The Role of Graphing Calculators in Mathematics Reform.

This essay describes the role of graphing calculators in mathematics reform. Among the topics discussed are the history of graphing calculators in mathematics education, recent technological innovations, and professional development opportunities. The case is made for a balanced approach between calculator use and paper-and-pencil techniques. (Contains 17 references.) (MM) Reproductions supplied by EDRS are the best that can be made from the original document. PERMISSION TO REPRODUCE AND DISSEMINATE THIS MATERIAL HAS BEEN G ANTED BY TO THE EDUCATIONAL RESOURCES INFORMATION CENTER (ERIC) 1 ‘The Role of Graphing Calculators in Mathematics Reform v. 4-1-98 Bert K. Waits and Franklin Demana Professors Emeritus of Mathematics Department of Mathematics, The Ohio State University 231 W. 18th Avenue, Columbus, OH 43210 [email protected] U.S. DEPARTMENT OF EDUCATION Office of Educational Research and Improvement E UCATIONAL RESOURCES INFORMATION CENTER (ERIC) This document has been reproduced as eived from the person or organization originating it. 0 Minor changes have been made to improve reproduction quality. Points of view or opinions stated in this document do not necessarily represent I official OERI position or policy. Introduction The authors began working together over fifteen years ago at The Ohio State University with computer visualization (computer generated graphs) to enhance the teaching and learning of mathematics (algebra, analytic geometry, and calculus). We found early in our work that students at typical high schools rarely had regular access to a computer lab during their classes. In fact, most teachers we knew indicated they seldom used computers and when they did, it was for “demonstration” only. They reported it was almost impossible to schedule their mathematics classes in a computer lab because the labs were usually fully scheduled with non-mathematics classes. Software and its high cost presented additional problems. Some software required training that many teachers found difficult or inconvenient to obtain. Graphing calculators, first introduced in 1986 by Casio, started a revolution in the teaching and learning of mathematics in the United States and in many other countries as well. Graphing calculators are really inexpensive hand-held computers with built-in numerical solvers and graphing software. Graphing calculators could be viewed as computers available to all students because of their low cost, ease of use, and portability [Demana and Waits, 1992]. The National Council of Teachers of Mathematics’ Curriculum and Evaluation Standards released in 1989 for grades 9 12 includes the assumption that graphing calculators will be available to all students at appropriate times because they are personal computers that fit in a pocket or purse. Before graphing calculators, teachers had to rely exclusively on expensive computers (usually housed in a separate computer laboratory) to deliver computer enhanced visualization in mathematics teaching and learning. Only a few elite schools could provide such an experience to all mathematics students on a regular basis graphing calculators changed that! The pedagogical significance to the mathematics community of the small, inexpensive, hand-held graphing calculators should not be under estimated. Prior to 1996 graphing calculators provided only some of the important features of a computer algebra system (CAS) all but the symbol manipulating software of a CAS at far less cost and often in a more user friendly environment PC based computer algebra systems. In 1996, a remarkable hand-held “portable and affordable” complete CAS with CABRI computer dynamic geometry was introduced by Texas Instruments (the TI-92). The TI-92 uses the same computer CPU than the early Macintosh computers! Now other powerful hand-held CAS are available as well such as the new TI-89 and Casio CFX-9970. Copyright by Bert Waits and Franklin Demana, 1998 2 BEST COPY AVAILABLE 1 The internet and the new upgradable calculators from TI Texas Instruments recently announced a family of Flash Technology based calculators (the TI-73 for middle and early high school students, TI-89 for advanced high school and college students, and the TI-92 PLUS module with advanced mathematics software for the existing TI-92s) that will end calculator box obsolesce. Do you remember what we did with our wonderful TI-81s when the “more wonderful” TI-82 was introduced (and then that was followed by the TI83…)? These new Flash Technology based calculators can be easily renewed with NEW computer software via the intemet and also will be able to use software applications from popular sources outside of TI that can be downloaded via the interne. For example, Sunburst Communications is making Some of their more popular software titles available to run on the TI-73. It is important to note that Flash Technology means that calculator functionality can expand as curriculum needs change. We are entering a new era of technology value added! We believe that students must use computers on a regular basis for both in-class work and for homework outside of class if there are to be significant changes in the mathematics that students learn today. The introduction of 1. the first graphing calculator by Casio in 1986, 2. the first hand-held pocket complete CAS calculator by Texas Instruments in 1996, and 3. the first FLASH based upgradable calculators by Texas Instruments in 1998 are all extremely significant. Here for the first time in their eras were serious “portable and affordable” computers with pedagogical software designed to enhance the teaching and learning of mathematics. The C2PC and C3E Projects Our first computer graphing project (known as the Computer and Calculator Pre-Calculus C2PC Project) began in the mid eighties at Ohio State. The materials developed in that project evolved into a textbook, Precalculus Mathematics, A Graphing Approach (now is its fourth edition; Demana, Waits, Clemens, & Foley, 1997) and is now in use in many high schools in the US. The first edition of that textbook in 1988 is recognized as the first widely adopted high school or university textbook to require the fully integrated use of computer graphing or graphing calculator technology by students on a regular basis. A subsequent project which began in 1990 (known as the Computer and Calculator enhanced Calculus C3E Project) also resulted in a calculus textbook that fully integrates graphing calculators (now is its second edition; Finney, Demana, Waits, and Kennedy, 1999). It is interesting to note that by 1989 we were almost a 100% graphing calculator based project. Today most algebra and calculus textbooks in the US fully integrate graphing calculators and assume their use by students. Many mathematics education research studies have been conducted as an outgrowth of the C2PC project. Professor Penny Dunham nicely summarizes them in her paper that appeared in the Proceedings of the Fourth Annual Conference on Technology in Collegiate Mathematics (Dunham, 1992). Copyright by Bert Waits and Franldin Demana, 1998 2