Theorems In School
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Theorems In School
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Author : Paolo Boero
language : en
Publisher: Sense Publishers
Release Date : 2007
Theorems In School written by Paolo Boero and has been published by Sense Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Education categories.
This book, addressing mathematics educators, teacher-trainers and teachers, is published as a contribution to the endeavour of renewing the teaching of proof (and theorems) on the basis of historical-epistemological, cognitive and didactical considerations.
Theorems In School
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Author :
language : en
Publisher: BRILL
Release Date : 2007-01-01
Theorems In School written by and has been published by BRILL this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-01 with Education categories.
During the last decade, a revaluation of proof and proving within mathematics curricula was recommended; great emphasis was put on the need of developing proof-related skills since the beginning of primary school. This book, addressing mathematics educators, teacher-trainers and teachers, is published as a contribution to the endeavour of renewing the teaching of proof (and theorems) on the basis of historical-epistemological, cognitive and didactical considerations. Authors come from eight countries and different research traditions: this fact offers a broad scientific and cultural perspective. In this book, the historical and epistemological dimensions are dealt with by authors who look at specific research results in the history and epistemology of mathematics with an eye to crucial issues related to educational choices. Two papers deal with the relationships between curriculum choices concerning proof (and the related implicit or explicit epistemological assumptions and historical traditions) in two different school systems, and the teaching and learning of proof there. The cognitive dimension is important in order to avoid that the didactical choices do not fit the needs and the potentialities of learners. Our choice was to firstly deal with the features of reasoning related to proof, mainly concerning the relationships between argumentation and proof. The second part of this book concentrates on some crucial cognitive and didactical aspects of the development of proof from the early approach in primary school, to high school and university. We will show how suitable didactical proposals within appropriate educational contexts can match the great (yet, underestimated!) young students’ potentialities in approaching theorems and theories.
18 Theorems Of Geometry
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Author : William Smith
language : en
Publisher: Xlibris Corporation
Release Date : 2010-06-25
18 Theorems Of Geometry written by William Smith and has been published by Xlibris Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-25 with Education categories.
A School Geometry
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Author : Henry Sinclair Hall
language : en
Publisher: CUP Archive
Release Date : 1929
A School Geometry written by Henry Sinclair Hall and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 1929 with categories.
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 And Proving In Mathematics Education
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Author : Gila Hanna
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-06-14
Proof And Proving In Mathematics Education written by Gila Hanna and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-14 with Education categories.
*THIS BOOK IS AVAILABLE AS OPEN ACCESS BOOK ON SPRINGERLINK* One of the most significant tasks facing mathematics educators is to understand the role of mathematical reasoning and proving in mathematics teaching, so that its presence in instruction can be enhanced. This challenge has been given even greater importance by the assignment to proof of a more prominent place in the mathematics curriculum at all levels. Along with this renewed emphasis, there has been an upsurge in research on the teaching and learning of proof at all grade levels, leading to a re-examination of the role of proof in the curriculum and of its relation to other forms of explanation, illustration and justification. This book, resulting from the 19th ICMI Study, brings together a variety of viewpoints on issues such as: The potential role of reasoning and proof in deepening mathematical understanding in the classroom as it does in mathematical practice. The developmental nature of mathematical reasoning and proof in teaching and learning from the earliest grades. The development of suitable curriculum materials and teacher education programs to support the teaching of proof and proving. The book considers proof and proving as complex but foundational in mathematics. Through the systematic examination of recent research this volume offers new ideas aimed at enhancing the place of proof and proving in our classrooms.
Teaching And Learning High School Mathematics
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Author : Charlene E. Beckmann
language : en
Publisher: John Wiley & Sons
Release Date : 2009-11-02
Teaching And Learning High School Mathematics written by Charlene E. Beckmann and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-11-02 with Education categories.
Too many high school students, faced with mathematics in courses at the level of algebra and beyond, find themselves struggling with abstract concepts and unwilling to pursue further study of mathematics. When students curtail their course taking in mathematics, they may be impacting their college and career options. Thus, high school mathematics teachers have the responsibility to help students recognize the value and importance of mathematics while also designing instruction that makes mathematics accessible to all students. Ball and Bass (2000), as well as other mathematics educators, have recognized that mathematics teachers not only need to know mathematics content and mathematics pedagogy (i.e., teaching strategies) but they also need to know how these ideas are integrated. This mathematical knowledge for teaching is the knowledge that teachers of mathematics need and it differs from the knowledge that research or applied mathematicians must know. This text is designed to provide teachers with insights into this mathematical knowledge for teaching. Teaching and Learning High School Mathematics is likely different from many other texts that you have used. It integrates both content and pedagogy to help you develop and build your own understanding of teaching. The text is designed to help you develop “deep conceptual understanding of fundamental mathematics” (Ma 1999) so that you are able to approach mathematics from multiple perspectives with many tools. Such flexibility in teaching is essential if teachers are to help all students become mathematically proficient. Throughout this book, you are encouraged to work in cooperative teams. This strategy is designed to help you develop a mathematics learning community and build a professional network that will be a valuable resource during your professional career. Hopefully, you will experience the benefits of engaging in rich mathematical discussions with peers and consider how to encourage such learning environments in your own classrooms. Lesson planning is another element pervasive throughout this text. To help teachers plan for effective student-centered lessons, the Question Response Support (QRS) Guide is introduced in Lesson 1.1 and used throughout the remainder of the lessons. The QRS Guide is a tool on which teachers may record tasks or questions (Q) for students, expected and observed student responses (R), and teacher support (S) in the form of additional “just enough” questions to support students in their progress on the task. In each unit, teachers expand their repertoire of teaching and learning elements and strategies and incorporate these elements as they plan additional lesson segments. In Unit 4 lesson planning is formally introduced as teachers put together elements from previous units into complete, cohesive lesson plans.
Traditions In German Speaking Mathematics Education Research
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Author : Hans Niels Jahnke
language : en
Publisher: Springer
Release Date : 2019-02-13
Traditions In German Speaking Mathematics Education Research written by Hans Niels Jahnke and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-13 with Education categories.
This open access book shares revealing insights into the development of mathematics education research in Germany from 1976 (ICME 3 in Karlsruhe) to 2016 (ICME 13 in Hamburg). How did mathematics education research evolve in the course of these four decades? Which ideas and people were most influential, and how did German research interact with the international community? These questions are answered by scholars from a range of fields and in ten thematic sections: (1) a short survey of the development of educational research on mathematics in German speaking countries (2) subject-matter didactics, (3) design science and design research, (4) modelling, (5) mathematics and Bildung 1810 to 1850, (6) Allgemeinbildung, Mathematical Literacy, and Competence Orientation (7) theory traditions, (8) classroom studies, (9) educational research and (10) large-scale studies. During the time span presented here, profound changes took place in German-speaking mathematics education research. Besides the traditional fields of activity like subject-matter didactics or design science, completely new areas also emerged, which are characterized by various empirical approaches and a closer connection to psychology, sociology, epistemology and general education research. Each chapter presents a respective area of mathematics education in Germany and analyzes its relevance for the development of the research community, not only with regard to research findings and methods but also in terms of interaction with the educational system. One of the central aspects in all chapters concerns the constant efforts to find common ground between mathematics and education. In addition, readers can benefit from this analysis by comparing the development shown here with the mathematical education research situation in their own country.
Pennsylvania School Journal
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Author :
language : en
Publisher:
Release Date : 1856
Pennsylvania School Journal written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1856 with Education categories.
The Noether Theorems
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Author : Yvette Kosmann-Schwarzbach
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-17
The Noether Theorems written by Yvette Kosmann-Schwarzbach and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-17 with Mathematics categories.
In 1915 and 1916 Emmy Noether was asked by Felix Klein and David Hilbert to assist them in understanding issues involved in any attempt to formulate a general theory of relativity, in particular the new ideas of Einstein. She was consulted particularly over the difficult issue of the form a law of conservation of energy could take in the new theory, and she succeeded brilliantly, finding two deep theorems. But between 1916 and 1950, the theorem was poorly understood and Noether's name disappeared almost entirely. People like Klein and Einstein did little more then mention her name in the various popular or historical accounts they wrote. Worse, earlier attempts which had been eclipsed by Noether's achievements were remembered, and sometimes figure in quick historical accounts of the time. This book carries a translation of Noether's original paper into English, and then describes the strange history of its reception and the responses to her work. Ultimately the theorems became decisive in a shift from basing fundamental physics on conservations laws to basing it on symmetries, or at the very least, in thoroughly explaining the connection between these two families of ideas. The real significance of this book is that it shows very clearly how long it took before mathematicians and physicists began to recognize the seminal importance of Noether's results. This book is thoroughly researched and provides careful documentation of the textbook literature. Kosmann-Schwarzbach has thus thrown considerable light on this slow dance in which the mathematical tools necessary to study symmetry properties and conservation laws were apparently provided long before the orchestra arrives and the party begins.