INVOLVING NINE SCHOOL SYSTEMS, THE PROJECT WAS TO PROVIDE STUDENTS WITH EXPERIENCES THAT REFLECTED A VALID INTERPRETATION OF GOOD MATHEMATICAL THINKING, TO MAKE EXTENSIVE DATA COLLECTIONS TO DOCUMENT THE NATURE OF THE EXPERIENCES, TO ACHIEVE THE MOST EFFECTIVE POSSIBLE QUALITY CONTROL IN ASSURING THE RELEVANCE AND EFFECTIVENESS OF THE EXPERIENCES, AND TO INTEGRATE THIS DEMONSTRATION INTO THE PROJECT'S PROGRAM OF INSERVICE TEACHER TRAINING AND THE DEVELOPMENT OF CURRICULUM MATERIALS. AN ORGANIZATIONAL STRUCTURE BETWEEN THE PROJECT AND THE PARTICIPATING SCHOOL SYSTEMS WAS DEVELOPED TO PROVIDE FOR COMPETENT STAFFING OF EACH SCHOOL AND TO ARRANGE FOR PROJECT MATERIALS TO BE TAUGHT TO STUDENTS IN GRADES 4 THROUGH 7 FOR 1 HOUR WEEKLY. TEACHERS WERE PROVIDED WITH WEEKLY OR BI-WEEKLY INSERVICE TRAINING. SYSTEMATIC, FORMAL INSTRUCTION WAS NOT INCLUDED, INSTEAD, A PROBLEM WAS PRESENTED, AND THE CLASS, WORKING AS A GROUP, SOLVED IT THE BEST WAY THEY COULD. SOME CHILDREN EMERGED AS LEADERS, WHILE OTHERS CHOSE NOT TO PARTICIPATE AND WERE NOT FORCED TO DO SO. CHILDREN HAD A MEASURE OF FREEDOM TO THINK ABOUT A PROBLEM AND TO SOLVE IT. AFTER AN ANALYSIS OF FIRST YEAR DATA ( OF THE 5 YEAR PROJECT), INDICATIONS ARE THAT CREATIVE USE OF MATHEMATICAL IDEAS IS STRONGLY DEPENDENT UPON SCHOOL EXPERIENCES--THAT, UNDER CERTAIN CONDITIONS, A SIGNIFICANT FRACTION OF CHILDREN FROM GRADES 4 THROUGH 7 CAN PROFIT FROM THE IDEAS PRESENTED, THAT INTEGRATION OF EXPLORATORY MATHEMATICS INTO THE SCHOOL PROGRAM CAN BE ACHIEVED WITH REASONABLE SUCCESS, AND THAT INSERVICE TEACHER EDUCATION IS VERY HELPFUL.