Putting the Fun Into Functions Through the Use of Manipulatives, Computers, and Calculators Connie C. Widmer Northern Kentucky University Highland Heights, Kentucky Linda J.Sheffield Northern Kentucky University Highland Heights, Kentucky For six years, the authors have conducted a series of professional development workshops for teachers in Grades K-8. This article summarizes some of the research from those workshops and gives an overview of the approach taken. The institutes emphasized basic reasoning skills based upon the NCTM Standards and the Kentucky Education Reform Act, integrating manipulative materials and technology. The article demonstrates the integration of manipulates and technology using patterns, relations and functions as examples. "Johnny told me he *s never liked math before." "Ann Marie’s mother said she’s doing much better at math this year." "I’ve never had so much fun teaching math!" The reason for these comments? Enthusiastic teachers in Grades K-8 were basing their mathemat- ics lessons on the use ofmanipulatives, supplemen- ted by appropriate calculator and computer activities. Mathematics Institutes for Teachers Encouraging teachers to build their lessons on hands-on activities was one of the goals of the Mathematics Institutes for Teachers, conducted at Northern Kentucky University during the summers of 1989 through 1994. Funded by grants from the U. S. Department of Education and the Eisenhower Math- ematics and Science Education Act, the institutes strove to promote mathematical reasoning through the integration ofmanipulatives, calculators, and computers into the mathematics curriculum. The 1989,1990,1993, and 1994 institutes were for teachers and administrators in Grades K-4; the 1991 and 1992 institutes focused on Grades 5-8. Prior to the institutes, teacher-participants com- pleted surveys concerning their use ofmanipulatives, calculators and computers in their teaching of mathe- matics. Table 1 shows the percentages of teachers using each of these tools less than once a week. Data from the first three years was typical of the entire program. To improve this situation, participants worked with calculators, a variety ofmanipulatives, and technology including interactive video ("Project Vision," a program developed for Kentucky’s primary grades), turtle robots, LEGO TC Logo, a modem, and adaptive computer devices designed for students with special needs. The first activities in the institute emphasized basic reasoning skills such as identifying attributes, comparing, sequencing, recognizing patterns and relationships, extending patterns, hypothesizing and hypothesis testing. These reasoning skills were then extended to include number sense, estimation, basic facts and computation, followed by geometry, measurement, graphing, probability and statistics. Activities were designed to demonstrate how ma- nipulative materials and technology could be inte- grated to help students create their own understand- ing of ideas. An example of this approach for the primary grades, based on patterns, relationships, and functions, follows. Table 1. Percent of Participants Using Manipulates, Calculators, and Computers Less Than Once a Week: Prior to Institute Group 1: Group 2: Group 3: N Elementary (1989) (n = 103) Elementary (1990) (n=89) Middle School (1991) (n=40) lanipulatives 37 47 84 Calculators 88 97 63 49 59 74 Computers School Science and Mathematics