Affordances of computer-based and physical geoboards in problem-solving activities in the middle grades

Recent technological advancements have made it feasible to use computer-based manipulatives for mathematics instruction. But despite the ready availability of computer-based manipulatives, the question still remains: how can we make effective use of technological resources in mathematics classrooms, including computers, in order to better promote student learning?; This research was designed to investigate affordances, the potential for effective use, of computer-based manipulatives compared with physical manipulatives, in order to use these manipulatives to engage student participation in mathematics classroom activities. Two sixth-grade classes received mathematics instruction based on a series of student-centered lessons in order to provide students with an opportunity to discover a formula for the area of a parallelogram. One class used a computer-based geoboard, and the other class used a physical geoboard. Two experts in mathematics teaching and learning observed all the classes. Based on the idea of Japanese Lesson Study, these two observers and the researcher, who taught all the classes, discussed their findings to identify affordances of these two types of geoboards in problem-solving activities.; A major finding of the research was that the computer-based and physical geoboards have different affordances. For example, the capability of putting a color inside a shape might be an affordance of the computer-based geoboard. Allowing students to make a shape easily, by just looking at its form, might be an affordance of the physical geoboard. Considering affordances of the two types of geoboards, this study suggests that the computer-based geoboard is an appropriate tool for a class designed to develop a formula for finding the area of a parallelogram by transforming a shape. The physical geoboard, on the other hand, has the potential to be a useful tool to help students develop the concept of area and learn ways to find the area of a rectangle and a square. Therefore, in order to maximize students learning in problem solving, these two types of geoboard should be used in complementary roles in the classroom. Research needs to be carried out to identify instructional activities that take advantages of the affordances of both kinds of geoboards.