Cognitive Contribution of Diagrammatic Reasoning Model towards Geometry ITS

Abstract:

The statement that "Mathematics education in secondary school might make students familiar with the deductive method" surely makes sense and is fairly accepted by many mathematics teachers.  On the other hand, there exist some mathematics educators who are skeptical about this practical postulation.  Van Hiele argued that the educational value of geometry is not only found in the deductive method, and proposed the developmental levels of geometric thinking to argue that "the development of logical thinking must be considered as the result of a learning process."  He emphasized that students' deductive thinking ability in geometry ought to be based on their naive spatial concept.  In this proposal, we discuss a cognitive contribution of the diagrammatic reasoning model for an geometry ITS.  The model is organized with the structural knowledge (called diagrammatic schema; DS, for short) which represents diagrammatic information as well as the logical implications among geometric relations.

On-line paper

PDF (2.0MB WinZip)

PDF (10.1MB uncompressed)