| Description |
1 online resource |
| Series |
Dutch Design in Mathematics Education |
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Dutch Design in Mathematics Education (Sense Publishers (Rotterdam, The Netherlands))
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| Contents |
Contents -- Geometry between application and proof, a general introduction -- About this book -- Geometry in Dutch education -- Mathematical contents of the course -- A short note on axioms and deduction -- Dynamic geometry software -- The aftermath of the Profi project -- The authors -- Geometry, classical topics and new applications -- Modeling, abstracting, reasoning -- The Dutch geometry curriculum -- Geometry of Territories -- How to prove 1 and 2? -- The discrete parabola -- Some conclusions -- Literature |
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Given: circle with butterfly or: how do you learn proving?What came before? -- Form as tool -- Heuristics -- Recognizing -- Learning to note -- Find a link -- ????????? Yesssssss!!!!! -- Translating -- Conjectures and Cabri (or Geogebra) -- Finally: teacher and student -- Geometrical footnotes -- Literature -- Distances, edges and domains Advanced geometry, part I -- Chapter 1: Voronoi diagrams -- 1. In the desert -- Summary of chapter 1 -- Preview -- Extra exploration exercises: Recovering the centers -- Chapter 2: Reasoning with distances |
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Introduction to this sectionStarting-points: triangle inequality and Pythagoras -- The perpendicular bisector -- Perpendicular bisectors in the triangle -- The circumscribed circle -- Chapter 3: Computer practical Voronoi diagrams -- Summary -- Chapter 4: A special quadrilateral -- Summary of chapter 4 -- overview of theorems in this chapter -- Chapter 5: Exploring isodistance lines -- Summary of chapter 5 -- Chapter 6: Shortest paths -- shortest road length -- meeting more lines on shortest routes -- The principle of Fermat -- billiards problems |
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Summary of chapter 6Example solutions -- Chapter 1: Voronoi diagrams -- Chapter 2: Reasoning with distances and angles -- Chapter 3: Computer practical Voronoi diagrams -- Chapter 4: A special quadrilateral -- Chapter 5: Exploring isodistance lines -- Chapter 6: shortest paths -- Worksheets part I -- worksheet A: Folding to Voronoi -- worksheet B: Exact Voronoi diagram for the desert -- worksheet C: map of the Netherlands -- worksheet D: isodistance lines round a square) -- worksheet E: triangle, feet, sectors -- worksheet F: an ant on a shoebox |
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""Worksheet G: triangles and mirrors""""Thinking in circles and lines Advanced geometry, part II""; ""Chapter 1: Using what you know""; ""1. In advance""; ""1. Finding arguments and writing down proofs""; ""motivations, given""; ""Chapter 2: The circle scrutinized""; ""an application with angle bisector and perpendicular bisector""; ""Chapter 3: Finding proofs""; ""links in short""; ""�splitting conditions� in short""; ""finding proofs""; ""preview""; ""Chapter 4: Conjectures on screen""; ""thinking up conjectures and investigating""; ""movement with left traces"" |
| Summary |
This book shows how geometry can be learned by starting with real world problems which are solved by intuition, common sense reasoning and experiments. Gradually the more formal demands of mathematical proofs get their proper place and make it possible to explore new applications. This process helps students to feel the need for precise definitions and procedures, to contribute to the construction of an axiomatic system, and to experience the power of systematic reasoning. The course is designed for students in a Nature & Technology strand which prepares for studying the sciences or technology at university level. Its goal was basically to reintroduce?proof? in a meaningful way in the late 1990s Dutch secondary education curriculum. Following the educational view of the Freudenthal Institute this is not done by stating Euclid?s axioms on page one, but rather a starting point is chosen in students? intuitions and tentative solutions of problems that are experienced as real and relevant. The photograph on the cover shows students exploring one of the problems from the midpart of the course in the computerlab |
| Analysis |
onderwijs |
|
education |
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Education (General) |
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Onderwijs (algemeen) |
| Notes |
English |
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Online resource; title from PDF title page (SpringerLink, viewed February 26, 2015) |
| Subject |
Geometry -- Textbooks
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Geometry -- Problems, exercises, etc.
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MATHEMATICS -- Geometry -- General.
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Geometry
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| Genre/Form |
exercise books.
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Problems and exercises
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Textbooks
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Textbooks.
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Problems and exercises.
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Problèmes et exercices.
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| Form |
Electronic book
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| Author |
Kindt, Martin, author
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|
Reuter, Wolfgang, author
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| ISBN |
9789462098602 |
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9462098603 |
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