APPROVED - UNT Digital Library - University of North Texas

452 Pages·2000·5.98 MB·English

by  Addie Hare

REVEALING WHAT URBAN EARLY CHILDHOOD TEACHERS THINK
ABOUT MATHEMATICS AND HOW THEY TEACH IT:
IMPLICATIONS FOR PRACTICE
Addie Y. V. McGriff Hare, B.S., M.A.
Dissertation Prepared for the Degree of
DOCTOR OF EDUCATION
UNIVERSITY OF NORTH TEXAS
December, 1999
APPROVED:
George Morrison, Major Professor
Linda Schertz, Committee Member
Allen Sullivan, Committee Member
Deborah Atkins, Committee Member
Rebecca Glover, Coordinator of the program in Early
Childhood Education
Michael Altekruse, Chair of Counseling, Development,
and Higher Education
M. Jean Keller, Dean of the College of Education
C. Neal Tate, Dean of the Robert B. Toulouse School of
Graduate Studies
Hare, Addie Y. V. McGriff, Revealing what urban early childhood teachers think
about mathematics and how they teach it: Implications for practice. Doctor of Education
(Early Childhood Education), December 1999, 443 pp., 39 tables, references, 197 titles.
Hersh (1986) states, (cid:147)One(cid:146)s conception of what mathematics is affects one(cid:146)s
conception of how it should be presented. One(cid:146)s manner of presenting it is an indication
of what one believes to be most essential in it.(cid:148) In this research study, three hundred
ninety-seven urban early childhood teachers were given a survey that examined their
attitudes toward mathematics and mathematics teaching, their views of mathematics,
views of teaching mathematics, and views of children learning mathematics. The
purpose of this study was to identify the attitudes and beliefs of early childhood teachers
in two urban school districts to determine if mathematics reform efforts made a
difference in teachers(cid:146) attitudes and beliefs about mathematics and its teaching.
Questionnaires were mailed directly to teachers in one school district and principals
distributed questionnaires in the other. Summary scores were calculated for parts of the
instrument. The researcher performed descriptive statistics, comparative analysis, and
conducted frequency distributions, t-tests, ANOVA, and Pearson Correlations.
Findings revealed that teachers with 30 or more years of teaching experience had
more positive attitudes toward mathematics than teachers with 1-3 years of experience.
African American teachers had more positive attitudes toward mathematics and its
teaching than other ethnic groups. Teachers who held a minor or major in mathematics
had more positive attitudes toward mathematics and its teaching than teachers without a
minor or major in mathematics. Teachers in District-A favored constructivist learning
while teachers in District-B favored rote learning. Both school districts(cid:146) teachers favored
the problem-solving approach to teaching mathematics.
If instruction is to be transformed, reformers need to understand teachers(cid:146) beliefs
about mathematics. Beliefs, which are essential for teachers(cid:146) development, seldom
change without significant intervention (Lappan and Theule-Lubienski, 1994).
Therefore, school districts must be informed about the changes necessary for the reform
of mathematics teaching and identify and implement through staff developments and
other measures what they perceive mathematics to be and how it should be taught.
Copyright by
Addie Y. V. McGriff Hare
1999
ii
ACKNOWLEDGMENTS
First I would like to thank God for seeing me through this project. Without him
this degree would have been impossible. Second, thanks go out to my immediate family,
Sam, Robert, and Ricks. You understood how important this degree was and you stood
the test of time; thanks for your love and understanding. Also to Sam, my dear husband,
thanks for riding out the ups and downs with me. You gave me the strength to carry on.
Special thanks to my extended family, the McGriffs, for their encouragement, support,
and above all their understanding. I did miss a lot of family gatherings and family duties.
Daddy, thanks for confiding in me that you wanted to see at least one of your eleven
children with a Doctorate degree. This was the final push I needed in order to pursue
something I had always dreamed of doing(cid:151)I took the challenge. To my late Grandma
Allie and brothers Harvest and Johnny Wayne thanks for your support and
encouragement as well as I sort to improve myself. Sorry you did not get the chance and
live to celebrate this joyous occasion with me. Also thanks goes out to my co-workers
and friends, especially my buddy Alcina McFarland, for their support and help.
I would like to express my gratitude to my committee members, Dr. George
Morrison, Dr. Linda Schertz, Dr. Deborah Atkins, and Dr. Allen Sullivan, a co-worker in
the school district. Dr. Sullivan you were the catalyst of this study and you went the
extra mile to keep me steered in the right direction. Many thanks to you all! I wish to
also thank Craig Henderson at the University of North Texas Computing Center for his
continued help and patience. Last, but not least, thank you Dr. Paul Ernest for allowing
me to adapt your questionnaire and for communicating with me by e-mail. Without your
help I probably would yet be developing a questionnaire.
iii
TABLE OF CONTENTS
Page
LIST OF TABLES(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133). vi
Chapter
1. INTRODUCTION(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133). 1
Statement of the Problem
Rationale for the Study
Reformation of Mathematics Education
Early Childhood Mathematics Teaching
Early Childhood and Mathematics Learning
Definition of Terms
Purpose and Research Questions
Significance of the Study
2. REVIEW OF LITERATURE(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133).... 46
The Urban Early Childhood Teacher and Mathematics
Teacher Expectations for Student Achievement
Socioeconomic Status and Achievement
Teachers(cid:146) Knowledge and Qualifications in Mathematics
A Discussion of Attitudes, Beliefs and Knowledge
Specific Studies About Teachers(cid:146) Conceptions of Mathematics
3. METHOD(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133). 86
Participants
Instrumentation
Data Collection Procedures
4. RESULTS(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)... 100
Analysis of Data
District A Results
District B Results
Summary of Findings
District A
iv
District B
5. DISCUSSION(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133). 143
Conclusion
Implications
Recommendations for Future Research
APPENDICES(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133) 170
Appendix A: Additional Definitions
Appendix B: Survey Instrument
Appendix C: Panel of Experts and Evaluation Checklist
Appendix D: Teachers(cid:146) Responses to Survey Items
REFERENCES(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133) 420
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LIST OF TABLES
Table Page
1. Survey Participants by Demographics Categories - District A(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133).101
2. Teacher Responses for Attitudes toward Mathematics - District A(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)..105
3. Attitude toward Mathematics and Years of Experience(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)...106
4. Years of Experience, Attitude toward Mathematics, and Least Squares Means 106
5. Attitude toward Mathematics and Ethnicity(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133).106
6. Ethnicity, Attitude toward Mathematics, and Least Squares Means(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)107
7. Attitude toward Mathematics and Major/Minor(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)...107
8. Major/Minor, Attitude toward Mathematics, and Least Square Means(cid:133)(cid:133)(cid:133)(cid:133)108
9. Teacher Responses for Attitudes to Teaching Mathematics - District A(cid:133)(cid:133)(cid:133)..109
10. Attitudes to Teaching Mathematics and Type Class(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)110
11. Type Class, Attitude to Teaching Mathematics, and Least Squares Means(cid:133)....110
12. Attitude to Teaching Mathematics and Ethnicity(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)111
13. Ethnicity, Attitude to Teaching Mathematics, and Least Squares Means(cid:133)(cid:133)...111
14. Attitude to Teaching Mathematics and Major/Minor(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)..111
15. Major/Minor, Attitude to Teaching Mathematics, and Least Squares Means(cid:133).112
16. Paired Samples Test - District A/View of Mathematics(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)..113
17. Descriptive Statistics - District A/View of Mathematics(cid:133).(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)... 113
18. District A - Frequencies/Views of Mathematics(cid:133)..(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)114
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19. Paired Samples Test - District A/View of Teaching Mathematics(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)..115
20. Descriptive Statistics - District A/View of Teaching Mathematics(cid:133)(cid:133)(cid:133)(cid:133)(cid:133).118
21. District A - Frequencies/Views of Teaching Mathematics(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)..118
22. Paired Samples Test - District A/View of Learning Mathematics(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)..120
23. Descriptive Statistics - District A/View of Learning Mathematics(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)..121
24. District A (cid:150) Frequencies/Views of Learning Mathematics(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)..121
25. Survey Participants by Demographics Categories - District B(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)122
26. Teacher Responses for Attitudes toward Mathematics - District B(cid:133)(cid:133)(cid:133)(cid:133)(cid:133).125
27. Teacher Responses for Attitudes to Teaching Mathematics - District B(cid:133)(cid:133)(cid:133).126
28. Paired Samples Test - District B/View of Mathematics(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)..127
29. Descriptive Statistics - District B/View of Mathematics(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133).128
30. District B - Frequencies/Views of Mathematics(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)..128
31. Paired Samples Test - District B/View of Teaching Mathematics(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)..129
32. Descriptive Statistics - District B/View of Teaching Mathematics(cid:133)(cid:133)(cid:133)(cid:133)(cid:133).132
33. District B - Frequencies/Views of Teaching Mathematics(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)..133
34. Paired Samples Test - District B/View of Learning Mathematics(cid:133)(cid:133)(cid:133)(cid:133)(cid:133).. 134
35. Descriptive Statistics - District B/View of Learning Mathematics(cid:133)(cid:133)(cid:133)(cid:133)(cid:133).135
36. District B - Frequencies/Views of Learning Mathematics(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)..136
37. Summary of Significance Effects(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)(cid:133)136
38. District A-Teacher Responses to Each Survey Item (Frequencies & Percents).197
39. District B-Teacher Responses to Each Survey Item (Frequencies & Percents)..308
vii
CHAPTER I
INTRODUCTION
Mathematics is at the heart of many successful careers and successful lives
(National Council of Teachers of Mathematics [NCTM], 1998a). However, mathematics
seems to be the number one academic subject disliked by children (National Urban
League, 1999; ERIC Clearinghouse on Rural Education and Small Schools, 1989), and
misunderstood by so many--even those in the profession of teaching. A person(cid:146)s
understanding of the nature of mathematics predicates that person(cid:146)s view of how teaching
should take place in the classroom (Hersh, 1986). It is not, as some may believe, ones
opinion of the best way to teach. Hersh (1986) states that (cid:147)one(cid:146)s conception of what
mathematics is affects one(cid:146)s conception of how it should be presented. One(cid:146)s manner of
presenting it is an indication of what one believes to be most essential in it.... The issue,
then, is not, What is the best way to teach? but, What is mathematics really all about?(cid:148)
(p. 13)
Hersh (1986) also defines mathematics as ideas, not marks made with pencils or
chalk, not physical triangles or physical sets, but ideas (which may be represented or
suggested by physical objects). He listed three main properties of mathematical activity
or mathematical knowledge:
1. Mathematical objects are invented or created by humans.
2. They are created, not arbitrarily, but arise from activity with already existing
1