1995 Fiscal Year Final Research Report Summary
A STUDY ON MATHEMATICAL ACTIVITIES USING GEOBOARDS
| Project/Area Number |
06680246
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
教科教育
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| Research Institution | OSAKA KYOIKU UNIVERSITY |
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Principal Investigator |
HAZAMA Setuko OSAKA KYOIKU UNIVERSITY FACULTY OF EDUCATION PROFESSOR, 教育学部, 教授 (40030382)
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| Co-Investigator(Kenkyū-buntansha) |
HASHIMOTO Yoshihiro OSAKA KYOIKU UNIVERSITY FACULTYOF EDUCATION ASSOCIATED PROFESSOR, 教育学部, 助教授 (00030479)
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| Project Period (FY) |
1994 – 1995
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| Keywords | Teaching Geometry / Geoboards Geometry / Mathematical Activities / Mathematization / Taxicab Geometry / Pick's Theorem / Transforming Shapes With The Same Units Perimeter / Lattice polygons |
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| Research Abstract |
Some distinctive features of playing with geoboards (square lattice points) have been made out clearly. On the base of the features, (1) the framework of mathematical activities and (2) contents in each shchool levels have been set up as follows.
[For lower and middle grades of elementary school]
(1) Playing with geoboards ; observation and classification of shapes on the boards
(2) Forming and transforming shapes on the boards (*)
The areas of rectangles with the same units perimeter (*)
*For upper grades of elementary school and for lower grades of secondary school*
(1) Working with geoboards and dotty papers ; analysis, classification and generalization of relations ; guess and test, discussion and inductive argument
(2) Transforming shapes with the same units perimeter ; Don't be square on a 4*4 board (*)
Farey suquence ; Discovery approach to the Pick's theorem (*)
*For upper grades of secondary school and for high school grades*
(1) Working with dotty papers ; analysis, classification and generalization of relations ; verification or modification of conjectures ; a deductical construction of local branch
(2) Transforming lattice polygons with the same units perimeter ; The equivalence of Euler's and Pick's theorem ; The number of the Routes on the board (*) ; Taxicab geometry
These results of the plactical lessons on the above content (*) in each school levels lead to the conclusion that we can keep learners very close to everythings that is being done, investigating them affectively, perceptively, actively, verbally, in fact totally, intheir contemplation of a challenge, in other words learners have experiecs in mathematization.
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