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University Microfilms International 300 N, ZEEB RD INFORMATION TO USERS This was produced from a copy of a document sent to us for microfilming. While the most advanced technological means to photograph and reproduce this document have been used, the quality is heavily dependent upon the quality of the material submitted. The following explanation of techniques is provided to help you understand markings or notations which may appear on this reproduction. 1.Thc sign or "target” for pages apparently lacking from the document photographed is "Missing Page(s)”. If it was possible to obtain the missing pagc(s) or section, they arc spliced into the film along with adjacent pages. This may have necessitated cutting through an image and duplicating adjacent pages to assure you of complete continuity. 2. 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For any illustrations that cannot be reproduced satisfactorily by xerography, photographic prints can be purchased at additional cost and tipped into your xerographic copy. Requests can be made to our Dissertations Customer Services Department. 5. Some pages in any document may have indistinct print. In all cases we have filmed the best available copy. University Microfilms international 300 N, ZEEB RD.. ANN ARBOR. Ml 4B106 8121772 B r ew er, K a t h l e e n * Ho f f m a n A STUDY OF THE EFFECT OF PROBLEM SOLVING INSTRUCTION ON THE STUDENTS ABILITY TO SOLVE MATHEMATICAL VERBAL PROBLEMS The Ohio State University PH.D. 1981 University Microfilms International 300 X. Zceb Road, Ann Atbor, M l 48106 Copyright 1981 by Brewer, Kathleen Hoffman All Rights Reserved PLEASE NOTE: In alt cases this material has been filmed in the best possible way from the available copy. Problems encountered with this document have been identified here with a check mark V ... 1. 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Other______________________________________ _ _____________________________ University Microfilms International A STUDY OF THE EFFECT OF PROBLEM SOLVING INSTRUCTION ON THE STUDENT'S ABILITY TO SOLVE MATHEMATICAL VERbIl PROBLEMS Dissertation Presented in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in the j Graduate School of The Ohio State University by Kathleen Hoffman Brewer, B.S., II.A. •kicicfe The Ohio State University 1981 Reading Committee : Approved by Dr. Lorren L. Stull Dr. C. Ray Williams Dr. Suzanne Damarin Dr. James Kerber * AdviseAdviser Early and Middle Childhood Education ACKNOWLEDGMENTS X would like to express my sincere appreciation to my adviser, Dr. Lorren L. Stull for his encouragement and guidance In the planning and execution of this investi­ gation. I am also grateful to Dr. C. Ray Williams who was instrumental in my decision to pursue graduate studies and who encouraged and supported me every step of the way. In addition, I am indebted to Dr. Suzanne Damarln for her helpful suggestions and guidance during the plan­ ning, data collection and composition stages of the re­ search. Her professional assistance was Invaluable. Special mention must also be given to the principal, teachers and students of the participating school in this investigation. Their cooperation made this research pro­ ject both possible and an enjoyable experience. I would also like to recognize the untiring efforts of my sister. Sister Margaret Hoffman, O.S.F., who spent hours critiquing, questioning and proofreading this dis­ sertation. A final word of thanks to my husband, John, and my entire family for their loving support and understanding. ii VITA March 4, 1948 .................. Born - Columbus, Ohio 1970............................B.S. The Ohio State Univer­ sity, Columbus, Ohio 1970-1978 ..................... Elementary Teacher, Columbus, Ohio Public Schools 1978............................ 11.A. The Ohio State Univer­ sity, Columbus, Ohio 1978-1980 ..................... Teaching Associate, Early and Middle Childhood Education, The Ohio State University, Columbus, Ohio 1980-1981 ..................... Mathematics Specialist Columbus Public Schools FIELDS OF STUDY Major Field: Early and Middle Childhood Education Studies in Early and Middle Childhood Education Dr. Lorren L. Stull, Dr. C. Ray Williams Studies in Mathematics Education Dr. Suzanne Damarin iii TABLE OF CONTENTS Page ACKNOWLEDGMENTS......................................... ii VITA....................................................... Ill LIST OF TABLES............................................. vi CHAPTER I. Introduction, Background and Statement of the Problem.................................. I Introduction and Background................... 1 Statement of the Problem....................... 11 II. Review of Research ................................ 13 Theoretical Framework ....................... 14 Heuristic Teaching................. .......... 20 Characteristics Related to Students' Problem Solving Performance...................26 III. Methodology............... 31 Subjects........................................ 31 Classroom Procedures........................... 33 Description of Treatments ................... 34 Instruments....................................41 Analysis of the Data........................... 46 Summary of the Two Methods of Instruction . 48 Summary of Teacher Behavior in Experimental Situations....................................51 Schedule for the Study. .............. 56 IV. Analysis of the D a t a ...................... 58 Statistical Findings for the Interviews . 58 Statistical Findings for the Written Test . 76 APPENDICES A. Procedure for Assignimg Groups .................. 103 Seating Chart ................................ 106 iv B. A Sample of the Questions Posed in Treatment A. 107 Examples of Problems Used Throughout the Study.......................................... 110 C. Scoring of Interview Problems.....................113 Interview Checklist . ..........................117 Sample Interview Transcripts................... 118 Interscorer Reliability Chart ................. 125 D. Iowa Problem Solving Tests and the Statistical Data for Each Test................................ 127 BIBLIOGRAPHY...............................................141 v LIST OF TABLES Table Page 1 Descriptive Statistics of Pre-Interview Scores and Pcfst-Interview Scores............... 60 2 Analysis of Covariance Table for Total Post-Interview Scores......................... .62 3 Partial Sum of Squares for ANCOVA of Total Post-Interview Scores......................... .62 4 Cell Means (Cell Sizes) of Total Pre-Interview Scores.......................................... 63 5 Cell Means (Cell Sizes) of Total Post-Interview Scores.......................................... 63 6 Analysis of Covariance Table of Post-Interview Scores on Criterion 1, "Understanding the Problem"........................................ 7 Partial Sum of Squares for ANCOVA of Post- InterView Scores on Criterion 1, "Under­ standing the Problem"......................... 8 Cell Means (Cell Sizes) for Pre-Interview Scores on Criterion 1, "Understanding the Problem"........................................ 9 Cell Means (Cell Sizes) for Post-Interview Scores on Criterion 1, "Understanding the Problem"........................................ 10 Analysis of Covariance Table of Post-Interview Scores on Criterion 2, "Devising a Plan". 68 11 Partial Sum of Squares for ANCOVA of Fost- Interview Scores on Criterion 2, "Devising A Plan.......................................... 68 12 Cell Means (Cell Sizes) for Pre-Interview Scores on Criterion 2, "Devising a Plan". 69 vi 13 Cell Means (Cell Sizes) for Post-Interview Scores on Criterion 2, "Devising a Plan". 69 14 Analysis of Covariance Table of Post- InterV.iew Scores on Criterion 3, "Carrying Out the P l a n " . ................................... 71 15 Partial Sum of Squares of ANCOVA of Post- Xnterview Scores on Criterion 3, "Carrying Out the Plan...................................... 71 16 Cell Means (Cell Sizes) for Pre-Interview Scores on Criterion 3, "Carrying Out the Plan.............................................. 72 17
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