RESEARCH ON CURRICULUM DEVELOPMENT OF FIGURES AND SPACE FROM THE VIEWPOINT CULTIVATING SPATIAL THINKING IN MATHEMATICS EDUCATION
Grant-in-Aid for Scientific Research (C)
|Allocation Type||Single-year Grants|
|Research Institution||Osaka Kyoiku University|
HAZAMA Setsuko OSAKA KYOIKU UNIVERSITY, EDUCATION, PROFESSOR, 教育学部, 教授 (40030382)
HASHIMOTO Yoshihiro OSAKA KYOIKU UNIVERSITY, EDUCATION, ASSOCIATE PROFESSOR, 教育学部, 助教授 (00030479)
|Project Period (FY)
2003 – 2004
Completed(Fiscal Year 2004)
|Budget Amount *help
¥2,700,000 (Direct Cost : ¥2,700,000)
Fiscal Year 2004 : ¥1,300,000 (Direct Cost : ¥1,300,000)
Fiscal Year 2003 : ¥1,400,000 (Direct Cost : ¥1,400,000)
|Keywords||CURRICULUM OF FIGURES AND SPACE / PUPILS' DEVELOPMENT OF SPATIAL THINKING / MENTAL OPERATIONS OF SPATIAL IMAGES / REPRESENTAITIONS AND THEIR TRANSFORMATION / VISUALIZATION / 表現と表現間に変換 / 数学教育 / 空間思考 / 空間的心像の形成と操作 / 数学的活動 / 空間図形の図表現|
Our results of the research are as follows.
1.We analyzed characteristics of pupils' development of spatial thinking from four viewpoints : spatial images, their mental operations, representations and their transformations, and basis of reasoning.
2.On the base of the characteristics of pupils' development of spatial thinking we constructed curriculum of figures and space for elementary, lower secondary and upper secondary schools according to the following plan.
(1)The curriculum is constructed of a frame of mathematical content and a frame of mathematical activities cultivating spatial thinking. Latter frame is composed of operational activities, representations and their transformation, enrichment activities and bases of reasoning.
(2)Enrichment activities aim to apply spatial thinking to concrete phenomena, plays, arts or computer graphics, etc.
3.The curriculum is characterized as follows.
(1)The mathematical operations of projection, section of solid, developing of solids, etc. are developed spirally in elementary, lower secondary and upper secondary schools levels.
(2)Representations and transformations between them are attached importance in order to cultivate spatial mental image and mental operations.
(3)Content and activities on sphere and spherical surface are enriched, for example, figures on the spherical surface in lower secondary and an elementary spherical surface in upper secondary schools.
(4)Activities on poly-cube is used effectively, for example, construct of poly-cube, its drawing, volume and idea of dimension in elementary school level.
4.We showed teaching-learning practices in elementary, lower secondary and upper secondary schools on some content and activities in the curriculum.
Research Products (12results)