Prospective Mathematics Teachers’ Knowledge of Algebra A Comparative Study in China and the United States of America

Rongjin Huang

Springer Spektrum | 2014 | 196 páginas | rar - pdf |1,76 Mb

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Rongjin Huang examines teachers’ knowledge of algebra for teaching, with a particular focus on teaching the concept of function and quadratic relations in China and the United States. 376 Chinese and 115 U.S.A. prospective middle and high school mathematics teachers participated in this survey. Based on an extensive quantitative and qualitative data analysis the author comes to the following conclusions: The Chinese participants demonstrate a stronger knowledge of algebra for teaching and their structure of knowledge of algebra for teaching is much more interconnected. They show flexibility in choosing appropriate perspectives of the function concept and in selecting multiple representations. Finally, the number of college mathematics and mathematics education courses taken impacts the teachers’ knowledge of algebra for teaching.

Contents

·        Knowledge Needed for Teaching

·        Mathematics Teacher Education in China and the U.S.A.

·        Instrumentation, Data Collection, and Data Analysis

·        Comparison of Knowledge of Algebra for Teaching (KAT) between China and the U.S.A.

·        Relationship among Different Components of KAT

·        Comparison of KTCF between China and the U.S.A.

Target Groups

·        Researchers, academics, and scholars of mathematics and didactics

·        Teachers

Mathematics Education: A Numerical Landscape

Robert Adjiage e Francois Pluvinage

Nova Science Pub Inc | 2009 | 92 páginas | rar - pdf | 492 kb

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This book concerns the field of mathematics education. Today, for almost any technology, attaining the most advanced level relies on using digital systems. Therefore, the authors focus on number acquisition and use, emphasise major discussions about related topics, and introduce our personal contribution. They consider three areas: numbers in society, at school, and in the field of education. Modern society needs two kinds of number users: the first has to deal with numbers, the second has to work with numbers. According to the framework for PISA assessment, dealing with numbers concerns every citizen facing situations in which the use of a quantitative... reasoning... would help clarify, formulate or solve a problem. Working with numbers is what a professional (marketing specialist, engineer, physician, artist...) does when he has to cope with numerical theoretical frameworks, or when he collaborates with a mathematician. This brings two types of questioning: what does competence in mathematics mean? What level of achievement is desirable in number-learning to meet either numerical need? The authors examine what is proposed for teaching such a broad subject to 7-to-18-year-olds. They first observe and question the educational system, the designer of curricula, scenarios for teaching, training programmes, and national assessments. Secondly, they question the notions of problem solving and modelling as mere responses to mathematics-teaching issues. The authors then focus on what really happens in a standard classroom, particularly how teachers apply recommendations and directives, and how the generalisation of assessments affects their practice. Three aspects are considered: epistemological, cognitive, and didactical. The authors distinguish four related levels which they have named: numeracy (competence linked to whole numbers), rationacy (competence linked to ratios and rational numbers), algebracy (competence linked to algebra), and functionacy (competence linked to calculus). The cognitive aspect evokes the essential issue of semiotic registers for representing and processing numerical objects, considers the discipline-of-expression aspect of mathematics, and other issues taken into account by numerous researchers, such as process and object. The didactical is devoted to exposing our conceptual framework for teaching numbers and understanding their learning. An experiment in ratio teaching is described and analysed.

CONTENTS
Preface vii
Chapter 1 Introduction 1
Chapter 2 Numbers in Society 5
Chapter 3 Curricula and Assessment; the Case of Modelling 13
Chapter 4 Studying Numbers: How Long and up to Which Degree
of Accuracy? 23
Chapter 5 Cognitive Aspects 31
Chapter 6 Mathematical Competence 39
Chapter 7 The Four Competences 47
Chapter 8 Conclusion 69
References 71
Index 77

Celestial Sleuth: Using Astronomy to Solve Mysteries in Art, History and Literature

Donald W. Olson

Springer | 2014 | 368 páginas | rar - pdf | 18,2 Mb

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For a general audience interested in solving mysteries in art, history, and literature using the methods of science, 'forensic astronomy' is a thrilling new field of exploration. Astronomical calculations are the basis of the studies, which have the advantage of bringing to readers both evocative images and a better understanding of the skies. 

Weather facts, volcano studies, topography, tides, historical letters and diaries, famous paintings, military records, and the friendly assistance of experts in related fields add variety, depth, and interest to the work. The chosen topics are selected for their wide public recognition and intrigue, involving artists such as Vincent van Gogh, Claude Monet, Edvard Munch, and Ansel Adams; historical events such as the Battle of Marathon, the death of Julius Caesar, the American Revolution, and World War II; and literary authors such as Chaucer, Shakespeare, Joyce, and Mary Shelley. This book sets out to answer these mysteries indicated with the means and expertise of astronomy, opening the door to a richer experience of human culture and its relationship with nature.
Each subject is carefully analyzed. As an example using the study of sky paintings by Vincent van Gogh, the analytical method would include:
- computer calculations of historical skies above France in the 19th century
- finding and quoting the clues found in translations of original letters by Van Gogh
- making site visits to France to determine the precise locations when Van Gogh set up his easel and what celestial objects are depicted.
For each historical event influenced by astronomy, there would be a different kind of mystery to be solved. As an example:
- How can the phase of the Moon and time of moonrise help to explain a turning point of the American Civil War - the fatal wounding of Stonewall Jackson at Chancellorsville in 1863?
For each literary reference to astronomy, it was determined which celestial objects were being described and making an argument that the author is describing an actual event. For example, what was the date of the moonlit scene when Mary Shelley first had the idea for her novel “Frankenstein?”

These and more fun riddles will enchant and delight the fan of art and astronomy.

Contents

Preface vii

Foreword ix

Acknowledgments xiii

Part I Astronomy in Art

1 Monet and Turner, Masters of Sea and Sky 3

2 Vincent van Gogh and Starry Skies Over France 35

3 Edvard Munch: Mysterious Skies in Norway 67

4 Yosemite Moonrises and Moonbows 113

Part II Astronomy in History

5 Moons and Tides in the Battle of Marathon,

Paul Revere’s Midnight Ride, and the Sinking of the Titanic 147

6 Lincoln, the Civil War Era, and American Almanacs 199

7 Th e Moon and Tides in World War II 237

Part III Astronomy in Literature

8 Literary Skies Before 1800 277

9 Literary Skies Aft er 1800 317

Index 351

Cool Structures: Creative Activities that Make Math & Science Fun for Kids

 Anders Hanson e Elissa Mann 

 (Cool Art With Math & Science)

Checkerboard Library | 2013 | 34 páginas | rar- pdf | 6,5 Mb

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Contents
COOL STRUCTURES-BITS AND PIECES PUT TOGETHER
PYRAMIDS-ANCIENT GEOMETRY
PROJECT 1-BUILD A PYRAMID
BRIDGEs-GET OVER IT!
PROJECT 2-BUILD A BRIDGE
SLING IT-STRUCTURES IN ACTION!
PROJECT 3-BUILD A CATAPULT
TOWERS-BUILDING HIGH
PROJECT 4-SPAGHETTI TOWER CHALLENGE
MATH TERMS
GLOSSARY
WEB SITES
INDEX

Sink or Float? Thought Problems in Math & Physics

Keith Kendig

Mathematical Association of America | 2008 | 390 páginas | rar - pdf | 18,6 Mb

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Sink or Float: Thought Problems in Math and Physics is a collection of problems drawn from mathematics and the real world. Its multiple-choice format forces the reader to become actively involved in deciding upon the answer. The book s aim is to show just how much can be learned by using everyday common sense. The problems are all concrete and understandable by nearly anyone, meaning that not only will students become caught up in some of the questions, but professional mathematicians, too, will easily get hooked. The more than 250 questions cover a wide swath of classical math and physics. Each problem s solution, with explanation, appears in the answer section at the end of the book.A notable feature is the generous sprinkling of boxes appearing throughout the text. These contain historical asides or little-known facts. The problems themselves can easily turn into serious debate-starters, and the book will find a natural home in the classroom

Contents
Preface vii
What Do You Think? A Sampler 1
Geometry 9
Numbers 33
Astronomy 45
Archimedes' Principle 67
Probability 85
Classical Mechanics 105
Electricity and Magnetism 123
Heat and Wave Phenomena 143
The Leaking Tank 179
Linear Algebra 197
What Do You Think? Answers 217
Geometry Answers 227
Numbers Answers 245
Astronomy Answers 253
Archimedes' Principle Answers 267
Probability Answers 273
Mechanics Answers 285
Electricity Answers 295
Heat and Wave Phenomena Answers 301
The Leaking Tank Answers 317
Linear Algebra Answers 323
Glossary 339
References 367
Problem Index 369
Subject Index 373
About the Author 375

Sophie's Diary a mathematical novel

Dora Musielak 

Mathematical Association of America | 2012 - 2ª edição | 292 páginas | rar - pdf | 1,82 Mb

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Sophie Germain, the first and only woman in history to make a substantial contribution to the proof of Fermat's Last Theorem, grew up during the most turbulent years of the French Revolution. Her mathematical genius was discovered by Lagrange around 1797. Published research about Germain focuses on her achievements, noting that she assumed a man's name at the École Polytechnique in Paris, to submit her own work to Lagrange. Yet, no biography has explained how Germain learned mathematics before that time to become so sure of her analytical skills to carry out such a daring act. Sophie s Diary is an attempt to answer this question: How did Germain learn enough mathematics to enter the world of Lagrange s analysis in the first place?

In Sophie s Diary, Germain comes to life through a fictionalized journal that intertwines mathematics with history of mathematics plus historically-accurate accounts of the brutal events that took place in Paris between 1789 and 1793. This format provides a plausible perspective of how a young Sophie could have learned mathematics on her own---both fascinated by numbers and eager to master tough subjects without a tutor s guidance. Her passion for mathematics is integrated into her personal life as an escape from societal outrage.

Sophie s Diary is suitable for a variety of readers---both students and teachers, mathematicians and novices---who will be inspired and enlightened on a field of study made easy as is told through the intellectual and personal struggles of an exceptional young woman.

Contents
Paris, France: 1789
1 Awakening 1
Paris, France: 1790
2 Discovery 49
Paris, France: 1791
3 Introspection 95
Paris, France: 1792
4 Under Siege 133
Paris, France: 1793
5 Upon the Threshold 173
6 Intellectual Discovery 187
Paris, France: 1794
7 Knocking on Heaven’s Door 215
Appendices
Author’s Note 241
Sophie Germain Biographical Sketch 249
Marie-Sophie Germain Timeline 267
Bibliography 269
Acknowledgements 275
Index 276

Leveled Texts for Mathematics: Geometry

Lori Barker

Shell Education | 2011 | 147 páginas | rar - pdf | 4,25 Mb

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Highlighting geometry, this resource provides the know-how to use leveled texts to differentiate instruction in mathematics. A total of 15 different topics are featured in and the high-interest text is written at four different reading levels with matching visuals. Practice problems are provided to reinforce what is taught in the passage.

Table of Contents
What Is Differentiation?...4
How to Differentiate Using This Product...5
General Information About Student Populations...6
Below-Grade-Level Students...6
English Language Learners...6
On-Grade-Level Students....7
Above-Grade-Level Students...7
Strategies for Using the Leveled Texts.....8
Below-Grade-Level Students...8
English Language Learners.... 11
Above-Grade-Level Students.... 14
How to Use This Product.... 16
Readability Chart.... 16
Components of the Product.... 16
Tips for Managing the Product.... 18
Correlations to Mathematics Standards... 19
Leveled Texts..... 21
Angles All Around.... 21
Understanding Triangles.... 29
To Cross or Not to Cross... 37
Quadrilaterals... 45
Classifying 2-D Shapes.... 53
Irregular Shapes... 61
Congruent and Similar Figures..... 69
Understanding 3-D Shapes.... 77
Understanding Prisms... 85
The Coordinate Plane.... 93
Circles... 101
Symmetry... 109
Reflections..... 117
Rotations... 125
Translations... 133
Appendices..... 141
References Cited... 141
Contents of Teacher Resource CD... 142