Mathematical Development in Young Children: Exploring Notations

by Brizuela, Barbara M.

• ISBN13: 9780807744512
• ISBN10: 0807744514
• Format: Paperback
• Copyright: 2004-04-01
• Publisher: Teachers College Pr

Summary

With profound implications for classroom practice, this text uses a series of interviews with Kindergarten and elementary school children to examine the significance of children's understanding and learning of mathematical notations in their development as matehmatics learners.

Author Biography

Barbara M. Brizuela is an assistant professor of education at Tufts University.

Table of Contents

Foreword, by Richard Lehrer	vii
Acknowledgments	ix
1. Overview	1	(10)
Research Focus	3	(3)
Connections to History of Mathematics and Notational Systems	6	(1)
A Definition for Notations	7	(2)
Organization of the Book	9	(2)
2. George: Written Numbers and the Written Number System	11	(16)
George's Fine-Motor Skills and Understanding of the Number System	13	(3)
George's Use of Dummy Numbers	16	(5)
The Role of Relative Position in George's Ideas About Written Numbers	21	(5)
Reflections	26	(1)
3. Paula: "Capital Numbers"	27	(15)
Making Sense of Conventions	28	(3)
Capital Numbers: Paula's Invented Tool	31	(4)
Inventions	35	(2)
Conventions	37	(1)
Reflections	38	(4)
4. Thomas: Commas and Periods in Numbers	42	(13)
Thomas's Developing Understanding of Periods and Commas in Numbers	43	(8)
Reflections	51	(4)
5. Sara: Notations for Fractions That Help Her "Think of Something"	55	(12)
WITH ANALUCIA SCHLIEMANN AND DAVID CARRAHER
Solving Algebraic Problems During Class	58	(5)
Solving Algebraic Problems During an Interview	63	(2)
Reflections	65	(2)
6. Jennifer and Her Peers: Data Tables and Additive Relations	67	(14)
WITH SUSANNA LARA-ROTH
Second Grade: Looking at Children's Self-Designed Tables	71	(6)
Jennifer in Third Grade	77	(3)
Reflections	80	(1)
7. Jennifer, Nathan, and Jeffrey: Relationships Among Different Mathematical Notations	81	(19)
Details of the Study	82	(1)
The Problem Presented to the Children	83	(1)
The Children's Reactions to the Problem	84	(3)
The Children's Notations	87	(4)
The Children's Interpretations of Jennifer's Graph	91	(7)
Reflections	98	(2)
8. Final Reflections	100	(7)
References	107	(10)
Index	117	(8)
About the Author	125