Geometric Reasoning And Proof

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Geometric Reasoning And Proof

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Author : Victor Ditoro
language : en
Publisher:
Release Date : 1994

Geometric Reasoning And Proof written by Victor Ditoro and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Elementary education of adults categories.

Teaching Geometric Reasoning

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Author : Matthew Lee Hawkins
language : en
Publisher:
Release Date : 2007

Teaching Geometric Reasoning written by Matthew Lee Hawkins and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with categories.

Keywords: proof writing, dynamic geometry software, proof with pictures, proof-by-picture method.

Reasoning And Geometric Proof In Mathematics Education

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Author : Kate Elizabeth Mansi
language : en
Publisher:
Release Date : 2003

Reasoning And Geometric Proof In Mathematics Education written by Kate Elizabeth Mansi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with categories.

Keywords: geometric reasoning, proof conceptions, proof achievement, mathematical reasoning, geometry, dynamic geometry, proof-readiness, van Hiele, Piaget, teacher preparation, secondary geometry, proof schemes.

Reasoning And Geometric Proof In Mathematics Education A Review Of The Literature

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Author :
language : en
Publisher:
Release Date : 2003

Reasoning And Geometric Proof In Mathematics Education A Review Of The Literature written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with categories.

The purpose of this literature review is to examine the role that reasoning and geometric proof play in the teaching and learning of mathematics. Specifically, I explore four questions: 1) What reasoning capabilities do students need to be ready for proof? 2) What evidence is there to show that high school students are not successful with proof and hold misconceptions about the nature of proof? 3) How can teachers' beliefs and understandings contribute to students' proof abilities? 4) What can be done to promote mathematical reasoning and improve students' proof writing skills? Through a comparison of the theories of Piaget and van Hiele, I discuss how students acquire mathematical and geometric reasoning skills and how this relates to their readiness to produce formal proofs. I then discuss research findings, which indicate that students are not typically at a high enough van Hiele level to be successful with proof by the time they get to high school. Further research is presented which examines common geometric and proof misconceptions among students, and how this relates to proof achievement. Teacher proof-conceptions and achievement are also discussed, citing studies with elementary, middle, and high school preservice and inservice teachers, and how this may affect students' proof performance. Finally, I discuss ways in which preservice and inservice teachers can help their students improve their mathematical and geometric reasoning skills, thus furthering their proof comprehension and achievement.

Machine Proofs In Geometry

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Author : Shang-Ching Chou
language : en
Publisher: World Scientific
Release Date : 1994

Machine Proofs In Geometry written by Shang-Ching Chou and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.

This book reports recent major advances in automated reasoning in geometry. The authors have developed a method and implemented a computer program which, for the first time, produces short and readable proofs for hundreds of geometry theorems.The book begins with chapters introducing the method at an elementary level, which are accessible to high school students; latter chapters concentrate on the main theme: the algorithms and computer implementation of the method.This book brings researchers in artificial intelligence, computer science and mathematics to a new research frontier of automated geometry reasoning. In addition, it can be used as a supplementary geometry textbook for students, teachers and geometers. By presenting a systematic way of proving geometry theorems, it makes the learning and teaching of geometry easier and may change the way of geometry education.

Proof In Geometry

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Author : A. I. Fetisov
language : en
Publisher: Courier Corporation
Release Date : 2012-06-11

Proof In Geometry written by A. I. Fetisov and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-11 with Mathematics categories.

This single-volume compilation of 2 books explores the construction of geometric proofs. It offers useful criteria for determining correctness and presents examples of faulty proofs that illustrate common errors. 1963 editions.

Teaching Geometric Reasoning Proof By Pictures

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Author :
language : en
Publisher:
Release Date : 2004

Teaching Geometric Reasoning Proof By Pictures written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with categories.

The purpose of this study was to investigate students' understanding of proof and proof writing using a new three-column method. The new three-column method consists of the traditional "statements" and "reasons" columns but also contains a "picture" column in which students must draw a picture that corresponds to the "statement." It is believed that this third column will act as a blue print providing students with a visual representation of how the proof is constructed. By examining this blueprint students will understand which steps are needed to complete the proof as well as the proper order of those steps. Thus, students develop a deeper understanding of the proof writing process. The study was conducted in a suburban school in central North Carolina and involved two standard geometry classes. The study lasted for a week and a half and was instituted during a chapter involving different triangle congruencies (i.e. SAS, SSS, etc). The three-column proof was taught to a 3rd period class containing 31 students. Their test and quiz scores were compared to a 2nd period class containing 23 students. After examining the average quiz and average test scores for the chapter it was shown that the 3rd period class did not out score the 2nd period class. Thus, the use of a three-column picture proof is as effective as the traditional approach. An important question pursuant to this outcome is whether there are other teaching/learning benefits from using picture proofs. For example, interviews with the cooperating teacher indicated that the three-column proof was very helpful for several students and also provided good teacher feedback as to students' understanding of theorems and postulates used in proof writing.

Geometry

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Author : Sonal Bhatt
language : en
Publisher: Dorling Kindersley Ltd
Release Date : 2014-07-01

Geometry written by Sonal Bhatt and has been published by Dorling Kindersley Ltd this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-01 with Mathematics categories.

Just about everyone takes a geometry class at one time or another. And while some people quickly grasp the concepts, most find geometry challenging. Covering everything one would expect to encounter in a high school or college course, Idiot's Guides: Geometry covers everything a student would need to know. This all-new book will integrate workbook-like practice questions to reinforce the lessons. In addition, a glossary of terms, postulates, and theorems provide a quick reference to need-to-know information as well. Easy-to-understand, step-by-step explanations walk the reader through: - Basics of Geometry - Reasoning and Proof - Perpendicular and Parallel Lines - Congruent Triangles - Properties of Triangles - Quadrilaterals - Transformations - Similarity - Right Triangles and Trigonometry - Circles - Area of Polygons and Circles - Surface Area and Volume

Geometry With Applications And Proofs

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Author : Aad Goddijn
language : en
Publisher: Springer
Release Date : 2014-12-03

Geometry With Applications And Proofs written by Aad Goddijn and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-03 with Education categories.

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.

Probing Pupils Geometric Reasoning

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Author : Nichola Clarke
language : en
Publisher:
Release Date : 2006

Probing Pupils Geometric Reasoning written by Nichola Clarke and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Logic, Symbolic and mathematical categories.