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 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 Culturally Responsive Teaching written by Geneva Gay and published by Teachers College Press. This book was released on 2010 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: The achievement of students of color continues to be disproportionately low at all levels of education. More than ever, Geneva Gay's foundational book on culturally responsive teaching is essential reading in addressing the needs of today's diverse student population. Combining insights from multicultural education theory and research with real-life classroom stories, Gay demonstrates that all students will perform better on multiple measures of achievement when teaching is filtered through their own cultural experiences. This bestselling text has been extensively revised to include expanded coverage of student ethnic groups: African and Latino Americans as well as Asian and Native Americans as well as new material on culturally diverse communication, addressing common myths about language diversity and the effects of "English Plus" instruction.

Download or read book Transforming Primary Mathematics written by Mike Askew and published by Routledge. This book was released on 2015-11-19 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fully updated to reflect the new curriculum, the revised edition of Transforming Primary Mathematics sets out key theories and cutting-edge research in the field to enable teachers to take a fresh look at how they teach mathematics. The book encourages teachers to reflect on their own beliefs and values about mathematics, and asks them to question whether their current methods meet the needs of all learners, and the challenge of having high expectations for all. It provides clear, practical approaches to help implement fundamental change in classroom environments, and offers motivational teaching styles to ensure meaningful mathematics learning. Chapters take an inspiring, sometimes controversial, and often unconventional look at the subject of mathematics, by: endorsing the use of a ‘new mathematics’ – one based on problem solving, modelling, inquiry and reasoning, not on abstract rules, memorising, and regurgitation arguing that there is more to maths teaching than ‘death by a thousand worksheets’ challenging norms, such as the practice of sorting children into sets based on their perceived mathematical ability asking whether mathematical ability is innate or a result of social practices examining what a ‘mastery’ approach might entail highlighting the role of variation in supporting learning advocating an environment where teachers are encouraged to take risks. Transforming Primary Mathematics is for all primary school teachers who want to make mathematics welcoming, engaging, inclusive and successful.

Download or read book Social Constructivism as a Philosophy of Mathematics written by Paul Ernest and published by SUNY Press. This book was released on 1998-01-01 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Extends the ideas of social constructivism to the philosophy of mathematics, developing a powerful critique of traditional absolutist conceptions of mathematics, and proposing a reconceptualization of the philosophy of mathematics.

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 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 Didactics of Mathematics as a Scientific Discipline written by Rolf Biehler and published by Springer Science & Business Media. This book was released on 2006-04-11 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 Success with Mathematics written by Heather Cooke and published by Routledge. This book was released on 2003-09-02 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many students find the leap between school and university level mathematics to be significantly greater than they expected. Success with Mathematics has been devised and written especially in order to help students bridge that gap. It offers clear, practical guidance from experienced teachers of mathematics in higher education on such key issues as: * getting started * ways of studying * assessment * mathematical communication * learning by doing * using ICT * using calculators * what next. After reading this book, students will find themselves better prepared for the change in pace, rigour and abstraction they encounter in degree level mathematics. They will also find themselves able to broaden their learning strategies and improve their self-directed study skills. This book is essential reading for anyone following, or about to undertake, a degree in mathematics, or other degree courses with mathematical content.

Download or read book Investigating Mathematics Teaching written by Barbara Jaworski and published by Routledge. This book was released on 2002-11-01 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Barbara Jaworski addresses a number of questions that are central to research on reform in mathematics education today. In this volume she attempts to chart critically yet honestly her own developing ideas as she undertakes a several-year-long enquiry into mathematics teaching and gives a very personal account of her developing conceptions, conjectures, thoughts and reflections. The author accounts for her research both genetically and biographically, simultaneously restructuring the development of her ideas and giving a rigorous, critical and reflective account.

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 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 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 Fundamental Constructs in Mathematics Education written by Sue Johnston-Wilder and published by Routledge. This book was released on 2004-01-22 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fundamental Constructs in Mathematics Education is a unique sourcebook crafted from classic texts, research papers and books in mathematics education. Linked together by the editors' narrative, the book provides a fascinating examination of, and insight into, key constructs in mathematics education and how they link together. The choice of constructs is based on (some of) the many constructs which have proved fruitful in research and which have informed choices made by teachers. The book is divided into two parts: learning and teaching. The first part includes views about how people learn - from Plato to Dewey, as well as constructivism, activity theory and French didactiques. The second part includes extracts concerned with initiating, sustaining and bringing to a conclusion learners' work on mathematical tasks. Fundamental Constructs in Mathematics Education provides access to a wide range of constructs in mathematics education and orients the reader towards important original sources.

Download or read book International Handbook of Mathematics Education written by Alan Bishop and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 1336 pages. Available in PDF, EPUB and Kindle. Book excerpt: ALAN J. BISHOP Monash University, Clayton, Victoria, Australia RATIONALE Mathematics Education is becoming a well-documented field with many books, journals and international conferences focusing on a variety of aspects relating to theory, research and practice. That documentation also reflects the fact that the field has expanded enormously in the last twenty years. At the 8th International Congress on Mathematics Education (ICME) in Seville, Spain, for example, there were 26 specialist Working Groups and 26 special ist Topic Groups, as well as a host of other group activities. In 1950 the 'Commission Internationale pour I 'Etude et l' Amelioration de l'Enseignement des Mathematiques' (CIEAEM) was formed and twenty years ago another active group, the 'International Group for the Psychology of Mathematics Education' (PME), began at the third ICME at Karlsruhe in 1976. Since then several other specialist groups have been formed, and are also active through regular conferences and publications, as documented in Edward Jacobsen's Chapter 34 in this volume.