Early Geometrical Thinking in the Environment of Patterns, Mosaics and Isometries.

Intro -- Main Topics You Can Find in This "ICME-13 Topical Survey" -- Contents -- 1 Early Geometrical Thinking in the Environment of Patterns, Mosaics and Isometries -- 1 Introduction -- 2 Theoretical Considerations About Early Geometrical Thinking -- 2.1 Why Early Geometry Is Related to Isometries -- 2.2 Impact of Visualisation on Geometrical Thinking -- 2.3 Theoretical Background of Research in Early Geometrical Thinking -- 3 Early Geometrical Thinking in Research -- 3.1 Research About Identifying and Creating Shapes -- 3.1.1 Introduction -- 3.2 Results of Research on the Understanding of Geometric Figures -- 3.2.1 Understanding of Two-Dimensional (2-D) Figures by Children -- 3.2.2 Understanding of Three-Dimensional (3-D) Figures by Children -- 3.2.3 Teachers' Understanding of Basic Geometric Concepts -- 3.3 Didactical Proposals for Teaching the Concept of Geometric Figures -- 3.4 Empirical Research about Creating Arrangements Based on a Variety of Regularities, Symmetries, and Repetitions -- 3.4.1 The Role of Patterns in Mathematical Development -- 3.5 Reason for Research Related to Geometrical Patterns -- 3.6 Results of Research in Geometrical Patterning -- 3.6.1 Is It Obvious How to Continue? -- 3.6.2 Perceiving Regularity -- 3.6.3 Arrangements of Surfaces -- 3.6.4 Geometrical Relations -- 3.6.5 Quantitative Analysis of the Protocols -- 3.6.6 Building Vocabulary, Development of Language -- 3.6.7 Connections with Other Geometrical Aspects -- 4 Summary and Looking Ahead -- References.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2023. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.