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Word Problem Solving of Students with Autistic Spectrum Disorders

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Word Problem Solving of Students with Autistic Spectrum Disorders Word Problem Solving of Students with Autistic Spectrum Disorders and Students with Typical Development Young Seh Bae Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy under the Executive Committee of the Graduate School of Arts and Sciences COLUMBIA UNIVERSITY 2013 © 2013 Young Seh Bae All rights reserved ABSTRACT Mathematical Word Problem Solving of Students with Autistic Spectrum Disorders and Students with Typical Development Young Seh Bae This study investigated mathematical word problem solving and the factors associated with the solution paths adopted by two groups of participants (N=40), students with autism spectrum disorders (ASDs) and typically developing students in fourth and fifth grade, who were comparable on age and IQ ( >80). The factors examined in the study were: word problem solving accuracy; word reading/decoding; sentence comprehension; math vocabulary; arithmetic computation; everyday math knowledge; attitude toward math; identification of problem type schemas; and visual representation. Results indicated that the students with typical development significantly outperformed the students with ASDs on word problem solving and everyday math knowledge. Correlation analysis showed that word problem solving performance of the students with ASDs was significantly associated with sentence comprehension, math vocabulary, computation and everyday math knowledge, but that these relationships were strongest and most consistent in the students with ASDs. No significant associations were found between word problem solving and attitude toward math, identification of schema knowledge, or visual representation for either diagnostic group. Additional analyses suggested that everyday math knowledge may account for the differences in word problem solving performance between the two diagnostic groups. Furthermore, the students with ASDs had qualitatively and quantitatively weaker structure of everyday math knowledge compared to the typical students. The theoretical models of the linguistic approach and the schema approach offered some possible explanations for the word problem solving difficulties of the students with ASDs in light of the current findings. That is, if a student does not have an adequate level of everyday math knowledge about the situation described in the word problem, he or she may have difficulties in constructing a situation model as a basis for problem comprehension and solutions. It was suggested that the observed difficulties in math word problem solving may have been strongly associated with the quantity and quality of everyday math knowledge as well as difficulties with integrating specific math-related everyday knowledge with the global text of word problems. Implications for this study include a need to develop mathematics instructional approaches that can teach students to integrate and extend their everyday knowledge from real- life contexts into their math problem-solving process. Further research is needed to confirm the relationships found in this study, and to examine other areas that may affect the word problem solving processes of students with ASDs. TABLE OF CONTENTS CHAPTER I. INTRODUCTION Background and Need...........................................................................................1 Word Problem Solving.. ............................................................................ 5 Definitions..... .............................................................................................7 Statement of the Problem ................................................................................... 11 CHAPTER II. REVIEW OF LITERATURE .................................................................. 13 Schematic Approaches to Word Problem Solving ............................................ 14 Schema Induction Theory and Analogical Thinking ............................... 15 Semantic Relations................................................................................... 16 Marshall's Schema Theory ....................................................................... 17 Summary .................................................................................................. 19 Linguistic Approaches to Word Problem Solving ..............................................20 Classic Models of Comprehension Process ............................................ 21 Situation Model ........................................................................................ 24 Mental Model ........................................................................................... 25 Brain Imaging Studies and Word Problem Solving ................................. 26 Summary ................................................................................................ 29 Research Studies on Factors Associated with Word Problem Solving ..............29 Word Reading/Decoding ......................................................................... 29 Sentence Comprehension ......................................................................... 31 Mathematics Vocabulary ......................................................................... 34 Arithmetic Computation .......................................................................... 36 i Everyday Math Knowledge ..................................................................... 39 Attitude toward Math ............................................................................... 40 Problem Type Schema Knowledge .......................................................... 43 Visual Representation .............................................................................. 44 Summary ................................................................................................ 48 Characteristics of Students with ASDs ............................................................. 49 Cognitive Theories Explaining High Functioning ASD .......................... 49 IQ and Overall Academic Abilities of Students with ASDs. ...................53 Sentence Comprehension, Word Reading, Semantics and Everyday Knowledge ..............................................................................................56 Visuospatial Abilities ..............................................................................58 Mathematics Abilities of Students with ASDs.........................................60 Summary and Rational ............................................................................. 62 Research Questions ............................................................................................ 66 CHAPTER III. METHOD ................................................................................................. 68 Participants ......................................................................................................... 68 Inclusion Criteria ..................................................................................... 69 Recruiting Procedures ............................................................................. 70 Research Design ................................................................................................. 72 Measures ............................................................................................................. 72 Screening.................................................................................................. 72 Dependent Variables ................................................................................ 75 Procedures .......................................................................................................... 82 Background Information .......................................................................... 82 ii Administration of Instruments ................................................................. 82 Administration Sequence ......................................................................... 82 Data Analysis .................................................................................................... 83 CHAPTER IV. RESULTS ................................................................................................. 84 Preliminary Analysis .......................................................................................... 84 Descriptive Statistics ................................................................................ 84 Main Analysis ..................................................................................................... 85 Research Question 1 ................................................................................ 85 Research Question 2 ................................................................................ 88 Research Question 3 ................................................................................ 89 Research Question 4 ................................................................................ 91 Additional Analysis ............................................................................................ 92 Analyses on Role of the Significant Factor in Differences ...... ...............93 Additional Analysis for Everyday Math Knowledge ............................... 93 Analysis for Visual Representation..... .....................................................95 Summary of Results ........................................................................................... 99 CHAPTER V. DISCUSSION .....................................................................................
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