Study of the Representational System in Mathematics Education
Grant-in-Aid for Scientific Research (C)
|Allocation Type||Single-year Grants|
|Research Institution||HIROSHIMA UNIVERSITY|
NAKAHARA Tadao Hiroshiama Univ.Education Professor, 教育学部, 教授 (90034818)
KOYAMA Masataka Hiroshiama Univ.Education Associate Prof., 教育学部, 助教授 (30186837)
IMAOKA Mitsunori Hiroshiama Univ.Education Associate Prof., 教育学部, 助教授 (20031817)
|Project Period (FY)
1995 – 1996
Completed(Fiscal Year 1996)
|Budget Amount *help
¥2,300,000 (Direct Cost : ¥2,300,000)
Fiscal Year 1996 : ¥1,100,000 (Direct Cost : ¥1,100,000)
Fiscal Year 1995 : ¥1,200,000 (Direct Cost : ¥1,200,000)
|Keywords||Representation / Mathematical Symbols / Interation / Understanding / 理解 / コミュニケーション|
In this study, we classified the modes of representaion used in mathematics teaching into five modes as follows.
E1.Realistic rep. : Representations using natural objects in the real world
E2.Manipulative rep. : Representations using artificial manipulative objects
1.Illustrative rep. : Representations using pictures, diagrams, and/or figures
S1.Linguistic rep. : Representations using written everyday language
S2.Symbolic rep. : Representations using mathematical symbols
Morevoer, we separated each mode of representation into children' internal representation and external representation. Based on the representational system, we examined characteristics and functional roles of each representational mode in mathematical lessons. Main findings can be summarized as :
(1) E1, E2 and I are strong iconizing. S1 and S2 are week iconizing.
(2) Following scheme will be suggested in the teaching-leraning process of mathematics ; E1 * E2 * I * S1 * S2
(3) Manipultive rep.and Illustrative rep.play important role in problem solving and understanding processes.
(4) The interactions in mathematical lessons are calssified into four types : 1.Decreased oppsition 2.Agreement 3.Integral enhancement 4.extensive enhancement.
Research Output (14results)