Bringing Out the Algebraic Character of Arithmetic: From Children's Ideas To Classroom Practice

by Schliemann; Analúcia D.

• ISBN13: 9780805858730
• ISBN10: 0805858733
• Edition: CD
• Format: Nonspecific Binding
• Copyright: 2006-08-17
• Publisher: Routledge

Table of Contents

Preface: Rethinking Early Mathematics Education	ix
1 Interpreting Research About Learning Algebra	1	(16)
Student Performance in Algebra	1	(2)
The Transitional Approach as a Response to Students' Difficulties	3	(4)
A More Radical Approach: Introduce Algebra in Elementary School	7	(2)
Young Children Doing Algebra	9	(2)
Our Approach	11	(6)
PART I: INTERVIEW STUDIES
2 Young Children's Understanding of Equivalences	17
Analúcia D. Schliemann, Monica Lins Lessa, Anna Paula Brito Lima, and Alane Siqueira
Contexts for Understanding Equivalence	19	(3)
Participants and Interview Questions	22	(4)
Children's Answers Across Ages and Contexts	26	(8)
Discussion	34
3 Can Young Students Solve Equations?	3	(62)
Analúcia D. Schliemann, David W. Carraher, Bárbara M. Brizuela, and Wendy Jones
Study 1: Recognizing Invariance Despite Change: Strategies and Representations	38	(9)
Study 2: "But How Much, How Many?": The Paradox Inherent in Representing Unknown Quantities	47	(12)
General Conclusions	59
PART II: CLASSROOM STUDIES
4 Addition Operations as Functions	65	(20)
A Bare Bones Example	67	(4)
Additive Functions and Word Problems	71	(7)
How Do the Above Examples Bear on Early Algebra?	78	(3)
Lessons for Early Algebra	81	(1)
Structure Versus Context	82	(3)
5 From Quantities to Ratio, Functions, and Algebraic Notation	85	(20)
Functions and Rate	86	(2)
Function and Ratio in Nonschool Settings	88	(2)
The Intervention and Its Results	90	(2)
First Week: Children's Initial Strategies	92	(3)
Second Week: Developing New Strategies and Algebraic Notation	95	(8)
Discussion	103	(2)
6 On Children's Written Notation to Solve Problems	105	(14)
Using Notations to Solve Problems	108	(3)
Using Notations to Show a Solution	111	(3)
Sara Explains Her Use of Notations to Solve Problems	114	(2)
Discussion	116	(3)
7 Discussion	119	(8)
Development Versus Learning	120	(1)
Contexts	121	(2)
The Roles of Representational Systems in Mathematical Learning	123	(1)
Future Developments	124	(3)
References	127	(12)
Author Index	139	(4)
Subject Index	143