Teaching Learners who Struggle with Mathematics: Systematic Intervention and Remediation

Helene J. Sherman, Lloyd I. Richardson e George J. Yard 

 Pearson | 2012 - 3ª edição | 265 páginas | rar - pdf | 5,3 Mb

link (password: matav)

This book is designed for aspiring and practicing K-6 teachers who will work or are working with students in need of remediation and intervention with common mathematical concepts students struggle with most, including place value, addition and subtraction of whole numbers, multiplication, division, fractions, and time and money. This book analyzes the roots and causes of frequent error patterns in student work and offers implementable solutions for solving them and teaching lifelong math skills. A Data Analysis Sheet is presented as an example for each problem area and followed by a Math Improvement Plan that offers guidance on how to instruct students in need of additional intervention and prepare them with lifelong mathematics skills

Contents
Chapter 1 The Dissimilar Learner and Mathematics Instruction . .1
Chapter 2 Place Value .. .19
Chapter 3 Addition of Whole Numbers  . .43
Chapter 4 Subtraction of Whole Numbers .. .64
Chapter 5 Multiplication . . .87
Chapter 6 Division .. . 113
Chapter 7 Rational Numbers .. . 137
Chapter 8 Decimal Fractions . .172
Chapter 9 Problem Solving . .. 198
Chapter 10 Time and Money .  . 211
Appendix A Sample DAS and MIP Tables . . . . 239
Appendix B Suggestions for Planning Academic Content Lessons . . 242

Index . . 246

Guided Math in Action Building Each Student’s Mathematical Proficiency with Small-Group Instruction

Nicki Newton

Routledge | 2013 | 159 páginas | rar - pdf | 2 Mb

link (password : matav)

Teachers, coaches, and supervisors will learn how to help elementary school students build mathematical proficiency with standards-based, differentiated, small-group instruction with the strategies in this book.

Both novice and veteran educators will gain in-depth knowledge for conducting effective guided math lessons, scaffolding learning in small groups, and assessing student learning. Lots of actual templates, graphic organizers, black-line masters, detailed lesson plans, and student work samples are included, as well as vignettes of mini-lessons, center time, small guided math groups, and share time.

This practical, hands-on guide will help you...

• Understand the framework of Guided Math lessons

• Gain an in-depth look at the role of assessment throughout the Guided Math process

• Develop an action plan to get started immediately

This is a must-have resource for all educators looking for a structure to teach small groups in math that meet the Common Core State Standards for Mathematics.

Contents
Supplemental Downloads 

1. Guided Math: An Introduction 
2. Guided Math in a Numerate Environment 
3. Managing the Math Workshop 
4. Forming Guided Math Groups 
5. Balanced Assessment: The Key to Grouping Students for Guided Math 
6. A Framework for Guided Math Lessons 
7. Building Mathematical Proficiency in Guided Math Groups 
8. What Are the Other Kids Doing? 
9. The First 20 Days of Math Workshop: Setting the Stage? for Effective Guided Math Groups 
Blackline Masters 
References

Today's Mathematics: Concepts, Methods, and Classroom Activities

James W Heddens; William R Speer; Daniel J Brahier

Wiley | 2009 - 12ª edição | páginas | rar - pdf |4,7 Mb

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Combining theory, methods and instructional activities in one convenient volume, Heddens, Speers and Brahier’s Twelfth Edition of "Today’s Mathematics" provides a valuable set of ideas and reference materials for actual classroom use. This combined coverage of content and methods creates a long-lasting resource, helping pre-service and in-service teachers see the relationship between what they teach and how they teach. Reflecting recent recommendations from the NCTM Standards, the text emphasizes how to introduce a concept at a given level to expand and reinforce it at successive levels.

Table of Contents

Chapter 1
Learning Mathematics 1
Societal Needs 2
Calls for Change 3
National and International Achievement 3
The Identification of Standards 5
Principles and Standards for School Mathematics 6
Implementing the Process Standards 8
Describing A Contemporary Mathematics Program 10
Levels of Abstraction 11
Theoretical Foundations for a Contemporary Mathematics Program 12
Theory into Practice 17
Closure 18
Teaching Competencies and Self-Assessment Tasks 19

Chapter 2
Teaching Mathematics 21
The NCTM Principles and Standards for School
Mathematics 22
The NCTM Professional Teaching Standards: Mathematics Teaching Today 23
An Example of a Teaching Standard 25
Lesson Planning Processes and Purposes 29
Issues in Designing Mathematics Lessons 33
Mathematics Objectives 35
The Role of Motivation and Follow-Up 36
The Assessment of Learning and Teaching 37
Adjusting Instruction to Meet Individual Needs 38
Classroom Instructional Aids 39
Closure 40
Teaching Competencies and Self-Assessment Tasks 41

Chapter 3
Assessing Mathematics 43
NCTM Assessment Standards for School Mathematics 44
An Example of an Assessment Standard 47
A Classroom Assessment Vignette 48
Purposes for Assessment 49
Assessment Strategies 51
Closure 58
Teaching Competencies and Self-Assessment Tasks 59

Chapter 4
Technology in K–8 Mathematics 61
A Brief History of Technology’s Influence on Education 62
Calculators and Exploration of Mathematical Concepts 63
Calculator Features and Functions 66
Examples of Effective Calculator Use 66
Tools for Measuring Motion 68
Computers and Mathematics Instruction 69
Instructional Software in the Mathematics Classroom 71
Application Software in the Mathematics Classroom 72
Virtual Manipulatives 73
Design Issues and Advantages of Virtual Manipulatives 74
Classification Attributes for Virtual Manipulatives 75
Capsule Descriptions of the National Library of Virtual Manipulatives 76
Multimedia in the Mathematics Classroom 81
The Internet in the Mathematics Classroom 82
Programming Computers and Calculators 83
Closure 84
Teaching Competencies and Self-Assessment Tasks 85

Chapter 5
Problem Solving and Mathematical
Language 87
The Nature of Problem Solving 88
Problem-Solving Strategies 91
Approaching Word Problems Effectively 98
Logic and Reasoning 101
The Language of Logic 101
The Language of Mathematics 103
Closure 107
Practice Exercises for Teachers 108
Teaching Competencies and Self-Assessment Tasks 111
Sample Instructional and Assessment Activities 112

Chapter 6
Number Sense, Numeration, and Place Value 115
A Foundation for Mathematics Development 116
Patterns and Other Relationships in the Primary Curriculum 117
Number Sense 118
Number Relations 123
Extending Numberness Concepts 125
Place-Value Numeration 125
Decimal Numeration 126
Ancient Numeration Systems 131
Number Bases Other Than Ten 134
Closure 137
Practice Exercises for Teachers 138
Teaching Competencies and Self-Assessment Tasks 141
Sample Instructional and Assessment Activities 142

Chapter 7
Addition and Subtraction of Whole
Numbers 145
Creating a Sound Base for Addition and
Subtraction 146
Meaning and Models for Addition 147
Developing Basic Addition Facts 148
Memorizing Basic Addition Facts Using Structures 149
Extending Basic Addition Facts Using Place Value 155
Regrouping in the Addition Process 156
Meaning and Models for Subtraction 157
Developing Basic Subtraction Facts 160
Memorizing Basic Subtraction Facts Using Structures 161
Extending Basic Subtraction Facts Using Place Value 162
Regrouping in the Subtraction Process 163
Closure 164
Practice Exercises for Teachers 166
Teaching Competencies and Self-Assessment Tasks 167
Sample Instructional and Assessment Activities 167

Chapter 8
Multiplication and Division of Whole Numbers 171
Meaning and Models for Multiplication 172
Developing and Memorizing Basic Multiplication Facts 175
Expanding Basic Multiplication Facts Through Place
Value 178
Regrouping in Multiplication 181
Meaning and Models for Division 183
Developing and Memorizing Basic Division Facts 186
Remainders in Division 187
Expanding Basic Division Facts Through Place Value 187
Closure 190
Practice Exercises for Teachers 191
Teaching Competencies and Self-Assessment Tasks 192
Sample Instructional and Assessment Activities 193

Chapter 9
Number Theory and Number Systems 197
The Language of Number Theory 199
The Sieve of Eratosthenes 200
Factor Trees 202
Prime Factorization 203
Divisibility ‘‘Rules’’ 205
Least Common Multiples and Greatest Common Factors 207
Number Systems 209
Closure 218
Practice Exercises for Teachers 218
Teaching Competencies and Self-Assessment Tasks 221
Sample Instructional and Assessment Activities 222

Chapter 10
Algebraic Reasoning: Generalizing
Patterns and Relationships 225
The Content of Algebra 226
Algebra in Problem Solving 228
Promoting Algebraic Thinking in the Lower Elementary Grades 229
Enhancing Algebraic Thinking in the Upper Elementary and Middle Grades 232
Closure 236
Practice Exercises for Teachers 238
Teaching Competencies and Self-Assessment Tasks 240
Sample Instructional and Assessment Activities 241

Chapter 11
Rational Numbers Expressed as
Fractions: Concepts 245
A Fraction of the History of Fractional Numbers 246
Rational Numbers—A Definition and Description 247
The Regions Model for Fractional Numbers 248
The Groups of Objects Model for Fractional Numbers 250
The Number Line Model for Fractional Numbers 251
Knowledge and Understandings Prior to Operations on Rational Numbers Expressed as Fractions 253
Closure 258
Practice Exercises for Teachers 260
Teaching Competencies and Self-Assessment tasks 262
Sample Instructional and Assessment Activities 263

Chapter 12
Rational Numbers Expressed as
Fractions: Operations 267
Addition of Fractional Numbers 269
Subtraction of Fractional Numbers 274
Multiplication of Fractional Numbers 278
Division of Fractional Numbers 282
Closure 285
Practice Exercises for Teachers 286
Teaching Competencies and Self-Assessment Tasks 288
Sample Instructional and Assessment Activities 288

Chapter 13
Rational Numbers Expressed as Decimals 291
Models That Give Decimals Meaning 292
Place Value—A Foundation for Decimals 293
Exponential Notation 295
Addition with Decimal Numbers 296
Subtraction with Decimal Numbers 297
Multiplication with Decimal Numbers 299
Division with Decimal Numbers 300
Relating Decimals and Fractions 301
Scientific Notation 303
Ratio, Proportion, and Percent 304
Closure 311
Practice Exercises for Teachers 312
Teaching Competencies and Self-Assessment Tasks 313
Sample Instructional and Assessment Activities 314

Chapter 14
Data Analysis: Graphs, Statistics, and Probability 317
A Child’s View of Statistics 318
Measures of Central Tendency in Data 319
Organizing and Interpreting Data 321
Taking a ‘‘Chance’’ 326
Experimental Probability 326
Theoretical Probability 327
Permutations and Combinations 328
Models for Exploring Probability 330
Closure 331
Practice Exercises for Teachers 332
Teaching Competencies and Self-Assessment Tasks 334
Sample Instructional and Assessment Activities 335

Chapter 15
Measurement 339
The Historical Development of Measurement Systems 340
Contemporary Measurement Systems 341
The Process of Measurement 345
Computing with Denominate Numbers 349
Money and Time as Measures 350
Closure 354
Practice Exercises for Teachers 354
Teaching Competencies and Self-Assessment Tasks 356
Sample Instructional and Assessment Activities 357

Chapter 16
Geometry: Basic Concepts and Structures 361
Early Experiences in Geometry 363
The ‘‘Building Blocks’’ of Geometry 364
Extending the Basics—Curves, Regions, and Rays 366
Angles and Angle Measure 369
Exploring Geometric Constructions 372
Symmetry and Transformational Geometry 374
Other Devices for Exploring Geometric Concepts 376
Closure 377
Practice Exercises for Teachers 378
Teaching Competencies and Self-Assessment Tasks 381
Sample Instructional and Assessment Activities 382

Chapter 17
Geometry: Polygons and Polyhedra 385
Defining Polygons 386
A Closer Look at Triangles 388
A Closer Look at Quadrilaterals 394
A Closer Look at Circles 395
Area, Perimeter, and Circumference Measurement 397
Defining Polyhedra 401
Closure 409
Practice Exercises for Teachers 410
Teaching Competencies and Self-Assessment Tasks 414
Sample Instructional and Assessment Activities 415

Becoming an Outstanding Mathematics Teacher

Jayne Bartlett

Routledge | 2013 | 185 páginas | rar - pdf | 1,4 Mb

link (password: matav)

Raising standards in mathematics is high on government education agendas and remains a key priority for schools. Schools strive to provide an outstanding education for their pupils preparing them to compete not only in a national but an international market. At the heart of this is the classroom and the classroom teacher. So how do you plan lessons that engage and motivate students and what makes a mathematics lesson outstanding?

Becoming an Outstanding Mathematics Teacher aims to help teachers develop approaches to teaching and learning that take into account individual students needs and abilities to best facilitate learning. Taking a fresh approach it offers a wide range of techniques for planning lessons that that allow them to use current resources (including themselves) in a more innovative way to produce outstanding results.

With a strong focus on activating learning and supporting pupils as they connect mathematical concepts and processes and develop their individual learning journeys the book covers:

• A step-by-step approach to planning for learning

• Assessment for learning and planning for progress

• Developing effective questioning strategies to promote thinking skills in pupils

• Techniques for differentiation to ensure all pupils make progress

• Using the classroom environment to develop a culture of learning

Packed full of practical strategies and activities that are easy to implement and including sample lesson plans, this timely new book is essential reading for newly qualified and experienced mathematics teachers that want to ensure outstanding teaching and learning in their classrooms.

Contents
List of figures and tables xi
Acknowledgements xiv
Introduction xv
1 Making connections 1
What makes a lesson outstanding? 2
The learning journey 4
Planning for learning 5
Joining the dots and making connections 6
Learning through thinking? 6
Connecting with reality 7
2 How does it all begin? 9
Bell work 9
Learning outcomes 15
Starter activities 18
The Big Question 19 
Benchmarking learning 21
Review 28
3 Learning in the main 30
Sequencing the learning 31
Mini-assessments 34
The main assessment activity 35
Working together 43
Independent learning 45
Individual learning preferences and mathematics 45
Linking with other departments 48
4 So how does it all end? 52
Returning to the Big Question 53
Plenary activities 56
Time for reflection 64
Reverse bell work 65
Home learning 65
5 What’s in a question? 68
No hands up 68
Wait and thinking time 69
Responding to an incorrect answer 69
Open and closed questions 70
Bloom’s taxonomy 71
Think, pair, share 75
Probing questions to develop a concept 76
Teacher input 81
6 How do I know? 83
Against what? 83
Learning outcomes and success criteria 84
Quality interaction with pupils 86
Target setting 86
The quality of assessments 88
Marking and feedback 89
Self-assessment and peer assessment 95
Reflection 97
Mini-assessment points 98
The final assessment activity 99
7 Thirty different minds? 100
Differentiation by ability 101
Differentiation by gender 105
Differentiation by resource 105
Differentiation by activity or task 112
Differentiation by learning preference 112
Differentiation by outcome 112
Differentiation by interest 113
Differentiation by grouping 113
Differentiation through questioning 114
Home learning 114
Special educational needs 116
Gifted and talented learners 117
8 The classroom environment 120
Classroom displays 120
The classroom climate 123
Seating arrangements 125
Classroom assistants 127
The outdoor learning environment 128
9 Pulling it all together 131
Expanding two linear expressions to produce
a quadratic expression 132
Indices 144
Dividing in a given ratio 147
Trigonometry 150
Solving equations 154
Conclusion 156
References 160
Index 162

Supporting English language learners in math class, grades 3/5

 Rusty Bresser, Kathy Melanese e Christine Sphar 

 Math Solutions | 2008 | 226 páginas | pdf | 2,4 Mb

link
link1

This lesson-based series gives teachers the essential tools for simultaneously meeting math content goals and language development goals. Teachers will get a wealth of strategies and activities for modifying their instruction as well as sentence frame structures and dozens of instant-use reproducibles. Grades 3-5

ContentsForeword / vii
Acknowledgments / xi
1 Teaching Math to English Language Learners / 1
2 Identifying and Describing Polygons: A Geometry Lesson / 18
3 Build a Shape, Part 1: A Geometry Lesson / 37
4 Build a Shape, Part 2: A Geometry Lesson / 50
5 Roll Two Dice: A Probability Lesson / 58
6 Building Iguanas with Pattern Blocks: An Algebra Lesson / 81
7 Round Things: A Measurement Lesson / 105
8 Helping English Language Learners Make Sense of Math Word Problems / 130
9 Writing and Solving Multiplication and Division Word Problems / 138
10 How to Modify Math Lessons to Support English Language Learners / 163
11 Frequently Asked Questions / 182
Appendix: Multiple-Meaning Words in Mathematics / 191
Blackline Masters / 193
Identifying and Describing Polygons Cards / 195
Identifying and Describing Polygons Record Sheet / 197
Roll Two Dice Record Sheet / 198
Round Things Record Sheet / 199
Lesson Template / 200
References / 201
Index / 205

Supporting English Language Learners in Math Class, Grades K-2

Rusty Bresser, Kathy Melanese e Christine Sphar

Math Solutions | 2008 | 218 páginas | pdf | 3,9 Mb

link direto
link
link1

This lesson-based series gives teachers the essential tools for simultaneously meeting math content goals and language development goals. Teachers will get a wealth of strategies and activities for modifying their instruction as well as sentence frame structures and dozens of instant-use reproducibles. Grades K-2

Contents
Foreword / vii
Acknowledgments / xi
1 Teaching Math to English Language Learners / 1
2 Capture and Double Capture: An Arithmetic Lesson / 18
3 From Rockets to Polygons: A Geometry Lesson / 34
4 Trade Up for a Nickel, Trade Up for a Dime, and Race for a Quarter: Number Sense Lessons About Money / 55
5 Would You Rather . . . ? A Data Analysis Lesson / 73
6 Cubes in a Tube: An Algebra Lesson / 88
7 Junk Sorting: An Algebra Lesson / 112
8 Helping English Language Learners Make Sense of Math Word Problems / 133
9 How to Modify Math Lessons to Support English Language Learners / 160
10 Frequently Asked Questions / 178
Appendix: Multiple-Meaning Words in Mathematics / 187
Blackline Masters / 189
Trade Up for a Nickel Game Board / 190
Trade Up for a Nickel Amount Cards / 191
Trade Up for a Dime Game Board / 192
Trade Up for a Dime Amount Cards / 193
Race for a Quarter Rules / 194
1–100 Chart / 195
References / 197
Index / 201

Writing Strategies for Mathematics

(Reading and Writing Strategies)

Trisha Brummer e Sarah Kartchner Clark

Shell Education | 2013 - 2ª edição | 259 páginas | rar - PDF | 6,4 Mb

link (password: matav)

1ª edição - 2008

Help students write mathematics content! This 2nd edition resource was created to support Common Core State Standards, provides an in-depth research base about literacy instruction, and includes key strategies to help students write and comprehend mathematics content. Designed in an easy-to-use format, this resource offers details approaches and activities with classroom examples by grade ranges and includes graphic organizer templates and digital resources to help teachers implement quickly and easily. Specific suggestions for differentiating instruction are also provided to help English language learners, gifted students, and students reading below grade level.
Table of Contents
Introduction
What Is Writing? . . . . . . . . . . . . . . . . . . . . . . . . . 5
Motivating Students to Write . . . . . . . . . . . . . . . 10
The Writing Process . . . . . . . . . . . . . . . . . . . . . 16
Writing Across the Curriculum . . . . . . . . . . . . . 20
Writing Instruction . . . . . . . . . . . . . . . . . . . . . . 25
How to Use This Book . . . . . . . . . . . . . . . . . . . 28
Correlation to Standards . . . . . . . . . . . . . . . . . . 29
Part 1: Writing to Learn
Developing Vocabulary
Developing Vocabulary Overview . . . . . . . . . . . 31
Word Wall . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Frayer Model . . . . . . . . . . . . . . . . . . . . . . . . 39
Concept of De nition Map . . . . . . . . . . . . . 43
List-Group-Label . . . . . . . . . . . . . . . . . . . . . 48
Vocabulary Self-Collection . . . . . . . . . . . . . 53
Possible Sentences . . . . . . . . . . . . . . . . . . . . 55
Word Trails . . . . . . . . . . . . . . . . . . . . . . . . . 59
Previewing and Reviewing
Previewing and Reviewing Overview . . . . . . . . 63
KWL Chart . . . . . . . . . . . . . . . . . . . . . . . . . 66
Think Sheet . . . . . . . . . . . . . . . . . . . . . . . . . 72
Free-Association Brainstorming . . . . . . . . . 76
Probable Passages . . . . . . . . . . . . . . . . . . . . 80
Guided Free Write . . . . . . . . . . . . . . . . . . . . 85
End-of-Class Re ection . . . . . . . . . . . . . . . . 89
Reader-Response Writing Chart . . . . . . . . . 92
Journal Writing
Journal Writing Overview . . . . . . . . . . . . . . . . . 96
Vocabulary Journal . . . . . . . . . . . . . . . . . . . 99
Dialogue Journal . . . . . . . . . . . . . . . . . . . . 103
Highlighted Journal . . . . . . . . . . . . . . . . . . 106
Key Phrase Journal . . . . . . . . . . . . . . . . . . 109
Double-Entry Journal . . . . . . . . . . . . . . . . 112
Critical Incident Journal . . . . . . . . . . . . . . 116
Three-Part Journal . . . . . . . . . . . . . . . . . . 119
Note-Taking
Note-Taking Overview . . . . . . . . . . . . . . . . . . 123
Cornell Note-Taking System . . . . . . . . . . . 125
Note-Taking System for Learning . . . . . . . 129
T-List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
Using Diagrams and Maps
Using Diagrams and Maps Overview . . . . . . . 137
Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
Venn Diagram . . . . . . . . . . . . . . . . . . . . . . 143
Triangular Venn Diagram . . . . . . . . . . . . . 147
Cause-and-Effect Map . . . . . . . . . . . . . . . . 151
Semantic Word Map . . . . . . . . . . . . . . . . . 155
Concept Map . . . . . . . . . . . . . . . . . . . . . . . 159
Problem-Solution Map. . . . . . . . . . . . . . . . 162
Time Order Map . . . . . . . . . . . . . . . . . . . . 168
Part 2: Writing to Apply
Authoring
Authoring Overview . . . . . . . . . . . . . . . . . . . . 173
Guided Writing Procedure . . . . . . . . . . . . 175
Reading-Writing Workbench . . . . . . . . . . . 178
Author’s Chair . . . . . . . . . . . . . . . . . . . . . . 182
Read, Encode, Annotate, Ponder . . . . . . . . 186
Summarizing
Summarizing Overview . . . . . . . . . . . . . . . . . 191
GIST . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
Key Words . . . . . . . . . . . . . . . . . . . . . . . . . 197
Guided Reading and Summarizing Procedure .. . . . . 199
Applying Knowledge
Applying Knowledge Overview . . . . . . . . . . . 204
Summary-Writing Microtheme . . . . . . . . . 208
Thesis-Support Microtheme . . . . . . . . . . . 210
Data-Provided Microtheme . . . . . . . . . . . . 212
Quandary-Posing Microtheme . . . . . . . . . 214
RAFT Assignment . . . . . . . . . . . . . . . . . . 216
Business Letter . . . . . . . . . . . . . . . . . . . . . 218
Friendly Letter . . . . . . . . . . . . . . . . . . . . . . 220
Data Report . . . . . . . . . . . . . . . . . . . . . . . . 222
Newspaper Article . . . . . . . . . . . . . . . . . . . 224
Mathematics Fiction Story . . . . . . . . . . . . 226
Research Report . . . . . . . . . . . . . . . . . . . . 228
Part 3: Assessing Writing
Assessing Writing
Assessing Writing Overview . . . . . . . . . . . . . . 230
Holistic Assessment . . . . . . . . . . . . . . . . . . 233
Analytic Assessment . . . . . . . . . . . . . . . . . 235
Primary Trait Assessment . . . . . . . . . . . . . 237
Self-Assessment . . . . . . . . . . . . . . . . . . . . . 239
Peer Assessment . . . . . . . . . . . . . . . . . . . . 242
Teacher Conference . . . . . . . . . . . . . . . . . . 244
Appendix A: Additional Resources . . . . . . . 246
Appendix B: References Cited . . . . . . . . . . . 247
Appendix C: Suggestions for Further Reading . . . 253
Appendix D: Contents of the Digital Resource CD .  . 254

Big ideas of early mathematics : what teachers of young children need to know

The Early Math Collaborative

Pearson | 2013 | 209 páginas | rar -pdf | 4,2 Mb


link (password: matav)

In this unique guide, classroom teachers, coaches, curriculum coordinators, college students, and teacher educators get a practical look at the foundational concepts and skills of early mathematics, and see how to implement them in their early childhood classrooms.

Big Ideas of Early Mathematics presents the skills educators need to organize for mathematics teaching and learning during the early years. For teachers of children ages three through six, the book provides foundations for further mathematics learning and helps facilitate long-term mathematical understanding.

Contents
About the Authors vii
Foreword ix
Preface x
INTRODUCTION 2
Chapter 1 SETS 12
Chapter 2 NUMBER SENSE 28
Chapter 3 COUNTING 46
Chapter 4 NUMBER OPERATIONS 64
Chapter 5 PATTERN 82
Chapter 6 MEASUREMENT 98
Chapter 7 DATA ANALYSIS 112
Chapter 8 SPATIAL RELATIONSHIPS 130
Chapter 9 SHAPE 146
CONCLUSION 168
Big Ideas Charts 174
Book Study Guide 184
Bibliography 190
Index 192

Learning Mathematics in Elementary and Middle Schools A Learner-Centered Approach

George S. Cathcart, Yvonne M. Pothier, James H. Vance e Nadine S. Bezuk

Pearson | 2010 - 5.ª edição | páginas | rar - pdf | 12,4 Mb

link (password: matav)

This popular text and it's new integrated online resource, MyEducationLab, promotes a learner-centered approach to teaching elementary and middle school mathematics. These resources provide valuable research-based instructional strategies, resources, and activities to help you learn to evaluate how children think mathematically and how to link that knowledge to developmentally appropriate teaching practices. A strong focus on NCTM Standards and developing critical tools to meet the individual needs of students ensures all students and teachers can be successful with math.

Brief Contents
1 Teaching Mathematics: Influences and Directions 1
2 Learning and Teaching Mathematics 15
3 Developing Mathematical Thinking and Problem-Solving Ability 39
4 Assessing Mathematics Understanding 60
5 Developing Number Concepts 76
6 Developing Understanding of Numeration 99
7 Developing Whole-Number Operations: Meaning of Operations 126
8 Developing Whole-Number Operations: Mastering the Basic Facts 149
9 Estimation and Computational Procedures for Whole Numbers 170
10 Developing Fraction Concepts 207
11 Developing Fraction Computation 234
12 Developing Decimal Concepts and Computation 259
13 Understanding Ratio, Proportion, and Percent 282
14 Developing Geometric Thinking and Spatial Sense 297
15 Developing Measurement Concepts and Skills 331
16 Collecting, Organizing, and Interpreting Data 363
17 Developing Algebraic Thinking 396
References 435
Index 443

What Primary Teachers Should Know About Maths

 

Aileen Duncan

Hodder Education | 1996 - 2ª edição | 216 páginas | rar - pdf | 22,3 Mb

link (password: matav)

This title offers support to those involved in teaching primary maths. This edition has been fully updated to accord with the new National Curriculum. Its question-and-answer format allows specific problem areas to be easily located. It explains unfamiliar mathematical terms and includes sample lesson plans.
Contents

Introduction 4
Section One —Aspects of mathematics

1 Introduction 6
2 About numbers 8
Whole numbers - cardinality, ordinality, counting; Whole numbers - place value ; Conservation ; Negative numbers ; Common fractions ; Decimal fractions ; Percentages 
3 Using numbers 31
Addition ; Subtraction ; Multiplication ; Division ; Number patterns ; Averages ; Probability ; Ratio ; Algebra - equations ; Money 
4 Measure 64
Length ; Area ; Weight ; Volume ; Time ; Scale
5 Shape, position and movement 88
Two-dimensional shapes: symmetry and tessellation; Triangles ; Quadrilaterals ; Circles ; 3D shapes; Lines ; Angles, compass points and bearings ; Networks and topology
6 Information handling 113
Pictorial representation ; Coordinates ; Graphs ; Databases and spreadsheets 126
Section Two - Teaching and learning7 Introduction 129
8 Focus on children listening and talking 130
Watching and listening to the teacher ; Talking with the teacher ; Talking with classmates; Devising and asking questions ; Reading
9 Focus on children doing and recording 144
Using resources ; Using a calculator ; Using a computer ; Playing a game; Writing practice examples;  Using a workcard, worksheet work/textbook; Recording mathematics; Problem solving 
Section Three - Sample lesson notes
10 Introduction 164
11 Lessons for 5 to 7-year-olds 165
12 Lessons for 7 to 11 -year-olds 181
Index 213

Math and Science for Young Children

Rosalind Charlesworth e Karen K. Lind

Cengage Learning | 2012 - 7ª edição | 658 páginas | rar - pdf | 22,5 Mb

link (password: matav)

MATH AND SCIENCE FOR YOUNG CHILDREN, Seventh Edition, is a unique reference that focuses on the integration of math and science in early childhood education programs, while addressing other important areas of child development during the crucial birth-through-eight age range. It also carefully addresses the ever-changing and significant national standards of the following organizations: The National Association for the Education of Young Children (NAEYC), National Council of Teachers of Math (NCTM), National Science Teachers Association (NSTA), American Association for the Advancement of Science (AAAS), and the National Research Council (NRC). A valuable resource for working professionals and involved parents, MATH AND SCIENCE FOR YOUNG CHILDREN, Seventh Edition, is the most current volume of information of its kind available on the market today.

Contents
Part I: CONCEPT DEVELOPMENT IN MATHEMATICS AND SCIENCE.
1. How Concepts Develop.
2. How Concepts Are Acquired.
3. Promoting Young Children's Concept Development through Problem Solving.
4. Assessing the Child's Developmental Level.
5. The Basics of Science.
6. How Young Scientists Use Concepts.
7. Planning for Science.
Part II: FUNDAMENTAL CONCEPTS AND SKILLS.
8. One-to-One Correspondence.
9. Number Sense and Counting.
10. Logic and Classifying.
11. Comparing.
12. Early Geometry: Shape.
13. Early Geometry: Spatial Sense.
14. Parts and Wholes.
15. Language and Concept Formation.
16. Fundamental Concepts in Science.
Part III: APPLYING FUNDAMENTAL CONCEPTS, ATTITUDES, AND SKILLS.
17. Ordering, Seriation, and Patterning.
18. Measurement: Volume, Weight, Length, and Temperature.
19. Measurement: Time.
20. Interpreting Data Using Graphs.
21. Applications of Fundamental Concepts in Preprimary Science.
22. Integrating the Curriculum through Dramatic Play and Thematic Units and Projects.
Part IV: SYMBOLS AND HIGHER-LEVEL ACTIVITIES.
23. Symbols.
24. Groups and Symbols.
25. Higher-Level Activities and Concepts.
26. Higher-Level Activities Used in Science Units and Activities.
Part V: MATHEMATICS CONCEPTS AND OPERATIONS FOR THE PRIMARY GRADES.
27. Operations with Whole Numbers.
28. Patterns.
29. Fractions.
30. Numbers above 10 and Place Value.
31. Geometry, Data Collection, and Algebraic Thinking.
32. Measurement with Standard Units.
Part VI: USING SKILLS, CONCEPTS, AND ATTITUDES FOR SCIENTIFIC INVESTIGATIONS IN THE PRIMARY GRADES.
33. Overview of Primary Science.
34. Life Science.
35. Physical Science.
36. Earth and Space Science.
37. Environmental Awareness.
38. Health and Nutrition.
Part VII: THE MATH AND SCIENCE ENVIRONMENT.
39. Materials and Resources for Math and Science.
40. Math and Science in Action.
41. Math and Science in the Home.
Appendix A: Developmental Assessment Tasks.
Appendix B: Children's Books and Software with Math and Science Concepts.
Appendix C: The National Research Council's National Science Education Standards (1996).
Glossary.
Index.

Mathematics Methods for Elementary and Middle School Teachers

 

Mary M. Hatfield, Nancy Tanner Edwards, Gary G. Bitter e  Jean Morrow 

Wiley | 2007 - 6ª edição| páginas | rar - pdf | 5,5 Mb

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This text provides preservice prekindergarten through grade eight teachers with ideas, techniques, and approaches to teaching mathematics appropriate for the 21st century, and strongly integrates technology with hands-on experience. This is the only text to include practice Praxis II-style test questions to prepare teacher candidates to pass the high-stakes test used for teacher certification. The new sixth edition has been updated with the National Council of Teachers of Mathematics (NCTM) Curriculum Focal Points, which provide focus on significant concepts for each grade level.


Table of Contents
1. Mathematics Education Today and into the Future.
2. Culturally Relevant Mathematics.
3. The Development of Mathematical Proficiency: Using Learning Research, Assessment, and Effective Instruction.
4. Middle School Mathematics.
5. Problem Solving.
6. Early Childhood Mathematics -- Number Readiness.
7. Operations and Number Sense.
8. Numeration and Number Sense.
9. Operations with Whole Numbers.
10. Common Fractions and Decimals.
11. Percent, Ratio, Proportion, and Rate.
12. Geometry and Spatial Reasoning.
13. Measurement.
14. Algebra and Algebraic Thinking.
15. Data Analysis, Statistics, and Probability.

Fostering Children's Number Sense in Grades K-2: Turning Math Inside Out

(New 2013 Curriculum & Instruction Titles)

Gregory Nelson

Pearson | 2013 | 173 páginas | rar - pdf | 2,5 Mb

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Fostering Children's Number Sense in Grades K-2 is a powerful, hands-on resource that helps in-service teachers, curriculum coaches, and math intervention specialists ensure children’s deep understanding of addition and subtraction in ways that enable long-term growth. Packed with child-centered instructional strategies, powerful and engaging learning materials, and revealing assessment tools, the book is clearly laid out and cross-referenced to the Common Core State Standards.

Contents

SECTION 1:  GETTING STARTED

Chapter 1:  Rethinking Number Sense

What math is not

Children’s readiness to be mathematicians

How we should teach math

What the experts and the research tell us

Math inside out

Chapter 2:  How to Teach Math This Way

Logistics

Space

Preparing the teaching materials

“Math time”

Work, not play

Learner-centered instruction

How we tend to teach…and why

Creating the learning community you want

Teacher-led lessons

The perils of group work

The role of the teacher as the children work

Keeping everyone safe

Authentic assessment

Teaching tips

Helping children talk about what they know

Three levels of vocabulary acquisition

Concrete before abstract

The same thing many ways

Errors are information

Competition

Answer keys, or no answer keys?

Study group discussion starters: Turning math inside out

SECTION 2:  EMERGENCE OF SECURE PLACE-VALUE AWARENESS

Chapter 3:  Place-Value Awareness Launch Points

What this is, and why it is important

What comes before, and how to get there

Logical quantification (K.NCC.4b)

Accurate counting to ten (K.NCC.1, K.NCC.4, K.NCC.5)

Connecting numerals to quantities (K.NCC.3)

Concepts and skills being reinforced at this developmental stage

The teen counting numbers have 10 as a base (K.NBT.1)

The use of zero as a place holder (1.NBT.2c)

The part-whole concept extended to the place value system (K.NBT.1, 1.NBT.2)

Place value versus face value (1.NBT.2)

The 10:1 relationship between units and tens (1.NBT.2a)

Directionality in reading multi-digit numerals (1.NBT.1)

Counting on using place value categories (K.CC.1, K.CC.2, 1.NBT.1)

Counting backwards through the decades

Estimating larger quantities

Greater than/less than in the place value system (1.NBT.3)

The relationship between hundreds and tens (2.NBT.1)

Launch points

Teen boards

Tens boards

Hands Up #1

“How Old Are We?” books

Hundreds board

Estimation activities (Unifix cubes; Cuisenaire rods; ten frames)

Race to a 100

Chapter 4:  Place-Value Awareness Check Points

Assessment probes

Cuisenaire teens

Hundred chain

Page walk

Hundreds board magic windows

Arrow math

Decade transition boards

How Many Now? — Variation #1

How Many Now? — Variation #2

How Many Now? — Variation #3

How Many Now? — Variation #4

Study group discussion starters: Secure place-value awareness

SECTION 3:  SECURE PART-WHOLE AWARENESS AND THE EMERGENCE OF ADDITION-SUBTRACTION FLUENCY

Chapter 5:  Addition-Subtraction Fluency Launch Points

What this is, and why it is important

What comes before, and how to get there

Basic part-whole awareness (K.OA.3)

Concepts and skills being reinforced in this chapter

Part-whole patterns for numbers up to 20 (K.OA.3, K.OA.4)

Decomposition and composition of numbers (K.OA.3, K.NBT.1, 1.OA.1, 1.OA.6)

The commutative property of addition (1.OA.3, 2.NBT.5, 2.NBT.6)

Addition and subtraction as inverse operations (1.OA.1, 1.OA.4, 1.OA.6, 1.NBT.4, 2.NBT.9)

Launch points

Hands Up #2 — Addition/subtraction

Ten-bar-in-a-cave game

Addition/subtraction using equal-arm balance scale

Addition/subtraction using ten-frames

Double-nines dominoes sorting

Domino trains or squares

Directional rods with addition/subtraction rack

Addition/subtraction using segmented Cuisenaire rods and 1-100 rack

Addition/subtraction using double-fives abacus

Chapter 6:  Addition-Subtraction Fluency Check Points

Assessment probes

Pursuit game

Ten-frame flash cards

Fact family triominoes

Parts Of calculator drill

Counting On calculator drill

Addition/subtraction war with playing cards

Addition/subtraction using torque balance scale

More teaching tips

Addition trumps subtraction

The perils of “Mad Minute” drills

Bridging from the concrete to paper-and-pencil

The real scoop on those dreaded word problems

The order in which number-sense based memorization develops

Study group discussion starters: Secure part-whole awareness and the emergence of addition-subtraction fluency

SECTION 4:  EXTENDING PLACE-VALUE AWARENESS
AND ADDITION-SUBTRACTION BEYOND THE HUNDREDS

Chapter 7:  Place-Value Fluency and Multi-Digit Addition-Subtraction Launch Points

Concepts and skills being reinforced in this chapter

A place value is determined by how many positions it is to the left of the units column (2.NBT.1, 2.NBT.4)

Zero as a place holder (2.NBT.1b, 2.NBT.3)

The maximum face value is 9 in any place-value column

10:1 exchange rates (2.NBT.1a, 2.NBT.7)

Exponential growth in a place-value system

The counting sequence in a place-value system

When combining or removing quantities, only digits in the same place-value location can be combined or decreased (2.NBT.5, 2.NBT.6, 2.NBT.7, 2.NBT.8, 2.NBT.9)

Composing and decomposing bundles of ten to move them from one place-value category to another can be done at any level of the place-value system as a tool of problem-solving (2.NBT.8, 2.NBT.11)

Standard algorithms can be used to efficiently solve multi-digit addition and subtraction problems, but alternative algorithms and strategies are sometimes preferable (2.NBT.10, 2.NBT.12, 2.NBT.13)

Launch points

200 board

Make-your-own place-value materials

Bank game with place-value blocks and place-value cards

Place-value materials sorter tray

Hundred and thousand extensions of ten-frames and Hand Game cards

Expanded notation strip

Modeling multi-digit addition-subtraction with exchanging

Mental math problem sets

Decimeter rods, meter rods, centimeter rods, metric measuring tape, and metric trundle wheel

Reading and writing really big numerals

Chapter 8:  Place-Value Fluency and Multi-Digit Addition-Subtraction Check Points

Assessment probes

Hundred-square in a cave game

Wacky numbers

I have, who has? game

Parts-of calculator drill

Skip-counting calculator drill

Target game

What’s wrong with this picture? sets

Final teaching tips

Words matter

Keeping children fluid

Teaching as improv

Collaboration and transformation

Keeping your eye on the prize

Study group discussion starters: Extended place-value awareness and addition-subtraction beyond the hundreds

Appendices

Appendix A:  Research-based teaching-learning paths

Appendix B:  Assessment templates — Use for individual child, tracking progress over time

Appendix C:  Assessment templates — Use for whole class, tracking outcomes of a particular lesson or activity