Mathematical Knowledge for Primary Teachers

Jennifer Suggate, Andrew Davis, Maria Goulding

Routledge | 2010 | 328 páginas | RAR - PDF | 3,28 Mb

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Descrição:

Now in its fourth edition, the bestselling text Mathematical Knowledge for Primary Teachers provides trainee teachers with clear information about the fundamental mathematical ideas taught in primary schools.With rigorous and comprehensive coverage of all the mathematical knowledge primary teachers need, the text goes beyond rules and routines to help readers deepen their understanding of mathematical ideas and increase their confidence in teaching these ideas. Fully updated to incorporate recommendations of the Williams review, new sections are included covering talk for learning in mathematics, with an emphasis placed on the language and vocabulary used in arithmetic contexts.Throughout the book, knowledge is linked to the TDA standards for Qualified Teacher Status, and features include:‘Check’ questions to test the reader’s understanding ‘Challenges’, to increase teachers’ confidence and stretch their mathematical abilities ‘Links with the classroom’ to emphasise the relevance of ideas to the classroom context Straightforward coverage from theory to practice for all aspects of the Mathematics framework.The book is accompanied by a Companion Website, which contains further visual activities and support, designed to scaffold and support the reader’s own understanding. Essential reading for all practising and trainee primary teachers, this book is ideal for those who wish to increase their mathematical understanding and confidence in presenting mathematics in the classroom.

Contents
Note to fourth edition Dedication Acknowledgements Introduction PART ONE: SETTING THE SCENE 1. Mathematical understanding 2. Language 3. Problem solving and proof PART TWO: NUMBER AND ALGEBRA 4. Properties of numbers and operations 5. Counting, place value, addition and subtraction 6. Multiplication and division 7. Integers 8. Fractions, decimals and percentages 9. Understanding algebra 10. Graphs and functions PART THREE: MEASUREMENT 11. Length 12. Area 13. Capacity and volume 14. Mass and weight 15. Angles and compass directions 16. Time PART FOUR: SHAPE 17. 2-D shape 18. 2-D shape applications and investigations 19. 3-D shape PART FIVE: DATA HANDLING 20. Data handling 21. Probability

Introduction to the History of Mathematics

Howard Eves

Holt, Rinehart & Winston | 1969 | 480 páginas | djvu | 8,9 Mb

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Descrição: This classic best-seller by a well-known author introduces mathematics history to math and math education majors. Suggested essay topics and problem studies challenge students. CULTURAL CONNECTIONS sections explain the time and culture in which mathematics developed and evolved. Portraits of mathematicians and material on women in mathematics are of special interest.

Mathematics Education as a Research Domain: A Search for Identity: An ICMI Study

(New ICMI Study Series)
Anna Sierpinska, Jeremy Kilpatrick

Springer | 1998 | 600 páginas |

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In 1978, in the foreword to Weeding and Sowing: A Preface to a Science of Mathematics Education, Hans Freudenthal wrote that his book is a preface to a science that does not exist. Almost 20 years later, does his claim still hold true? The present book is the result of the reflection of many individuals in mathematics education on this and related questions. Is mathematics education a science? Is it a discipline? In what sense? What is its place within other domains of research and academic disciplines? What accounts for its specificity? In the book, the reader will find a range of possible answers to these questions, a variety of analyses of the actual directions of research in different countries, and a number of visions for the future of research in mathematics education. The book is a result of an ICMI Study, whose theme was formulated as: `What is Research in Mathematics Education and What are Its Results?'. One important outcome of this study was the realization of the reasons for the difficulty of the questions that the study was posing, leading possibly to a set of other questions, better suited to the actual concerns and research practices of mathematics education researchers. The book addresses itself to researchers in mathematics education and all those working in their neighborhood who are concerned with the problems of the definition of this new scientific domain emerging at their borders.
Table of contents

Foreword.
I. The Study Conference.
II. Mathematics Education as a Research Discipline.
III. Goals, Orientations and Results of Research in Mathematics Education.
IV. Different Research Paradigms in Mathematics Education.
V. Evaluation of Research in Mathematics Education.
VI. Mathematics Education and Mathematics.
Continuing the Search.

Statistical Literacy at School: Growth and Goals

(Studies in Mathematical Thinking and Learning Series)

Jane M. Watson

Lawrence Erlbaum Associates | 2006 | 320 páginas | rar - pdf | 12,7 Mb

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This book reveals the development of students' understanding of statistical literacy. It provides a way to "see" student thinking and gives readers a deeper sense of how students think about important statistical topics. Intended as a complement to curriculum documents and textbook series, it is consistent with the current principles and standards of the National Council of Teachers of Mathematics.

The term "statistical literacy" is used to emphasize that the purpose of the school curriculum should not be to turn out statisticians but to prepare statistically literate school graduates who are prepared to participate in social decision making. Based on ten years of research--with reference to other significant research as appropriate--the book looks at students' thinking in relation to tasks based on sampling, graphical representations, averages, chance, beginning inference, and variation, which are essential to later work in formal statistics. For those students who do not proceed to formal study, as well as those who do, these concepts provide a basis for decision making or questioning when presented with claims based on data in societal settings.

Statistical Literacy at School: Growth and Goals:
*establishes an overall framework for statistical literacy in terms of both the links to specific school curricula and the wider appreciation of contexts within which chance and data-handling ideas are applied;
*demonstrates, within this framework, that there are many connections among specific ideas and constructs;
*provides tasks, adaptable for classroom or assessment use, that are appropriate for the goals of statistical literacy;
*presents extensive examples of student performance on the tasks, illustrating hierarchies of achievement, to assist in monitoring gains and meeting the goals of statistical literacy; and
*includes a summary of analysis of survey data that suggests a developmental hierarchy for students over the years of schooling with respect to the goal of statistical literacy.

Statistical Literacy at School: Growth and Goals is directed to researchers, curriculum developers, professionals, and students in mathematics education as well those across the curriculum who are interested in students' cognitive development within the field; to teachers who want to focus on the concepts involved in statistical literacy without the use of formal statistical techniques; and to statisticians who are interested in the development of student understanding before students are exposed to the formal study of statistics.

Contents

Preface vii

1 Purpose and Foundations 1

2 Sampling—A Good Start 27

3 Graphs—How Best to Represent the Data 55

4 Average—What Does It Tell Us? 97

5 Chance—Precursor to Probability 127

6 Beginning Inference—Supporting a Conclusion 187

7 Variation—The Underlying Phenomenon 217

8 Statistical Literacy—A Global Goal 247

Further Reading 275

References 281

Author Index 297

Subject Index 303

Mathematical Circles: Russian Experience

(Mathematical World, Vol. 7)
Dmitri Fomin, Sergey Genkin, Ilia V. Itenberg

American Mathematical Society | 1996 | 272 páginas | djvu | 1,92 Mb

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"This is a sample of rich Russian mathematical culture written by professional mathematicians with great experience in working with high school students ... Problems are on very simple levels, but building to more complex and advanced work ... [contains] solutions to almost all problems; methodological notes for the teacher ... developed for a peculiarly Russian institution (the mathematical circle), but easily adapted to American teachers' needs, both inside and outside the classroom."

--from the Translator's notes

What kind of book is this? It is a book produced by a remarkable cultural circumstance in the former Soviet Union which fostered the creation of groups of students, teachers, and mathematicians called "mathematical circles". The work is predicated on the idea that studying mathematics can generate the same enthusiasm as playing a team sport--without necessarily being competitive.

This book is intended for both students and teachers who love mathematics and want to study its various branches beyond the limits of school curriculum. It is also a book of mathematical recreations and, at the same time, a book containing vast theoretical and problem material in main areas of what authors consider to be "extracurricular mathematics". The book is based on a unique experience gained by several generations of Russian educators and scholars.

Statistique: Dictionnaire encyclopédique

Yadolah Dodge

Springer | 2010 | 643 páginas | pdf | 16 Mb

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La statistique joue un rôle de tout premier plan dans d’innombrables domaines, en sciences pures comme en sciences appliquées: des mathématiques à la physique, de la chimie à la biologie ou de l’économie à la sociologie, c’est un outil devenu indispensable. Pour avoir un accès pratique et rapide aux concepts et aux méthodes de la statistique, la formule la plus efficace est celle du dictionnaire: qu’il soit consulté ponctuellement ou bien utilisé dans le cadre d’une recherche approfondie, cet ouvrage contient l’information nécessaire - mieux, il procure plusieurs degrés d’explication adaptés à chaque besoin. À chaque entrée correspondent un historique de la notion traitée, des explications mathématiques, des domaines de validité et limitations, des exemples et des mots clés avec leur équivalent en anglais. La biographie de nombreux chercheurs illustres invite à suivre l’évolution de la statistique de ses débuts jusqu’à la période contemporaine, où elle a atteint sa pleine maturité. Un système de renvois permet de prolonger l’explication des termes considérés et d’acquérir une vue d’ensemble de chaque sujet étudié. Instrument de travail, ce dictionnaire est aussi un livre de référence pour qui veut connaître le langage et les méthodes d’une science en constante évolution et toujours sollicitée par les développements de l’actualité.

Learning and Teaching Mathematics: An International Perspective

P. Bryant, T. Nunes

Psychology Press | 1999 | 512 páginas |  pdf  | 8,6 Mb

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The authors of this volume, which is newly available in paperback, all hold the view that mathematics is a form of intelligent problem solving which plays an important part in children's lives outside the classroom as well as in it. Learning and Teaching Mathematicsprovides an exciting account of recent and radically different research on teaching and learning mathematics which will have a far reaching effect on views about mathematical education

Contents
The nature of mathematical concepts / Gérard Vergnaud
Systems of signs and mathematical reasoning / Terezinha Nunes
Mathematical understanding in the nursery school years / Peter Bryant
Word problems : a vehicle for promoting authentic mathematical understanding and problem solving in the primary school? / L. Verschaffel and E. De Corte
Children's understandings of turn and angle / Sandra Magina and Celia Hoyles
Knowing about proportions in different contexts / Janice A. Singer, Amy S. Kohn and Lauren B. Resnick
Mathematical concepts at the secondary school level : the learning of algebra and functions / Carolyn Kieran
Happy birthday to you : early mathematical thinking of Asian, South American, and US children / Herbert P. Ginsburg ... [et al.]
Learning arithmetic with an abacus / Giyoo Hatano
What children and teachers count as mathematics / Guida de Abreu, Alan J. Bishop and Geraldo Pompeu, Jr.
Social interactions and mathematics learning / M.L. Schubauer-Leoni and A.-N. Perret-Clermont
Meaning mathematically with computers / Richard Noss
Mediating between concrete and abstract / Koeno Gravemeije
Charming fractions or fractions being charmed? / L. Streefland
Didactic engineering / Régine Douady