丁香园AV

Two decades ago, a new type of computer software was introduced, one that offered a radically new way of representing mathematical objects. Dynamic Geometry Environments (DGEs) enable the creation of dynamic representations鈥攈itherto static objects such as triangles, points, and numbers can now move continuously on the computer screen; these objects can grow, change, and morph over time. Based on the testimonies of some of the great mathematicians of the past, imagining dynamic mathematical objects is central to coming to know about them and being able to work with them in problem-solving contexts. The static media of the past were not conducive to making such personal, dynamic images shareable with others. DGEs change all that.

Much research on the use of DGEs has focused on geometry learning at the secondary level. Given the limited amount of formal geometry taught prior to secondary school, and biases against the use of technology by young children, there has been very little research on the potential of DGEs in the primary school classroom. However, researchers are becoming increasingly concerned about the lost opportunities of current primary school curricula, a loss that is particularly troublesome given the enormous informal geometric ideas young children bring to formal schooling. Moreover, with the increased use of technology in elementary school classrooms as well as both the growing awareness of the importance of geometry, the time is ripe to study the role DGEs could play in improving student mathematics learning in the primary school. The basic tools of DGEs are more than appropriate for the primary school geometry curriculum. In fact, based on the strongly visual, kineasthetic and empirical nature of young children's interactions with the world and the importance of developing flexible geometric imagery at an early age, they are most appropriate for learners of this age, who often develop narrow conceptions of shapes through interaction with static representations.

The proposed research has three main foci. The first is to compare the learning trajectories of children's geometric thinking across age groups in the context of Dynamic Geometry Environment (DGE) use. This component of the proposed research will not only serve to identify the affordances of DGEs, it will contribute to the general understanding of how digital technologies change the way learners (and the way mathematics itself) changes. The second focus is on the long-term effect of DGE use on children's thinking and problem solving. We currently have limited understanding of how dynamic visual representations can affect children's strategies and imageries in various areas of the mathematics curriculum. The third focus is on the classroom interactions involving DGE use engaging the teacher, the students and the tasks. The goal is to develop teaching episodes involving suitably designed DGE-based tasks that will enable a better understanding of how teacher and student discourses in the classroom can promote more sophisticated mathematical thinking.