Relationships between the spatial and theoretical in geometry: the role of computer dynamic representations in problem solving
暂无分享,去创建一个
Diagrams play an important role in geometry teaching. An analysis of tasks and students’ behaviour in solving problems in two different environments, paper-and-pencil or computer, indicated that the dynamic nature of the software changes the relationship between diagrams and the theoretical aspects of the subject. Learning geometry seems to involve not only learning how to use theoretical statements in deductive reasoning, but also learning to recognise visually relevant spatial-graphical invariants attached to geometrical invariants. Observations of students revealed that this was not easy for them—moving between the spatial and the theoretical domains was not spontaneous and they tended to consider each domain independently.
[1] John Mason,et al. Exploiting mental imagery with computers in mathematics education , 1995 .
[2] Raymond Duval,et al. Geometrical Pictures: Kinds of Representation and Specific Processings , 1995 .
[3] M. Alessandra Mariotti,et al. Images and Concepts in Geometrical Reasoning , 1995 .
[4] E. Fischbein. The theory of figural concepts , 1993 .
[5] Tommy Dreyfus. Didactic Design of Computer-based Learning Environments , 1993 .