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Young Children's Acquisition of Mathematical Knowledge and Mathematics Education in Kindergarten Kuei-Er Chung Iowa State University Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 1994 Young children's acquisition of mathematical knowledge and mathematics education in kindergarten Kuei-Er Chung Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Pre-Elementary, Early Childhood, Kindergarten Teacher Education Commons, and the Science and Mathematics Education Commons Recommended Citation Chung, Kuei-Er, "Young children's acquisition of mathematical knowledge and mathematics education in kindergarten " (1994). Retrospective Theses and Dissertations. 10688. https://lib.dr.iastate.edu/rtd/10688 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. U-M-I MICROFILMED 1994 INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand corner and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back of the book. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6" x 9" black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. University Microfilms International A Bell & Howell Infornnation Company 300 North Zeeb Road. Ann Arbor, Ml 48106-1346 USA 313/761-4700 800.'521-0600 Order Number 9503541 Young children's acquisition of mathematical knowledge and mathematics education in kindergarten Chung, Kuei-Er, Ph.D. Iowa State University, 1994 UMI 300 N. ZeebRd. Ann Aibor, MI 48106 Young children's acquisition of mathematical knowledge and mathematics education in kindergarten by Kuei-Er Chung A Dissertation Submitted to the Graduate Faculty in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY Department: Human Development and Family Studies Major: Human Development and Family Studies (Early Childhood Education) Approved: Signature was redacted for privacy. Signature was redacted for privacy. Signature was redacted for privacy. For the/Gc2fauate College Iowa State University Ames, Iowa 1994 ii TABLE OF CONTENTS GENERAL INTRODUCTION 1 Explanation of Dissertation Format 2 References Cited 3 LITERATURE REVIEW ON YOUNG CHILDREN'S ACQUISITION OF 6 MATHEMATICAL KNOWLEDGE Introduction 6 Mathematical Knowledge 7 Mathematics Education Reformation 10 Goals of Mathematics Education 10 Young Children's Acquisition of Mathematical Knowledge 11 Knowledge Acquisition 12 Learning and the Learner 14 Social Interactions 21 Peers and Adults 23 Educational Implications: Learning with Meanings 25 Role of Teacher 25 Teachers' Cognitive Distancing Strategies 30 Peer Interactions 34 Problem-Solving Environments 37 Manipulatives 37 Computers and Calculators 39 Personally Meaningful Experiences 40 Planned Activities as Self-Directed Learning Opportunities 41 Play and Games 42 Individual Appropriateness 44 References Cited 45 iii LITERATURE REVIEW ON KINDERGARTEN MATHEMATICS EDUCATION, A 53 BRIDGE CONNECTING INFORMAL AND FORMAL MATHEMATICS Introduction 53 Informal Mathematical Knowledge 53 Early Childhood Mathematics Education 55 Developing Number Sense 56 Understanding Relations 58 Knowing Conventional Symbols 58 Solving Problems 61 NCTM School Mathematics Standards 62 Gap between Formal and Informal Mathematics Learning 64 Kindergarten Teachers' Classroom Practices 65 Summary 70 Conclusion 71 References Cited 72 DEVELOPMENTALLY APPROPRIATE PRACTICES AND MATHEMATICS 78 TEACHING AND LEARNING IN KINDERGARTEN CLASSROOMS Abstract 78 Introduction 78 NCTM Position on Early Childhood Mathematics Education 80 The Need for Examination of Kindergarten Mathematics Education 81 Review of Methodology 85 Objectives of the Study 89 Methodology 90 Subjects 90 Instruments 91 Procedures 94 Results 97 Demographics 97 iv Developmentally Appropriate Practices in Kindergarten 98 Classroom Behaviors 100 Relations between Developmentally Appropriate Practices and 104 Teachers' Classroom Behaviors Relations between Developmentally Appropriate Practices and 106 Children's Classroom Behaviors Comparison of Teaching Behaviors in Mathematics-Related and 110 Nonmathematics-Related Activities Comparison of Children's Learning Behaviors in Mathematics-Related 113 and Nonmathematics-Related Activities Relations between Teachers' Behaviors and Children's Behaviors 114 Relations between Teachers' Characteristics and Degree of 118 Developmentally Appropriate Practices Relations between Teachers' Characteristics and Classroom Behaviors 119 in Mathematics-Related Activities Discussion 120 Relations between Developmentally Appropriate Practices and 121 Teachers' Classroom Behaviors Relations between Developmentally Appropriate Practices and 122 Children's Classroom Behaviors Teaching and Learning in Mathematics-Related and Nonmathematics- 125 Related Activities Teachers' Cognitive Distancing and Children's Responses 126 Developmentally Appropriate Practices in Kindergarten 128 Conclusion 130 References Cited 133 GENERAL CONCLUSIONS 139 Limitations of the Study and Future Implications 143 References Cited 145 ACKNOWLEDGMENTS 148 APPENDIX A: PROCEDURES FOR RECRUITING SUBJECTS 149 APPENDIX B; CORRESPONDENCE 153 V APPENDIX C: INSTRUMENTS 163 APPENDIX D: CODING MANUAL FOR KINDERGARTEN CLASSROOM PROFILE 190 1 GENERAL INTRODUCTION Mathematical learning in the United States has been characterized by certain ineffective practices that are suspected causes of the poor achievement of American students compared with their peers in other countries (Song & Ginsburg, 1987; Stevenson, Stigler, Lee, Lucker, Kitamura, & Hsu, 1985; Stevenson, Lee, & Stigler, 1986; Stigler, Lee, Lucker, & Stevenson, 1982; Stigler, Lee, & Stevenson, 1987). Such ineffective practices include less time allotted to teaching and learning mathematics; less time spent using effective teaching methods such as direct teaching and use of manipulatives and of real-world problems; and more inappropriate behaviors during mathematics learning time (Stevenson et al, 1985; Stevenson et al., 1986; Stigler et al, 1982; Stigler et al, 1987). Moreover, lack of connection between children's informally learned mathematical knowledge and school-taught formal mathematics is a major concern (Song & Ginsburg, 1987). Kindergarten is a bridge linking children's informally learned mathematical knowledge to formal school-taught mathematics. Cross-cultural studies have demonstrated that preschool children in the United States can understand and apply mathematics better than children in other countries (Song & Ginsburg, 1987). But American children lose this advantage after kindergarten (Husen, 1967; Song & Ginsburg, 1987; Stevenson et al., 1985; Stevenson et al., 1986, Stigler et al., 1982). Baroody and Ginsburg (1990) suggest that this loss of advantage is the result of a notable gap between children's informal mathematical understanding and their school mathematics education. Educational organizations such as the National Association for the Education of Young Children (NAEYC) and the National Council of Teachers of Mathematics (NCTM), as well as other groups of educators (e.g., Bredekamp, 1986; Campbell & Carvey, 1992; Kamii, 1990; Katz & Chard, 1989) have advocated that mathematics education for young children should be integrated into other subjects. However, the majority of kindergartens are not developmentally 2 appropriate (Bryant, Clifford, & Peisner, 1991; Charlesworth, Hart, Burt, & Hernandez. 1991; Hyson, Hirsh-Pasel<, & Rescoria, 1990; Mayers, 1991; Rustier, iVlcGrevin, Lambiotte, 1992). Further, the majority of kindergarten teachers are unaware of teaching strategies that are effective in connecting children's experience to mathematics (Parker & Kurtz, 1990). As a result, many still emphasize methods such as memorization and drills in teaching mathematics and teach it as an isolated subject instead of integrating it into other learning activities. However, little research is available documenting actual classroom mathematics teaching and learning in kindergarten.. To gain a better understanding of young children's acquisition of mathematical knowledge and actual classroom mathematics teaching and learning in kindergarten, this dissertation aims to (1) examine existing literature on young children's acquisition of mathematical knowledge, (2) examine
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