The Influence of Ability Grouping on Math Achievement in a Rural Middle School

Transcription

1 Seon Hall Universiy Seon Hall Seon Hall Universiy Disseraions and Theses (ETDs) Seon Hall Universiy Disseraions and Theses Fall 2012 The nfluence of Abiliy Grouping on Mah Achievemen in a Rural Middle School Rober R. Prichard Seon Hall Universiy Follow his and addiional works a: hp://scholarship.shu.edu/disseraions Par of he Elemenary and Middle and Secondary Educaion Adminisraion Commons Recommended Ciaion Prichard, Rober R., "The nfluence of Abiliy Grouping on Mah Achievemen in a Rural Middle School" (2012). Seon Hall Universiy Disseraions and Theses (ETDs) hp://scholarship.shu.edu/disseraions/1817

2 f THE NFLUENCE OF ABLTY GROUPll\lG ON MATH ACHEVEMENT N A RURAL MDDLE SCHOOL ROBERT R. PRTCHARD Disseraion Commiee Charles M. Achilles, Ed.D., Menor Barbara Srober, Ed.D. James A. Douglass, Ed.D. Parick Darfier-Sweeney, Ed.D. Submied in Parial Fulfillmen ofhe Requiremens for he Degree of Docor ofeducaion Seon Hall Universiy 2012, " ~ i ~

3 SETON HALL UNVERSTY COLLEGE OF EDUCATON AND HUMAN SERVCES ~ OFFCE OF GRADUATE STUDES 1,! ~ APPROVAL FOR SUCCESSFUL DEFENSE fi Docoral Candidae, Rober Prichard, has successfully defended and made he required ~ modificaions o he ex of he docoral disseraion for he Ed.D. during his Summer Semeser DSSERTATON COMMTTEE (please sign and dae beside your name) Menor: Dr. Charles Achilles r,j( k ~jj~ f J, O~! Commiee Member: Dr. Barbara Srober ~A 7/ i1 ()i > Commiee Member:~ Dr. James Doue.las \.>- Commiee Member: Dr, Parick Darfler-Sweene Exernal Reader: l i 1 Er:l.l>. 7/~~/ Z- f r i ~ j ~ ~ if f i ~ f,! f The menor and any oher commiee members who wish o review revisions will sign and dae his documen only when revisions have been compleed, Please reurn his form o he Office of Graduae Sudies, where i will be placed in he candidae's file and submi a copy wih your final disseraion o be bound as page number wo. l i ~

4 ABSTRACT The researcher examined he academic performance oflow-racked sudens (n=156) using sandardized mah es scores o deermine wheher here is a saisically significan difference in achievemen depending on academic environmen, racked or nonracked. An analysis of variance (ANOVA) was calculaed, using a paired samples es for a single cohor as boh low- and high-racked sudens were reorganized from heerogeneous course assignmens in Grades 6 and 7 o an abiliy-grouped assignmen in Grade 8. The researcher conduced a non-experimenal sudy o analyze he influence of racking on he academic achievemen ofnon-acceleraed sudens as measured by Grade 8 sandardized mah scores. The researcher analyzed he daa using a longiudinal explanaory design. The daa used were he NYSTP Mah scores for a single cohor over a hree-year period in Grades 6 hrough 8. An analysis ofhe daa revealed ha soring he sudens ino wo groups for he purposes of mah insrucion - acceleraed and sandard curriculum - did no have a posiive influence on mah achievemen for eiher group. The lower-racked sudens demonsraed saisically significan decreases (p<.05) in performance on sandardized mah esing when assigned o a non-acceleraed course ofinsrucion. Furhermore, he paern ofdeclining mah achievemen for economically disadvanaged sudens enrolled in a racked environmen is significanly greaer han he paern ofdecline when compared o he group as a whole. n his insance, low SES sudens do no have he same access o a high qualiy curriculum as heir wealhier peers. This pus sudens who are already in crisis a an even greaer disadvanage. A a ime when offering greaer resources o low SES sudens would benefi hem he mos, hese 11

5 sudens are assigned o a lower-racked insrucional grouping. The findings of his sudy suppor he eliminaion of a racked academic environmen for middle schools endeavoring o improve he achievemen of academically a-risk sudens. i!!! ~ ~ o f, f ~ ~ ~ 1 " ~ i e

6 ACKNOWLEDGMENTS This research has renewed my sense of service o hose who are disenfranchised i, i 1 and lack he capaciy o be ruly successful- however ha may be defined in our U.S. educaion sysem. Perhaps one of he mos influenial scholars in research relaed o his field is my menor, Dr. Charles Achilles, who has helped me, and many ohers, o sor hrough he noise and confusion ofwha is relevan, and wha is no, when designing a sysem ha promoes excellence and equiy - wo variables ha should no be exclusive from each oher. Dr. Achilles has provided he consrucive feedback ha has guided me i r. l r i i oward educaional milesones; and for his, am graeful i!i am also indebed o Dr. Barbara Srober for her posiive aiude, calm spiri, and for inspiring in me a love for he profession. She provided a space for me in which was able o creae my bes inellecual argumens while being ever-mindful of he emoional elemens ha shape public school adminisraion. Lasly, am graeful o Drs. James Douglass and Parick Darfler-Sweeney, wo school adminisraors whom have known over he years who have helped me o reconcile heoreical perspecives presened in he research wih bes-pracices and inuiion. These sars are no always aligned; bu when hey are, grea hings happen for sudens. i! f ~ ~ ( ~ ~ i f V

7 DEDCATON dedicae his disseraion o Sharon, my loving wife, as well as o our son and daugher, Rober and Jane, who oo ofen had o sacrifice heir own needs during his process. Throughou his endeavor, and many oher challenging life-evens for ha maer, my wife and our children have mainained heir own personal commimens o excellence while supporing me in mine. They are he reason for all ha do and a reflecion ofall ha am. would also like o dedicae his o my moher and faher, Jacqueline and Rober, who enabled in me an undersanding ofhuman creaiviy as a funcion ofa disciplined mind and an open hear. v

8 Table of Conens ABSTRACT...ii ACKNOWLEDGMENTS....iv DEDCATON...v LST OF TABLES...ix LST OF FGURES...x CHAPTER 1. NTRODUCTON AND BACKGROUND... 1 nroducion...1 Saemen of he Problem...3 Purpose for he Sudy...7 Concepual Framework...7 Research Quesions Design and Mehodology Significance ofhe Sudy Delimiaions of he Sudy...12 Limiaions of he Sudy Summary CHAPTER 2. REVEW OF RESEARCH, THEORY, AND PRACTCE nroducion...16 The Hisory of Homogeneous Grouping and Abiliy Grouping...18 The Need for Heerogeneous nsrucional Grouping...22 Advanages and Disadvanages of Heerogeneous Grouping...25 Summary...28 V

9 CHAPTER 3. RESEARCH DESGN AND METHODS Overview...29 Descripion of he School Disric !~ f i!! Research Design...33 Mehods...35 nsrumenaion...36 nernal and Exernal Validiy...40 Daa Collecion...41 Daa Analysis...43 Swnmary...45 CHAPTER 4. RESULTS OF DATA ANALYSS...46 Hypohesis...46 Daa Collecion...46 Daa Analyses and Resuls...47 Swnmary...55 CHAPTER 5. SUMMARY, CONCLUSONS, DSCUSSON, AND RECOMMENDATONS FOR POLCY, PRACTCE, AND FURTHER RESEARCH...56 Swnmary...59 Conclusions...63 Recommendaions for Policy, Pracice, and for Furher Research...66 REFERENCES...75 Vll

10 APPENDCES Appendix A: Glossary ofterms Appendix B: RB non-review Cerificaion Appendix C: Disric Approval o Conduc Sudy Vlll

11 LST OF TABLES Table. Two-Year Cohor Trend by Risk-Caegory on NYS Mah Assessmen Table 2. Disribuion of Mean Scores NYS Mah Grade 6 ( ) Table 3. Disribuion ofmean Scores NYS Mah Grade 7 ( ) Table 4. Disribuion ofmean Scores NYS Mah Grade 8 ( ) Table 5: Types of Research Obained by Crossing Research Objecive and Time Dimension Table 6: Typography of abiliy groups o be sudied using mean scores on NYS Mah Assessmens..., Table 7: Paired Samples -Tes Comparing Grades 6 and 7 NYSTP Mah Scores Table 8: Paired Samples -Tes Comparing Grades 7 and 8 NYSTP Mah Scores Table 9: Paired Samples -Tes Comparing Grades 7 and 8 NYSTP Mah Scores (Low SES) X

12 LST OF FGURES Figure 1. Carroll's Model for School-Based Learning (1963)... 9 Figure 2. Suden nsrucional Grouping Changes for Mah 6, 7, and x

13 1 CHAPTER 1 NTRODUCTON AND BACKGROUND nroducion n response o he increasing pressure for public schools o produce masery levels of suden achievemen, school adminisraors have considered changing insrucional groupings. The federal governmen provides funding o schools wih lower han average financial resources, which ofen requires ha insrucional groupings include academic inervenion programs and oher remedial offerings for sudens. As such, many of hese schools receiving federal funding end o channel sudens ino less rigorous academic programs. Many policymakers, educaors, and researchers consider his pracice of abiliy grouping o be a form of racking. Tracking is he process of soring sudens by academic abiliy, a process ha many researchers consider o be derimenal o he learning needs of sudens. This process has also been deermined o be illegal when, as deermined in he case of Hobsen v. Hansen (1971), Judge J. Skelly Wrigh concluded ha "racially and socially homogeneous schools damage he minds and spiris of all children in lower racks for reduced educaion based on (inappropriae) ess, hus implemening he self fulfilling prophecy inheren in such misjudgmens. The scholasic achievemen of he disadvanaged child, Negro and Whie, is srongly relaed o he racial and socio-economic composiion of he suden body" (Cuban, 1975). n he school year, he Mexico Middle School, a middle school wih approximaely 600 sudens, Grades 5 hrough 8, acceped funding under he No Child Lef Behind (NCLB) legislaion for an adequae yearly progress (A YP) deficiency o be used o improve he achievemen of sudens wih disabiliies. Specifically, he N ew York

14 2 Sae Educaion Deparmen (NYSED) idenified his deficiency as lower han expeced achievemen by classified sudens on saewide high-sakes esing in he area of English Language Ars (ELA) in Grades 7 and 8. n order o remedy his siuaion mandaed by NCLB legislaion, he school's adminisraion used Tile funding o provide remediaion or Academic nervenion Services (AS) for underperforming sudens in an effor o mee A YP goals in ELA insrucion. The applicaion of hese funds ypically resuled in an emphasis on abiliy grouping, since underachieving sudens were someimes "pulled ou" of regular academic programming for he purpose of remediaion. School adminisraors assigned sudens o abiliy-grouped classes for ELA insrucion which, in um, dicaed he sudens' schedules for he res of he school day. Also, he op-performing sudens in Grade 8 mah were "pulled" ino a secion of negraed Algebra insrucion, he op rack for all eighh-grade sudens. While suden class assignmens remain largely heerogeneous, he school's adminisraors assigned he op performing eighh-grade sudens o more rigorous, acceleraed programs. Having removed a seleced group for more rigorous mah insrucion, he adminisraors hen assigned he remaining sudens o insrucional groups ha refleced he sudens' performance on ELA esing from he previous year, anoher sympom ofhe adminisraors' response o he NCLB mandae for inervenion. While school adminisraors made some aemp o place sudens ino heerogeneous class assignmens in mah, facors such as placemen for ELA academic services and racking for he highes performing mah sudens were dicaed by purely random assignmen. As such, he sudens' scores from he saewide ELA examinaion from he prior year became he primary facor ha a guidance counselor employed o deermine each suden's

15 3 schedule for mah. n he fall of2011, NYSED again lised he Mexico Middle School "in need of improvemen," as he school had again failed o mee is A YP requiremens on ELA assessmen for sudens wih disabiliies as well as hose sudens considered o be economically disadvanaged. By randomly assigning sudens ino more challenging coursework, he school's adminisraors sough o improve mah insrucion while eliminaing he harmful influence ofracking. NYSED classified he Mexico Middle School as "in saisfacory sanding" since he aggregae populaions exceeded A YP in mah and ELA on New York Sae nermediae level assessmens. However, performance indices for sudens considered disabled and/or economically disadvanaged were in he lowes performing subgroups in he school year. Sudens in hese subgroups received NCLB prescribed academic inervenions ha were more remedial han rigorous in naure. This emphasis on remediaion over acceleraion calls ino quesion he worhiness of Public Law (NCLB). Furher, he legal picure became complicaed, as he Sixh Federal Circui Cour had ruled ha pars ofnclb were unconsiuional. This was because he federal governmen had no provided clear noice o he saes ofhe cos implicaions when saes acceped NCLB funding. The siuaion was furher confused, as he Secreary of Educaion's inerpreaion of he NCLB unfunded mandaes provision was no correc (Walsh & Mark, 2008). Saemen of he Problem A-risk suden groups have minimal access o acceleraed mah classes a Mexico Middle School in Grade 8. Mos ofhe economically disadvanaged and learning-disabled

16 4 sudens are unlikely o mee he sandards of perfonnance on NYS middle-level assessmens as deennined by he NYSED, whereas wealhier, general educaion sudens are far more likely o exceed NYSED perfonnance sandards. The able below illusraes he percenages of sudens by caegory who scored less han a "Level 3" perfonnance index on he 2009 New York Sae Middle Level Mah Assessmen for Grades7 and 8. NYSED classifies a "Level 3" perfonnance index as "meeing he sandard" (NYSED, 2011). Table 1 Two-Year Cohor Trend by Risk-Caegory on NYS Mah Assessmen Sub-group Grade 7 no meeing he sandards No Disadvanaged 21% 39% Economically Disadvanaged 44% 60% General Educaion Sudens 21 % 41% Suden wih Disabiliies Source: (NYSED, 2011) Grade 8 no meeing he sandards 85% 86% The pracice of soring sudens according o abiliy coninues in spie of he research illusraing he manner in which low-rack classes fail o serve sudens. Furher, school adminisraors who sor sudens in his manner creae an even more damaging learning environmen for disabled and economically disadvanaged sudens (Rubin, 2008). Rubin and ohers have posied ha he pracice of racking persiss due o inheren insiuional poliics, beliefs, values, and culure as much as o "echnical, srucural, or organizaional needs" (Burris, Heuber, & Levin, 2004). nuiively, many educaors and parens finnly believe ha segregaing high achievers according o heir abiliies will

17 5 provide learning benefis no found in a less-challenging curriculum. Findings on he influence ofheerogeneous grouping upon suden achievemen have provided mixed resuls. Resuls from some sudies have suggesed improved achievemen for low-racked sudens in mixed-abiliy insrucional groups (Burris, Wener, Wiley, & Murphy, 2007; Marzano, Pickering, & Pollock, 2004; Oakes, 1985; Oakes, Wells, Jones, & Danow, 1997; Slavin, Lake, & Groff, 2009), while ohers have suggesed ha high-achieving sudens may well suffer in heerogeneous groups (Kulik, 1992; Loveless, 1999). Several researchers have even suggesed ha here is no saisically significan influence on highachieving sudens assigned o mixed-abiliy insrucional groups (Oakes, Wells, Jones, & Danow, 1997; Slavin, Lake, & Groff, 2009). However, here is now emerging research o srongly indicae ha deracking can and does improve achievemen resuls for marginalized sudens in wealhier, suburban communiies (Welner & Burris, 2006). Tracking or "abiliy grouping" coninues o be employed in schools o group sudens wih he same skill levels or abiliy for he purpose of achieving specific goals which are believed o be aainable by each suden in he group. Tracking akes on many differen forms, depending on he paricular school's or individual eacher's policies. Abiliy grouping can begin or ake he form ofsudens being grouped wihin a classroom where hey break ino small groups wihin he class o receive specific insrucion. Ofen, his ype ofdiffereniaed insrucion occurs in he earlies grades. However, as sudens progress ino higher grades hey may be grouped ino enirely separae classrooms where sudens of differen abiliy groups ake classes wih differen eachers, insrucional maerials, or a a differen pace. Evenually, hese sudens may be separaed ino differen courses or "racks" of insrucion. When racked sudens reach high school, some have

18 6 already been "racked" ino courses ha will lead o a college preparaory course ofsudy and exposure o he maerials ha will be esed on high school graduaion ess or college enrance exams, whereas oher sudens may be direced o vocaional opporuniies. The effec ofracking ofen has he uninended consequence of negaive aiudes and percepions, which may influence suden learning and subsequen scores on New York Sae sandardized esing in he area of middle level mahemaics (Boaler, 2007). n Mexico Cenral School Disric, adminisraors have aemped o address he negaive aiudes ha were eviden in "racked" classes in he middle school by scheduling nearly all sudens wih disabiliies ino heerogeneous classes. The majoriy of sudens were placed ino heerogeneous mah classes in Sepember 2008 when he middle school was iniially deemed in a sae of"correcive acion" by NYSED. However, concerns coninued o exis over he performance of a-risk sudens when hese sudens were assigned o mah classes ha did no include he op performing mah sudens. Before siuaions such as his can be addressed in he fuure, i is imperaive o have a beer, fuller undersanding of why sudens coninue o be sored by abiliy and wha challenges persis ha preven random assignmen of sudens. Therefore, he researcher's quesions were cenered on differences in suden achievemen on NYS sandardized esing as a funcion of sudens having greaer access o more challenging course work in mahemaics. The quesion ha warraned aenion and was reviewed in his sudy is as follows: How does he absence of higher-achieving sudens and lack of access o acceleraed coursework influence he achievemen of he general populaion of sudens in eighhgrade mah in a rural, high-povery middle school? As he highes performing sevenh

19 7 grade mah sudens had been "skimmed" off he op for he purposes of acceleraed mah placemen in eighh grade, his researcher's quesions were cenered on he impac of mah insrucion for "non-acceleraed" eighh-grade sudens. Simply saed, does he achievemen gap widen from Grade 7 o 8 for a-risk sudens who were "nonacceleraed?" How did sudens' scores differ in classes where sudens were grouped heerogeneously as compared o classes where he op-performing sudens had been removed? Previous research compared academic achievemen as i relaed o grouping pracices, bu none ofhe sudies provided daa o compare pre- and pos-grouping scores on NYS middle-level mah ess where he highes achieving sudens had been removed from wha would have oherwise been a mixed-abiliy class. Purpose The researcher's purpose for his sudy was o deermine if and how he achievemen of he general populaion of sudens may be influenced when he opperforming sudens are removed from he regular course of sudy ino acceleraed mah programming. Concepual Framework One ofhe concepual models used o frame his sudy is John Carroll's (1963) Model of School Learning. This model describes learning as a funcion of four variables: ime, capaciy, effor, and qualiy of resources (Figure 1). The researcher's purpose for his sudy is o deermine ifand how he achievemen ofhe general populaion of sudens may be influenced when he op-performing sudens are removed from he regular course of sudy ino acceleraed mah programming. This researcher considers all four variables as presened by Carroll's Model of School Learning: (1) resriced access ofracked

20 8 sudens o high-qualiy resources, (2) lack ofcapaciy due o limied preparaion or prior knowledge concerning mah conen, (3) reduced effor semming from low expecaions, (4) and reduced ime spen on developmen ofconen knowledge, especially during aferschool hours, which creaes a siuaion where a-risk sudens are likely o be unsuccessful. This being he case, his researcher would sugges ha sudens who are inherenly disadvanaged should have greaer access o a high-rack mah curriculum, no less, if ideals ofequal opporuniy o learn are o be achieved wihin a diversiy of educaional objecives. Carroll considered he ime needed for effecive learning o be a funcion ofabiliy o learn academic maerial, abiliy o undersand insrucion, and he qualiy of insrucion iself. One measure ofabiliy o learn academic maerial, according o Carroll, would be Q. The preparedness ofa suden o undersand insrucion describes he suden's abiliy o undersand wha he or she is augh. f a suden is persisenly assigned o low-rack classes, i is reasonable o sugges ha he or she may have limied abiliy o undersand insrucion if assigned o a high-rack course. Carroll did no specifically address heerogeneous insrucional grouping as a componen of learning; however, a low-racked insrucional grouping, in mah or any oher course of sudy, resrics all four componens ofcarroll's' model for school-based learning (1963).

21 9 -lnelle'cual abiliy -Personaliy - Healh and nuriion -Emoional sae of he learner -Referenced o i11>aricular learning ask or subjec -Sudens of lower capaciy who pu in grea effor mlly learn considerably more han hose of higher capaciy who do no pu in sudl effor -Effor is derivaive of moivaion and incenives, facors ha are ofen denoed in oher learning models -Qualiy of eaching -Characerisics of he curriwlum -Organizaion of insrucion -Availabiliy of maerials -CJlaraerisics of fellow sudens -Qualiy of he learning faciliy HOllle environmen Time devoed o suden effor Can be allocaed boh inside and ouside he classroom f Figure 1 Carroll's Modelfor School-Based Learning (1963) Carroll's model has become he groundwork for a number of oher research effors designed o classify he primary variables ha are deerminans of school learning. To his end, he work of Henry M. Levin on he characerisics of acceleraed educaion and he i! 1 applicabiliy of acceleraed educaion o a-risk sudens (1988) has served as he second concepual model for his sudy. Levin's repor on disadvanaged sudens' access o acceleraed courses (1988) in combinaion wih Carol Burris' research (2003) concerning how sudens' mah course-aking paerns and mah achievemen are affeced when sudens sudy mah in heerogeneously grouped classes serve as a framework for his researcher's sudy. While many researchers have examined he influence ofheerogeneous

22 10 insrucional grouping in schools, his sudy is unique in ha he research effor is cenered upon he effecs associaed wih low SES sudens sored ino a non-acceleraed middle school mah course. Burris (2006) showed ha he probabiliy of compleion of advanced mah courses increased significanly in all groups, including minoriy sudens, sudens of low socioeconomic saus, and sudens a all iniial achievemen levels when placed in heerogeneous insrucional groupings in high school mah. Research Quesions 1. Wha is he difference, if any, beween he NYS Middle Level Mah Assessmen performance for lower-achieving sudens in Grade 6 (heerogeneous insrucional grouping) and he performance for he same sudens in Grade 7 (also grouped heerogeneousl y)? 2. Wha is he difference, if any, beween he NYS Middle Level Mah Assessmen performance for lower-achieving sudens in Grade 7 (heerogeneous insrucional grouping) and he performance for he same sudens in Grade 8 (homogeneous insrucional grouping)? 3. Wha is he difference, ifany, beween he NYS Middle Level Mah Assessmen performance for economically disadvanaged sudens in Grade 7 (heerogeneous insrucional grouping) and he performance for he same sudens in Grade 8 (homogeneous insrucional grouping)? Design and Mehodology The researcher examined he academic performance of low-racked sudens (n=156) using sandardized mah es scores o deermine wheher here was a saisically significan difference in achievemen depending on academic environmen: racked or

23 11 non-racked. The researcher analyzed he daa using a non-experimenal, longiudinal explanaory design. The daa used were he NYSTP Mah scores for a single cohor over a hree-year period in Grades 6 hrough 8. Using quaniaive mehods, an analysis ofvariance (ANOVA) was calculaed, using a paired samples -es for a single cohor ha was reorganized from heerogeneous course assignmens in Grades 6 and 7 o an abiliy-grouped assignmen in Grade 8. The researcher conduced a non-experimenal sudy o analyze he influence of racking on he academic achievemen of non-acceleraed sudens as measured by Grade 8 sandardized mah scores. The researcher employed a quaniaive mehod using daa aken from NYS Assessmen scores for middle-school mahemaics examinaions. Scores were aken from a cohor ofapproximaely 150 sudens from heir sixh ( ), sevenh ( ) and eighh ( ) grade NYS Mah Assessmens and analyzed o beer undersand he process of abiliy grouping as sudens were promoed from grade o grade o include he manner in which sudens qualified for AS and acceleraed placemen in he final year of middle school, Grade 8. Archival suden records (Mah 6, 7, and 8 es scores by groupings) provided he basis for he collecion of quaniaive daa and provided insigh ino he subjecs ofhe sudy, general educaion sudens aending a Grades 5 hrough 8 middle school. Significance of he Sudy The significance ofhis research is cenered on how school adminisraors migh influence he achievemen gap for high-povery, marginalized sudens by examining how, ifa all, insrucional grouping influences suden achievemen in mah. n many high need-o-resource capaciy school disrics in New York Sae, much ofhe funding

24 12 resuling from he NCLB coninues o be allocaed oward enhancing academic inervenion programs for argeed sudens, saff developmen programs, equipmen purchases, and salaries for academic inervenion specialiss. However, many of hese iniiaives may serve o exacerbae condiions of inequiy in underperforming schools, as none promoe access o more challenging coursework (Bracey, 2008). Federal funding ofen means more dollars spen on remediaion for sudens who are already marginalized. A possible alernaive o his emphasis on remediaion would be o redirec funding oward he resrucuring of abiliy groups o ensure ha all sudens may have access o high-level coursework, specifically mah in he middle school. Several school disrics in New York Sae have addressed he need o resrucure by implemening programs such as he nernaional Baccalaureae. Furher, Levin's (1988) "acceleraed schools" research has provided a framework for undersanding equiable suden access o more rigorous coursework. Delimiaions of he Sudy The scope ofhis sudy is confined o a cohor of approximaely 150 sudens and heir experience wih mah in hree grade levels - Grades 6, 7 and 8 - wihin a New York Sae rural school disric during he , and school years. The researcher used quaniaive mehods o compare mah scores on NYS sandardized esing resuls from a single cohor of sudens ha were heerogeneously placed in sixh and sevenh grades o heir subsequen resuls in Grade 8 when some sudens were grouped by abiliy and ohers received AS in accordance wih NCLB and NYSED saues. All suden resuls were drawn from a middle school in Oswego Couny, New York.

25 13 While he curriculum sandards for New York Sae middle school mah are consisen, he mehod ofinsrucion varies from class o class. The researcher did no consider variaions in insrucional pracices. For his sudy, sandardized es scores sored in he New York Sae Suden nformaion Sysem (NYSSS) were colleced from mah classes in which sudens were randomly placed regardless ofpreviously demonsraed abiliy or level of AS or relaed services prescribed in accordance wih suden disabiliies. Sudens' ideniies were coded by a hird pary from he Oswego Couny Board ofcooperaive Educaional Services and included suden classificaion informaion offamily wealh and disabiliies, if applicable. The researcher conduced his sudy in a rural middle school ranked as a School in Need of mprovemen Year One (SN 1) by NYSED, and he findings may no be applicable o oher schools and school disrics. Furher, he school was classified as having a "focused" improvemen saus by NYSED in Sepember 2011, since suden scores in wo a-risk caegories SWD and economically disadvanaged - failed o make A YP. There was no review of suden scores in academic areas beyond mah in Grades 6 hrough 8. Beyond his, validiy issues may persis in ha he researcher did no consider any oher confounding variables ha migh have possibly influenced suden achievemen, mos noable ofwhich included gender and race. The sudy was furher delimied since he informaion was obained from mah classes in a single middle school. Archival daa was colleced from all mah secions for a period ofhree consecuive years. The daa ha he researcher used o measure annual suden achievemen were he raw scores on he NYS Mah assessmens, he same scores ha he school's guidance saff used o place sudens according o abiliy in Grade 8.

26 14 Limiaions of he Sudy The resuls of his sudy are no generalizable o oher grade levels. Furher, here may be oher inervening variables ha could influence suden achievemen, such as suden percepions of heir own mah abiliies (Rubin, 2003) or less-han-random assignmen o heerogeneous mah classes. There are also oher facors ha conribue o suden performance beyond insrucional grouping ha are discussed in Chaper 3. The demographics ofhe school disric were a limiaion ofhis research. The sudens who were no placed in he acceleraed program in Grade 8 in were he subjecs ofhe sudy (There may be oher facors ha impac suden achievemen beyond srucural consideraions, bu abiliy grouping was he only facor considered in his sudy). The manner in which abiliy grouping impacs economically disadvanaged and disabled sudens was a furher consideraion ofhis researcher. Summary There is a growing emphasis on using suden achievemen daa o measure eacher effeciveness. n order o fairly measure eacher performance using "value-added" evaluaion models, web-designed inferenial saisics mus be employed in order o effecively compare growh in suden achievemen. The researcher gahered archival daa from suden and course records via he New York Sae Suden nformaion Sysem (NYSSS) for he years 2008 o The informaion was organized ino a repor of five chapers. n Chaper 1, he researcher addressed he inroducory maerial and he background informaion along wih he problem saemen, purpose, raionale, research quesions, significance, definiions, limiaions, delimiaions, naure, and organizaion of he sudy. n Chaper 2, he researcher provided a review of he research, heory, and

27 15 lieraure ha perain o deracking and he achievemen gap for marginalized sudens, especially as i perains o economically disadvanaged or learning-disabled sudens. n Chaper 3, he researcher presened a descripion ofhe design and mehodology used for his quaniaive sudy, including objecives, populaion, validiy, and reliabiliy. Chaper 4 includes he daa and analyses. n Chaper 5, he researcher has summarized he findings, discussed oucomes, and relaed hem o prior sudies. Based on he conclusions, he researcher has suggesed recommendaions o educaors on ways o narrow he achievemen gap for marginalized sudens in middleschool mah programs and makes recommendaions for policy pracice and oher research. This researcher's focus has been o invesigae some of he issues ha develop when school-disric personnel aemp o bring rigorous mah courses o all sudens, paricularly when sudens in he same classroom have various degrees of compuaional skills. Pracicing classroom eachers should be able o find meaning in hese analyses in order o assis hem o bring sraegies o heir own mixed-abiliy mah classes. School disric adminisraors should be able o use he resuls o plan job-embedded professional developmen and oher suppor sysems for eachers. Resuls ofhis research should allow researchers and praciioners o creae new quesions and expose new areas for fuure research.

28 16 CHAPTER 2 REVEW OF RESEARCH, THEORY, AND PRACTCE nroducion Each year in he Unied Saes, school disric adminisraors consruc elaborae maser schedules in order o organize sudens and eachers ino effecive eaching and learning cohors. Many of hese school leaders group sudens heerogeneously wih he inenion of addressing gaps in achievemen. School guidance counselors, eachers, and adminisraors assign sudens ino groups according o suden resuls on sandardized achievemen ess, eacher evaluaions, and pas performance in school. Once an adminisraor or eacher assigns a suden o a paricular rack, sudens will likely remain in ha grouping permanenly. This is eviden as early as kindergaren when eachers develop a differeniaed program of insrucion for sudens based on enrance evaluaions, kindergaren screening crieria, and sandardized ess ha will ulimaely creae a permanen rack ha will influence access o curricular opporuniies. Wha his means for an a-risk suden sudying mah in he conex of a low-wealh, rural middle school is a he hear ofhis sudy. n his chaper he researcher has reviewed perinen lieraure in order o develop a framework for analysis ofsuden achievemen when he opperforming sudens are removed from he regular course ofsudy ino acceleraed mah programmmg. The researcher has jusified inclusion, or exclusion, oflieraure based on several crieria as warraned wihin he conex of hisorical significance and pracical significance. Furher, he researcher has considered he hisory ofracking and how homogeneous grouping has become commonplace in U.S. schools. The primary

29 17 deerminan for inclusion in his review was based upon he daa provided in he lieraure which, in um, enabled he researcher o se he broad conex for he sudy. The firs secion ofhe sudy presens a review of he hisory of research regarding equiable suden access o educaional resources. n his insance, lieraure ha was considered for inclusion in he review was cenered on sociological facors such as economic, socieal, and poliical forces ha influence jus how sudens are grouped for he purposes of insrucion. Lieraure ha he researcher considered for inclusion in his secion criically examined he hisory ofhe opic ofinsrucional grouping. The researcher has chosen o focus on he shifs from heerogeneiy in he one-room school house o he abiliy-grouped insrucional seing during he indusrializaion ofamerica, and he manner in which school adminisraors have more recenly employed assigning sudens o mixed-abiliy insrucional groups as a means o improve suden achievemen. Lieraure ha was excluded from his hisorical review were hose sudies ha did no specifically address oucomes for sudens. n mos cases hese sudies focused upon economic or social prosperiy as a resul of sudens being grouped for he purposes of insrucion. n he second secion of he lieraure review, he lieraure ha has been included by he researcher specifically addresses he achievemen concerns ha are presened in a racked or de-racked classroom. Here he researcher has framed he argumen for analyzing suden achievemen in a heerogeneous insrucional seing and has included a review ofhe lieraure ha addresses he socio-economic impac ofhe racked/de-racked classroom. n he second secion, he researcher has examined he research lieraure ha illusraes he imporance ofcreaing insrucional grouping ha reflecs he diverse learning needs ofsudens in a single classroom. Again, in his secion, he researcher has

30 18 excluded hose sudies ha do no specifically address suden oucomes, wheher direcly associaed wih suden achievemen or relaed gains beyond he classroom. n he hird secion of his sudy, he researcher considers he research ha addresses he advanages and disadvanages ofgrouping sudens wihou consideraion for heir iniial perceived academic abiliy. Here, he researcher has reviewed he lieraure associaed wih he issues ha confron educaors aemping o implemen heerogeneous insrucional groups. Excluded from his secion ofhe review were case sudies ha would oherwise advocae for abiliy~grouped insrucional seings ha do no presen a causal relaionship beween racking and improved suden achievemen for a larger suden populaion. This ype of"advocacy lieraure" which only addresses achievemen for sudens wih excepionaliies (e.g., gifed and alened programming or sudens who are severely disabled) was no considered for review by his researcher. The Hisory of Homogeneous Grouping and Abiliy Grouping The pracice of soring and grouping sudens by measured and perceived abiliy has long been quesioned by educaional researchers (Bowles & Ginis, 1976; Cicourel & Kisuse, 1963). The issue of racking gained momenum as a opic of research following he publicaion ofkeeping Track by Oakes in 1985 (Mehan, 1996; Slavin & Karwei, 1985; Wener & Oakes, 1996; Wheelock, 1992). These researchers posied ha racking segregaes sudens wihin schools and delivers a subsandard educaion for sudens in he lower racks. Researchers of high rack/low rack sudies argue ha lower-rack sudens, mainly he poor or hose classified as disabled, receive an unchallenging, non-collegebound curriculum delivered by subsandard eachers, while sudens in he higher racks, predominanly higher SES, paricipae in a more rigorous, high-qualiy curriculum augh

31 19 by more skilled eachers. n his manner, according o hese researchers, racking is one of he mechanisms wherein inequaliies presen in our schools and in sociey are perpeuaed. Rural schools have a long radiion ofmixing sudens of differen abiliy levels for he purposes of insrucion largely due o financial efficiencies gained by assigning as many sudens o a single eacher as could fi ino a classroom. n he 1800s, mos Americans lived in rural areas, and communiies were served hrough one-room school buildings. Schools were organized differenly han hey are oday: local school board policies were no codified, few eachers were formally rained, suden aendance was no compulsory and was no inended o inerfere wih family farming effors. However, by he end ofhe nineeenh cenury, America had "schooling for more people han any oher naion, and... paerns ofeducaion were remarkably uniform in purpose, srucure, and curriculum, despie he realiy of local conrol in housands ofseparae communiies" (Tyack & Hanso, 1982, p.17). Beyond his, he research associaed wih insrucional grouping in sparsely populaed, geographically expansive, and low-wealh rural schools hroughou U.S. hisory has been largely ignored in he lieraure. Much aenion in he research lieraure has been dedicaed o he influence of indusrializaion and urbanizaion ofu.s. sociey and he impac ha each has had on he schooling of American sudens (Kozol, 1991). Tracking sudens, namely immigrans, ino differen groups for insrucion developed as America's school sysem expanded o accommodae he growing numbers ofehnically and economically diverse suden groups. This growh was a resul of immigraion, urbanizaion, he child labor law movemen, and massive indusrial growh beween 1890 and 1940 (Tyack & Hanso, 1982). The one-room schoolhouse model where sudens of differing abiliy levels, ages,

32 20 and socio-economic saus were all educaed ogeher (usually wihin walking disance from heir homes) was no longer viewed as an effecive means of educaing large numbers of sudens from culurally diverse backgrounds in an urban seing. Addiionally, educaors promoed he pracice of child rearing as he role ofhe school in seings where parens were increasingly unable o spend ime because of work-relaed consrains (Tyack & Hanso, 1982). Upon reflecion, we see ha he role of schools has changed radically hroughou American hisory, paricularly in ligh of he expanded role of curriculum ha was designed o produce a ciizenry ha was capable of democraic and socially accepable behavior. Educaion policymakers mainained a growing emphasis on assimilaing immigrans ino a common American culure (Tyack & Hanso). Much of he curriculum prior o he 1960s was cenered on developing ciizens who would embrace he democraic principles which were challenged by he evens ha were shaping economic and poliical landscapes in Europe. However, he impac ha hese shifs in world evens had on he rural educaional sysems in he Unied Saes remained largely unnoiced by researchers. The research lieraure is largely silen regarding hisorical changes in rural schools ha remained largely unouched by he forces of indusrializaion, urbanizaion, immigraion, and he perceived hrea o he developmen of an American culure. More han any previous decade, he 1960s saw a growing awareness of he socieal problems associaed wih segregaed schools in he souhern Unied Saes and large urban ceners ha yielded a number ofeducaional reforms and cour cases. Despie hese reforms and judicial acions, racking coninues oday o be presen in many U.S. schools, even hough research beginning as early as he 1980s argues agains his pracice (Sevens

33 21 & Wood, 1992; Berends, Lucas, Sullivan, & Briggs 2005). Mos researchers who have invesigaed racking in secondary schools have aemped o undersand and idenify he educaional consequences of placing sudens in high-rack and low-rack curricula as well as he underlying raionale upon which schools rely o sor and assign sudens o a paricular rack. To his end, research suggess ha he framework of aending o he individual differences of sudens only exacerbaes he inequiies beween suden groups (Desimone, Payne, Fedoravicius, Henrich, & Finn-Sevenson, 2004; Gamoran & Mare 1989). Findings from several sudies furher sugges ha he process of soring sudens by perceived academic apiude or vocaional ineres conribues o he achievemen gap beween sudens in vocaional and academic racks (Oakes, 2005; Gamoran & Mare, 1989; Chunn, 1989; Gamoran, 1987). These sudies sugges ha high-rack classes like Advanced Placemen and B (nernaional Baccalaureae) courses end o arac sudens from high SES households and are augh by beer-qualified eachers. Conversely, lowrack courses are augh by less-qualified insrucors, and course work is largely vocaional in naure (Carbonaro & Gamoran, 2002; Dreeben & Gamoran, 1986; Gamoran, 1986, 1989; Gamoran & Nysrand, 1991; Gamoran, Nysrand, Berends, & LePore, 1995; Gamoran, Porer, Smihson, & Whie, 1997; Hallinan, 1994; Oakes, 2005; Page, 1990). These same sudies also find ha low-rack classes end o be represened by a-risk sudens from disadvanaged socioeconomic backgrounds and ha high-rack courses end o be represened by wealhier sudens. Generally speaking, hese high-rack courses place a greaer emphasis on higher-order hinking skills and encourage sudens o pursue a college rajecory beyond high school (Oakes, 2005). Several sudies also sugges ha

34 22 hese racks end o be permanen in ha sudens say in assigned racks (Aya10n & Gamoran, 2000; Braddock, 1990; Yonezawa, Wells, & Serna, 2002). However, in hese aforemenioned sudies, he researcher mus quesion he pracical significance ofhe research lieraure in ha hese sudies did no address he disadvanages associaed wih rural povery for low-racked sudens. Schiller (1999) found ha mos courses, including mah, have a characerisically verical sequence from eighh grade o high school. This verical srucure ends o limi movemen beween high- and low-racked courses of sudy. Uncerainies coninue o exis as o how low-ses, rural sudens are influenced by being assigned o low-racked mah courses, and hese concerns are no specifically addressed in he research lieraure. The Need for Heerogeneous nsrucional Grouping Tracking in many U.S. schools akes he form of a pracice called "abiliy grouping." Abiliy grouping permis sudens o self-sor hrough he enrollmen in a range of courses, from remedial o advanced, wih placemen deermined hough individual suden course selecion (Lucas, 1999; Yonezawa, Wells, & Serna, 2002). Much like radiional means of racking, grouping paerns associaed wih class and race are reproduced despie he elemen of choice ha is offered o sudens and families (Lucas; Oakes, Wells, Jones, & Danow, 1997; Wheelock, 1992). When offered he opporuniy, lower-achieving, a-risk sudens end o selec low-rack, vocaional elecives, which raises concerns among educaors and researchers who see a persisence of inequaliies in schools. This researcher has observed a higher-han-average number ofnon-academic course offerings in he Mexico High School, which presens a concern, as he low-rack sudens who have compleed non-acceleraed coursework in mah a he Mexico Middle

35 23 School end o avoid college prep courses when given he opion in high school. Alhough racking remains a common pracice in he majoriy of American schools, he number of deracors coninues o increase (Goodlad & Oakes, 1988; Mehan, Hubbard, Villanueva, & Mehan, 1994; Oakes, 1986, 1992; Slavin, 1991, 1995). Researchers argue ha racking serves as a means of soring sudens by race and class. Moreover, many researchers claim ha sudens in differen racks do no receive he same qualiy ofeducaion (Oakes, 1985; Loerscher, 2008; Mulkey, Casambis, Seelman, & Crain, 2005). These researchers conend ha sudens in lower-racked classrooms are subjec o characerisically lower-qualiy insrucion and curriculum. is his experience, framed by social ineracions, ha perpeuaes a lowered self-eseem. The oucome for sudens is a sysem ha is boh demoralizing and demoivaing. Furher, hese researchers argue ha i is he sudens who are already a-risk who end up in he lowes racks (Alexander, Enwisle, & Olson, 2001; Oakes, Gamoran, & Page, 1992). Furher, many researchers argue ha he pracice ofracking is inherenly unfair and ha i plays a significan role in he perpeuaion of social inequaliies (Burris, Weiner, & Murphy, 2008). n response o lingering quesions and concerns associaed wih homogeneous and/or abiliy grouping, some schools have implemened heerogeneous grouping sraegies. Heerogeneous grouping has been implemened in numerous schools and school disrics using a variey of approaches and sraegies ranging from he oal eliminaion of abiliy grouping, commonly referred o as deracking, o abiliy-grouped programs ha provide greaer access o upper-rack classes for sudens in he lower-rack (Rubin, 2006). There is growing evidence ha adminisraors and eachers are favoring

36 24 heerogeneous grouping as a prescripive soluion o he adverse influences of racking. This is furher reinforced by more recen research ha srongly suggess ha heerogeneous grouping promoes improved suden achievemen (Alvarez & Mehan, 2006; Boaler, 2007). Y onezawa defines deracking as "he process of replacing racked course programs or so called abiliy-grouped classes wih mixed abiliy classes or he creaion of heerogeneous classes" (Yonezawa, Wells, & Serna, 2002). School adminisraors have aemped o address he inequaliies associaed wih homogeneously grouped sudens by placing hem in mixed abiliy insrucional groupings. This is ofen referred o as he "deracking movemen" (Goodlad & Oakes, 1988; Rubin, 2008). Opponens of abiliy grouping argue ha all sudens, regardless of academic abiliy, should have equal access o he mos rigorous and highes-qualiy curriculum ha maximizes each suden's poenial in school and beyond. (Burris, Heuber, & Levin, 2004). Specific o his sudy, here was a limied amoun of research addressing school communiies ha perceive excellence and equiy as compeing educaional values (Wener & Burris). However, Faye Brady (2010) suggesed ha here was no saisically significan influence on achievemen for regular educaion sudens when sudens wih learning disabiliies were included in heerogeneously grouped mah and ELA courses. Brady's work srongly indicaed ha excellence and equiy can be achieved in heerogeneously grouped classrooms (2010). The researcher of his sudy considered he appropriaeness of he research mehods ha Brady (2010) used o warran he claim ha including lower-achieving sudens wih higher-achieving sudens does no negaively impac he performance of he high-achievers. As a resul of Brady's (2010) sudy, his

37 25 researcher has considered he converse argumen: The exclusion ofhigh-achievers from he regular eighh grade mah classes migh negaively influence he performance ofhe lower-achieving sudens. Boaler (2007) conduced research on models ofeaching used in mixed-abiliy, high school mah classes where inequaliies were reduced and suden achievemen improved. However, since many of hese sudies used daa solely from high school classes, given he parameers ofhis sudy, uncerainies exised ha quesioned how inequaliies and achievemen migh be addressed a he middle school level. Regardless of grade level or subjec maer, sudies by Henry M. Levin demonsraed convincingly ha a-risk sudens mus learn a a faser rae han more privileged sudens, no a a rae ha drags hem farher behind (Levin & Hopfenberg, 1991). This approach, he Acceleraed Schools Projec, was designed o channel all sudens ino more rigorous academic programming regardless of iniial achievemen levels. Advanages and Disadvanages of Heerogeneous Grouping Wheelock (1994) defined heerogeneous grouping as "a mehod of grouping sudens wih varying abiliies, learning syles, backgrounds, and racial and ehnic origins, wih an emphasis on challenging curriculum and insrucion for all sudens" (p. 76). Lucas (1999) suggesed ha he presence of advanced-level courses does no mean ha a school is racked. School adminisraors may assign sudens o heerogeneous grouped classes bu mus emphasize curricular differeniaion. n schools ha provide high-racked courses such as Advanced Placemen or B, adminisraors ensure ha sudens ofall abiliy levels receive guidance and preparaion for hose courses. According o Waanbe (2006), school adminisraors in de-racked schools do no provide separae advanced

38 26 level courses; raher, all sudens are placed ino he same college-bound heerogeneous course sequence. Advocaes ofheerogeneous grouping sugges ha i permis high-achieving sudens he opporuniy o engage in enhanced social developmen while offering lowerachieving sudens increased (a) self-eseem and confidence, (b) leadership opporuniies, (c) moivaion, (d) educaional benefis, and (e) rus in he educaional sysem (Adams Byers, Whisell, & Moon, 2004; Oakes, 1985; Slavin, 1987). Researchers have noed several advanages when educaors ransiion from homogeneous grouping o heerogeneous grouping including: (a) improved social/emoional developmen (Boaler, 2006; Oakes, 2000; Slavin, 1990; Villa & Thousand, 2003), (b) more equiable access o high-rack coursework (DiMarino & Miles, 2004; Loan, 2006), (c) reduced suden misbehavior (Berends & Lapore, 1995; Glahorn, 1995), (d) improved aendance raes (Gamoran, Nysrand, Berends, & LePore, 1995; Glahorn, 1995), (e) reduced school dropou raes (Slavin, 1990), and (f) improved academic performance (Burris, Wener, Wiley, & Murphy, 2007). The disadvanages associaed wih heerogeneous insrucional groupings in schools are largely implemenaion concerns. nequiies may persis even when adminisraors make every effor o ensure heerogeneiy in insrucional groupings. Therefore, in a classroom ha conains a diverse group oflearners, i is vial ha he eacher undersands he echniques ofdiffereniaed insrucion. The differen learning characerisics ofsudens placed in mixed-abiliy classes require differeniaed insrucional echniques (Denig, 2004; Marzano, Pickering, & Pollock, 2004; Lauria, 2010; Farkas, 2003). There are many quesions and differing opinions concerning how o