Download or read book Mathematics as a Constructive Activity written by Anne Watson and published by Routledge. This book was released on 2006-04-21 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explains and demonstrates the teaching strategy of asking learners to construct their own examples of mathematical objects. The authors show that the creation of examples can involve transforming and reorganizing knowledge and that, although this is usually done by authors and teachers, if the responsibility for making examples is transferred to learners, their knowledge structures can be developed and extended. A multitude of examples to illustrate this is provided, spanning primary, secondary, and college levels. Readers are invited to learn from their own past experience augmented by tasks provided in the book, and are given direct experience of constructing examples through a collection of many tasks at many levels. Classroom stories show the practicalities of introducing such shifts in mathematics education. The authors examine how their approach relates to improving the learning of mathematics and raise future research questions. *Based on the authors' and others' theoretical and practical experience, the book includes a combination of exercises for the reader, practical applications for teaching, and solid scholarly grounding. *The ideas presented are generic in nature and thus applicable across every phase of mathematics teaching and learning. *Although the teaching methods offered are ones that engage learners imaginatively, these are also applied to traditional approaches to mathematics education; all tasks offered in the book are within conventional mathematics curriculum content. Mathematics as a Constructive Activity: Learners Generating Examples is intended for mathematics teacher educators, mathematics teachers, curriculum developers, task and test designers, and classroom researchers, and for use as a text in graduate-level mathematics education courses.
Download or read book Engaging Young Children in Mathematics written by Douglas H. Clements and published by Routledge. This book was released on 2004 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: Engaging Young Children in Mathematics: Standards for Early Childhood Mathematics Education brings together the combined wisdom of a diverse group of experts involved with early childhood mathematics. The book originates from the landmark 2000 Conference on Standards for Pre-kindergarten and Kindergarten Mathematics Education, attended by representatives from almost every state developing standards for young children's mathematics; federal government officials; mathematicians; mathematics educators; researchers from mathematics education, early childhood education, and psychology; curriculum developers; teachers; policymakers; and professionals from organizations such as the National Conference of Teachers of Mathematics and the National Association for the Education of Young Children. The main goal of the Conference was to work collectively to help those responsible for framing and implementing early childhood mathematics standards. Although it has its roots in the Conference, the expanded scope of the standards and recommendations covered in this book includes the full range of kindergarten to grade 2. The volume is organized into two main parts and an online appendix (http://www.gse.buffalo.edu/org/conference/). Part One, Major Themes and Recommendations, offers a framework for thinking about pre-kindergarten - grade 2 mathematics education and specific recommendations. Part Two, Elaboration of Major Themes and Recommendations, provides substantive detail regarding young students' understandings of mathematical ideas. Each Part includes five parallel subsections: "Standards in Early Childhood Education"; "Math Standards and Guidelines"; "Curriculum, Learning, Teaching, and Assessment"; "Professional Development"; and "Toward the Future: Implementation and Policy." As a whole the book: * presents comprehensive summaries of research that provide specific guidelines for standards, curriculum, and teaching; * takes the recent reports and recommendations for early childhood mathematics education to the next level; * integrates practical details and research throughout; and * provides a succinct, but thorough review of research on the topics, sequences, and learning trajectories that children can and should learn at each of their first years of life, with specific developmental guidelines that suggest appropriate content for each topic for each year from 2-year-olds to 7-year-olds. This is an indispensable volume for mathematics educators, researchers, curriculum developers, teachers and policymakers, including those who create standards, scope and sequences, and curricula for young children and professional teacher development materials, and students in mathematics education, early childhood trainers, teacher educators, and faculty in mathematics education.
Download or read book Mathematics Teacher Noticing written by Miriam Sherin and published by Routledge. This book was released on 2011-02 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to examine research on mathematics teacher noticing---how teachers pay attention to and make sense of what happens in the complexity of instructional situations.
Download or read book The Essential Guide to Secondary Mathematics written by Colin Foster and published by Routledge. This book was released on 2013 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combining research-based theory with fresh, practical guidance for the classroom, this is a stimulating resource for all student and practising teachers looking for new ideas and inspiration.
Download or read book Debates in Mathematics Education written by Dawn Leslie and published by Routledge. This book was released on 2013-10-01 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: Debates in Mathematics Education explores the major issues that mathematics teachers encounter in their daily lives. It engages with established and contemporary debates, promotes and supports critical reflection and aims to stimulate both novice and experienced teachers to reach informed judgements and argue their point of view with deeper theoretical knowledge and understanding. Written by experts in the field of mathematics education, it investigates and offers fresh insight into topics of central importance, including: Gender, social inequality and mathematics Mathematics, politics and climate change The history and culture of mathematics Using popular culture in the mathematics classroom The concept of ‘ability’ and its impact on learning What we mean by ‘teaching for understanding’ Choosing and using examples in teaching The fitness of formal examinations. Designed to stimulate discussion and support you in your own research, writing and practice, Debates in Mathematics Education will be a valuable resource for any student or practising teacher engaged in initial teacher training, continuing professional development or Masters level study. It also has much to offer to those leading initial teacher education programmes, and to beginning doctoral students looking for a survey of the field of mathematics education research.
Download or read book Didactics of Mathematics as a Scientific Discipline written by Rolf Biehler and published by Springer Science & Business Media. This book was released on 1993-11-30 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: Didactics of Mathematics as a Scientific Discipline describes the state of the art in a new branch of science. Starting from a general perspective on the didactics of mathematics, the 30 original contributions to the book, drawn from 10 different countries, go on to identify certain subdisciplines and suggest an overall structure or `topology' of the field. The book is divided into eight sections: (1) Preparing Mathematics for Students; (2) Teacher Education and Research on Teaching; (3) Interaction in the Classroom; (4) Technology and Mathematics Education; (5) Psychology of Mathematical Thinking; (6) Differential Didactics; (7) History and Epistemology of Mathematics and Mathematics Education; (8) Cultural Framing of Teaching and Learning Mathematics. Didactics of Mathematics as a Scientific Discipline is required reading for all researchers into the didactics of mathematics, and contains surveys and a variety of stimulating reflections which make it extremely useful for mathematics educators and teacher trainers interested in the theory of their practice. Future and practising teachers of mathematics will find much to interest them in relation to their daily work, especially as it relates to the teaching of different age groups and ability ranges. The book is also recommended to researchers in neighbouring disciplines, such as mathematics itself, general education, educational psychology and cognitive science.
Download or read book Counterexamples in Calculus written by Sergiy Klymchuk and published by American Mathematical Soc.. This book was released on 2010-12-31 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: Counterexamples in Calculus serves as a supplementary resource to enhance the learning experience in single variable calculus courses. This book features carefully constructed incorrect mathematical statements that require students to create counterexamples to disprove them. Methods of producing these incorrect statements vary. At times the converse of a well-known theorem is presented. In other instances crucial conditions are omitted or altered or incorrect definitions are employed. Incorrect statements are grouped topically with sections devoted to: Functions, Limits, Continuity, Differential Calculus and Integral Calculus. This book aims to fill a gap in the literature and provide a resource for using counterexamples as a pedagogical tool in the study of introductory calculus.
Download or read book Presenting Children to Maths Stronger Character for Better Learning written by David Shattock and published by John Catt. This book was released on 2023-09-22 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is not a universally popular subject, neither within nor outside of school. There are those who love it but many do not, and it is not uncommon for people to take a perverse pride in being bad at it. This book argues that, while much-needed improvements to mathematics teaching are necessary to address such issues, they are insufficient without also imbuing children with the character required to learn it effectively. Teachers of mathematics are responsible not only for applying skilful pedagogy but also for developing a productive learning culture within the mathematics classroom. We need to consider the emotional and social impact on children of teachers' own attitudes and beliefs about mathematics and how children should be taught it. Sometimes provocative and irreverent but always stimulating and lucid, Presenting Children to Maths is an original and profound discussion about how students' ability and success in mathematics depends largely on how their disposition and will are shaped towards learning it.
Download or read book From Foundations to Philosophy of Mathematics written by Joan Roselló and published by Cambridge Scholars Publishing. This book was released on 2011-10-18 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: From Foundations to Philosophy of Mathematics provides an historical introduction to the most exciting period in the foundations of mathematics, starting with the discovery of the paradoxes of logic and set theory at the beginning of the twentieth century and continuing with the great foundational debate that took place in the 1920s. As a result of the efforts of several mathematicians and philosophers during this period to ground mathematics and to clarify its nature from a certain philosophical standpoint, the four main schools in the philosophy of mathematics that have largely dominated the twentieth century arose, namely, logicism, intuitionism, formalism and predicativism. It was due precisely to the insufficiencies of the first three foundational programs and the objections raised against them, that interest in Platonism was renewed in the 1940s, mainly by Gödel. Not only does this book pay special attention to the foundational programs of these philosophies of mathematics, but also to some technical accomplishments that were developed in close connection with them and have largely shaped our understanding of the nature of mathematics, such as Russell’s type theory, Zermelo’s set theory and Gödel’s incompleteness theorems. Finally, it also examines some current research programs that have been pursued in the last decades and have tried, at least to some extent, to show the feasibility of the foundational programs developed in the schools mentioned above. This is the case of neologicism, constructivism, and predicativist and finitist reductionism, this last one developed closely with the research program of reverse mathematics.
Download or read book Debates in Mathematics Education written by Gwen Ineson and published by Routledge. This book was released on 2020-06-15 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new and updated second edition of Debates in Mathematics Education explores the major issues that mathematics teachers encounter in their daily lives. By engaging with established and contemporary debates, this volume promotes and supports critical reflection and aims to stimulate both novice and experienced teachers to reach informed judgements and argue their point of view with deeper theoretical knowledge and understanding. Divided into five accessible sections, this book investigates and offers fresh insight into topics of central importance in mathematics education, with this second edition including new discussions and chapters on: Classic and contemporary issues of pedagogy, politics, philosophy and sociology of mathematics education International comparisons of achievement Digital technologies for teaching Mastery in mathematics Pop culture and mathematics Whether mathematics can be harmful Designed to stimulate discussion and support you in your own research, writing and practice through suggested questions and activities throughout, Debates in Mathematics Education will be a valuable resource for any student or practising teacher, and those engaged in initial teacher education, continuing professional development or Master's level study. This book also has much to offer to those leading mathematics departments in schools and initial teacher education programmes, and to beginning doctoral students looking for a survey of the field of mathematics education research.
Download or read book Constructing Mathematical Knowledge written by Paul Ernest and published by Routledge. This book was released on 2012-10-12 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 1994. This book and its companion volume, Mathematics, Education and Philosophy: An International Perspective are edited collections. Instead of the sharply focused concerns of the research monograph, the books offer a panorama of complementary and forward-looking perspectives. They illustrate the breadth of theoretical and philosophical perspectives that can fruitfully be brough to bear on the mathematics and education. The empathise of this book is on epistemological issues, encompassing multiple perspectives on the learning of mathematics, as well as broader philosophical reflections on the genesis of knowledge. It explores constructivist and social theories of learning and discusses the rile of the computer in light of these theories.
Download or read book Making the Connection written by Marilyn Paula Carlson and published by MAA. This book was released on 2008 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: The chapters in this volume convey insights from mathematics education research that have direct implications for anyone interested in improving teaching and learning in undergraduate mathematics. This synthesis of research on learning and teaching mathematics provides relevant information for any math department or individual faculty member who is working to improve introductory proof courses, the longitudinal coherence of precalculus through differential equations, students' mathematical thinking and problem-solving abilities, and students' understanding of fundamental ideas such as variable and rate of change. Other chapters include information about programs that have been successful in supporting students' continued study of mathematics. The authors provide many examples and ideas to help the reader infuse the knowledge from mathematics education research into mathematics teaching practice. University mathematicians and community college faculty spend much of their time engaged in work to improve their teaching. Frequently, they are left to their own experiences and informal conversations with colleagues to develop new approaches to support student learning and their continuation in mathematics. Over the past 30 years, research in undergraduate mathematics education has produced knowledge about the development of mathematical understandings and models for supporting students' mathematical learning. Currently, very little of this knowledge is affecting teaching practice. We hope that this volume will open a meaningful dialogue between researchers and practitioners toward the goal of realizing improvements in undergraduate mathematics curriculum and instruction.
Download or read book Creativity and Technology in Mathematics Education written by Viktor Freiman and published by Springer. This book was released on 2018-09-03 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides new insights on creativity while focusing on innovative methodological approaches in research and practice of integrating technological tools and environments in mathematics teaching and learning. This work is being built on the discussions at the mini-symposium on Creativity and Technology at the International Conference on Mathematical Creativity and Giftedness (ICMCG) in Denver, USA (2014), and other contributions to the topic. The book emphasizes a diversity of views, a variety of contexts, angles and cultures of thought, as well as mathematical and educational practices. The authors of each chapter explore the potential of technology to foster creative and divergent mathematical thinking, problem solving and problem posing, creative use of dynamic, multimodal and interactive software by teachers and learners, as well as other digital media and tools while widening and enriching transdisciplinary and interdisciplinary connections in mathematics classroom. Along with ground-breaking innovative approaches, the book aims to provide researchers and practitioners with new paths for diversification of opportunities for all students to become more creative and innovative mathematics learners. A framework for dynamic learning conditions of leveraging mathematical creativity with technology is an outcome of the book as well.
Download or read book Radical Constructivism in Mathematics Education written by E. Glasersfeld and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is the science of acts without things - and through this, of things one can define by acts. 1 Paul Valéry The essays collected in this volume form a mosaik of theory, research, and practice directed at the task of spreading mathematical knowledge. They address questions raised by the recurrent observation that, all too frequently, the present ways and means of teaching mathematics generate in the student a lasting aversion against numbers, rather than an understanding of the useful and sometimes enchanting things one can do with them. Parents, teachers, and researchers in the field of education are well aware of this dismal situation, but their views about what causes the wide-spread failure and what steps should be taken to correct it have so far not come anywhere near a practicable consensus. The authors of the chapters in this book have all had extensive experience in teaching as well as in educational research. They approach the problems they have isolated from their own individual perspectives. Yet, they share both an overall goal and a specific fundamental conviction that characterized the efforts about which they write here. The common goal is to find a better way to teach mathematics. The common conviction is that knowledge cannot simply be transferred ready-made from parent to child or from teacher to student but has to be actively built up by each learner in his or her own mind.
Download or read book Constructivism in Mathematics Vol 1 written by A.S. Troelstra and published by Elsevier Science. This book was released on 1988-07-15 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: These two volumes cover the principal approaches to constructivism in mathematics. They present a thorough, up-to-date introduction to the metamathematics of constructive mathematics, paying special attention to Intuitionism, Markov's constructivism and Martin-Lof's type theory with its operational semantics. A detailed exposition of the basic features of constructive mathematics, with illustrations from analysis, algebra and topology, is provided, with due attention to the metamathematical aspects. Volume 1 is a self-contained introduction to the practice and foundations of constructivism, and does not require specialized knowledge beyond basic mathematical logic. Volume 2 contains mainly advanced topics of a proof-theoretical and semantical nature.
Download or read book Resources for Teaching Mathematics 11 14 written by Colin Foster and published by Bloomsbury Publishing. This book was released on 2011-09-22 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: This resource contains 50 ready-to-use mathematics lesson plans suitable for the whole department to use with learners aged 11-14. Each plan consists of a teacher's sheet which breaks down the lesson into time-allocated sections from starter through to homework, together with a photocopiable (or downloadable) student task sheet to give out. There is also a companion website with extra material to support the lesson plans in the book, giving teachers the time and confidence to try new activities in the classroom with minimal preparation. The lesson tasks are open-ended and encourage deep mathematical thinking, allowing learners to explore different topics creatively through solving problems in their own way. This is an essential resource for any busy teacher of mathematics.
Download or read book Resources for Teaching Mathematics 14 16 written by Colin Foster and published by A&C Black. This book was released on 2010-10-07 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt:
