RELATIONSHIPS BETWEEN CERTAIN INTELLECTUAL PROCESSES AND ACHIEVEMENT OF INSTRUCTIONAL OBJECTIVES FOR SELECTED MATHEMATICS TOPICS TAUGHT IN THE HIGHER ELEMENTARY GRADES WERE EXAMINED. INSTRUMENTS WERE CHOSEN TO ASSESS MATHEMATICS ACHIEVEMENT AND INTELLECTUAL PROCESSES. THESE WERE ADMINISTERED BY CLASSROOM TEACHERS TO 765 STUDENTS IN THE FOURTH, FIFTH, AND SIXTH GRADES WHO HAD SATISFIED SPECIFIC SELECTION CRITERIA. MATHEMATICS ACHIEVEMENT DATA WERE GATHERED ON (1) NUMERICAL OPERATIONS AND ASSUMPTIONS, (2) GEOMETRY, (3) RELATIONS, (4) NUMERATION, (5) MEASUREMENT, AND (6) OPERATIONS WITH FRACTIONS. DATA GATHERED ON INTELLECTUAL PROCESSES WERE (1) PERCEPTUAL DISCRIMINATION, (2) MEMORY SPAN, (3) ASSOCIATIVE MEMORY, (4) ASSOCIATIVE MEMORY PLUS CONVERSION, (5) REASONING ON NUMERICAL RELATIONS AND WORD GROUPINGS, (6) VERBAL MEANING, AND (7) SPATIAL RELATIONS. A SINGLE CLASSIFICATION ANALYSIS OF VARIANCE WAS USED TO ANALYZE RELATIONSHIPS AMONG THE THREE GRADES' MEANS. THE RESULTS OF THE STUDY INDICATED THAT THE PREDOMINANT PSYCHOLOGICAL COMPONENTS (INTELLECTUAL PROCESSES) OF THE FACETS OF MATHEMATICAL ACHIEVEMENT SAMPLED WERE FACILITY IN NUMERICAL REASONING AND IN DISCERNING VERBAL MEANING. RESULTS WERE CONSISTENT WITH DATA REPORTED IN COMPARABLE INVESTIGATIONS CONDUCTED EARLIER. (JH)