1 This dissertation has been microfilmed exactly as received 70-6763 DICKERSCHEID, Harold, 1927- CURRICULAR IMPLICATIONS OF MATHEMATICAL CONCEPTS OF THE PRESCHOOL CHILD. The Ohio State University, Ph.D., 1969 Education, theory and practice University Microfilms, Inc,, Ann Arbor, Michigan Copyright by Harold Dickerscheid 1970 CURRICULAR implications o f mathematical CONCEPTS OF THE PRESCHOOL CHILD DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Harold Dickerscheid, B.S., M.Ed. The Ohio State University 1969 Approved by Adviser College of Education ACKNOWLEDGMENTS The writer gratefully acknowledges his adviser, Dr, Paul R, Klohr, Curriculum and Foundations Faculty, for his insightful suggestions and critical analyses throughout the planning and writing of this study. Special acknowledgment is made to Dr, Nathan Lazar who gave impetus and encouragement to the study. Appreciation is extended to Dr, James K, Duncan for his time in reading and evaluating the manuscript. Gratitude is given to the staff and student teachers of the Campbell Hall Child Development Laboratory and to the children who participated in this study. Special thanks is given to Mrs, Donna Deichert, head teacher, and Mrs, Gretchen Batra, graduate assistant, for their cooperation with testing and observations. Thanks are also due to Mrs. Arlene Flocken and the children in her Head Start classes at Windsor School for their contribution. To my wife, Jean, and children Annette, Daniel, and Pamela, a special thanks— for patience, understanding and sacrifice which made possible my fulfillment of a long sought goal. li VITA January 21t 192? • • • Born— Hamilton, Ohio 1950 »••*••••• B*S.t The Ohio State University, Columbus, Ohio 1951-1955 Teacher, Mathematics, Elm Valley High School, Ashley, Ohio 1955 *•••••••• M.Ed*, Miami University, Oxford, Ohio 1955-1965t 1967-1968 • Teacher, Mathematics, Columbus Public Schools, Columbus, Ohio 1958-1959 • •*••• National Science Foundation Participant 1965-1967 *••••• Teaching Assistant, The Ohio State University, Columbus, Ohio 1968-1969 • *••#• Assistant Professor, Urbana College, Urbana, Ohio FIELDS OF STUDY Major Fieldt Curriculum and Foundations Studies in Curriculum and Foundations* Professor Paul P. Klohr Studies in Mathematics Education* Professor Nathan Lazar Studies in Higher Education* Professor Karl Openshaw H i CONTENTS Pago ACKNOWLEDGMENTS ............................................ 11 VITA .............................................. Ill TABLES .................................................... v CHAPTER I INTRODUCTION AND STATEMENT OF PROBLEM ............ 1 Origin of the Problem •••••••••••« 1 Statement of the Problem •••••••■•• 3 Importance of the Study ••••••••••• 3 Design of the Study 9 Limitations of the Study •••••»•••• 10 Definition of Terms ••••••••••••• 11 Organization of the Dissertation •••••• 12 II REVIEW OF THE L I T E R A T U R E ........................... 13 History of the Nursery School ..................13 Child Development Research .......... 23 Current Preschool Mathematics Programs • • • 33 Nursery School Textbooks Mathematical Concepts Possessed by the Preschooler ••••••• ............. •• 33 Analysis of Concepts from the Literature • • 5^ Analysis of Individual Concepts .•••••• 59 III ANALYSIS OF MATHEMATICAL CONCEPTS IN USE IN THE CHILD DEVELOPMENT LABORATORY .................... 68 Exploratory Study ............................ 68 Preschool Inventory ••••••••••••• 69 Results of Preschool Inventory in the Child Development Laboratory 71 Results of Preschool Inventory in Head Start Centers ••••••••••»•••• 79 IV CONCEPTUAL FRAMEWORK AND ILLUSTRATIVE CURRICULAR MATERIAL FOR PILOT PRESCHOOL MATHEMATICS PROGRAM 101 V SUMMARY, CONCLUSIONS, AND IMPLICATIONS .......... 152 BIBLIOGRAPHY ................................... 159 iv TABLES Page Rote counting ability of 3, 4, and 5-year oldB • 41 Reaulte of Preschool Inventory with the three- year-olds at laboratory school during summer quarter, 1968, with 1 denoting a correct response ••• 72 Results of Preschool Inventory with the three- year-olds at laboratory school during spring quarter, 1968, with 1 denoting a correct response 73 Results of Preschool Inventory with the four- year-olds at laboratory school during summer quarter, 1968, with 1 denoting a correct response 74 Results of Preschool Inventory with the four- year-olds at laboratory school during spring quarter, 1968, with 1 denoting a correct response ••••••••••••••»•••• 75 Total number of correct responses to the Pre­ school Inventory by 25 three-year-olds and 29 four-year-olds of the laboratory school . • • 76 Serial order of correct responses to the Pre­ school Inventory questions one through nine­ teen by the laboratory and Head Start threes and fours •••••••••••••••••• 77 Results of Preschool Inventory with the three- and four-year-olds in operation Head Start, summer, 1968, with 1 denoting a correct response 80 Total number of correct responses to the Pre­ school Inventory by 6 three-year-olds and 7 four-year-olds of Head Start •••■••••• 81 Total number of questions missed on the Pre­ school Inventory by children having a score of fifteen to nineteen •••»••••••«• 84 v TABLES (continued) Table Page 11 Total number of questions correct on the Pre­ school Inventory by children having a score of one to four •••••••••••>■•••• 86 12 Mean age and mean score on Preschool Inventory, and mean quarters in preschool of five classes 91 13 Mean scores of the boys and girls on the Pre­ school Inventory 92 vi CHAPTER I INTRODUCTION AND STATEMENT OF PROBLEM Origin of the Problem The preschool is currently being critically scrutinised by educators, psychologists, sociologists, and many other interested groups in an attempt to reformulate the curriculum. The preschool years are being studied to see what potential for learning there is during these first six years of a child's life. Psychologists are stating that a child's approximate full potential for learning is determined by the time he is five years of age, and hence, the experiences the child has had up to this time are very crucial to the experiences he will have the remainder of his life. Behavioral scientists theorise that if certain intellectual pursuits are not undertaken at this crucial time, some concepts will not be acquired in later years. Other concepts may be only partially acquired. Since research is indicating the early years as the time of greatest physical and intellectual growth, appropriate stimulation must be pro­ vided during these years if all children are not to.be labelled "culturally deprived." Although there have been sporadic attempts in the past to place mathematics in the preschool curriculum (Froebel, Dewey, Montessori), the impact on the preschools is negligible. 1 2 As late as thirty years ago, there was great disagreement whether arithmetic should be systematic or incidental in the primary grades* This debate has now sifted down to the pre­ schooler and his experiences with arithmetic*^ Much of the present emphasis on the preschooler may be attributed to a concern for the disadvantaged* Money made available by the Federal government, private endowments, uni­ versities, and business has precipitated increased interest in the intellectual capabilities of the disadvantaged preschool child* This, in turn, has caused some persons to become con­ cerned with improving programs for all preschool children* The time for the pre-school experiment is doubly right* That it is needed for the sake of the excluded and de­ prived is self-evident; but the movement is gathering momentum at the very moment when educational psychologists are offering persuasive evidence that all children can learn— and often want to learn— much more, much sooner* What has been Introduced as a lifesaving device for those at the bottom of our society*s ladder may, in time, help to loosen the rigidity of the educational structure as a whole*^ There is a broad spectrum on positions taken by pre­ schools concerning mathematics* Some are concerned solely with child care and do nothing with mathematical learning* Others, such as those based on the Mchild study" movement, have moved cautiously to incorporate mathematics in the curriculum by ^William Brownell, Arithmetic in Grades I and II (Durham, N. C*i Duke University Research Studios in Education, 19^1 )• 2 Fred Hechinger, Pre-School Education Today (Garden City, N. Y.j Doubleday, 1966), p* 12* placing their main emphasis on incidental learning. One bold, present day program (Bereiter and Engelmann)^ places its emphasis on rote memorization of facts. Statement of the Problem The purpose of this study is to investigate the mathe­ matical concepts of a selected group of preschool children and to design a pilot mathematics curriculum. Three objectives will give direction to this study. They are: (1) To investigate how a child builds his earliest number concepts. 12) To design curricular materials to aid in the learning of mathematical concepts. (3) To identify how mathematical concepts can be effectively incorporated in a nursery school program. Importance of the Study Bernard Spodek succinctly underlines the importance of critical investigation of the preschooler and curricular ex­ periences that are possibly mandatory if all children are not to be classified as deprived. Early childhood education is coming to be seen less as a privilege and more as an individual right and possibly even as a.responsibility