Mathematics Curriculum in School Education

(Advances in Mathematics Education)

 Yeping Li e Glenda Lappan

Springer | 2014 | 651 páginas | rar - pdf | 8,8 Mb

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• Identifying what is important in mathematics for teaching and learning in different education systems;

• Understanding mathematics curriculum and its changes that are valued over time in different education systems;

• Identifying and analyzing effective curriculum practices;

• Probing effective infrastructure for curriculum development and implementation.

Mathematics curriculum, which is often a focus in education reforms, has not received extensive research attention until recently. Ongoing mathematics curriculum changes in many education systems call for further research and sharing of effective curriculum policies and practices that can help lead to the improvement of school education.

This book provides a unique international perspective on diverse curriculum issues and practices in different education systems, offering a comprehensive picture of various stages along curriculum transformation from the intended to the achieved, and showing how curriculum changes in various stages contribute to mathematics teaching and learning in different educational systems and cultural contexts.

The book is organized to help readers learn not only from reading individual chapters, but also from reading across chapters and sections to explore broader themes, including:

Mathematics Curriculum in School Education brings new insights into curriculum policies and practices to the international community of mathematics education, with 29 chapters and four section prefaces contributed by 56 scholars from 14 different education systems. This rich collection is indispensable reading for mathematics educators, researchers, curriculum developers, and graduate students interested in learning about recent curriculum development, research, and practices in different education systems.

It will help readers to reflect on curriculum policies and practices in their own education systems, and also inspire them to identify and further explore new areas of curriculum research for improving mathematics teaching and learning.

Contents

Part I Introduction and Perspectives

Mathematics Curriculum in School Education: Advancing Research and Practice from an International Perspective .. . 3

Yeping Li and Glenda Lappan

Curriculum Design and Systemic Change . . 13

Hugh Burkhardt

Mathematics Curriculum Policies and Practices in the U.S.: The Common Core State Standards Initiative  . . 35

Barbara J. Reys

Reflections on Curricular Change. . 49

Alan H. Schoenfeld

Part II Curriculum and Policy

Mathematics Curriculum Policies: A Framework with Case Studies from Japan, Korea, and Singapore  . . 79

Khoon Yoong Wong, Masataka Koyama, and Kyeong-Hwa Lee

Decision Making in the Mathematics Curricula among the Chinese Mainland, Hong Kong, and Taiwan . . 93

Hak Ping Tam, Ngai-Ying Wong, Chi-Chung Lam, Yunpeng Ma, Lije Lu, and Yu-Jen Lu

Potential Impact of the Common Core Mathematics Standards on the American Curriculum . . 119

Hung-Hsi Wu

Brief Considerations on Educational Directives and Public Policies in Brazil Regarding Mathematics Education  . . 143

Antonio Vicente Marafioti Garnica

The Australian Curriculum: Mathematics—How Did it Come About? What Challenges Does it Present for Teachers and for the Teaching of Mathematics? . . 157

Max Stephens

Part III Curriculum Development and Analysis

Three Pillars of First Grade Mathematics, and Beyond  . . 183

Roger Howe

Forging New Opportunities for Problem Solving in Australian Mathematics Classrooms through the First National Mathematics Curriculum. . 209

Judy Anderson

Freedom of Design: The Multiple Faces of Subtraction in Dutch Primary School Textbooks . . 231

Marc van Zanten and Marja van den Heuvel-Panhuizen

Changes to the Korean Mathematics Curriculum: Expectations and Challenges . . 261

JeongSuk Pang

The Singapore Mathematics Curriculum Development—A Mixed Model Approach . . 279

Ngan Hoe Lee

School Mathematics Textbook Design and Development Practices in China . . 305

Yeping Li, Jianyue Zhang, and Tingting Ma

Part IV Curriculum, Teacher, and Teaching

Teachers as Participants in Textbook Development: The Integrated Mathematics Wiki-book Project . . . 333

Ruhama Even and Shai Olsher

Mathematics Teacher Development in the Context of District Managed Curriculum  . . 351

Mary Kay Stein, Julia Kaufman, and Miray Tekkumru Kisa

Curriculum, Teachers and Teaching: Experiences from Systemic and Local Curriculum Change in England  . . 377

Margaret Brown and Jeremy Hodgen

Teaching Mathematics Using Standards-Based and Traditional Curricula: A Case of Variable Ideas . . 391

Jinfa Cai, Bikai Nie, John C. Moyer, and Ning Wang

Supporting the Effective Implementation of a New Mathematics Curriculum: A Case Study of School-Based Lesson Study at a Japanese Public Elementary School . . 417

Akihiko Takahashi

Does Classroom Instruction Stick to Textbooks? A Case Study of Fraction Division . . 443

Rongjin Huang, Z. Ebrar Yetkiner Ozel, Yeping Li, and Rebecca V. Osborne

Part V Curriculum and Student Learning

Curriculum Intent, Teacher Professional Development and Student Learning in Numeracy . . 473

Vince Geiger, Merrilyn Goos, and Shelley Dole

The Impact of a Standards-Based Mathematics Curriculum on Classroom Instruction and Student Performance: The Case of Mathematics in Context . . 493

Mary C. Shafer

Curriculum and Achievement in Algebra 2: Influences of Textbooks and Teachers on Students’ Learning about Functions  . . 515

Sharon L. Senk, Denisse R. Thompson, and Jamie L.W. Wernet

Learning Paths and Learning Supports for Conceptual Addition and Subtraction in the US Common Core State Standards and in the Chinese Standards  . . 541

Karen C. Fuson and Yeping Li

The Virtual Curriculum: New Ontologies for a Mobile Mathematics . . 559

Nathalie Sinclair and Elizabeth de Freitas

Part VI Cross-national Comparison and Commentary

Forty-Eight Years of International Comparisons in Mathematics Education from a United States Perspective: What Have We Learned?  . . 581

Zalman Usiskin

(Mathematics) Curriculum, Teaching and Learning  . . 607

Ngai-Ying Wong, Qiaoping Zhang, and Xiaoqing Li

Improving the Alignment Between Values, Principles and Classroom Realities . . 621

Malcolm Swan

Index . . . 637

Author Index . . . . 643

Author Biographies. . . 649

Bridge to Abstract Mathematics

(Mathematical Association of America Textbooks)

Ralph W. Oberste-Vorth, Aristides Mouzakitis e Bonita A. Lawrence

Mathematical Association of America | 2012 | 253 páginas | pdf | 3,6 Mb

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Mathematics is a science that concerns theorems that must be proved within a system of axioms and definitions. With this book, the mathematical novice will learn how to prove theorems and explore the universe of abstract mathematics. The introductory chapters familiarise the reader with some fundamental ideas, including the axiomatic method, symbolic logic and mathematical language. This leads to a discussion of the nature of proof, along with various methods for proving statements. The subsequent chapters present some foundational topics in pure mathematics, including detailed introductions to set theory, number systems and calculus. Through these fascinating topics, supplemented by plenty of examples and exercises, the reader will hone their proof skills. This complete guide to proof is ideal preparation for a university course in pure mathematics, and a valuable resource for educators.

• A complete guide to constructing proofs
• Introduces students to the world of abstract mathematics
• Prepares students for further study in linear algebra, calculus and topology

Table of Contents
Some notes on notation
To the students
For the professors
Part I. The Axiomatic Method:
1. Introduction
2. Statements in mathematics
3. Proofs in mathematics
Part II. Set Theory:
4. Basic set operations
5. Functions
6. Relations on a set
7. Cardinality
Part III. Number Systems:
8. Algebra of number systems
9. The natural numbers
10. The integers
11. The rational numbers
12. The real numbers
13. Cantor's reals
14. The complex numbers
Part IV. Time Scales:
15. Time scales
16. The Delta Derivative
Part V. Hints:
17. Hints for (and comments on) the exercises
Index.

Math for Life: Crucial Ideas You Didn't Learn in School

Jeffrey Bennett


Roberts and Company Publishers | 2011 | 189 páginas 

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• How can we solve the national debt crisis? 

• Should you or your child take on a student loan? 

• Is it safe to talk on a cell phone while driving? 

• Are there viable energy alternatives to fossil fuels? 

• Could simple policy changes reduce political polarization? 

These questions may all seem very different, but they share two things in common. First, they are all questions with important implications for either personal success or our success as a nation. Second, they all concern topics that we can fully understand only with the aid of clear quantitative or mathematical thinking. In other words, they are topics for which we need math for life--a kind of math that looks quite different from most of the math that we learn in school, but that is just as (and often more) important.
     In Math for Life, award-winning author Jeffrey Bennett simply and clearly explains the key ideas of quantitative reasoning and applies them to all the above questions and many more. He also uses these questions to analyze our current education system, identifying both shortfalls in the teaching of mathematics and solutions for our educational future.
     No matter what your own level of mathematical ability, and no matter whether you approach the book as an educator, student, or interested adult, you are sure to find something new and thought-provoking in Math for Life.
Table of Contents
Preface
1 (Don’t Be) “Bad at Math”
2 Thinking with Numbers
3 Statistical Thinking
4 Managing Your Money
5 Understanding Taxes
6 The U.S. Deficit and Debt
7 Energy Math
8 The Math of Political Polarization
9 The Mathematics of Growth
Epilogue: Getting “Good at Math”
To Learn More
Acknowledgments
Also by Jeffrey Bennett
Index
Index of Examples

Manifold Mirrors: The Crossing Paths of the Arts and Mathematics

 Felipe Cucker

Cambridge University Press | 2013 | 424 páginas | pdf | 31 Mb

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Most works of art, whether illustrative, musical or literary, are created subject to a set of constraints. In many (but not all) cases, these constraints have a mathematical nature, for example, the geometric transformations governing the canons of J. S. Bach, the various projection systems used in classical painting, the catalog of symmetries found in Islamic art, or the rules concerning poetic structure. This fascinating book describes geometric frameworks underlying this constraint-based creation. The author provides both a development in geometry and a description of how these frameworks fit the creative process within several art practices. He furthermore discusses the perceptual effects derived from the presence of particular geometric characteristics. The book began life as a liberal arts course and it is certainly suitable as a textbook. However, anyone interested in the power and ubiquity of mathematics will enjoy this revealing insight into the relationship between mathematics and the arts.

The Mathematics Teacher in the Digital Era: An International Perspective on Technology Focused Professional Development

(Mathematics Education in the Digital Era, 2)

Alison Clark-Wilson, Ornella Robutti e Nathalie Sinclair

 Springer | 2014 | 419 páginas | rar - pdf | 4,5 Mb

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This volume addresses the key issue of the initial education and lifelong professional learning of teachers of mathematics to enable them to realize the affordances of educational technology for mathematics. With invited contributions from leading scholars in the field, this volume contains a blend of research articles and descriptive texts.

In the opening chapter John Mason invites the reader to engage in a number of mathematics tasks that highlight important features of technology-mediated mathematical activity.

This is followed by three main sections

·        an overview of current practices in teachers’ use of digital technologies in the classroom and explorations of the possibilities for developing more effective practices drawing on a range of research perspectives (including grounded theory, enactivism and Valsiner’s zone theory).

·        a set of chapters that share many common constructs (such as instrumental orchestration, instrumental distance and double instrumental genesis) and research settings that have emerged from the French research community, but have also been taken up by other colleagues.

·        meta-level considerations of research in the domain by contrasting different approaches and proposing connecting or uniting elements

Contents

Introduction .... 1

Alison Clark-Wilson , Ornella Robutti , and Nathalie Sinclair

Interactions Between Teacher, Student, Software and Mathematics: Getting a Purchase on Learning with Technology .... 11

John Mason

Part I Current Practices and Opportunities for Professional Development

Exploring the Quantitative and Qualitative Gap Between Expectation and Implementation: A Survey of English Mathematics Teachers’ Uses of ICT ....... 43

Nicola Bretscher

Teaching with Digital Technology: Obstacles and Opportunities .............. 71

Michael O.J. Thomas and Joann M. Palmer

A Developmental Model for Adaptive and Differentiated Instruction Using Classroom Networking Technology ... 91

Allan Bellman , Wellesley R. Foshay , and Danny Gremillion

Integrating Technology in the Primary School Mathematics Classroom: The Role of the Teacher ..... 111

María Trigueros , María-Dolores Lozano , and Ivonne Sandoval

Technology Integration in Secondary School Mathematics: The Development of Teachers’ Professional Identities .... 139

Merrilyn Goos

Teaching Roles in a Technology Intensive Core Undergraduate Mathematics Course .... 163

Chantal Buteau and Eric Mulle

Part II Instrumentation of Digital Resources in the Classroom

Digital Technology and Mid-Adopting Teachers’ Professional Development: A Case Study .. 189

Paul Drijvers , Sietske Tacoma , Amy Besamusca , Cora van den Heuvel , Michiel Doorman , and Peter Boon

Teaching Mathematics with Technology at the Kindergarten Level: Resources and Orchestrations ..... 213

Ghislaine Gueudet , Laetitia Bueno-Ravel , and Caroline Poisard

Teachers’ Instrumental Geneses When Integrating Spreadsheet Software........ 241

Mariam Haspekian

A Methodological Approach to Researching the Development of Teachers’ Knowledge in a Multi-Representational Technological Setting .... 277

Alison Clark-Wilson

Teachers and Technologies: Shared Constraints, Common Responses ..... 297

Maha Abboud-Blanchard

Didactic Incidents: A Way to Improve the Professional Development of Mathematics Teachers ..... 319

Gilles Aldon

Part III Theories on Theories

Meta-Didactical Transposition: A Theoretical Model for Teacher Education Programmes ...... 347

Ferdinando Arzarello, Ornella Robutti, Cristina Sabena, Annalisa Cusi,

Rossella Garuti, Nicolina Malara, and Francesca Martignone

Frameworks for Analysing the Expertise That Underpins Successful Integration of Digital Technologies into Everyday Teaching Practice ....... 373

Kenneth Ruthven

Summary and Suggested Uses for the Book ...... 395

Alison Clark-Wilson , Ornella Robutti , and Nathalie Sinclair

Glossary ....... 403

Index ........ 407

50 mathematical ideas you really need to know

Quercus | 2008 | 320 páginas

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Tony Crilly is Reader in Mathematical Sciences at Middlesex University, having previously taught at the University of Michigan, the City University in Hong Kong, and the Open University. His principal research interest is the history of mathematics, and he has written and edited many works on fractals, chaos and computing. He is the author of the acclaimed biography of the English mathematician Arthur Cayley

Contents
Introduction
01 Zero
02 Number systems
03 Fractions
04 Squares and square roots
05 π
06 e
07 Infinity
08 Imaginary numbers
09 Primes
10 Perfect numbers
11 Fibonacci numbers
12 Golden rectangles
13 Pascal’s triangle
14 Algebra
15 Euclid’s algorithm
16 Logic
17 Proof
318 Sets
19 Calculus
20 Constructions
21 Triangles
22 Curves
23 Topology
24 Dimension
25 Fractals
26 Chaos
27 The parallel postulate
28 Discrete geometry
29 Graphs
30 The four-colour problem
31 Probability
32 Bayes’s theory
33 The birthday problem
34 Distributions
35 The normal curve
36 Connecting data
37 Genetics
38 Groups
439 Matrices
40 Codes
41 Advanced counting
42 Magic squares
43 Latin squares
44 Money mathematics
45 The diet problem
46 The travelling salesperson
47 Game theory
48 Relativity
49 Fermat’s last theorem
50 The Riemann hypothesis

APOS Theory: A Framework for Research and Curriculum Development in Mathematics Education

Springer | 2014 | 270 páginas | pdf | 1,7 Mb

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In spite of the fact that APOS Theory has been used extensively in numerous scholarly publications, in the design of textbooks, and in teaching practice, there is no single references that contains all the relevant information about its components, and provides guidance about its application. The goal of this book is to present the main elements of APOS theory. It should be useful for researchers who work with, or would like to learn more about, this theoretical approach, people who are interested in the way which mathematical conceptions are constructed according to this theory, Mathematics Education researchers, graduate students in Mathematics Education, and Mathematics instructors.

Chapter 1 Introduction.- Chapter 2 From Piaget’s Theory to APOS Theory: Reflective Abstraction in Learning Mathematics and the Historical Development of APOS Theory.- Chapter 3 Mental Structures and Mechanisms: APOS Theory and the Construction of Mathematical Knowledge.- Chapter 4 Genetic Decomposition.- Chapter 5 The Teaching of Mathematics Using APOS Theory.- Chapter 6 The APOS Paradigm for Research and Curriculum Development.- Chapter 7 Schemas, Their Development and Interaction.- Chapter 8 Totality as a Possible New Stage and Levels in APOS Theory.- Chapter 9 Use of APOS Theory to Teach Mathematics at Elementary School.- Chapter 10 Frequently Asked Questions.- Chapter 11 Conclusions.- Chapter 12 Annotated Bibliography.- References.- Index.