Descripciones mejoradas de Syndetics:

The new eighth edition of this successful book presents the tools to help children learn mathematical concepts and skills while utilizing important problem-solving techniques. In the process, it challenges the readers and further stimulates their interest in mathematics. The book is built around three main themes: helping children make sense of mathematics, incorporating field-experiences, and emphasizing major ideas detailed in the National Council of Teachers of Mathematics Principles and Standards for School Mathematics.

Tabla de contenidos provista por Syndetics

• Chapter 1 School Mathematics in a Changing World(p. 1)
• Introduction
• Focus Questions
• What Is Mathematics?(p. 2)
• What Determines the Mathematics Being Taught?(p. 3)
• Needs of the Subject(p. 3)
• Needs of the Child(p. 5)
• Needs of Society(p. 7)
• Your Role(p. 8)
• Where Can You Turn?(p. 9)
• National Guidelines for School Mathematics(p. 9)
• State and Local Guidelines(p. 9)
• Research(p. 9)
• Cultural and International Resources(p. 9)
• History(p. 10)
• Textbooks and Other Materials(p. 10)
• Electronic Materials(p. 11)
• Professional Organizations(p. 11)
• Professional Development(p. 12)
• Other Teachers(p. 12)
• What Is Your Role Now?(p. 12)
• A Glance at Where We've Been
• Things to Do: From What You've Read
• Things to Do: Going Beyond This Book
• Annotated Resources
• Chapter 2 Helping Children Learn Mathematics with Understanding(p. 15)
• Snapshot of a Lesson
• Introduction
• Focus Questions
• How Can We Support the Diverse Learners in Our Classrooms?(p. 16)
• Creating a Positive Learning Environment(p. 17)
• Avoiding Negative Experiences that Increase Anxiety(p. 18)
• Establishing Clear Expectations(p. 19)
• Treating All Students as Equally Likely to Have Aptitude for Mathematics(p. 19)
• Helping Students Improve Their Ability to Retain Mathematical Knowledge and Skills(p. 20)
• How Can We Help Children Acquire Both Procedural Knowledge and Conceptual Knowledge?(p. 21)
• In the Classroom 2-1 Different Kinds of Four-sided Figures(p. 22)
• How Do Children Learn Mathematics?(p. 22)
• Building Behavior(p. 23)
• Constructing Understanding(p. 25)
• How Can We Help Children Make Sense of Mathematics?(p. 27)
• In the Classroom 2-2 Patterns with Blocks(p. 29)
• Recommendation 1 Teach to the Developmental Characteristics of Students(p. 27)
• Recommendation 2 Actively Involve Students(p. 29)
• Recommendation 3 Move Learning from Concrete to Abstract(p. 31)
• Recommendation 4 Use Communication to Encourage Understanding(p. 32)
• A Glance at Where We've Been
• Things to Do: From What You've Read
• Things to Do: Going Beyond This Book
• Book Nook for Children
• Annotated Resources
• Chapter 3 Planning and Teaching(p. 37)
• Snapshot of a Lesson
• Introduction
• Focus Questions
• Preparing to Teach: Questions to Ask Before Planning Begins(p. 39)
• In the Classroom 3-1 Place Value(p. 41)
• Do I Understand the Mathematics I Am Teaching?(p. 39)
• What Are the Developmental Characteristics of My Students?(p. 40)
• What Do My Students Already Know?(p. 40)
• What Kinds of Tasks Will I Give My Students?(p. 42)
• How Will I Encourage My Students to Talk, What Kinds of Questions Will I Ask, and How Will I Group My Students?(p. 44)
• What Materials Will My Students and I Use?(p. 46)
• Planning for Effective Teaching(p. 51)
• The Importance of Planning(p. 51)
• Levels of Planning(p. 52)
• Planning Different Types of Lessons(p. 52)
• Meeting the Needs of All Students(p. 59)
• Assessment and Analysis in Planning(p. 62)
• A Glance at Where We've Been
• Things to Do: From What You've Read
• Things to Do: Going Beyond This Book
• Book Nook for Children
• Annotated Resources
• Chapter 4 Assessment: Enhanced Learning and Teaching(p. 68)
• Snapshot of a Lesson
• Introduction
• Focus Questions
• Assessment of Learning: Summative Assessment(p. 70)
• Assessment for Learning: Formative Assessment(p. 73)
• Phases of Assessment(p. 73)
• Making Instructional Decisions(p. 74)
• Monitoring Student Progress(p. 74)
• Evaluating Student Achievement(p. 75)
• Ways to Assess Students' Abilities and Dispositions(p. 75)
• In the Classroom 4-1 Primary Interview on Place Value(p. 80)
• Observation(p. 77)
• Questioning(p. 78)
• Interviewing(p. 78)
• Performance Tasks(p. 81)
• Self-Assessment and Peer Assessment(p. 82)
• Work Samples(p. 84)
• Portfolios(p. 84)
• Writings(p. 86)
• Teacher-Designed Written Tests(p. 87)
• Standardized Achievement Tests(p. 88)
• Keeping Records and Communicating about Assessments(p. 89)
• Recording the Information(p. 89)
• Communicating the Information(p. 91)
• Cultural Connections(p. 93)
• A Glance at Where We've Been
• Things to Do: From What You've Read
• Things to Do: Going Beyond This Book
• Book Nook for Children
• Annotated Resources
• Chapter 5 Processes of Doing Mathematics(p. 97)
• Snapshot of a Lesson
• Introduction
• Focus Questions
• Problem Solving(p. 99)
• In the Classroom 5-1 Rolling the Dice(p. 101)
• Reasoning and Proof(p. 104)
• Reasoning Is About Making Generalizations(p. 106)
• Reasoning Leads to a Web of Generalizations(p. 106)
• Reasoning Leads to Mathematical Memory Built on Relationships(p. 106)
• Learning through Reasoning Requires Making Mistakes and Learning from Them(p. 107)
• Communication(p. 107)
• Connections(p. 109)
• Representations(p. 111)
• Creating and Using Representations(p. 112)
• Selecting, Applying, and Translating Among Representations(p. 112)
• Using Representations to Model and Interpret Phenomena(p. 113)
• Cultural Connections(p. 113)
• A Glance at Where We've Been
• Things to Do: From What You've Read
• Things to Do: Going Beyond This Book
• Book Nook for Children
• Annotated Resources
• Chapter 6 Helping Children with Problem Solving(p. 119)
• Snapshot of a Lesson
• Introduction
• Focus Questions
• What Is a Problem and What Is Problem Solving?(p. 121)
• Teaching Mathematics through Problem Solving(p. 123)
• In the Classroom 6-1 Which Rectangle Is Biggest?(p. 128)
• Factors for Success in Problem Solving(p. 124)
• Choosing Appropriate Problems(p. 125)
• Finding Problems(p. 129)
• Having Students Pose Problems(p. 130)
• Using Calculators and Computers(p. 131)
• Strategies for Problem Solving(p. 132)
• Act It Out(p. 133)
• Make a Drawing or Diagram(p. 134)
• Look for a Pattern(p. 135)
• Construct a Table(p. 136)
• Guess and Check(p. 136)
• Work Backward(p. 137)
• Solve a Similar but Simpler Problem(p. 137)
• In the Classroom 6-2 Solve A Similar But Simpler Problem(p. 138)
• The Importance of Looking Back(p. 139)
• Looking Back at the Problem(p. 140)
• Looking Back at the Answer(p. 140)
• Looking Back at the Solution Process(p. 140)
• Looking Back at One's Own Thinking(p. 140)
• Helping All Students with Problem Solving(p. 141)
• Managing Time(p. 141)
• Managing Classroom Routines(p. 141)
• Managing Student Needs(p. 141)
• Cultural Connections(p. 143)
• A Glance at Where We've Been
• Things to Do: From What You've Read
• Things to Do: Going Beyond This Book
• Book Nook for Children
• Annotated Resources
• Chapter 7 Counting and Number Sense in Early Childhood and Primary Grades(p. 149)
• Snapshot of a Lesson
• Number Sense
• Focus Questions
• Prenumber Concepts(p. 153)
• In the Classroom 7-1 Who Am I?(p. 154)
• In the Classroom 7-2 Alike-and-Difference Trains(p. 155)
• Classification(p. 153)
• Patterns(p. 156)
• Comparisons(p. 157)
• Early Number Development(p. 158)
• Conservation(p. 158)
• Group Recognition(p. 159)
• Counting(p. 160)
• In the Classroom 7-3 Numbers on a Calendar(p. 163)
• In the Classroom 7-4 Counting on ... and on ... and on(p. 164)
• In the Classroom 7-5 Counting on and Back(p. 165)
• In the Classroom 7-6 Hunting for Numbers(p. 165)
• In the Classroom 7-7 Skip Counting(p. 166)
• Counting Principles(p. 160)
• Counting Stages(p. 161)
• Counting Strategies(p. 163)
• Counting Practice(p. 166)
• Developing Number Benchmarks(p. 167)
• Making Connections(p. 167)
• Cardinal, Ordinal, and Nominal Numbers(p. 170)
• Writing Numerals(p. 171)
• Cultural Connections(p. 172)
• A Glance at Where We've Been
• Things to Do: From What You've Read
• Things to Do: Going Beyond This Book
• Book Nook for Children
• Annotated Resources
• Chapter 8 Extending Number Sense: Place Value(p. 177)
• Snapshot of a Lesson
• Introduction
• Focus Questions
• Our Numeration System(p. 179)
• Nature of Place Value(p. 180)
• Modeling-Ungrouped and Pregrouped(p. 181)
• Modeling-Proportional and Nonproportional(p. 181)
• Grouping or Trading(p. 183)
• Beginning Place Value (Early Childhood)(p. 183)
• A Place to Start(p. 183)
• In the Classroom 8-1 Using A Hundred Chart(p. 186)
• In the Classroom 8-2 What's in a Score?(p. 187)
• Extending Place Value(p. 188)
• In the Classroom 8-3 Counting by Hundreds(p. 191)
• Counting and Patterns(p. 190)
• Regrouping and Renaming(p. 192)
• Reading and Writing Numbers(p. 193)
• In the Classroom 8-4 The Power of 10 on the Thousand Chart(p. 193)
• Rounding(p. 196)
• Cultural Connections(p. 198)
• A Glance at Where We've Been
• Things to Do: From What You've Read
• Things to Do: Going Beyond This Book
• Book Nook for Children
• Annotated Resources
• Chapter 9 Operations: Meanings and Basic Facts(p. 203)
• Snapshot of a Lesson
• Introduction
• Focus Questions
• Helping Children Develop Number Sense and Computational Fluency(p. 205)
• Facility with Counting(p. 206)
• Experience with a Variety of Concrete Situations(p. 207)
• Familiarity with Many Problem Contexts(p. 207)
• Experience in Talking and Writing about Mathematical Ideas(p. 207)
• Developing Meanings for the Operations(p. 208)
• Addition and Subtraction(p. 208)
• Multiplication and Division(p. 209)
• In the Classroom 9-1 Rectangles and More Rectangles(p. 211)
• Mathematical Properties(p. 212)
• Overview of Basic Fact Instruction(p. 213)
• Start Where the Children Are(p. 214)
• Build Understanding of the Basic Facts(p. 215)
• Focus on How to Remember Facts(p. 215)
• In the Classroom 9-2 Games for Practicing Basic Facts(p. 217)
• Thinking Strategies for Basic Facts(p. 218)
• Thinking Strategies for Addition Facts(p. 218)
• Thinking Strategies for Substraction Facts(p. 222)
• Thinking Strategies for Multiplication Facts(p. 223)
• Thinking Strategies for Division Facts(p. 226)
• Cultural Connections(p. 229)
• A Glance at Where We've Been
• Things to Do: From What You've Read
• Things to Do: Going Beyond This Book
• Book Nook for Children
• Annotated Resources
• Chapter 10 Computation Methods: Calculators, Mental Computation, and Estimation(p. 233)
• Snapshot of a Lesson
• Introduction
• Focus Questions
• Balancing Your Instruction(p. 236)
• Calculators(p. 237)
• In the Classroom 10-1 Calculators Versus Mental Computation-When to Use Which(p. 239)
• Using Calculators Requires Thinking(p. 238)
• Using Calculators Can Raise Student Achievement(p. 238)
• Calculators Are Not Always the Fastest Way of Doing Computations(p. 238)
• Calculators Are Useful for More Than Just Doing Computations(p. 239)
• Mental Computation(p. 240)
• Strategies and Techniques for Mental Computation(p. 240)
• Encouraging Mental Computation(p. 242)
• In the Classroom 10-2 How Would You do it (Whole Numbers)?(p. 244)
• In the Classroom 10-3 How Would You do it (Fractions)?(p. 244)
• Estimation(p. 245)
• Front-End Estimation(p. 247)
• Adjusting(p. 247)
• In the Classroom 10-4 Front-End Estimation(p. 248)
• Compatible Numbers(p. 248)
• Flexible Rounding(p. 249)
• Clustering(p. 251)
• Choosing Estimation Strategies(p. 251)
• Cultural Connections(p. 252)
• A Glance at Where We've Been
• Things to Do: From What You've Read
• Things to Do: Going Beyond This Book
• Book Nook for Children
• Annotated Resources
• Chapter 11 Standard and Alternative Computational Algorithms(p. 257)
• Snapshot of a Lesson
• Introduction
• Focus Questions
• Teaching Algorithms with Understanding(p. 259)
• Using Materials(p. 260)
• Using Place Value(p. 260)
• Addition(p. 260)
• In the Classroom 11-1 Capture 5(p. 262)
• In the Classroom 11-2 Starters(p. 264)
• Standard Addition Algorithm(p. 263)
• Partial-Sum Addition Algorithm(p. 263)
• Higher-Decade Addition(p. 265)
• Subtraction(p. 265)
• In the Classroom 11-3 Look for Patterns(p. 265)
• In the Classroom 11-4 Racing with Base-Ten Blocks(p. 267)
• Standard Subtraction Algorithm(p. 265)
• Partial-Difference Subtraction Algorithm(p. 268)
• Multiplication(p. 269)
• In the Classroom 11-5 What's Missing?(p. 270)
• Multiplication with One-Digit Multipliers(p. 269)
• Multiplication by 10 and Multiples of 10(p. 270)
• Multiplication with Zeros(p. 271)
• Multiplication with Two-Digit Multipliers(p. 271)
• Multiplication with Large Numbers(p. 272)
• Division(p. 272)
• In the Classroom 11-6 The Missing Digits Game(p. 276)
• In the Classroom 11-7 Making Examples(p. 276)
• In the Classroom 11-8 Easy Does It!(p. 277)
• Division with One-Digit Divisors(p. 273)
• Division with Two-Digit Divisors(p. 277)
• Making Sense of Division with Remainders(p. 277)
• Checking(p. 278)
• In the Classroom 11-9 The Remainder Game (For 2 to 4 Players)(p. 278)
• Choosing Appropriate Methods(p. 279)
• Building Computational Proficiency(p. 279)
• In the Classroom 11-10 What Number Am I!(p. 280)
• Cultural Connections(p. 279)
• A Glance at Where We've Been
• Things to Do: From What You've Read
• Things to Do: Going Beyond This Book
• Book Nook for Children
• Annotated Resources
• Chapter 12 Fractions and Decimals: Meanings and Operations(p. 286)
• Snapshot of a Lesson
• Introduction
• Focus Questions
• Conceptual Development of Fractions(p. 288)
• In the Classroom 12-1 Three-Fourths(p. 292)
• In the Classroom 12-2 Fraction Bars(p. 293)
• In the Classroom 12-3 Sharing Rods(p. 293)
• In the Classroom 12-4 Comparing Models(p. 296)
• In the Classroom 12-5 Can You Divide It?(p. 298)
• In the Classroom 12-6 Whole Hog(p. 299)
• Three Meanings of Fractions(p. 289)
• Models of the Part-Whole Meaning(p. 290)
• Making Sense of Fractions(p. 291)
• Ordering Fractions and Equivalent Fractions(p. 295)
• Benchmarks(p. 299)
• Mixed Numbers and Improper Fractions(p. 299)
• Operations with Fractions(p. 300)
• Addition and Subtraction(p. 300)
• Multiplication(p. 302)
• Division(p. 304)
• Conceptual Development of Decimals(p. 305)
• In the Classroom 12-7 A New Twist on Old Rhymes(p. 305)
• In the Classroom 12-8 Can You Beat the Toss?(p. 306)
• Relationship to Common Fractions(p. 306)
• Relationship to Place Value(p. 307)
• Ordering and Rounding Decimals(p. 308)
• Operations with Decimals(p. 309)
• In the Classroom 12-9 What's Your Answer?(p. 309)
• Addition and Subtraction(p. 309)
• Multiplication and Division(p. 309)
• In the Classroom 12-10 Plug-in Puzzles(p. 311)
• Cultural Connections(p. 311)
• A Glance at Where We've Been
• Things to Do: From What You've Read
• Things to Do: Going Beyond This Book
• Book Nook for Children
• Annotated Resources
• Chapter 13 Ratio, Proportion, and Percent: Meanings and Applications(p. 315)
• Snapshot of a Lesson
• Introduction
• Focus Questions
• Ratios(p. 318)
• In the Classroom 13-1 Know Your Coins(p. 319)
• Proportions(p. 320)
• Percents(p. 325)
• In the Classroom 13-2 Using Percents(p. 328)
• In the Classroom 13-3 Estimating Percents(p. 329)
• Understanding Percents(p. 326)
• Applying Percents(p. 329)
• Cultural Connections(p. 331)
• A Glance at Where We've Been
• Things to Do: From What You've Read
• Things to Do: Going Beyond This Book
• Book Nook for Children
• Annotated Resources
• Chapter 14 Algebraic Thinking(p. 335)
• Snapshot of a Lesson
• Introduction
• Focus Questions
• Problems, Patterns, and Relations(p. 338)
• In the Classroom 14-1 Thinking About Patterns(p. 339)
• Problems(p. 338)
• Patterns(p. 338)
• Relations(p. 340)
• In the Classroom 14-2 Balance Me(p. 341)
• Language and Symbols of Algebra(p. 342)
• In the Classroom 14-3 In-Out Machine(p. 343)
• Equality and Inequality(p. 342)
• Variables(p. 344)
• Expressions and Equations(p. 344)
• Modeling, Generalizing, and Justifying(p. 344)
• In the Classroom 14-4 Painting Cubes(p. 348)
• In the Classroom 14-5 From a Rule to a Graph(p. 351)
• Routine Problems(p. 344)
• Patterns and Pattern Problems(p. 346)
• Nonroutine Problems(p. 348)
• Functions(p. 349)
• Properties of Numbers and Number Theory(p. 351)
• Cultural Connections(p. 354)
• A Glance at Where We've Been
• Things to Do: From What You've Read
• Things to Do: Going Beyond This Book
• Book Nook for Children
• Annotated Resources
• Chapter 15 Geometry(p. 358)
• Snapshot of a Lesson
• Introduction
• Focus Questions
• Properties of Two- and Three-Dimensional Shapes(p. 361)
• In the Classroom 15-1 Solid Mystery(p. 365)
• In the Classroom 15-2 What Can You Discover?(p. 366)
• In the Classroom 15-3 Gumdrops and Toothpicks(p. 367)
• In the Classroom 15-4 Build Your Own Pyramid(p. 368)
• In the Classroom 15-5 Find Me(p. 368)
• In the Classroom 15-6 Less is Best (A Game for Two or More)(p. 370)
• In the Classroom 15-7 How Many Lines?(p. 371)
• In the Classroom 15-8 Show My Sides(p. 371)
• In the Classroom 15-9 How Many Degrees in a Quadrilateral?(p. 372)
• In the Classroom 15-10 Piezles(p. 373)
• In the Classroom 15-11 What's My Altitude?(p. 374)
• In the Classroom 15-12 Classify Me(p. 375)
• In the Classroom 15-13 Can You Find It?(p. 375)
• Three-Dimensional Shapes(p. 362)
• Two-Dimensional Shapes(p. 368)
• Locations and Spatial Relationships(p. 376)
• In the Classroom 15-14 Shapes on a Grid(p. 377)
• Transformations(p. 378)
• Visualization and Spatial Reasoning(p. 379)
• In the Classroom 15-15 Shape Maker(p. 380)
• Using Geometric Instructional Tools(p. 379)
• Using Mental Images(p. 380)
• Cultural Connections(p. 381)
• A Glance at Where We've Been
• Things to Do: From What You've Read
• Things to Do: Going Beyond This Book
• Book Nook for Children
• Annotated Resources
• Chapter 16 Measurement(p. 386)
• Snapshot of a Lesson
• Introduction
• Focus Questions
• The Measurement Process(p. 390)
• In the Classroom 16-1 Perceptual Comparison of Lengths(p. 391)
• In the Classroom 16-2 Direct Comparison of Length(p. 391)
• In the Classroom 16-3 Indirect Comparison of Length(p. 392)
• In the Classroom 16-4 Comparing Height and Circumference(p. 393)
• In the Classroom 16-5 Are We the Same Size?(p. 395)
• In the Classroom 16-6 Measuring Length with Arbitrary Units(p. 397)
• In the Classroom 16-7 Make Your Own(p. 401)
• In the Classroom 16-8 Breaking up is not Hard to Do(p. 403)
• Identifying Attributes(p. 390)
• Choosing a Unit(p. 396)
• Comparing an Object to a Unit and Finding the Number of Units(p. 398)
• Reporting Measurements(p. 403)
• Comparing Measurements(p. 404)
• In the Classroom 16-9 Solving Conversion Problems with Square Units(p. 405)
• Equivalences(p. 404)
• Conversions(p. 405)
• Estimating Measurements(p. 406)
• Connecting Attributes(p. 407)
• In the Classroom 16-10 Estimating Measurements(p. 407)
• In the Classroom 16-11 With My Area, I Can Change My Shape!(p. 408)
• Area and Shape(p. 408)
• Volume and Shape(p. 408)
• Perimeter and Area(p. 408)
• Volume and Surface Area(p. 409)
• In the Classroom 16-12 Same Volume, Different Shape(p. 409)
• In the Classroom 16-13 Do you Know How to Connect Perimeter and Area?(p. 409)
• In the Classroom 16-14 What is the Connection Between Volume and Area?(p. 410)
• Cultural Connections(p. 409)
• A Glance at Where We've Been
• Things to Do: From What You've Read
• Things to Do: Going Beyond This Book
• Book Nook for Children
• Annotated Resources
• Chapter 17 Data Analysis, Statistics, and Probability(p. 414)
• Snapshot of a Lesson
• Introduction
• Focus Questions
• Data Analysis(p. 418)
• In the Classroom 17-1 Let's Find Out(p. 418)
• Posing a Question and Collecting Data(p. 418)
• Surveys(p. 418)
• Experiments(p. 419)
• Simulations(p. 419)
• Displaying Data(p. 419)
• In the Classroom 17-2 Sharing Data(p. 426)
• Quick and Easy Graphing Methods(p. 420)
• Plots(p. 421)
• Picture Graphs(p. 423)
• Bar Graphs(p. 424)
• Histograms(p. 424)
• Pie Graphs(p. 424)
• Line Graphs(p. 426)
• Graphical Roundup(p. 426)
• Analyzing and Communicating Results(p. 428)
• Data Sense(p. 428)
• Analysis(p. 428)
• Misleading Graphs(p. 428)
• Communicating Results(p. 429)
• Descriptive Statistics(p. 430)
• In the Classroom 17-3 Peanuts(p. 434)
• Measure of Variation: Range(p. 430)
• Measures of Central Tendency or Averages(p. 430)
• Choosing Averages(p. 433)
• Probability(p. 435)
• In the Classroom 17-4 What's the Average?(p. 435)
• In the Classroom 17-5 What are the Chances?(p. 436)
• In the Classroom 17-6 What's More Likely?(p. 437)
• In the Classroom 17-7 What's the Probability?(p. 439)
• In the Classroom 17-8 Rolling and Recording(p. 439)
• In the Classroom 17-9 Are you a Winner?(p. 440)
• In the Classroom 17-10 Can you Make Predictions?(p. 441)
• Probability of an Event(p. 436)
• Randomness(p. 440)
• Independence of Events(p. 440)
• Misconceptions about Probability(p. 442)
• Cultural Connections(p. 442)
• A Glance at Where We've Been
• Things to Do: From What You've Read
• Things to Do: Going Beyond This Book
• Book Nook for Children
• Annotated Resources
• References(p. 447)
• Appendix A Standards and Expectations, National Council of Teachers of Mathematics, 2000(p. 463)
• Index(p. 471)
• Appendix B Masters

Notas de autor provistas por Syndetics

Robert E. Reys is currently Professor of Math Education at the University of Missouri.  He received his B.S. in Education and his M.A. in Mathematics, both from Central Missouri State University.  He also received his Ed.D. in Mathematics Education from the University of Missouri.  Reys has been on the University of Missouri faculty since 1966. He has taught numerous undergraduate and graduate mathematics education courses and has served as advisor for more than 400 secondary mathematics majors, 100 MEd and 30 PhD students in mathematics education. Reys has also served as visiting professor at the University of Georgia, Fulbright Research/Lecturer in Mexico during 1989-90); University of Tsukuba (Japan; 1991-92) and a Fulbright Research/Lecturer in Sweden (1995). He was a visiting summer professor at the University of Saskatchewan (Canada) and the University of Regina (Canada). During the last ten years Reys has conducted workshops and seminars for teachers/researchers on mathematical topics from elementary to secondary school throughout the United States, and several countries including Australia, Canada, Cyprus, England, Germany, Hungary, Italy, Japan, Mexico, Panama, Philippines, Puerto Rico, Sweden, Taiwan and Yemen.