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A STUDY ON MATHEMATICAL ACTIVITIES USING GEOBOARDS

Research Project

Project/Area Number 06680246
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field 教科教育
Research InstitutionOSAKA KYOIKU UNIVERSITY

Principal Investigator

HAZAMA Setuko  OSAKA KYOIKU UNIVERSITY FACULTY OF EDUCATION PROFESSOR, 教育学部, 教授 (40030382)

Co-Investigator(Kenkyū-buntansha) HASHIMOTO Yoshihiro  OSAKA KYOIKU UNIVERSITY FACULTYOF EDUCATION ASSOCIATED PROFESSOR, 教育学部, 助教授 (00030479)
Project Period (FY) 1994 – 1995
Project Status Completed (Fiscal Year 1995)
Budget Amount *help
¥2,200,000 (Direct Cost: ¥2,200,000)
Fiscal Year 1995: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 1994: ¥1,200,000 (Direct Cost: ¥1,200,000)
KeywordsTeaching Geometry / Geoboards Geometry / Mathematical Activities / Mathematization / Taxicab Geometry / Pick's Theorem / Transforming Shapes With The Same Units Perimeter / Lattice polygons / ジオボード(格子点) / 算数・数学教育 / ジオボード / 格子点の数学
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.

Report

(3 results)
  • 1995 Annual Research Report   Final Research Report Summary
  • 1994 Annual Research Report
  • Research Products

    (7 results)

All Other

All Publications (7 results)

  • [Publications] 狭間節子: "ジオボード(格子点)の数学的活動の研究-ジオボード上の図形の等周変形-" 『数学教育研究』 大阪教育大学数学教室編. 第25号. 19-36 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] 高橋晋: "四角形くずし" 『数学教育研究』 大阪教育大学数学教室編. 第25号. 37-50 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] HAZAMA,SETUKO: "A STUDY ON MATHEMATICAL ACTIVITIES USING GEOBOARDS : Transforming lattice polygons with the same units perimeter" Osaka Journal of Mathematics Education. no.25. 19-36 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] TAKAHASHI,SUSUMU: "Don't be square on the 3*3,4*4 and 5*5 boadrs" Osaka Journal of Mathematics Education.no.25. 37-50 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] 狭間節子: "ジオボード(格子点)の数学的活動の研究-ジオボード上の図形の等周変形" 『数学教育研究』大阪教育大学数学教室編. 25. 19-36 (1996)

    • Related Report
      1995 Annual Research Report
  • [Publications] 高橋 晋: "四角形くずし" 『数学教育研究』大阪教育大学数学教室編. 25. 37-50 (1996)

    • Related Report
      1995 Annual Research Report
  • [Publications] 狭間節子編著: "小学校算数実践指導全集第7巻 空間観念を育てる立体図形の指導" 日本教育図書センター, 294 (1995)

    • Related Report
      1995 Annual Research Report

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Published: 1994-04-01   Modified: 2016-04-21  

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