Mathematical development in young children : exploring notations / Bárbara M. Brizuela ; foreword by Richard Lehrer.

Format:

Book

Author/Creator:

Brizuela, Bárbara M.

Series:

Ways of knowing in science and mathematics series

Language:

English

Subjects (All):

Mathematical notation.

Mathematics--Study and teaching (Elementary).

Physical Description:

xi, 125 pages : illustrations ; 23 cm.

Place of Publication:

New York : Teachers College Press, [2004]

Summary:

With profound implications for classroom practice, this text examines the significance of children's understanding and learning of mathematical notations in their development as mathematics learners. Using a series of interviews and in-depth conversations with kindergarten and elementary school children, the author investigates young children's understanding of different mathematical notations, including written numbers and the written number system, commas and periods in numbers, notations for fractions, data tables, number lines, and graphs. Logically organized according to the ages of the children, with each chapter focusing on one to three children and one aspect of notations, this seminal work discusses key concepts

Contents:

Connections to History of Mathematics and Notational Systems 6

2. George: Written Numbers and the Written Number System 11

George's Fine-Motor Skills and Understanding of the Number System 13

George's Use of Dummy Numbers 16

The Role of Relative Position in George's Ideas About Written Numbers 21

3. Paula: "Capital Numbers" 27

Making Sense of Conventions 28

Capital Numbers: Paula's Invented Tool 31

Inventions 35

Conventions 37

4. Thomas: Commas and Periods in Numbers 42

Thomas's Developing Understanding of Periods and Commas in Numbers 43

5. Sara: Notations for Fractions That Help Her "Think of Something" / With Analucia Schliemann, David Carraher 55

Solving Algebraic Problems During Class 58

Solving Algebraic Problems During an Interview 63

6. Jennifer and Her Peers: Data Tables and Additive Relations / With Susanna Lara-Roth 67

Second Grade: Looking at Children's Self-Designed Tables 71

Jennifer in Third Grade 77

7. Jennifer, Nathan, and Jeffrey: Relationships Among Different Mathematical Notations 81

The Problem Presented to the Children 83

The Children's Reactions to the Problem 84

The Children's Notations 87

The Children's Interpretations of Jennifer's Graph 91.

Notes:

Includes bibliographical references (pages 107-115) and index.

ISBN:

0807744522

0807744514

OCLC:

53932683