TWO STUDIES DEAL WITH THE THOUGHT PROCESSES CHILDREN DISPLAY WHEN FACED WITH PROBLEMS INVOLVING THE CONCEPTS OF QUANTITY AND NUMBER. INVOLVING CHILDREN IN KINDERGARTEN, FIRST GRADE AND SECOND GRADE, THE STUDIES USE PIAGET'S THEORIES IN BOTH A CROSS-SECTIONAL AND A LONGITUDINAL APPROACH TO STUDY CHILDREN'S THINKING IN AN EDUCATIONAL SETTING. TO DETERMINE THE VALIDITY OF THE STAGES OF THOUGHT AS DESCRIBED BY PIAGET, THE STUDIES DEAL WITH ONE ASPECT OF A CHILD'S THINKING, HIS ABILITY TO CONSERVE NUMBER AND QUANTITY AS REVEALED IN THREE TASKS. STUDIED ALSO ARE HOW THAT ABILITY RELATES ITSELF TO OTHER INTELLECTUAL ABILITIES AND TO SCHOOL READINESS AND ACHIEVEMENT, AND HOW THAT ABILITY CHANGES AND DEVELOPS OVER TIME. RESULTS OF THE CROSS-SECTIONAL STUDY CONFIRMED THE RELEVANCE OF PIAGET'S THEORY TO THE STUDY OF YOUNG CHILDREN. RESULTS OF THE LONGITUDINAL STUDY CONFIRMED CROSS-SECTIONAL RESULTS AND UNDERLINED THE RELEVANCE OF THE CHILD'S PROGRESS IN CONSERVATION OF NUMBER AND QUANTITY TO HIS PERFORMANCE IN THE CLASSROOM. THE DOCUMENT INCLUDES A BIBLIOGRAPHY AND TABLES. THIS DOCUMENT IS AVAILABLE FROM TEACHER'S COLLEGE PRESS, TEACHER'S COLLEGE, COLUMBIA UNIVERSITY, NEW YORK 10027. (EF)