Geometry with Applications and Proofs : a Advanced Geometry for Senior High School, Student Text and Background Information /
Goddijn, Aad,
Geometry with Applications and Proofs : a Advanced Geometry for Senior High School, Student Text and Background Information / Advanced Geometry for Senior High School, Student Text and Background Information Aad Goddijn; Martin Kindt; Wolfgang Reuter. - 1 online resource - Dutch Design in Mathematics Education ; 6 Educational Research E-Books Online, Collection 2005-2017, ISBN: 9789004394001 . - Dutch Design in Mathematics Education ; 6. Educational Research E-Books Online, Collection 2005-2017, ISBN: 9789004394001. .
Preliminary Material -- Geometry between application and proof, a general introduction / Aad Goddijn -- Geometry, classical topics and new applications / Martin Kindt -- Given: circle with butterfly or: how do you learn proving? / Aad Goddijn -- Distances, edges and domains -- Voronoi diagrams -- Reasoning with distances -- Computer practical Voronoi diagrams -- A special quadrilateral -- Exploring isodistance lines -- Shortest paths -- Example solutions -- Worksheets part I -- Thinking in circles and lines -- Using what you know -- The circle scrutinized -- Finding proofs -- Conjectures on screen -- Proving conjectures -- Clues for chapter 3 and 5 -- Conflict lines and reflections -- Preface -- Edge and conflict -- Parabola, ellipse and hyperbola -- Analytic geometry -- Conic sections.
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.
9789462098602
10.1007/978-94-6209-860-2 DOI
Geometry.
QA455
516
Geometry with Applications and Proofs : a Advanced Geometry for Senior High School, Student Text and Background Information / Advanced Geometry for Senior High School, Student Text and Background Information Aad Goddijn; Martin Kindt; Wolfgang Reuter. - 1 online resource - Dutch Design in Mathematics Education ; 6 Educational Research E-Books Online, Collection 2005-2017, ISBN: 9789004394001 . - Dutch Design in Mathematics Education ; 6. Educational Research E-Books Online, Collection 2005-2017, ISBN: 9789004394001. .
Preliminary Material -- Geometry between application and proof, a general introduction / Aad Goddijn -- Geometry, classical topics and new applications / Martin Kindt -- Given: circle with butterfly or: how do you learn proving? / Aad Goddijn -- Distances, edges and domains -- Voronoi diagrams -- Reasoning with distances -- Computer practical Voronoi diagrams -- A special quadrilateral -- Exploring isodistance lines -- Shortest paths -- Example solutions -- Worksheets part I -- Thinking in circles and lines -- Using what you know -- The circle scrutinized -- Finding proofs -- Conjectures on screen -- Proving conjectures -- Clues for chapter 3 and 5 -- Conflict lines and reflections -- Preface -- Edge and conflict -- Parabola, ellipse and hyperbola -- Analytic geometry -- Conic sections.
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.
9789462098602
10.1007/978-94-6209-860-2 DOI
Geometry.
QA455
516