Concept formation of triangles and quadrilaterals in the second grade

In order to understand the concept of an n-gon it can be characterized by a commutative diagram which is composed of four ways of judging a given figure as an n-gon, and it is examined through some cases on the introductory instruction on the concept of triangles and quadrilaterals. In each of these cases, it was observed that some children gave persuading arguments containing a critical idea and the concept formation corresponded to a structure-preserved transformation in the diagram. Following the diagram, four stages on the concept formation and its development are introduced. According to two operations in the diagram, essentially two kinds of teaching tools can be distinguished. Putting these issues together, an experimental instruction is designed and implemented.