PIAGET HAS PROPOSED THAT THE CONCEPT OF NUMBER IS PREDICATED ON THE CONCEPT OF CONSERVATION OF SUBSTANCE--THAT IS, THE CONCEPT THAT THE AMOUNT OR NUMBER REMAINS THE SAME DESPITE SPATIAL REARRANGEMENTS. BECAUSE OF THE CURRENT EMPHASIS ON REVISION OF MATHEMATICS CURRICULUM AND OF THE APPARENT VALUE OF NUMBER TRAINING TO PRESCHOOL DISADVANTAGED CHILDREN, THIS STUDY WAS CREATED TO INVESTIGATE (1) WHETHER TRAINING PROGRAMS CAN EFFECTIVELY TEACH 3- TO 6-YEAR-OLD CHILDREN THE CONCEPT OF CONSERVATION OF SUBSTANCE, AND (2) IF SO, WHETHER SOME TRAINING PROCEDURES ARE MORE EFFECTIVE WITH CERTAIN POPULATIONS THAN OTHER PROCEDURES. ACCORDING TO PIAGET, TRAINING PROGRAMS ALONE ARE NOT SUFFICIENT TO TEACH CHILDREN THE CONSERVATION CONCEPT. ALL OF THE ACTIVITIES OF A CHILD, HIS GRADUAL INTELLECTUAL DEVELOPMENT, LEAD TO THE ACQUISITION OF THE CONCEPT. TO INVESTIGATE PIAGET'S IDEAS ON THE FORMATION OF THE CONCEPT OF CONSERVATION OF SUBSTANCE, 416 CHILDREN OF AGES THREE TO SIX AND OF VARIED SOCIOECONOMIC LEVELS WERE ADMINISTERED ONE OF FOUR TRAINING PROCEDURES AFTER A PRETEST. THE FOUR TRAINING PROCEDURES USED WERE (1) SMEDSLUND'S COGNITIVE CONFLICT METHOD, (2) SIGEL'S MULTIPLE CLASSIFICATION METHOD, (3) BEILIN'S VERBAL RULE INSTRUCTION METHOD, AND (4) BRUNER'S LANGUAGE ACTIVATION METHOD. AT THREE TIME INTERVALS AFTER THIS TRAINING PERIOD, POSTTESTS WERE ADMINISTERED TO ASCERTAIN THE QUALITY AND EXTENT OF THE CHILD'S LEARNING OF THE CONCEPT. THE CONCLUSION REACHED FROM COMPARING THE TEST RESULTS FOR THE FOUR TRAINING GROUPS TO THE RESULTS FROM A CONTROL GROUP WAS THAT THE TRAINING PROCEDURES, ALONE, WERE INEFFECTIVE, REGARDLESS OF THE POPULATION TYPE, IN TEACHING THE CHILDREN THE CONSERVATION-OF-SUBSTANCE CONCEPT. (WD)