ACCORDING TO PIAGET, THE CONCEPT OF CONSERVATION IS A PREREQUISITE TO MATHEMATICAL UNDERSTANDING. THIS STUDY SOUGHT TO DETERMINE WHETHER THE ABILITY OF FIRST GRADE CHILDREN TO SOLVE ADDITION PROBLEMS WAS DEPENDENT ON THEIR MASTERY OF CONSERVATION OF NUMEROUSNESS. SECONDARY PURPOSES WERE TO INVESTIGATE THE EFFECT IN PROBLEM STATEMENTS OF (1) PHYSICAL OR PICTORIAL AIDS, AND (2) THE PRESENCE OR ABSENCE OF TRANSFORMATIONS. A TEST OF CONSERVATION OF NUMEROUSNESS THAT DIVIDED CHILDREN INTO 4 LEVELS WAS DEVELOPED IN A PILOT STUDY. THE POPULATION FOR THE MAIN STUDY WAS 2,166 FIRST GRADE CHILDREN WHO HAD PROGRESSED THROUGH ABOUT 3/4 OF AN ARITHMETIC CURRICULUM. ALL WERE GIVEN AN IQ TEST, WHICH WAS USED TO DEFINE 3 IQ LEVELS, AND THEN 341 CHILDREN WERE RANDOMLY SELECTED AND GIVEN (1) THE CONSERVATION OF NUMEROUSNESS TEST, (2) A TEST WITH 18 ADDITION PROBLEMS, EACH HAVING EITHER (A) PHYSICAL, (B) PICTORIAL, OR (C) NO AIDS, AND EITHER HAVING OR LACKING A TRANSFORMATION, AND (3) A TEST OF ADDITION FACTS. AN ANALYSIS OF VARIANCE EVALUATIONS BASED ON A SUBSAMPLE OF 121 CHILDREN INDICATED THAT BOTH THOSE AT THE LOWEST LEVEL OF CONSERVATION MASTERY AND THOSE AT THE LOWEST IQ LEVEL PERFORMED SIGNIFICANTLY LESS WELL ON TESTS (2) AND (3) ABOVE. FOR THE PROBLEM-SOLVING TEST, PROBLEMS HAVING A TRANSFORMATION WERE SIGNIFICANTLY EASIER THAN THOSE WITHOUT, AND PROBLEMS HAVING NO AIDS WERE SIGNIFICANTLY HARDER THAN THOSE WITH PHYSICAL OR PICTORIAL AIDS. CORRELATION OF .49 WAS FOUND BETWEEN THE PROBLEM-SOLVING AND ADDITION FACTS TESTS, WHICH WAS FELT TO INDICATE THAT ACTUAL PROBLEM-SOLVING RATHER THAN SIMPLE DRILL WAS NECESSARY TO LEARNING ADDITION FACTS. (DR)