The effects of a mathematical word problem solving strategy on problem solving performance by middle school students with mild disabilites PDF
Preview The effects of a mathematical word problem solving strategy on problem solving performance by middle school students with mild disabilites
THEEFFECTSOFAMATHEMATICALWORDPROBLEMSOLVING STRATEGYONPROBLEMSOLVINGPERFORMANCEBY MIDDLESCHOOLSTUDENTSWITHMILDDISABILITIES BY ADDISONKENTWATANABE ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF DOCTOROFPHILOSOPHY UNIVERSITYOFFLORIDA 1991 Copyright1991 by AddisonKentWatanabe ACKNOWLEDGEMENTS Numerouspersonshavecontributedtomakingthedissertation endeavorasuccessfulexperience. Thecombinationoftheir individualandcollectiveeffortsprovidedthesupportneededto completethisproject. Iwouldliketothankmycommitteemembers,Dr.Linda Crocker,Dr.CaryReichard,Dr.StuartSchwartz,andDr.Paul Sindelarfortheirsupportandguidance. Theirvaluablefeedback andencouragementhavebeengreatlyappreciated. SpecialthanksareextendedtoDr.WilliamWolkingandCarolyn Harrisfortheirtechnicalexpertiseindatapresentationandanalysis forthisproject. Theyhavealsoprovidedagreatdealof encouragementasIworkedonthisresearchstudy. IwouldalsoliketothankLoisFrankfromA.QuinnJones School,JackiePattonfromWestwoodMiddleSchool,andTradena IveyfromHawthorneJunior-SeniorHighSchoolfortheirassistance withtheimplementationofthisproject. Appreciationisalso extendedtoLoisFilanowicz,TheresaLischka,DeliaMcClelland,and SueWatanabewhoprovidedassistancewithgraphicdesign, interobserver,andinterscorerreliabilityprocedures. Ill HeartfeltthanksareextendedtoDr.CecilMercer,whoasmy mentor,coach,andfriendhelpedmelearnhowtoasktheright questions,howtothink,howtowrite,howtoresearch,andhowto teach. Hisintellect,wittysenseofhumor,positiveattitude, sensitivity,productivity,andprofessionahsmhavebeenan inspirationthroughoutmydoctoralprogram. CecilMercerhas helpedmetorefineandpolishmystrengths,andforthisIwill alwaysbeappreciative. Mymostheartfeltexpressionsofgratitude,love,andrespectare reservedformywife,Susan,andformyson,Sakae,foralloftheir lovingsupport. Theirpatience,encouragement,andunderstanding, whileIspentcountlesshoursdevelopingmaterials,analyzingdata, andwriting,havemadeparticipationinthedoctoralprogramtmlya "familyaffair". IV TABLEOFCONTENTS Page ACKNOWLEDGEMENTS iii LISTOFTABLES viii LISTOFFIGURES xii ABSTRACT xiv CHAPTERS I INTRODUCTION 1 StatementoftheProblem 4 Rationale 5 DefinitionofTerms 7 Deliminations 10 Limitations 11 Summary 11 II REVIEW OF THE LITERATURE 13 SelectionofRelevantLiterature 14 ReviewofStudiesAssociatedwithMathematicsInstmction and Learning Disabled Individuals 15 ReviewofGenerahzationLiterature 37 ExaminationofSpecificComponentsDealingwith MathematicalWordProblemsSolving 46 ExaminationofEffectiveInstructionalProceduresto PromoteSkillAcquisitionandGeneralizationofNewSkills 64 Summary 67 III METHODSANDPROCEDURES 71 Introduction 71 Setting 72 SubjectDescriptionandSelection 74 V DescriptionofWordProblem-SolvingStrategy 88 Instructional Procedures 92 Instruments 94 ReliabilityofProcedures 103 TrainingofPersonnel 104 Materials 106 ScoringProceduresofInstruments 106 Experimental Design 109 DataAnalysis 114 IV RESULTS 117 Introduction 117 InterscorerReliability 117 InterobserverAgreementofInstructional Procedures 119 ResultsforQuestionOneforSubjectsandtheAcquisition ofaMathematicalWordProblemSolvingStrategy 120 SummaryofOverallResultsforQuestionOne 166 ResultsforIndividualSubjectsPertainingtoRetention ofaMathematicalWordProblemSolvingStrategy 168 SummaryofOverallResultsforQuestion2 182 ResultsforIndividualSubjectsPertainingtotheGeneralization ofaMathematicalWordProblem SolvingStrategy toMultistepWordProblems 184 SummaryofOverallResultsforQuestion3 208 Summary 210 V DISCUSSION 211 Introduction 211 ReviewofPurpose,Literature,andMethods 211 SummaryandAnalysisofResults 217 Implications 222 Limitations 230 SuggestionsforFutureResearch 230 REFERENCES 233 VI APPENDICES A SIGNSINSTRUCTIONALPROCEDURESAND MATERIALS 249 B INSTITUTIONALREVIEWBOARD 286 C COUNTY SCHOOL BOARD 288 D PARENTPERMISSION 292 E CHILDASSENT 295 F SAMPLEBASELINE,ACQUISITION,AND MAINTENANCE,ANDGENERALIZATION PROBES 297 G INTERSCORERINSTRUCTIONSANDFORM 310 H INTEROBSERVERRECORDINGFORM 314 BIOGRAPHICAL SKETCH 316 vii LISTOFTABLES TABLE Page 1 Research-MathAbility 18 2 Research-DirectInstruction 23 3 Research-CognitiveandCognitiveBehaviorStrategies 28 4 Research-Mnemonics 33 5 Research-GeneralizationStudies 39 6 Comparisons of Methods following Polya's and Garofalo & Lester's 4 step methods for solving mathematical word problems 45 7 Research-KeyWordIdentification 4g 8 Research-Graphic Representations 58 9 Comparisons of Methods with Components of SIGNSStrategy 7q 10 Test Scores for Subjects' Level of IntellectualFunctioning 77 11 Subjects' Achievement and Prescreening Test Scores 78 12 TheSIGNSStrategy g9 13 Instruments 101 14 Scoring of Instruments 107 15 Steps for Implementation of Experimental Study 115 Vlll 16 Interscorer Reliabilities for 27 Baseline, Acquisition, and Maintenance (BAM),and Generalization (G) Probes 118 17 Interobserver Agreement on Instructional Procedures 119 18 Summary of Visual Analysis of Baseline (BL), Intervention (I), and Maintenance (M) Data Plotted in Figure 2 for Subject 1: Usage ofSIGNS marks 124 19 Summary of Visual Analysis of Baseline (BL), Intervention (I), and Maintenance (M) Data Plotted inFigures forSubject 1: Problems solved 125 20 Summary of Visual Analysis of Baseline (BL), Intervention (I), and Maintenance (M) Data Plotted in Figure 2 for Subject 2: Usage ofSIGNS marks 127 21 Summary of Visual Analysis of Baseline (BL), Intervention (I), and Maintenance (M) Data Plotted inFigures forSubject2: Problems solved 128 22 Summary of Visual Analysis of Baseline (BL), Intervention (I), and Maintenance (M) Data Plotted in Figure 2 for Subject S: Usage ofSIGNS marks 1S1 2S Summary of Visual Analysis of Baseline (BL), Intervention (I), and Maintenance (M) Data Plotted inFigures forSubjectS: Problems solved 132 24 Summary of Visual Analysis of Baseline (BL), Intervention (I), and Maintenance (M) Data Plotted in Figure 4 for Subject 4: Usage ofSIGNS marks 1S7 25 Summary of Visual Analysis of Baseline (BL), Intervention (I), and Maintenance (M) Data Plotted inFigures forSubject4: Problems solved 138 IX 26 Summary of Visual Analysis of Baseline (BL), Intervention (I), and Maintenance (M) Data Plotted in Figure 4 for Subject 5: Usage ofSIGNS marks 141 27 Summary of Visual Analysis of Baseline (BL), Intervention (I), and Maintenance (M) Data Plotted inFigures forSubject5: Problems solved 142 28 Summary of Visual Analysis of Baseline (BL), Intervention (I), and Maintenance (M) Data Plotted in Figure 4 for Subject 6: Usage ofSIGNS marks 145 29 Summary of Visual Analysis of Baseline (BL), Intervention (I), and Maintenance (M) Data Plotted inFigures forSubject6; Problems solved 146 30 Summary of Visual Analysis of Baseline (BL), Intervention (I), and Maintenance (M) Data Plotted in Figure 6 for Subject 7: Usage ofSIGNS marks 151 31 Summary of Visual Analysis of Baseline (BL), Intervention (I), and Maintenance (M) Data Plotted inFigure7forSubject7:Problems solved 152 32 Summary of Visual Analysis of Baseline (BL), Intervention (I), and Maintenance (M) Data Plotted in Figure 6 for Subject 8: Usage ofSIGNS marks 155 33 Summary of Visual Analysis of Baseline (BL), Intervention (I), and Maintenance (M) Data Plotted inFigure7forSubject8: Problems solved 156 34 Summary of Visual Analysis of Baseline (BL), Intervention (I), and Maintenance (M) Data Plotted in Figure 6 for Subject 9: Usage ofSIGNS marks 159 X
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