626


REFERENCES
































Fri 18 Dec 2009 181626


































Fri 18 Dec 2009 181626






Fri 18 Dec 2009 181626















Fri 18 Dec 2009 181626






Fri 18 Dec 2009 181626


PP

END

IX

Tab

leA

1D

efin

itio

ns

ofVa

riab

les

and

Para

met

ers

Des

crip

tion

Rela

tions

hip

toO

ther

Mod

elVa

riabl

esEq

nN

o

Abi

lity

Ab

ility

Inv

aria

ntpr

oper

tyof

each

stud

ent

Stan

dard

norm

alFi

xed

mod

elva

riabl

edi

strib

utio

nse

ta

stud

entrsquos

ldquocre

atio

nrdquo(i

ee

ntry

into

the

syst

em)

AA

chie

vem

ent

isre

late

dto

abili

tyM

ore

able

stud

ents

gene

rally

For

inco

min

gst

uden

tsan

dst

uden

tsin

thei

rfir

stye

ar

1ac

hiev

em

ore

inac

adem

icte

rms

Ther

eis

also

ara

ndom

com

pone

nt

a ic

t=1

=Ab

ility

i0

6+

ε

04

(ε~

N(0

1))

to

achi

evem

ent

Ach

ieve

men

tde

pend

sno

ton

lyon

abili

ty

but

onw

hat

the

stud

ents

have

lear

ned

over

the

cour

seof

thei

rhi

ghIn

subs

eque

ntye

ars

scho

oled

ucat

iona

lcar

eers

toth

atpo

int

a ic

t=

Abili

tyi

abw

t+

(1ndasha

bwt)

andash ict

-10

6+

ε

04

2

GG

rad

esar

em

appe

dfr

omth

eem

piric

algr

ade

dist

ribut

ions

for

each

g ic

t=

G(a

icit

rsquoabulli

ct)

3co

urse

inth

etw

osc

hool

sst

udie

don

the

basi

sof

the

rank

orde

rof

achi

evem

ent

Gis

am

appi

ngfu

nctio

nth

atre

turn

sth

eap

prop

riate

grad

efo

rth

est

uden

trsquospo

sitio

nin

the

rank

orde

r(b

yac

hiev

emen

t)fo

ra

give

nco

urse

ina

give

nsc

hool

RtR

ewar

dto

lera

nce

depe

nds

onpr

ior

perf

orm

ance

and

stud

entrsquos

succ

ess

rtit

=pe

rfit

(1

ndashadw

t)+

adap

t it

adw

t4

inad

aptin

gto

chan

ges

inst

anda

rds

resu

lting

from

upw

ard

ordo

wnw

ard

trac

km

oves

(ada

ptab

ility

)

Perf

Rel

ativ

ep

erfo

rman

ceca

ptur

esth

ede

gree

tow

hich

the

stud

ents

perf

it=

(gic

tndashgndash ibull

t)

(1ndashp

e)+

(gic

tndashgndash c

t)pe

5ex

ceed

ed(o

rno

t)th

eir

prio

rpe

rfor

man

cean

dth

eir

perf

orm

ance

rela

tive

toth

eir

cour

seco

hort

adap

tA

dap

tab

ility

The

degr

eeto

whi

chth

est

uden

trsquospe

rfor

man

cech

ange

sad

apt i

t=

perf

itndash

perf

it-1

6fr

omon

epe

riod

toth

ene

xtA

dow

nwar

dm

ove

shou

ldca

use

are

duct

ion

inpe

rfor

man

ceb

utth

em

ore

adap

tabl

est

uden

tw

illsu

ffer

alo

wer

drop

than

will

ale

ssad

apta

ble

one

Con

vers

ely

anad

apta

ble

stud

ent

will

not

doas

wel

lin

alo

wer

trac

kas

one

who

refu

ses

toch

ange

his

orhe

rst

anda

rds

just

beca

use

heor

she

has

mov

eddo

wn

atr




PP

END

IX

Tab

leA

1C

onti

nue

d

Des

crip

tion

Mod

elPa

ram

eter

s(E

quat

ions

24

and

5)

RT[a

b]

Rew

ard

tole

ran

ceth

resh

old

sA

nex

ogen

ous

para

met

erth

atse

tsth

ebo

unds

ofac

cept

able

educ

atio

nale

xper

ienc

eVa

lues

outs

ide

this

rang

etr

igge

rtr

ack

chan

ges

ais

the

valu

eof

rtdo

wn

bth

atof

rtup

Edu

catio

nale

xper

ienc

eva

lues

low

erth

anrt

dow

ntr

igge

ra

mov

eto

alo

wer

-tra

ckco

urse

Val

ues

high

erth

anrt

uptr

igge

ra

mov

eto

ahi

gher

-tra

ckco

urse

abw

tA

bili

tyw

eig

ht

Am

odel

para

met

erth

atad

just

sth

ede

gree

tow

hich

achi

evem

ent

isa

func

tion

ofra

wab

ility

and

how

muc

ha

func

tion

ofpr

ior

lear

ning

(ach

ieve

men

t)

adw

tA

dap

tati

onw

eig

ht

Am

odel

para

met

erad

just

ing

the

degr

eeto

whi

chad

apta

tion

mod

erat

esth

eim

pact

ofpe

rfor

man

ceco

mpa

rison

s(r

elat

ive

tose

lfan

dre

lativ

eto

peer

s)on

the

way

the

educ

atio

nale

xper

ienc

eis

perc

eive

dby

the

stud

ent

pePe

eref

fect

wei

gh

tA

mod

elpa

ram

eter

adju

stin

gth

eex

tent

tow

hich

perf

orm

ance

isju

dged

rela

tive

toa

stud

entrsquos

prio

rpe

rfor

man

ceas

oppo

sed

toa

stud

entrsquos

perf

orm

ance

rela

tive

tohe

ror

his

peer

s


Fri 18 Dec 2009 181626


REFERENCES
































Fri 18 Dec 2009 181626


































Fri 18 Dec 2009 181626






Fri 18 Dec 2009 181626






Fri 18 Dec 2009 181626


PP

END

IX

Tab

leA

1D

efin

itio

ns

ofVa

riab

les

and

Para

met

ers

Des

crip

tion

Rela

tions

hip

toO

ther

Mod

elVa

riabl

esEq

nN

o

Abi

lity

Ab

ility

Inv

aria

ntpr

oper

tyof

each

stud

ent

Stan

dard

norm

alFi

xed

mod

elva

riabl

edi

strib

utio

nse

ta

stud

entrsquos

ldquocre

atio

nrdquo(i

ee

ntry

into

the

syst

em)

AA

chie

vem

ent

isre

late

dto

abili

tyM

ore

able

stud

ents

gene

rally

For

inco

min

gst

uden

tsan

dst

uden

tsin

thei

rfir

stye

ar

1ac

hiev

em

ore

inac

adem

icte

rms

Ther

eis

also

ara

ndom

com

pone

nt

a ic

t=1

=Ab

ility

i0

6+

ε

04

(ε~

N(0

1))

to

achi

evem

ent

Ach

ieve

men

tde

pend

sno

ton

lyon

abili

ty

but

onw

hat

the

stud

ents

have

lear

ned

over

the

cour

seof

thei

rhi

ghIn

subs

eque

ntye

ars

scho

oled

ucat

iona

lcar

eers

toth

atpo

int

a ic

t=

Abili

tyi

abw

t+

(1ndasha

bwt)

andash ict

-10

6+

ε

04

2

GG

rad

esar

em

appe

dfr

omth

eem

piric

algr

ade

dist

ribut

ions

for

each

g ic

t=

G(a

icit

rsquoabulli

ct)

3co

urse

inth

etw

osc

hool

sst

udie

don

the

basi

sof

the

rank

orde

rof

achi

evem

ent

Gis

am

appi

ngfu

nctio

nth

atre

turn

sth

eap

prop

riate

grad

efo

rth

est

uden

trsquospo

sitio

nin

the

rank

orde

r(b

yac

hiev

emen

t)fo

ra

give

nco

urse

ina

give

nsc

hool

RtR

ewar

dto

lera

nce

depe

nds

onpr

ior

perf

orm

ance

and

stud

entrsquos

succ

ess

rtit

=pe

rfit

(1

ndashadw

t)+

adap

t it

adw

t4

inad

aptin

gto

chan

ges

inst

anda

rds

resu

lting

from

upw

ard

ordo

wnw

ard

trac

km

oves

(ada

ptab

ility

)

Perf

Rel

ativ

ep

erfo

rman

ceca

ptur

esth

ede

gree

tow

hich

the

stud

ents

perf

it=

(gic

tndashgndash ibull

t)

(1ndashp

e)+

(gic

tndashgndash c

t)pe

5ex

ceed

ed(o

rno

t)th

eir

prio

rpe

rfor

man

cean

dth

eir

perf

orm

ance

rela

tive

toth

eir

cour

seco

hort

adap

tA

dap

tab

ility

The

degr

eeto

whi

chth

est

uden

trsquospe

rfor

man

cech

ange

sad

apt i

t=

perf

itndash

perf

it-1

6fr

omon

epe

riod

toth

ene

xtA

dow

nwar

dm

ove

shou

ldca

use

are

duct

ion

inpe

rfor

man

ceb

utth

em

ore

adap

tabl

est

uden

tw

illsu

ffer

alo

wer

drop

than

will

ale

ssad

apta

ble

one

Con

vers

ely

anad

apta

ble

stud

ent

will

not

doas

wel

lin

alo

wer

trac

kas

one

who

refu

ses

toch

ange

his

orhe

rst

anda

rds

just

beca

use

heor

she

has

mov

eddo

wn

atr




PP

END

IX

Tab

leA

1C

onti

nue

d

Des

crip

tion

Mod

elPa

ram

eter

s(E

quat

ions

24

and

5)

RT[a

b]

Rew

ard

tole

ran

ceth

resh

old

sA

nex

ogen

ous

para

met

erth

atse

tsth

ebo

unds

ofac

cept

able

educ

atio

nale

xper

ienc

eVa

lues

outs

ide

this

rang

etr

igge

rtr

ack

chan

ges

ais

the

valu

eof

rtdo

wn

bth

atof

rtup

Edu

catio

nale

xper

ienc

eva

lues

low

erth

anrt

dow

ntr

igge

ra

mov

eto

alo

wer

-tra

ckco

urse

Val

ues

high

erth

anrt

uptr

igge

ra

mov

eto

ahi

gher

-tra

ckco

urse

abw

tA

bili

tyw

eig

ht

Am

odel

para

met

erth

atad

just

sth

ede

gree

tow

hich

achi

evem

ent

isa

func

tion

ofra

wab

ility

and

how

muc

ha

func

tion

ofpr

ior

lear

ning

(ach

ieve

men

t)

adw

tA

dap

tati

onw

eig

ht

Am

odel

para

met

erad

just

ing

the

degr

eeto

whi

chad

apta

tion

mod

erat

esth

eim

pact

ofpe

rfor

man

ceco

mpa

rison

s(r

elat

ive

tose

lfan

dre

lativ

eto

peer

s)on

the

way

the

educ

atio

nale

xper

ienc

eis

perc

eive

dby

the

stud

ent

pePe

eref

fect

wei

gh

tA

mod

elpa

ram

eter

adju

stin

gth

eex

tent

tow

hich

perf

orm

ance

isju

dged

rela

tive

toa

stud

entrsquos

prio

rpe

rfor

man

ceas

oppo

sed

toa

stud

entrsquos

perf

orm

ance

rela

tive

tohe

ror

his

peer

s


Fri 18 Dec 2009 181626


REFERENCES
































Fri 18 Dec 2009 181626


































Fri 18 Dec 2009 181626






Fri 18 Dec 2009 181626


PP

END

IX

Tab

leA

1D

efin

itio

ns

ofVa

riab

les

and

Para

met

ers

Des

crip

tion

Rela

tions

hip

toO

ther

Mod

elVa

riabl

esEq

nN

o

Abi

lity

Ab

ility

Inv

aria

ntpr

oper

tyof

each

stud

ent

Stan

dard

norm

alFi

xed

mod

elva

riabl

edi

strib

utio

nse

ta

stud

entrsquos

ldquocre

atio

nrdquo(i

ee

ntry

into

the

syst

em)

AA

chie

vem

ent

isre

late

dto

abili

tyM

ore

able

stud

ents

gene

rally

For

inco

min

gst

uden

tsan

dst

uden

tsin

thei

rfir

stye

ar

1ac

hiev

em

ore

inac

adem

icte

rms

Ther

eis

also

ara

ndom

com

pone

nt

a ic

t=1

=Ab

ility

i0

6+

ε

04

(ε~

N(0

1))

to

achi

evem

ent

Ach

ieve

men

tde

pend

sno

ton

lyon

abili

ty

but

onw

hat

the

stud

ents

have

lear

ned

over

the

cour

seof

thei

rhi

ghIn

subs

eque

ntye

ars

scho

oled

ucat

iona

lcar

eers

toth

atpo

int

a ic

t=

Abili

tyi

abw

t+

(1ndasha

bwt)

andash ict

-10

6+

ε

04

2

GG

rad

esar

em

appe

dfr

omth

eem

piric

algr

ade

dist

ribut

ions

for

each

g ic

t=

G(a

icit

rsquoabulli

ct)

3co

urse

inth

etw

osc

hool

sst

udie

don

the

basi

sof

the

rank

orde

rof

achi

evem

ent

Gis

am

appi

ngfu

nctio

nth

atre

turn

sth

eap

prop

riate

grad

efo

rth

est

uden

trsquospo

sitio

nin

the

rank

orde

r(b

yac

hiev

emen

t)fo

ra

give

nco

urse

ina

give

nsc

hool

RtR

ewar

dto

lera

nce

depe

nds

onpr

ior

perf

orm

ance

and

stud

entrsquos

succ

ess

rtit

=pe

rfit

(1

ndashadw

t)+

adap

t it

adw

t4

inad

aptin

gto

chan

ges

inst

anda

rds

resu

lting

from

upw

ard

ordo

wnw

ard

trac

km

oves

(ada

ptab

ility

)

Perf

Rel

ativ

ep

erfo

rman

ceca

ptur

esth

ede

gree

tow

hich

the

stud

ents

perf

it=

(gic

tndashgndash ibull

t)

(1ndashp

e)+

(gic

tndashgndash c

t)pe

5ex

ceed

ed(o

rno

t)th

eir

prio

rpe

rfor

man

cean

dth

eir

perf

orm

ance

rela

tive

toth

eir

cour

seco

hort

adap

tA

dap

tab

ility

The

degr

eeto

whi

chth

est

uden

trsquospe

rfor

man

cech

ange

sad

apt i

t=

perf

itndash

perf

it-1

6fr

omon

epe

riod

toth

ene

xtA

dow

nwar

dm

ove

shou

ldca

use

are

duct

ion

inpe

rfor

man

ceb

utth

em

ore

adap

tabl

est

uden

tw

illsu

ffer

alo

wer

drop

than

will

ale

ssad

apta

ble

one

Con

vers

ely

anad

apta

ble

stud

ent

will

not

doas

wel

lin

alo

wer

trac

kas

one

who

refu

ses

toch

ange

his

orhe

rst

anda

rds

just

beca

use

heor

she

has

mov

eddo

wn

atr




PP

END

IX

Tab

leA

1C

onti

nue

d

Des

crip

tion

Mod

elPa

ram

eter

s(E

quat

ions

24

and

5)

RT[a

b]

Rew

ard

tole

ran

ceth

resh

old

sA

nex

ogen

ous

para

met

erth

atse

tsth

ebo

unds

ofac

cept

able

educ

atio

nale

xper

ienc

eVa

lues

outs

ide

this

rang

etr

igge

rtr

ack

chan

ges

ais

the

valu

eof

rtdo

wn

bth

atof

rtup

Edu

catio

nale

xper

ienc

eva

lues

low

erth

anrt

dow

ntr

igge

ra

mov

eto

alo

wer

-tra

ckco

urse

Val

ues

high

erth

anrt

uptr

igge

ra

mov

eto

ahi

gher

-tra

ckco

urse

abw

tA

bili

tyw

eig

ht

Am

odel

para

met

erth

atad

just

sth

ede

gree

tow

hich

achi

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Fri 18 Dec 2009 181626


REFERENCES
































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PP

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Fri 18 Dec 2009 181626


REFERENCES
































Fri 18 Dec 2009 181626


































Fri 18 Dec 2009 181626






Fri 18 Dec 2009 181626


REFERENCES
































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Fri 18 Dec 2009 181626

Documents

Organization by Design: Supply- and Demand-side Models of ... · tic models of educational career systems and to validate them via comparisons to observed reality. COURSE-TAKING LITERATURE