Pathways to Number

This volume celebrates the 50th anniversary of the famous and influential work of Jean Piaget and Alina Szeminska, The Child's Conception of Number.It is a tribute to those two authors as well as to the entire Geneva school that pioneered the genetic study of cognitive structures in children. Dealing with the process of the child's construction of the notion of number -- a very important subject for the child as well as for the teacher, the researcher, and the practicing psychologist -- it summarizes the progress that has been made and outlines new research directions in this area. The book is a compilation of the work of the foremost international researchers in this area and includes a wide spectrum of viewpoints and schools of thought. It also introduces several new authors from Europe, including students of Piaget, to the American academic community.

Introduction	p. 1
Learning About Numbers: Lessons for Mathematics Education From Preschool Number Development	p. 19
A Tool For Number Construction: Finger Symbol Sets	p. 41
Conservation and the Notion of """"Half""""	p. 67
Learning Stages in the Construction of the Number Sequence	p. 83
The Development of Preschoolers' Counting Skills and Principles	p. 99
Relationships Between Counting and Cardinality From Age 2 to Age 8	p. 127
Number Conservation: Distinguishing Quantifier From Operator Solutions	p. 151
Early Principles Aid Initial but Not Later Conceptions of Number	p. 171
Subitizing: The Discontinuity After Three	p. 191
From Number to Numbers in Use: Solving Arithmetic Problems	p. 209
The Appropriation of the Concept of Number: A Lengthy Process	p. 219
The Multiple Roots of Natural Numbers and Their Multiple Interpretations	p. 229
Number Transcribing by Children: Writing Arabic Numbers Under Dictation	p. 245
Understanding the Microgenesis of Number: Sequence Analyses	p. 265
Learning Addition and Subtraction: Effects of Number Words and Other Cultural Tools	p. 283
Remedying Common Counting Difficulties	p. 307
Some Unforeseen Variants on the Number Construction Scenario	p. 325
Assessment and Perspectives	p. 349
References	p. 363
Addendum	p. 385
Author Index	p. 387
Subject Index	p. 395
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