## Students with Learning Disabilities encompass

The Impact of Using the Calculator as an Accommodation on the Math Achievement ofStudents with Learning DisabilitiesSubmitted byRoxana RussellDissertation ProposalDoctorate of EducationGrand Canyon UniversityPhoenix, ArizonaDecember 20, 2013iiTable of ContentsList of Tables ………………………………………………………………………………………………………..vChapter 1: Introduction to the Study…………………………………………………………………………1Introduction ……………………………………………………………………………………………………..1Background of the Study …………………………………………………………………………………..2Problem Statement ……………………………………………………………………………………………5Purpose of the Study …………………………………………………………………………………………7Research Question(s) and Hypotheses …………………………………………………………………9Advancing Scientific Knowledge ……………………………………………………………………..11Significance of the Study …………………………………………………………………………………12Rationale for Methodology ………………………………………………………………………………14Nature of the Research Design for the Study………………………………………………………15Definition of Terms…………………………………………………………………………………………18Assumptions, Limitations, Delimitations …………………………………………………………..21Summary and Organization of the Remainder of the Study ………………………………….23Chapter 2: Literature Review …………………………………………………………………………………25Introduction and Background to the Study …………………………………………………………25Theoretical Foundations and/or Conceptual Framework ………………………………………29Theories explaining mathematical learning disabilities. …………………………..30Accommodations: Possible solution to overcome math deficits. ………………33Review of the Literature ………………………………………………………………………………….34Learning disabilities. …………………………………………………………………………..36Education of students with learning disabilities. …………………………………….60iiiLegislation and testing. ……………………………………………………………………….71Accommodations. ………………………………………………………………………………75The use of the calculator as a testing accommodation. …………………………….81Summary ……………………………………………………………………………………………………….90Chapter 3: Methodology ……………………………………………………………………………………….92Introduction ……………………………………………………………………………………………………92Statement of the Problem …………………………………………………………………………………93Research Questions and Hypotheses …………………………………………………………………95Research Methodology ……………………………………………………………………………………98Research Design……………………………………………………………………………………………..99Population and Sample Selection…………………………………………………………………….101Instrumentation …………………………………………………………………………………………….104IEP records. ……………………………………………………………………………………..104Testing scores…………………………………………………………………………………..105Validity ……………………………………………………………………………………………………….106Reliability…………………………………………………………………………………………………….107Data Collection Procedures…………………………………………………………………………….108Data Analysis Procedures ………………………………………………………………………………110Preparation of data. …………………………………………………………………………..111Data analysis. …………………………………………………………………………………..111Ethical Considerations …………………………………………………………………………………..113Limitations …………………………………………………………………………………………………..115ivSummary ……………………………………………………………………………………………………..116Appendix A ……………………………………………………………………………………………………….142vList of TablesTable 1. Calculator as Testing Accommodation across United States ……………………….. 811Chapter 1: Introduction to the StudyIntroductionStudents with Learning Disabilities encompass the largest single category ofstudents with special educational needs in most countries, accounting for an estimate of4-7% of school aged children. (Buttner and Hasselhorn, 2011). These same authors,citing Kavale and Forness (2006), noted that in United States, about 50% of the childrenidentified for special education services are children with a Learning Disability. By thefederal law, No Child Left Behind Act of 2001 (NCLB) (2001), all students, includingthose with disabilities, are expected to participate in assessments in reading/language arts,mathematics, and science. The Individuals with Disabilities Education Improvement Actof 2004 (IDEA) specifically governs the individual services that each student withdisabilities may need and are specified through an Individual Education Plan (IEP).IDEA requires that all children with disabilities are to be included in general and statewide assessment programs, with appropriate accommodations (IDEA, 2004).Accommodations are practices and procedures in the areas of presentation, response,setting, and timing/scheduling that provide equitable access during instruction andassessments for students with disabilities (South Carolina Department of Education,2009b).The topic investigated by the proposed study concerns the impact of the use of thecalculator as math accommodation in grades six through eight during instruction andassessment, on the math academic achievement of students with Specific LearningDisabilities (SLD) or Learning Disabilities (LD), the latter term being utilized more oftenby researchers.2Background of the StudyAccommodations are tools and procedures that provide equal access to instructionand assessment for students with disabilities (Cortiella, 2005). Under the NCLB Act(2001), public school students must participate in annual testing in specific academicareas and grades, and the students with disabilities must be provided the accommodationsstated in their individual educational plans (IEPs) when taking these assessments. The useof calculator is a fairly âcontroversial accommodationâ (Christensen, Braam, Scullin, &Thurlow, 2011, p.23) and it is implemented differently across United States of America.The implementation during state standardized testing in grades three to twelfth variessignificantly from one state to another. At the federal level, according to the most recenttechnical report completed by the National Center of Education Outcomes, in 2009, 10states allowed the calculator to be used as an accommodation (the student must be giventhe score she or he earned, the studentâs score must be aggregated with all the otherscores, and the score must be used for accountability purposes), 23 states allowed it incertain circumstances, (the accommodation is allowed on some assessments and notothers), three states allowed it with implications for scoring (if the accommodation isused, the student automatically receives a certain score (e.g., zero or below basic) or thescore is not aggregated), six states allowed it with implications for scoring and in certaincircumstances, one state allowed it as unique aggregated (a non-standard accommodationis used, but the student is given his or her earned score, and the studentâs score isaggregated and used for accountability purposes) and four states prohibited thisaccommodation (see Table 1.)The effectiveness of this accommodation has been investigated in severalaccommodation studies, and the results have been mixed (Bouck, 2010; Bouck & Yadav,32008; Parks, 2009; SCDE, 2011b). Bouck (2010) indicated that four-function and graphiccalculators were equally beneficial to eighth grade students with and without disabilities,Bouck and Yadav (2008) suggested that all seventh grade students (with and withoutdisabilities) benefited from the use of a graphic calculator, (2008) and Bouck and Bouck(2008) indicated that the four-function calculators were beneficial for sixth grade students(Bouck and Yadav, 2008). Engelhard, Fincher, and Domaleski (2011) indicated thatcalculators were beneficial for students with disabilities in grades three and four, but notin sixth and seventh grade, while Parks (2009) concluded that calculators did not show asignificant impact on the problem solving skills of students with Learning Disabilities orwith Attention Deficit Hyperactivity Disorder and SCDE (2011b) reviewing differentincrease/decrease patterns for each grade level between third grade and eighth gradeconcluded that calculators had no significant effects on the math abilities of students withdisabilities.Another study, limited to only students with Learning Disabilities, who utilizedthis accommodation for the majority of the academic year, might uncover moreinformation about the impact of this accommodation. Unlike Bouck (2010), Bouck andBouck and Yadav (2008) and Bouck and Bouck (2008), who only introduced thecalculator at testing time, the population of this study would have used the calculator forthe entire academic year prior end of year testing. This design is based on Ellingtonâs(2003) meta-analysis conclusion that the greatest effects of using the calculators wereseen after long term use (9 weeks or longer). The research design in the studies of Bouck(2008, 2010) and Parks (2009) did not explicitly mention the construct validity of theassessment used while using the calculator. By contrast, the assessment instrument usedby Foster and Kim (2008) and Go (2009) to investigate the math performance had been4researched and proven to maintain construct validity for grades five through eight whenthe calculator as an accommodation was used. Unlike the South Carolina Department ofEducationâs study, which included the entire student population with disabilities and didnot check for IEP services during the compared years, the proposed investigation willfocus on only one type of disability and will ensure special education services wereimplemented during the years compared. Moreover, unlike the South CarolinaDepartment of Educationâs study, which compared the percentage of students that Metversus Not Met after the use of accommodation, the proposed study will compare normalcurve equivalent scores, not cut off scores that are very wide apart to ensure a betterreflection of the studentsâ progress.In short, studies of the use of the calculator as an accommodation have producedmixed results in part because the sample did not differentiate between the nature of thedisability, the conditions under which the accommodation was used, or the type ofachievement measure. The proposed investigation will thus be limited to only studentswith Learning Disabilities who were in grades six through eight at the time of PASS2012 testing, who had an IEP and were provided special education math services duringthe academic years of 2010-2011 and 2011-2012 and used the calculator as anaccommodation only during the academic year of 2011-2012. Moreover, the investigatorwill not examine the change in the percent of students whose scores Met performanceexpectations (hereafter referred to as Met or âthe Met categoryâ), but will look at changesin the studentsâ Normal Curve Equivalent scores obtained in 2011 and in 2012 after theimplementation of this accommodation, which may be a better way to evidence theirprogress.5To further explore the impact of this accommodation, the proposed research willaddress the impact of services provided and placement of the students by separating dataabout the students into three categories, based on the type of services/educational settingthe students were provided with: Self-contained, resource, and inclusion students. Thescores of the three groups will be compared to possibly differentiate the impact of thisaccommodation based on the services/educational placement they received.Problem StatementIt is not known to what extent the use of a calculator as an accommodation duringmath instruction and assessment impacts the academic achievement of students withLearning Disabilities in grades six and seven as revealed by end of the year standardizedstate assessments. Extant current research, although limited when compared to theresearch done on other types of accommodations such as oral presentation or computerassisted presentation (Cormier et al., 2010), points in several directions. Some studieshave indicated that students with and without disabilities benefited from the use of thecalculator on an assessment (Bouck, 2010; Bouck & Bouck, 2008, Bouck & Yadav,2008). Other studies (Parks, 2009; SCDE, 2011b) indicated that calculators did notbenefit students with disabilities. One particular investigation, focusing on students withdisabilities in South Carolina and using the same math assessment as the proposed study,Palmetto Assessment of State Standards (PASS) (SCDE, 2011b), has shown that the useof calculator as an accommodation did not appear to improve the performance ofstudents. However, SCEDâs research sampled all students with disabilities in grades threethrough eight who had the calculator as an accommodation/modification either in the yearof 2009 or 2010, without consideration for other factors, such as IEP services, or timespent in the general education setting. The investigators concluded that this6accommodation did not appear to be related to improved Math PASS performance, butthe results may be misleading since the difference between the cut-off scores is quitewide. For instance, in grade six, a score of Not Met is a standard score of 300 -599, andthe Met standard score is between 600-657 (PASS, 2009). An investigation on thedifference in the normal curve equivalent score after the use of this accommodationwould evidence the actual progress made by students. All other studies except the SCDE(2011b) introduced the calculator only at the time of the assessment and measured itsimpact on similar tests, but by definition, to be an appropriate accommodation for testing,the strategy has to be used consistently in instruction, therefore an accurate assessment ofthe effectiveness of this accommodation can only be made after this accommodation wasconsistently used in instruction and not just at the time of testing.Given that students with Learning Disabilities encompass the largest singlecategory of students with special educational needs, it is important to understand how thispopulation, in particular, may benefit from the calculator as an accommodation. Asdiscussed earlier, an accommodation such as the use of calculator may impact differentstudent populations in different ways but existing literature does not shed light on thisrelationship between the type of students and the effectiveness of the use of calculator.The proposed investigation will focus only on students with Learning Disabilities andwill contribute to a better understanding of the utility of this accommodation for thisparticular type of disability. The investigation will also focus only on grade levels wherethe math academic content is far beyond simple computation skills, and where the use ofthe calculator is considered a standard accommodation that allows special educationstudents to receive standardized scores for the assessments. In South Carolina, on themath state standardized assessment, the calculator is allowed as a standard7accommodation for grades five through eight, but a modification to the assessmentinstrument for grade four because the use of calculator invalidates the construct validityof the test. Since the evaluation of fifth grade learning outcome depends on the fourthgrade test score which was not standardized, the fifth grade group was excluded from theproposed study. The provision of special education services in the area of math will be aprerequisite for both years being compared, such that the implementation of thisaccommodation during instruction and assessment would be the only variation in thesestudentsâ instruction and assessment. In 2010-2011, the students received specialeducation services without the use of calculator during instruction and assessment, thenthe calculator was implemented as part of the special education services in 2011-2012.Instead of investigating the change in percentages of students scoring Met after thisaccommodation was implemented, the researcher will investigate the change in theNormal Curve Equivalent scores that will be calculated from the scale scores received onthe math PASS assessment in 2011 and 2012. Furthermore, the students will be separatedin three categories, based on the type of services/educational setting the students wereprovided with: self-contained, resource and inclusion students and their scores will becompared to possibly differentiate the impact of this accommodation based on theservices/educational placement they received.Purpose of the StudyThe purpose of this quantitative, non-experimental, causal comparative study is toexamine the impact of a standard accommodation (the use of a four-function calculator)and the math academic achievement among 6th , 7th and 8th grade students with LearningDisabilities, in a rural district of South Carolina for the year 2011-2012, as compared tothe math achievement in the previous year 2010-2011. A standard accommodation8represents one type of practice and procedure in the areas of presentation, response,setting, and timing/scheduling that provide equitable access during instruction andassessments for students with disabilities without invalidating their testing score (SouthCarolina Department of Education, 2009b).The proposed study will focus exclusively on students with Learning Disabilitiesto more carefully discern the impact of this particular accommodation within that targetedpopulation. This proposed investigation will additionally look at Individual EducationalPlans in both years to ensure that the sample of students had an IEP and received servicesfor the area of math, in both academic years, the only difference being the presence ofthis particular accommodation during instruction and testing. The researcher willcompare the Normal Curve Equivalent scores calculated based on the scale scoresreceived on the math state standardized assessment completed in 2011 without thisaccommodation during the school year 2010-2011 and the 2012 scores after thisaccommodation was fully implemented in the academic year 2011-2012 prior to testingand during testing, in order to identify the impact of this accommodation.Considering the overall rate at which the use of the accommodation increased(from 19.7% in 2009 to 22.5% in 2010 and 26.2% in 2011) for the standardized mathtesting of students with disabilities in grades five through eight (SCDE, 2011b), it is veryimportant to investigate the true effectiveness of this accommodation, and ensure that anineffective accommodation is not overly prescribed. This studyâs results may support theimplementation of this accommodation during instruction and assessment or may prompta more thorough analysis of the reasons behind this decision-making process.9Research Question(s) and HypothesesThere are two main research questions the author will answer through this study.The first research question is:R1: Does the use of a calculator as a math accommodation during instruction andassessment have an effect on math achievement of students with Learning Disabilities, asmeasured by the end of year standardized math assessment?The following hypotheses will support this research question:H1: There is a significant difference between the math achievement of studentswith Learning Disabilities with the use of calculators as part of the math accommodationsand the math achievement of the same students without the use of the calculator.H0: There is not a significant difference between the math achievement ofstudents with Learning Disabilities with the use of calculators as part of the mathaccommodations and the math achievement of the same students without the use of thecalculator.The second research question examines three types of special education programsin which students use the calculator accommodation. These are: (1) the general educationclass (inclusion), (2) the special education support room (resource) in addition to theirgeneral education classroom, and (3) the special education self-contained setting (selfcontained). These special education programs are chosen according to the level ofachievement the students display: higher achieving students are served under theinclusion model, while the lowest achievers are placed in the self-contained setting.The second research question is:R2: Does the effect of calculator use on math achievement, as measured by theend of year standardized math assessment, vary across the type of special education10program where the calculator was implemented as an accommodation for students withLearning Disabilities?This research question will be supported by the following hypotheses:H2: There is a significant difference among the three types of special educationprograms in terms of the effect of calculator use on the studentsâ math achievement.H0: There is not a significant difference among the three types of specialeducation programs in terms of the effect of calculator use on studentsâ mathachievement.The independent variable is defined as the utilization of the four-functioncalculator as an accommodation during math instruction and assessment. The dependentvariable is defined by math academic achievement expressed by the normal curveequivalent calculated based on the scale score received on the standardized statewidemath assessment given in South Carolina, named Palmetto Assessment of State Standards(PASS). The measure is the normal curve equivalent score difference between schoolyear 2011-2012 and school year 2010-2011. This assessment was chosen because it isbelieved to be the most representative assessment of studentâs knowledge and skills afterone year of instruction. The normal curve equivalent score was chosen versus a scalescore or performance level because it is a score that can be compared across tests and itcan be averaged (Peca, 2005). In a typical learning situation, a studentâs normal curveequivalent score indicates his or her standing among the population of students in thesame grade and this score stays constant from year to year when all students are makingregular progress. If a studentâs normal curve equivalent score changes from one year tothe next, the achievement during that year is considered enhanced (if the change ispositive) or hindered (if the change is negative). It is therefore important to study the11typically developing students and those with special needs, with the latter populationfurther categorized based on the type of needs requires by the students.

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