Mathematics As A Constructive Activity

Download Mathematics As A Constructive Activity ebook PDF or Read Online books in PDF, EPUB, and Mobi Format. Click Download or Read Online button to Mathematics As A Constructive Activity book pdf for free now.

Mathematics As A Constructive Activity

Author : Anne Watson
ISBN : 9781135630027
Genre : Education
File Size : 65.13 MB
Format : PDF
Download : 285
Read : 693

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.
Category: Education

Mathematics Classrooms Students Activities And Teachers Practices

Author : Fabrice Vandebrouck
ISBN : 9789462092815
Genre : Education
File Size : 86.25 MB
Format : PDF, ePub, Docs
Download : 423
Read : 1100

With cooperation of Aline Robert, Janine Rogalski, Maha Abboud-Blanchard, Claire Cazes, Monique Chappet-Pariès, Aurélie Chesnais, Christophe Hache, Julie Horoks, Eric Roditi & Nathalie Sayac. This book presents unique insights into a significant area of French research relating the learning and teaching of mathematics in school classrooms and their development. Having previously had only glimpses of this work, I have found the book fascinating in its breadth of theory, its links between epistemological, didactic and cognitive perspectives and its comprehensive treatment of student learning of mathematics, classroom activity, the work of teachers and prospective teacher development. Taking theoretical perspectives as their starting points, the authors of this volume present a rich array of theoretically embedded studies of mathematics teaching and learning in school classrooms. Throughout this book the reader is made aware of many unanswered questions and challenged to consider associated theoretical and methodological issues. For English-speaking communities who have lacked opportunity to access the French literature the book opens up a wealth of new ways of thinking about and addressing unresolved issues in mathematics learning, teaching and teacher education. I recommend it wholeheartedly! (Extract from Barbara Jaworski’s preface.)
Category: Education

Constructing Mathematical Knowledge

Author : Paul Ernest
ISBN : 9781135716196
Genre : Education
File Size : 29.51 MB
Format : PDF, Mobi
Download : 813
Read : 734

This book provides a panorama of complimentary and forward looking perspectives on the learning of mathematics and epistemology from some of the leading contributors to the field. It explores constructivist and social theories of learning, and discusses the role of the computer in the light of these theories. It brings analyses from psychoanalysis, Hermeneutics and other perspectives to bear on the issues of mathematics and learning. It enquires into the nature of enquiry itself, and an important emergent theme is the role of language. Finally it relates the history of mathematics to its teaching and learning. The book both surveys current research and indicates orientations for fruitful work in the future.
Category: Education

Visible Learning For Teachers

Author : John Hattie
ISBN : 1003024475
Genre : EDUCATION
File Size : 43.55 MB
Format : PDF, ePub, Mobi
Download : 333
Read : 204

In November 2008, John Hattie's ground-breaking book Visible Learning synthesised the results of more thanfifteen years research involving millions of students and represented the biggest ever collection of evidence-based research into what actually works in schools to improve learning. Visible Learning for Teachers takes the next step and brings those ground breaking concepts to a completely new audience. Written for students, pre-service and in-service teachers, it explains how to apply the principles of Visible Learning to any classroom anywhere in the world. The author offers concise and user-friendly summaries of the most successful interventions and offers practical step-by-step guidance to the successful implementation of visible learning and visible teaching in the classroom. This book: links the biggest ever research project on teaching strategies to practical classroom implementation champions both teacher and student perspectives and contains step by step guidance including lesson preparation, interpreting learning and feedback during the lesson and post lesson follow up offers checklists, exercises, case studies and best practice scenarios to assist in raising achievement includes whole school checklists and advice for school leaders on facilitating visible learning in their institution now includes additional meta-analyses bringing the total cited within the research to over 900 comprehensively covers numerous areas of learning activity including pupil motivation, curriculum, meta-cognitive strategies, behaviour, teaching strategies, and classroom management. Visible Learning for Teachers is a must read for any student or teacher who wants an evidence based answer to the question; 'how do we maximise achievement in our schools?'
Category: EDUCATION

Success With Mathematics

Author : Heather Cooke
ISBN : 041529861X
Genre : Education
File Size : 61.97 MB
Format : PDF, ePub, Docs
Download : 532
Read : 1295

This study guide has been designed to support students studying mathematics to prepare themselves for self-directed study and provides guidance and ideas to help make their learning efficient and effective.
Category: Education

Mathematics Education And Language

Author : Tony Brown
ISBN : 9789401007269
Genre : Education
File Size : 22.94 MB
Format : PDF, ePub, Mobi
Download : 540
Read : 1156

Contemporary thinking on philosophy and the social sciences has primarily focused on the centrality of language in understanding societies and individuals; important developments which have been under-utilised by researchers in mathematics education. In this revised and extended edition this book reaches out to contemporary work in these broader fields, adding new material on how progression in mathematical learning might be variously understood. A new concluding chapter considers how teachers experience the new demands they face.
Category: Education

Perspectives On Mathematics Education

Author : H. Christiansen
ISBN : 9789400945043
Genre : Education
File Size : 48.5 MB
Format : PDF, ePub, Mobi
Download : 292
Read : 929

BACOMET cannot be evaluated solely on the basis of its publications. It is important then that the reader, with only this volume on which to judge both the BACOMET activities and its major outcome to date, should know some thing of what preceded this book's publication. For it is the story of how a group of educators, mainly tutors of student-teachers of mathematics, com mitted themselves to a continuing period of work and self-education. The concept of BACOMET developed during a series of meetings held in 1978-79 between the three editors, Bent Christiansen, Geoffrey Howson and Michael Otte, at which we expressed our concern about the contributions from mathematics education as a discipline to teacher education, both as we observed it and as we participated in it. The short time which was at the teacher-educator's disposal, allied to the limited knowledge and experience of the students on which one had to build, raised puzzling problems concerning priorities and emphases. The recognition that these problems were shared by educators from many different countries was matched by the fact that it would be fruitless to attempt to search for an internationally (or even nationally) acceptable solution to our problems. Different contexts and traditions rule this out.
Category: Education

Mathematics For Tomorrow S Young Children

Author : C.S. Mansfield
ISBN : 9789401722117
Genre : Education
File Size : 59.26 MB
Format : PDF
Download : 112
Read : 988

Social constructivism is just one view of learning that places emphasis on the social aspects of learning. Other theoretical positions, such as activity theory, also emphasise the importance of social interactions. Along with social constructivism, Vygotsky's writings on children's learning have recently also undergone close scru tiny and researchers are attempting a synthesis of aspects ofVygotskian theory and social constructivism. This re-examination of Vygotsky's work is taking place in many other subject fields besides mathematics, such as language learning by young children. It is interesting to speculate why Vygotsky's writings have appealed to so many researchers in different cultures and decades later than his own times. Given the recent increased emphasis on the social nature of learning and on the interactions between student, teacher and context factors, a finer grained analysis of the nature of different theories of learning now seems to be critical, and it was considered that different views of students' learning of mathematics needed to be acknowledged in the discussions of the Working Group.
Category: Education

Reflective Teaching In Schools

Author : Andrew Pollard
ISBN : 9781441175397
Genre : Education
File Size : 83.97 MB
Format : PDF, Docs
Download : 464
Read : 211

Building on best-selling texts over three decades, this thoroughly revised new edition is essential reading for both primary and secondary school teachers in training and in practice, supporting both initial school-based training and extended career-long professionalism. Considering a wide range of professionally relevant topics, Reflective Teaching in Schools presents key issues and research insights, suggests activities for classroom enquiry and offers guidance on key readings. Uniquely, two levels of support are offered: · practical, evidence-based guidance on key classroom issues – including relationships, behaviour, curriculum planning, teaching strategies and assessment processes; · routes to deeper forms of expertise, including evidence-informed 'principles' and 'concepts' to support in-depth understanding of teacher expertise. Andrew Pollard, former Director of the UK's Teaching and Learning Research Programme, led development of the book, with support from primary and secondary specialists from the University of Cambridge, UK. Reflective Teaching in Schools is part of a fully integrated set of resources for primary and secondary education. Readings for Reflective Teaching in Schools directly complements and extends the chapters in this book. Providing a compact and portable library, it is particularly helpful in school-based teacher education. The website, reflectiveteaching.co.uk, offers supplementary resources including reflective activities, research briefings, advice on further reading and additional chapters. It also features a glossary, links to useful websites, and a conceptual framework for deepening expertise. This book is one of the Reflective Teaching Series – inspiring education through innovation in early years, schools, further, higher and adult education.
Category: Education

Learning In The Early Years

Author : Jeni Riley
ISBN : 0761941061
Genre : Education
File Size : 43.55 MB
Format : PDF, ePub, Mobi
Download : 997
Read : 1299

This book will help early years educators understand the nature, form, and content of the curriculum for children aged 3 to 7 and the most appropriate ways of presenting it.
Category: Education

Cultural Perspectives On The Mathematics Classroom

Author : Steve Lerman
ISBN : 9789401711999
Genre : Education
File Size : 48.19 MB
Format : PDF, Kindle
Download : 533
Read : 457

Mathematics teaching and learning have been dominated by a concern for the intellectual readiness of the child, debates over rote learning versus understanding and, recently, mathematical processes and thinking. The gaze into today's mathematics classroom is firmly focused on the individual learner. Recently, however, studies of mathematics in social practices, including the market place and the home, have initiated a shift of focus. Culture has become identified as a key to understanding the basis on which the learner appropriates meaning. The chapters in this timely book attempt to engage with this shift of focus and offer original contributions to the debate about mathematics teaching and learning. They adopt theoretical perspectives while drawing on the classroom as both the source of investigation and the site of potential change and development. The book will be of fundamental interest to lecturers and researchers and to teachers concerned with the classroom as a cultural phenomenon.
Category: Education

Epistemological Foundations Of Mathematical Experience

Author : Leslie P. Steffe
ISBN : 9781461231783
Genre : Psychology
File Size : 34.94 MB
Format : PDF, Mobi
Download : 106
Read : 635

On the 26th, 27th, and 28th of February of 1988, a conference was held on the epistemological foundations of mathematical experience as part of the activities of NSF Grant No. MDR-8550463, Child Generated Multiplying and Dividing Algorithms: A Teaching Experiment. I had just completed work on the book Construction of Arithmetical Meanings and Strategies with Paul Cobb and Ernst von Glasersfeld and felt that substantial progress had been made in understanding the early numerical experiences of the six children who were the subjects of study in that book. While the book was in preparation, I was also engaged in the teaching experiment on mUltiplying and dividing algorithms. My focus in this teaching experiment was on investigating the mathematical experiences of the involved children and on developing a language through which those experiences might be expressed. However, prior to immersing myself in the conceptual analysis of the mathematical experiences of the children, I felt that it was crucial to critically evaluate the progress that we felt we had made in our earlier work. It was toward achieving this goal that I organized the conference. When trying to understand the mathematical experiences of a child, one can do no better than to interact with the child in a mathematical context guided by the intention to specify the child's current knowledge and the progress the child might make.
Category: Psychology

Amongst Mathematicians

Author : Elena Nardi
ISBN : 9780387371436
Genre : Education
File Size : 34.22 MB
Format : PDF, ePub, Mobi
Download : 420
Read : 226

This book offers a unique perspective on ways in which mathematicians: perceive their students' learning; teach; reflect on their teaching practice. Elena Nardi achieves this by employing two fictional, yet entirely data-grounded, characters to create a conversation on these important issues. The construction of these characters is based on large bodies of data including intense focused group interviews with mathematicians and extensive analyses of students' written work, collected and analyzed over a substantial period.
Category: Education

The Sociology Of Mathematics Education

Author : Paul Dowling
ISBN : 9781135710026
Genre : Education
File Size : 31.68 MB
Format : PDF, ePub, Mobi
Download : 142
Read : 1319

Until the 1960s, maths was studied as an academic subject in a desire to have more mathematicians. The current trend, however, has moved away from viewing maths as a purely intellectual endeavour and towards developing a more mathematically competent workforce and citizenry. This trend has seen a large increase in the number of maths schemes being produced by the major educational publishers, which attempt to make maths easier and more approachable by using language instead of symbols. So why do so many children still fail at maths? The author contends that to understand this, teachers need to analyze and evaluate the maths textbooks they are currently using. The author shows the reader how to systematically analyze and evaluate these textbooks. This interrogation of classroom resources, should have important implications for teaching strategies and for textbook design and use.
Category: Education

Perspectives In Primary Education

Author : L. Borghi
ISBN : 9789401020695
Genre : Education
File Size : 45.78 MB
Format : PDF, ePub
Download : 902
Read : 823

PURPOSE OF THE STUDY Primary education in Europe, as in the United States and other conti nents, is passing through a period of profound change, affecting some of the fundamental educational aims at primary school level and teaching structure, content and methods. The purpose of this study is to sketch a broad picture of the Euro pean educational scene which may be brought about by the impact of innovation in industrialised countries. We are only too aware of the difficulties inherent in our task. Even when projections and forecasts are firmly rooted in an analysis of existing data, they are liable to be contradicted by the facts. We shall attempt to allow for those alternative situations which may provide the context for the organisation and functioning of primary education. We make no claim to portray the European primary school at the end of the twentieth or at the beginning of the twenty-first century. We shall do no more than analyse existing achievements and experiments based on research in the associated fields of education, psychology and sociology and from this analysis extrapolate a series of forecasts based on objective factors of a social and intellectual nature, offering realistic hypotheses for the future. Our aim is to provide sound guidelines for those who are to build a better future for our children.
Category: Education

Reconceiving Mathematics Instruction

Author : Raffaella Borasi
ISBN : 1567501672
Genre : Education
File Size : 68.11 MB
Format : PDF, ePub, Docs
Download : 690
Read : 1228

As dissatisfaction with the current status of school mathematics grows worldwide, educators and professionals alike are calling for reforms and instructional changes. Yet, significant changes can only be achieved if each educator of school mathematics personally rethinks various aspects of mathematics instruction, and identifies concrete ways in which their current practice could be modified. Before such visions can be meaningfully implemented in classrooms, it is important that mathematics teachers and educators examine critically both the assumptions and implications of the vision for school mathematics that the reports propose. This book is intended to support educators in such a challenging enterprise by focusing attention on errors and their use in mathematics instruction. Throughout the book, an approach to errors as opportunities for learning and inquiry will be developed and employed both as a means to create the kinds of instructional experiences advocated for school mathematics reform, and as a heuristic to invite reflections about school mathematics as well as mathematics as a discipline. REVIEWS: ...Raffaella Borasi's newest book offers important contributions to the current debate on school mathematics reform. - Journal for Research in Mathematics Education There are some great bits of philosophy in this book... - Mathematics Teaching
Category: Education

Proceedings Of The Fifth International Congress On Mathematical Education

Author : CARASS
ISBN : 9781475742381
Genre : Juvenile Nonfiction
File Size : 81.41 MB
Format : PDF, Kindle
Download : 130
Read : 1213

International Congresses on Mathematical Education (ICMEs), under the auspices of the International Commission on Mathematical Instruction, are held every four years. Previous Congresses have been held in France (Lyons), England (Exeter), the Federal Republic of Germany (Karlsruhe), and the United States of America (Berkeley). The Fifth International Congress on Mathematical Education (lCME 5) was held in Adelaide, Australia, from August 24-30, 1984. More than 1800 participants from over 70 countries participated in the Congress, while some additional 200 people attended social functions and excursions. The program for ICME 5 was planned and structured by an International Program Committee, and implemented by the National Program Committee in Australia. For the main body of the program, Chief Organisers, assisted by Australian Coordinators, were invited to plan and prepare the individual components of the program which addressed a wide range of topics and interest areas. Each of these teams involved many individuals from around the world in the detailed planning and preparation of the working sessions for their area of program responsibility. For the actual working sessions at the Congress, the smallest group had some 60 members, while the largest had well over 300. In addition to the working sessions, there were three major plenary addresses, several specially invited presentations, and over 420 individual papers in the form of short communications, either as posters or brief talks.
Category: Juvenile Nonfiction

Developing Thinking In Algebra

Author : John Mason
ISBN : 1412911710
Genre : Mathematics
File Size : 65.3 MB
Format : PDF, ePub, Docs
Download : 133
Read : 173

By integrating pedagogy and subject knowledge through experiencing a variety of tasks for learners, this book makes it possible for all learners to succeed in thinking algebraically.
Category: Mathematics

The Roles Of Representation In School Mathematics

Author : Albert A. Cuoco
ISBN : UOM:39015053387166
Genre : Mathematics
File Size : 90.11 MB
Format : PDF, ePub, Mobi
Download : 218
Read : 465

Educators and scholars discuss the roles of "invented" and "presented" representations, the kind the child creates versus the kind the teacher gives to students, as an aspect of the internalization of mathematical reasoning. Representations are the devices which people use to help them gain insights, and by examining the interplay between modeling and representation, the roles for representation can be defined.
Category: Mathematics