算数における関数的概念の発達の様相 ― 思考水準とシンボル化の視点から ―

抄録

　　The purpose of this research is to clarify the aspect of symbolization of tables, formulas,and graphs,and signalization in development of a functional concept on the basis of the theory of levels of thinking by van Hiele (1986).　In development of the functional concept, I think that symbolization is that it is to recognize the situation in tables, formulas, and graphs, and when the situation that a symbol works on other expression appeared, I consider that a symbol functions as a signal.

　　In order to clarify the aspect of symbolization and signalization, I observed and analyzed the lessons of a fourth grader “how to change” and the fifth grader “formula using ○ and △”, and　investigated the aspect of development of a children’s functional concept.

　　As a result, the following knowledge was acquired :

・ In order to symbolize graphs, it is important that children consider motions of hands (gestures) as the concept of the function and the change.

・ In order to symbolize formulas, it is important that children focus on the structure of the situation by unitizing and norming (Lamon, 1994).

・ By following a change of the phases of thinking (van Hiele, 1986), children found that it was difficult to exceed “free orientation (phase 4)”.