Teaching and Learning Middle School Mathematics through Cyber Learning System: The Concept of Centroid

Abstract

As the development of technology accelerates, people have expected that technology could impact on teaching and learning of mathematics, and further students deeper understanding (Ayersman, 1996; Borba, 1995; Clements & Del Campo, 1989; Hannafin, Hill, & Land, 1997; Johnson-Gentile, Clements, & Battista, 1994). Along with these aspects that technology might bring to the educational field, it was expected that students proactive participation in mathematics classroom and creativity in exploration could be accomplished (Bransford, Stein, Delcos, & Littlefield, 1986; Dreyfes & Gullo, 1984; Kwon, Kim, & Kim, 2002). One of the softwares that brought peoples attention to the research study in mathematics education relating to students understanding in 1980s was the LOGO, so called Turtle Geometry (Papert, 1980). This software is especially limited to geometry and the level is appropriate for low graders in elementary school. One thing that stands out in LOGO is to guide students to know geometrical figures conceptually by stimulating students thinking power and leading their voluntary participations rather than students get the results by inputting the data into the machine or mechanically memorize the concepts of geometrical figures. In the sense that not only LOGO was the newly introduced mechanical tool but also it encouraged students active participation, people began to foresee the other possibilities that they could do with this. One of the first things that we can easily observe in the technology-based classroom is the change of proportion of the power in the classrooms between teachers and students (Hannafin, Hill, & Land, 1997). With the appearance of increasingly powerful, useful, and adaptable technologies, unprecedented learning environments which are different from those of traditional classrooms have emerged. Especially these systems, called open-ended learning environments (OELEs) (Hannafin, 1992), provide�@electronic tools and resources with which students attempt to address authentic situated problems�@(Hannafin, Hill, & Land, 1997, p. 94). As we can guess easily, the power in the traditional classrooms is almost centered to teachers, that is, the teacher who is in charge of leads a class from the beginning to the end and students are asked to do as they are told. Whereas, although it depends on the design of class in the technology-based classroom, much proportion of power in classrooms is naturally divided into the hands of students. This change requires not only the reformed curriculum so that new environments can play roles that are expected but also the preparation of teachers and active participation of students are necessary for successful teaching and learning of mathematics.