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

• Superior document: ICME-13 Topical Surveys Series
• Author: Swoboda, Ewa.
• TeilnehmendeR: Vighi, Paola.
• Place / Publishing House: Cham : : Springer International Publishing AG,, 2016.; Ã2016.
• Year of Publication: 2016
• Edition: 1st ed.
• Language: English
• Series: ICME-13 Topical Surveys Series
• Physical Description: 1 online resource (57 pages)

Table of Contents

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.