Both Computer and Traditional Technology Are Inevitable for Mathematics Teaching : Revisiting why we use technology

We use technology to improve mathematics education. The first part of this lecture, the logical inconsistencies for introducing technology come from the difference of society, curriculum and technology itself will be mentioned. Because inconsistencies logically existed, we should develop the judicious position of using technology. The judicious users will be teachers and students. The second part, I would illustrate the Japanese approach by focusing on teachers. The later half, I would addressed the importance of judicious using of technology if it is to be a necessity in enhancing students mathematical explorations and developing mental object in order to support their mathematization. The basic theories of mathematics education will be applied to explain this position. To illustrate the importance of both the traditional and computer technology, I would use the perspective drawing and mechanical motions as for the example. 1. Beyond the inconsistencies of using technology in classroom Technology is a part of necessary tools for knowledge based society. It is true that technology has been pushing globalization and changing society. It is necessary to prepare children, and technology should be introduced into classroom in preparation of the changing society. On the other hands, we should be concerned about some of the logical inconsistencies based on the difference of society, aims of reform and technology itself. First inconsistency is the mismatch between technology and society of academy and teachers. There is a simplistic motion of introducing technology into classroom because of the existence of some advanced countries in using certain special technology. Even if using technology itself is mathematically interesting, its usage in classroom is meaningful in some countries but not in some other countries. In 1990s, the reform movements of using of innovative technology had influenced the world. The reform of AP-Calculus in USA influenced the other countries. It spreads the use of graphing calculators to limited countries which shared the similar setting and target in their reforms but not with countries having different setting and target. In the case of East Asia, many students have good achievement in their mathematics curriculum without innovative technology. In these countries, teachers are reluctant to use technology even if they well recognize the significance of technology for instance the power of visualization and importance of exploration. In comparison to East Asia, there are many countries in which the mathematics teachers are not well prepared for teaching mathematics. It is not uncommon that mathematics educators who teach elementary mathematics to future prospective teachers do not have good experience in geometrical proof themselves. Judicious technology using (Lynda Ball, Kaye Stacy. 2005) is a general necessary expectation in the teaching content for the knowledge based society when we teach students both on how to use technology and thinking mathematically. On the other hands, if teachers use technology such as Dynamic Geometry Software in their classroom and does not well understand geometrical proof, their exploration with DGS will be limited hence the meaning of judicious using itself is not similar to other countries. Second inconsistency is the mismatch between curriculum and technology. Introducing new technology into classroom sometimes means the change in the teaching content and aims of education. There is a simplistic motion to use technology as an alternative to paper and pencil approach. When students explore the free fall phenomena using the digitizing system of the motion of graphing calculator, the approximation by the four degree function is better than the quadrilateral function. Here, teachers are teaching students how to explore the phenomena with graphing calculator on its statistical meaning or its mathematical modeling but not teaching them to consider mathematical structure of the free fall phenomena. If we introduce technology as a necessary tool for learning, it changes the content of mathematics teaching itself. If calculus teacher want to use the free fall phenomena as a model of fundamental theorem of calculus, he hopes that pre-calculus teachers teach it as an example of the quadrilateral function. Many teachers who are teaching upper level of mathematics deny teachers who are teaching lower level mathematics, change the content with technology. Upper level mathematics usually uses lower level mathematics as the mental object for the base of constructing upper level mathematics. In some countries, the movement of introducing technology is ongoing with the regression of mathematics teaching content. Third inconsistency is among innovations. Even if one learned how to use the innovative technology it gets out dated very fast. On the integrity and fair competition of technological innovation, new technology is tentatively new until new products come and governments have to spend too much for every revision.