FROM A STUDY OF GUILFORD'S MODEL OF THE STRUCTURE OF INTELLECT, THE HYPOTHESIS WAS FORMED THAT THE ABILITIES MOST IMPORTANT TO LEARNING MATHEMATICS AND MOST LIKELY TO BE CULTIVATED IN MATHEMATICS CLASS ARE THOSE WHICH REQUIRE THE OPERATIONS OF COGNITION AND CONVERGENT PRODUCTION PERFORMED ON SYMBOLIC AND SEMANTIC CONTENT. A BATTERY OF TESTS SELECTED TO REPRESENT SEVERAL COMBINATIONS OF THESE OPERATIONS AND CONTENTS WAS ASSEMBLED TO PROVIDE DATA BY WHICH THE HYPOTHESIS MIGHT BE TESTED. TWO SAMPLES OF PUPILS ABOUT TO BEGIN THE STUDY OF ALGEBRA WERE TESTED. ONE SAMPLE WAS DRAWN FROM SCHOOLS IN WHICH THE MATERIALS AND METHODS DEVELOPED BY THE UNIVERSITY OF ILLINOIS COMMITTEE ON SCHOOL MATHEMATICS (UICSM) WERE IN USE, AND THE OTHER FROM SCHOOLS WHICH USED OTHER MATERIALS. AT THE END OF THE SAME SCHOOL YEAR, THE SUBJECT-MATTER PROFICIENCIES OF THOSE PUPILS WERE MEASURED BY APPROPRIATE CRITERION TESTS, AND THE SAME EXPERIMENTAL TESTS WERE ADMINISTERED TO ANOTHER SAMPLE OF PUPILS FROM THE SAME SCHOOLS. PUPILS ENROLLED IN UICSM COURSES EXCELLED IN MORE THAN HALF OF THE EXPERIMENTAL MEASURES. THE PROJECT HYPOTHESIS WAS TENTATIVELY SUPPORTED. ONE OF THE CONCLUSIONS STATED WAS THAT THE EXPECTATION THAT MEASURES OF COGNITION OF SYMBOLIC SYSTEMS WOULD BE VALID PREDICTORS OF ALGEBRA ACHIEVEMENT WAS NOT SUBSTANTIATED. (TC)