Details

Autor(en) / Beteiligte

• Guille-Biel Winder, Claire
• Assude, Teresa

Titel

Articulations Between Tangible Space, Graphical Space and Geometrical Space : Resources, Practices and Training

Ort / Verlag

Newark : John Wiley & Sons, Incorporated,

Erscheinungsjahr

2023

Beschreibungen/Notizen

• Cover -- Title Page -- Copyright Page -- Contents -- Preface -- Part 1. Articulations between Tangible Space, Graphical Space and Geometric Space -- Chapter 1. The Geometry of Tracing, a Possible Link Between Geometric Drawing and Euclid's Geometry? -- 1.1. Introduction -- 1.2. Geometry in middle school -- 1.2.1. What underlying axiomatics? -- 1.2.2. An example -- 1.2.3. The current lack of consistency -- 1.3. Geometry of tracing, a possible link between material geometry and Euclid's geometry? -- 1.3.1. Figure visualization and figure restoration -- 1.3.2. The geometrical use of tracing instruments, a first step to make sense to an axiomatic -- 1.3.3. Distinguishing between the hypothesis and the conclusion -- 1.3.4. Restoration, description, construction of figures and geometric language -- 1.4. Dialectics of action, formulation and validation with regards to the reproduction of figures with instruments -- 1.4.1. Formulation situations and possible variations -- 1.4.2. Validation situations -- 1.5. From tracing to the characterization of objects and geometric relationships -- 1.5.1. On the concepts of segments, lines and points -- 1.5.2. On the notion of perpendicular lines -- 1.6. Towards proof and validation situations in relation to figure restoration -- 1.6.1. Equivalence between two construction programs and the need for proof -- 1.6.2. Validation situations involving programs for the construction of a square and introducing a proof process -- 1.7. Conclusion -- 1.8. References -- Chapter 2. How to Operate the Didactic Variables of Figure Restoration Problems? -- 2.1. Introduction -- 2.2. Theoretical framework -- 2.2.1. Studying a specific type of problem: figure restoration -- 2.2.2. Studying the concepts involved in figure restoration problems -- 2.3. Values of the didactic variables of the first problem family.
• 2.3.1. Values of the didactic variables for the "figure" and the "beginning of the figure" -- 2.3.2. Value for the didactic variable "instruments made available" -- 2.3.3. Rules of action and theorems-in-action associated with development on the geometrical usage of the ruler -- 2.4. Conclusion -- 2.5. References -- Chapter 3. Early Geometric Learning in Kindergarten: Some Results from Collaborative Research -- 3.1. The emergence of the first questions -- 3.2. Theoretical insights -- 3.2.1. Global understanding and visual perception of geometric shapes -- 3.2.2. Operative understanding and visual perception of geometric shapes -- 3.2.3. Topological understanding and visual perception of geometric shapes -- 3.2.4. Haptic perception -- 3.2.5. Association of visual and haptic perceptions: towards a sequential understanding of geometric shapes -- 3.3. The role of language in early geometric learning -- 3.3.1. But which lexicon? -- 3.3.2. Verbal and gestural language -- 3.4. Assembling shapes -- 3.4.1. Free assembly of shapes -- 3.4.2. Assembling triangles -- 3.5. Gestures to learn -- 3.6. Conclusion -- 3.7. References -- Chapter 4. Using Coding to Introduce Geometric Properties in Primary School -- 4.1. Coding in geometry -- 4.2. Two examples of communication activities requiring the use of coding -- 4.2.1. A co-constructed coding -- 4.2.2. Personal coding -- 4.3. Conclusion: perspectives on the introduction of coding in geometry -- 4.4. References -- Chapter 5. Freehand Drawing for Geometric Learning in Primary School -- 5.1. Introduction -- 5.2. Drawings in geometry and their functions -- 5.3. Freehand drawing in research -- 5.4. Exploring the milieu around a freehand reproduction task of the Mitsubishi symbol on a blank white page -- 5.4.1. Freehand drawing reveals a reasoning between spatial knowledge and geometric knowledge.
• 5.4.2. Freehand drawing as a dynamic process to build and transform knowledge -- 5.5. Conclusion -- 5.6. References -- Part 2. Resources and Artifacts for Teaching -- Chapter 6. Use of a Dynamic Geometry Environment to Work on the Relationships Between Three Spaces (Tangible, Graphical and Geometrical) -- 6.1. Added value with a dynamic geometry environment: the ecological and economical point of view -- 6.2. Tangible space, graphical space and geometric space -- 6.3. Designing situations for first grade primary school -- 6.3.1. Our choices for designing situations -- 6.3.2. Presentation of situations -- 6.4. Analysis of the situations for the first-grade class -- 6.4.1. Instrumental dimension: perceptive-gestural level -- 6.4.2. Instrumental dimension: spatial-geometric relationships -- 6.4.3. Instrumental dimension: exploration and graphical space -- 6.4.4. Instrumental dimension: tool-geometric space symbiosis -- 6.4.5. Praxeological dimension -- 6.4.6. Praxeological dimension: observe and describe -- 6.5. Conclusion -- 6.6. References -- Chapter 7. Robotics and Spatial Knowledge -- 7.1. Introduction -- 7.2. Theoretical framework and development for a categorization of spatial tasks -- 7.2.1. Spatial knowledge -- 7.2.2. Types of spatial tasks -- 7.2.3. Types of tasks and techniques -- 7.3. Research methodology -- 7.4. Analysis: reproducing an assembly -- 7.4.1. Test item -- 7.4.2. Test results -- 7.4.3. Analysis of the results -- 7.5. Conclusion -- 7.6. References -- Chapter 8. Contribution of a Human Interaction Simulator to Teach Geometry to Dyspraxic Pupils -- 8.1. Introduction -- 8.2. General research framework -- 8.2.1. Teaching geometry -- 8.2.2. Dyspraxia and consequences for geometry -- 8.3. What alternatives are there for teaching geometry? -- 8.3.1. Using tools in a digital environment -- 8.3.2. Dyadic work arrangement.
• 8.4. Designing the human interaction simulator -- 8.4.1. General considerations -- 8.4.2. Choice of instrumented actions -- 8.4.3. Interaction choices -- 8.4.4. Ergonomic considerations -- 8.5. Initial experimental results -- 8.5.1. Data collected -- 8.5.2. Jim's diagnostic evaluation -- 8.5.3. Analysis of the first experimentation -- 8.5.4. Conclusion -- 8.6. References -- Chapter 9. Research and Production of a Resource for Geometric Learning in First and Second Grade -- 9.1. Presentation of the ERMEL team's research on spatial and geometric learning from preschool to second grade -- 9.1.1. Origins of the research -- 9.1.2. Introduction to the chapter -- 9.2. Learning to trace straight lines -- 9.2.1. Significance of the straight line -- 9.2.2. Initial hypotheses -- 9.2.3. The RAYURE situation -- 9.2.4. Using straight lines -- 9.2.5. A few summary elements -- 9.3. Plane and solid figures -- 9.3.1. Findings and assumptions -- 9.3.2. The SQUARE AND QUASI-SQUARE situation -- 9.3.3. The emergence of criteria for comparing solids: the IDENTIFYING A SOLID situation -- 9.3.4. Identification of cube properties: the CUBE AND QUASI-CUBE situation -- 9.3.5. Progression on solids and plane figures -- 9.4. The appropriation of research results by the resource -- 9.5. Conclusion -- 9.6. References -- Chapter 10. Tool for Analyzing the Teaching of Geometry in Textbooks -- 10.1. General framework and theoretical tools -- 10.1.1. Didactic co-determination scale, mathematical and didactic organizations -- 10.1.2. Reference MO and theoretical tools for analysis -- 10.2. Analysis criteria: definition and methodology -- 10.2.1. Institutional conformity -- 10.2.2. Educational adequacy -- 10.2.3. Didactic quality -- 10.3. Introducing the analysis grid -- 10.3.1. Analysis of tasks and task types -- 10.3.2. Analysis of techniques -- 10.3.3. Analysis of knowledge.
• 10.3.4. Analysis of ostensives -- 10.3.5. Analysis of organizational and planning elements -- 10.3.6. Summary -- 10.4. Conclusion -- 10.5. References -- Part 3. Teaching Practices and Training Issues -- Chapter 11. Study on Teacher Appropriation of a Geometry Education Resource -- 11.1. Introduction -- 11.2. Research background -- 11.2.1. Study on dissemination possibilities in ordinary education -- 11.2.2. Resource design approach -- 11.2.3. A working methodology based on assumptions -- 11.2.4. Designing a situation using the didactic engineering approach for development -- 11.3. Focus on the adaptability of this situation to ordinary education -- 11.3.1. Details about the theoretical framework and the research question -- 11.3.2. Presentation on the follow-up of teachers, details of the research question and the methodology -- 11.3.3. Presentation of the analysis methodology -- 11.4. Elements of the analysis -- 11.4.1. Analysis a priori of the situation and anticipatory analysis of the teacher's activity -- 11.4.2. Analysis of practices -- 11.5. Conclusion -- 11.6. References -- Chapter 12. Geometric Reasoning in Grades 4 to 6, the Teacher's Role: Methodological Overview and Results -- 12.1. Introduction -- 12.2. Theoretical choices and the problem statement -- 12.2.1. Geometrical paradigms -- 12.2.2. The different spaces -- 12.2.3. Study on reasoning -- 12.2.4. The role of the teacher -- 12.2.5. Problem statement -- 12.3. Methodology -- 12.3.1. General principle -- 12.3.2. The situations -- 12.3.3. Analysis methodology -- 12.4. Conclusion -- 12.5. References -- Chapter 13. When the Teacher Uses Common Language Instead of Geometry Lexicon -- 13.1. Introduction -- 13.2. An attempt to categorize the uses of common vernacular terms in place of geometry lexicon terms within teacher discourse -- 13.2.1. The phenomenon of didactic reticence.
• 13.2.2. The phenomenon of semantic analogy: comparison with common concepts to construct meaning for mathematical knowledge.
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