Demystify Math, Science, and Technology: Creativity, Innovation, and Problem-Solving

Dennis Adams e Mary Hamm

R&L Education | 2013 -2ª edição | 161 páginas | rar - pdf | 921 kb

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In a rapidly evolving local and global economy, skills related to mathematical problem solving, scientific inquiry, and technological innovation are becoming more critical for success in and out of school. Thus, Demystify Math, Science, and Technology addresses the need to cultivate these skills in young students so that ingenuity, teamwork, and imaginative skills become part of their arsenal in dealing with real world challenges. This whole package of attributes is essential for learners imagining new scenarios and future work in areas that don't even exist yet. Another important issue is that teachers now deal with students who span the entire spectrum of learning. Students differ widely in levels of preparedness, personal interests, and cultural ways of seeing and experiencing the world. One size does not fit all. Teachers need to learn to turn diversity into an advantage because innovation builds on the social nature of learning; the more diverse the inputs, the more interesting the outputs. The authors also believe that no one should be sidelined with basic skill training in a way that keeps them away from the creative and collaborative engagement associated with problem solving, inquiry, and the technological products of math and science.

Contents
Preface v
1 Creativity, Innovation, and Differentiation: Problem
Solving and Inquiry with Math, Science, and Technology 1
2 Creative and Innovative Thinking: Differentiated Inquiry, Open-Ended Problem Solving, and Innovation 27
3 Mathematics: Problem Solving, Collaboration, Creativity, and Communication 57
4 Science: Inquiry, Differentiation, Innovation, and the Future 85
5 Technology and Education: Powerful Tools for Encouraging Creativity and Innovation 115

About the Authors 151

Problem Posing: Reflections and Applications

 Stephen I. Brown e Marion I. Walter

Psychology Press |1993 |355 páginas | rar - pdf | 14,88 Mb

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As a result of the editors' collaborative teaching at Harvard in the late 1960s, they produced a ground-breaking work -- The Art Of Problem Posing -- which related problem posing strategies to the already popular activity of problem solving. It took the concept of problem posing and created strategies for engaging in that activity as a central theme in mathematics education. 

Based in part upon that work and also upon a number of articles by its authors, other members of the mathematics education community began to apply and expand upon their ideas. This collection of thirty readings is a testimony to the power of the ideas that originally appeared. In addition to reproducing relevant materials, the editors of this book of readings have included a considerable amount of interpretive text which places the articles in the context of problem solving. While the preponderance of essays focus upon mathematics and mathematics education, some of them point to the relevance of problem posing to other fields such as biology or psychology. In the interpretive text that accompanies each chapter, they indicate how ideas expressed for one audience may be revisited or transformed in order to ready them for a variety of audiences.


Contents
PREFACE ix
INTRODUCTION xili
Reflections on the Power of Problem Posing xiv
On the Audience for the Book xv
A Note on Reading the Collection xvi
A Caveat of Sorts xvii
CHAPTER I. REFLECTIONS INTRODUCTORY COMMENTS 1
SECTION 1: PEDAGOGICAL FOCUS: THE DESIGN OF A COURSE 
EDITORS' COMMENTS 3
ESSAYS
1. In the Classroom: Student as Author and Critic Stephen I. Brown and Marion I. Walter 7
2. Problem Posing in Mathematics Education Stephen I. Brown and Marion I. Walter 16
SECTION 2: ELABORATIONS AND APPLICATIONS OF PROBLEM POSING SCHEMES
EDITORS' COMMENTS 28

ESSAYS:
3. On Building Curriculum Materials That Foster Problem Posing, E. Paul Goldenberg 31
4. Removing the Shackles of Euclid: 8: "Strategies", David S. Fielker 39
5. "What if Not?" A Technique for Involving and Motivating Students in Psychology Courses, Werner Feibel 52
SECTION 3: RATIONALE: TOWARDS A MULTIPLISTIC VIEW OF THE WORLD
EDITORS' COMMENTS 59
ESSAYS:
6. A Problem Posing Approach to Biology Education, John R. Jungck 64
7. An Experience with Some Able Women Who Avoid Mathematics, Dorothy Buerk 70
8. The Invisible Hand Operating in Mathematics Instruction: Student's Conceptions and Expectations, Raffaella Borasi 83
9. The Logic of Problem Generation: From Morality and Solving to De-Posing and Rebellion, Stephen I. Brown 92
10. Vice into Virtue, or Seven Deadly Sins of Education Redeemed, Israel Scheffler 104
CHAPTER II. ALGEBRA AND ARITHMETIC 117
INTRODUCTORY COMMENTS
SECTION 1: ASKING WHY
EDITORS' COMMENTS 118
ESSAYS:
11. Number Sense and the Importance of Asking "Why?" David J. Whitin 121
12. Creating Number Problems, Marian Small 130
13. Making Your Own Rules, Dan Brutlag 134
14. 1089: An Example of Generating Problems, Rick N. Blake 141
SECTION 2: MISTAKES
EDITORS' COMMENTS 152
ESSAYS:
15. Mathematical Mistakes, Lawrence Nils Meyerson 153
16. Algebraic Explorations of the Error  Raffaella Borasi
SECTION 3: TINKERING WITH WHAT HAS BEEN TAKEN FOR GRANTED
EDITORS' COMMENTS 164
ESSAYS:
17. Problem Stories: A New Twist on Problem Posing, William S. Bush and Ann Fiala 167
18. How to Create Problems, Stephen I. Brown 174
19. Beyond Problem Solving: Problem Posing, Barbara M. Moses, Elizabeth Bjork, and E. Paul Goldenberg 178
20. Mathematical Investigations: Description, Rationale, and Example, Barry V. Kissane 189
21. Curriculum Topics Through Problem Posing, Marion Walter 204
22. Is the Graph of y = cx Straight? Alex Friedlander and Tommy Dreyfus 204
SECTION 4: YOUR TURN
EDITORS' COMMENTS 220
ESSAY:
23. Because a Door Has To Be Open or Closed, An Intriguing Problem Solved by Some Inductive Exploration, Charles Cassidy and Bernard R. Hodgson 222
CHAPTER III. GEOMETRY: EDITORS' COMMENTS 229
INTRODUCTORY COMMENTS
SECTION 1: LOOKING BACK
EDITORS' COMMENTS 231
ESSAYS:
24. The Looking-Back Step in Problem Solving, Larry Sowder 235
25. Reopening the Equilateral Triangle Problem: What Happens If . . . , Douglas L Jones and Kenneth L Shaw 240
26. Mathematics and Humanistic Themes: Sum Considerations, Stephen I. Brown 249
SECTION 2: THE INTERTWINE OF PROBLEM POSING AND PROBLEM SOLVING 
EDITORS' COMMENTS 279
ESSAYS:
27. Problem Posing in Geometry, Larry Hoehn 281
28. Students Microcomputer-Aided Exploration in Geometry, Daniel Chazan 289
SECTION 3: SOMETHING COMES FROM NOTHING
EDITORS' COMMENTS
ESSAY:
29. Generating Problems From Almost Anything, Marion Walter
SECTION 4: YOUR TURN
EDITORS' COMMENTS
ESSAY:
30. A Non-Simply Connected Geoboard-Based on the Not" Idea, Philip A. Schmidt
AUTHOR INDEX
SUBJECT INDEX
NOTES ON CONTRIBUTORS

Outro livro dos mesmo editores

The art of problem posing por Stephen I Brown; Marion I Walter Idioma: Inglês   Editora: Mahwah, N.J. : Lawrence Erlbaum, 2005.

Problem Solving and Comprehension

Arthur Whimbey, Jack Lochhead, e Ron Narode

 Routledge |  2013 - 7.ª edição | 441 páginas | rar - pdf | 948 kb

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pdf - 6,8 Mb - link

6.ª edição - 1999

This popular book shows students how to increase their power to analyze problems and comprehend what they read using the Think Aloud Pair Problem Solving [TAPPS] method. First it outlines and illustrates the method that good problem solvers use in attacking complex ideas. Then it provides practice in applying this method to a variety of comprehension and reasoning questions, presented in easy-to-follow steps. As students work through the book they will see a steady improvement in their analytical thinking skills and become smarter, more effective, and more confident problem solvers. Not only can using the TAPPS method assist students in achieving higher scores on tests commonly used for college and job selection, it teaches that problem solving can be fun and social, and that intelligence can be taught.

Changes in the Seventh Edition: New chapter on "open-ended" problem solving that includes inductive and deductive reasoning; extended recommendations to teachers, parents, and tutors about how to use TAPPS instructionally; Companion Website with PowerPoint slides, reading lists with links, and additional problems.

CONTENTS

Preface to the Seventh Edition ix

Preface to the Sixth Edition xi

1. Test Your Mind—See How It Works 1

2. Errors in Reasoning 11

3. Problem-Solving Methods 21

4. Verbal Reasoning Problems 43

5. Six Myths About Reading 139

6 Analogies 143

7. Writing Relationship Sentences 157

8. How to Form Analogies 173

9. Analysis of Trends and Patterns 195

10. Deductive and Hypothetical Thinking Through Days of the Week 223

11. Solving Mathematical Word Problems 241

12. Open-Ended Problem Solving 335

13. The Post-WASI Test 356

14. Meeting Academic and Workplace Standards: How This Book Can Help 364

15. How to Use Pair Problem Solving: Advice for Teachers, Parents, Tutors, and Helpers of All Sorts 383

Appendix 1. Answer Key 400

Appendix 2. Compute Your Own IQ 420

References 421

Second Handbook of Research on Mathematics Teaching and Learning

Frank K. Jr. Lester

Information Age Publishing | 2007 | 1381 páginas | rar - pdf | 11,4 Mb

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The audience remains much the same as for the 1992 Handbook, namely, mathematics education researchers and other scholars conducting work in mathematics education. This group includes college and university faculty, graduate students, investigators in research and development centers, and staff members at federal, state, and local agencies that conduct and use research within the discipline of mathematics.
The intent of the authors of this volume is to provide useful perspectives as well as pertinent information for conducting investigations that are informed by previous work. The Handbook should also be a useful textbook for graduate research seminars. In addition to the audience mentioned above, the present Handbook contains chapters that should be relevant to four other groups: teacher educators, curriculum developers, state and national policy makers, and test developers and others involved with assessment.

Taken as a whole, the chapters reflects the mathematics education research community's willingness to accept the challenge of helping the public understand what mathematics education research is all about and what the relevance of their research fi ndings might be for those outside their immediate community.
The intent of the authors of this volume is to provide useful perspectives as well as pertinent information for conducting investigations that are informed by previous work. The Handbook should also be a useful textbook for graduate research seminars. In addition to the audience mentioned above, the present Handbook contains chapters that should be relevant to four other groups: teacher educators, curriculum developers, state and national policy makers, and test developers and others involved with assessment.
Taken as a whole, the chapters reflects the mathematics education research community's willingness to accept the challenge of helping the public understand what mathematics education research is all about and what the relevance of their research fi ndings might be for those outside their immediate community.
Taken as a whole, the chapters reflects the mathematics education research community's willingness to accept the challenge of helping the public understand what mathematics education research is all about and what the relevance of their research fi ndings might be for those outside their immediate community. 

CONTENTS

Preface. 
Acknowledgements.
Part I: Foundations. 
Putting Philosophy to Work: Coping With Multiple Theoretical Perspectives, Paul Cobb.
Theory in Mathematics Education Scholarship, Edward A. Silver & Patricio G. Herbst
Method, Alan H. Schoenfeld. 
Part II: Teachers and Teaching. 
Assessing Teachers' Mathematical Knowledge: What Knowledge Matters and What Evidence Counts? Heather C. Hill, Laurie Sleep, Jennifer M. Lewis, & Deborah Loewenberg Ball. 
The Mathematical Education and Development of Teachers, Judith T. Sowder.
Understanding Teaching and Classroom Practice in Mathematics, Megan Loef Franke, Elham Kazemi and Daniel Battey. 
Mathematics Teachers' Beliefs and Affect, Randolph A. Philipp. 
Part III: Influences on Student Outcomes. 
How Curriculum Influences Student Learning, Mary Kay Stein, Janine Remillard and Margaret Smith. 
The Effects of Classroom Mathematics Teaching on Students' Learning, James S. Hiebert and Douglas A. Grouws. 
Culture, Race, Power, and Mathematics Education, Diversity in Mathematics Education Center for Learning and Teaching. 
The Role of Culture in Teaching and Learning Mathematics, Norma G. Presmeg. 
Part IV: Students and Learning. 
Early Childhood Mathematics Learning, Douglas H. Clements and Julie Sarama. 
Whole Number Concepts and Operations, Lieven Verschaffel, Brian Greer, and Erik DeCorte.
Rational Numbers and Proportional Reasoning: Toward a Theoretical Framework for Research, Susan J. Lamon. Early Algebra, David W. Carraher and Analucia D. Schliemann. 
Learning and Teaching of Algebra at the Middle School through College Levels: Building Meaning for Symbols and Their Manipulation, Carolyn Kieran. 
Problem Solving and Modeling, Richard Lesh and Judith Zawejewski. 
Toward Comprehensive Perspectives on the Learning and Teaching of Proof, Guershon Harel and Larry Sowder. 
The Development of Geometric and Spatial Thinking, Michael T. Battista. 
Research in Probability: Responding to Classroom Realities, Graham A. Jones, Cynthia W. Langrall and Edward S. Mooney. 
Research on Statistics Learning and Reasoning, J. Michael Shaughnessy. 
Mathematics Thinking and Learning at Post-secondary Level, Michele Artigue, Carmen Batanero and Phillip Kent. 
Part V: Assessment. 
Keeping Learning on Track: Classroom Assessment and the Regulation of Learning, Dylan Wiliam. 
High Stakes Testing in Mathematics, Linda Dager Wilson. 
Large-scale Assessment of Mathematics Education, Jan DeLange. 
Part VI: Issues and Perspectives. 
Issues in Access and Equity in Mathematics Education, Alan J. Bishop and Helen J. Forgasz. 
Research on Technology in Mathematics Education: The Perspective of Constructs, Rose Mary Zbiek, M. Kathleen Heid, Glendon Blume and Thomas P. Dick. 
Engineering Change in Mathematics Education: Research, Policy, and Practice, William F. Tate and Celia Rousseau. 
Educational Policy Research and Mathematics Education, Joan Ferrini-Mundy & Robert Floden. 
Mathematics Content Specification in the Age of Assessment, Norman L. Webb. 
Reflections on the State and Trends in Research on Mathematics Teaching and Learning: From Here to Utopia, Mogens Niss.

101 Activities for Teaching Creativity and Problem Solving

Arthur B. VanGundy

Pfeiffer | 2004 | 410 páginas | pdf | 3,7 Mb

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Employees who possess problem-solving skills are highly valued in today?s competitive business environment. The question is how can employees learn to deal in innovative ways with new data, methods, people, and technologies? In this groundbreaking book, Arthur VanGundy -- a pioneer in the field of idea generation and problem solving -- has compiled 101 group activities that combine to make a unique resource for trainers, facilitators, and human resource professionals. The book is filled with idea-generation activities that simultaneously teach the underlying problem-solving and creativity techniques involved. Each of the book?s 101 engaging and thought-provoking activities includes facilitator notes and advice on when and how to use the activity. Using 101 Activities for Teaching Creativity and Problem Solving will give you the information and tools you need to:

• Generate creative ideas to solve problems.
• Avoid patterned and negative thinking.
• Engage in activities that are guaranteed to spark ideas.
• Use proven techniques for brainstorming with groups.

Contents
Acknowledgments.

Getting Started.

Chapter 1: Creativity and Problem Solving.

Why Use Creativity Techniques?

Generating Creative Ideas.

Creativity Training in Organizations.

A Typology of Idea Generation Activities.

Chapter 2: Six Key Principles for Encouraging Creativity.

1. Separate Idea Generation from Evaluation.

2. Test Assumptions.

3. Avoid Patterned Thinking.

4. Create New Perspectives.

5. Minimize Negative Thinking.

6. Take Prudent Risks.

Chapter 3: Linking Problems, Solutions, and Activities.

Defining Problems.

Problem Solving.

Creativity and Serendipity.

A Few of My Favorite Activities.

A Guide for Selecting Activities.

How to Evaluate and Select Ideas in a Group.

Getting Ready: Different Uses Warm-Up Exercise.

Activity Selection Guide.

Individual and Group Activities.

Chapter 4: Basic Idea Generation: “No Brainers”.

1. Bend It, Shape It.

2. Brain Borrow.

3. Copy Cat.

4. Dead Head Deadline.

5. Get Crazy.

6. Idea Diary.

7. Mental Breakdown.

8. Music Mania.

9. Name Change.

10. Stereotype.

11. Switcheroo.

12. Wake-Up Call.

Chapter 5: Ticklers: Related and Unrelated Stimuli.

13. Excerpt Excitation.

14. Idea Shopping.

15. A Likely Story.

16. PICLed Brains.

17. Picture Tickler.

18. Rorschach Revisionist.

19. Say What?

20. Text Tickler.

21. Tickler Things.

Chapter 6: Combinations.

22. Bi-Wordal.

23. Circle of Opportunity.

24. Combo Chatter.

25. Ideas in a Box.

26. Ideatoons.

27. Mad Scientist.

28. Noun Action.

29. Noun Hounds.

30. Parts Is Parts.

31. Parts Purge.

32. Preppy Thoughts.

33. SAMM I Am.

34. 666.

35. Word Diamond.

Chapter 7: Free Association Activities: “Blue Skies”.

36. Brain Mapping.

37. Doodles.

38. Essence of the Problem.

39. Exaggerate That.

40. Fairy Tale Time.

41. Idea Links.

42. Imaginary Mentor.

43. Lotus Blossom.

44. Say Cheese.

45. Sense Making.

46. Skybridging.

47. Tabloid Tales.

48. We Have Met the Problem and It Is We.

49. What if . . . ?

Chapter 8: Grab Bag: Miscellaneous Activities.

Backward Activities.

50. Law Breaker.

51. Problem Reversals.

52. Turn Around.

Just Alike Only Different Activities.

53. Bionic Ideas.

54. Chain Alike.

55. I Like It Like That.

56. What Is It?

Group Only Activities.

Chapter 9: Brainstorming with Related Stimuli.

57. Be #1.

58. Blender.

59. Drawing Room.

60. Get Real!!

61. Idea Showers.

62. Modular Brainstorming.

63. Pass the Hat.

64. Phillips 66.

65. Play by Play.

66. Rice Storm.

67. Spin the Bottle.

68. Story Boards.

69. That’s the Ticket!

70. What’s the Problem?

Chapter 10: Brainstorming with Unrelated Stimuli.

71. Battle of the Sexes.

72. Best of. . . .

73. Brain Splitter.

74. Force-Fit Game.

75. Grab Bag Forced Association.

76. It’s Not My Job.

77. Rolestorming.

78. Roll Call.

79. Sculptures.

80. Super Heroes.

Chapter 11: Brainwriting with Related Stimuli.

81. As Easy As 6–3–5.

82. Brain Purge.

83. Group Not.

84. Idea Mixer.

85. Idea Pool.

86. Museum Madness.

87. Organizational Brainstorms.

88. Out-of-the-Blue Lightning Bolt Cloudbuster.

89. You’re a Card, Andy!

90. Your Slip Is Showing.

Chapter 12: Brainwriting with Unrelated Stimuli.

91. Altered States.

92. Balloon, Balloon, Balloon.

93. Bouncing Ball.

94. Brainsketching.

95. Doodlin’ Around the Block.

96. Greeting Cards.

97. The Name Game.

98. Pass the Buck.

99. Post It, Pardner!

100. Puzzle Pieces.

101. The Shirt Off Your Back.

References.

About the Author.

Pfeiffer Publications Guide.

Principles of Mathematical Problem Solving

Martin J. Erickson, Joe Flowers

(página de Martin Erickson : erickson.sites.truman.edu)

Pearson | 1998 | 252 Páginas | djvu | 3 Mb

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This book presents the principles and specific problem-solving methods that can be used to solve a variety of mathematical problems. The book provides clear examples of various problem-solving methods accompanied by numerous exercises and their solutions. Principles of Mathematical Problem Solving introduces and explains specific problem-solving methods (with examples), and gives a set of exercises and complete solutions for each method. The idea is that by studying the principles and applying them to the exercises, the reader will gain problem-solving ability as well as general mathematical insight. Eventually, the reader should be able to produce results that have "the whole air of intuition." Organized according to specific techniques in separate chapters, techniques include induction and the pigeonhole principle, among others. Arranged in order of increasing difficulty, the book presents a wide variety of problem sets designed to illustrate significant mathematical ideas. Each chapter also includes a moderate amount of the "theory" behind each problem-solving principle it presents. An essential resource for every student of mathematics and every professional who needs to solve mathematical problems.

Contents
Preface
1 Data
2 Direct and Indirect Reasoning
3 Contradiction
4 Induction
5 Specialization and Generalization
6 Symmetry
7 Parity
8 Various Moduli
9 Pigeonhole Principle
10 Two-Way Counting
11 Inclusion–Exclusion Principle
12 Algebra of Polynomials
13 Recurrence Relations and Generating Functions
14 Maxima and Minima
15 Means, Inequalities, and Convexity
16 Mean Value Theorems
17 Summation by Parts
18 Estimation
19 Deus Ex Machina
20 More Problems
Glossary
Bibliography

Outros livros de Martin J. Erickson:

Beautiful Mathematics
Aha! Solutions

50 Problem-Solving Lessons: The Best from 10 Years of Math Solutions Newsletters

Marilyn Burns

Math Solutions | 1996 | 192 páginas | PDF | 1,5 Mb

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For many years, Marilyn Burns has produced a newsletter for teachers. Each newsletter contains classroom-tested activities from teachers across the country. This compilation presents the newsletters' best problem-solving lessons for grades 1-6. The lessons span the strands of the math curriculum and are illustrated with children's work. 


Introduction 1
Grade Level and Strand Charts 3
Grade Levels for Activities 4
Strands in Activities 6
The Lessons 9
A Beginning Experience with Recording 11
Counting Cats 13
Where’s the Penny? 15
How Many Pockets? 17
Planting Bulbs 19
Making Recording Books 21
Comparing Alphabet Letters 23
How Many Dots? 27
The Raccoon Problem 31
Lessons with Geoboards 33
Hands and Beans 37
Counting Feet 41
Sharing an Apple 43
How Many Animals? 47
Sharing 50 Cents 49
Exploring Halves 53
Dividing Cakes 55
Roll for $1.00 57
The Rubber Band Ball 61
How Many Days of School? 63
The Place Value Game 65
The Name Graph 69
Calculators in Math Class 73
Pioneers, Candles, and Math 77
The Game of Leftovers 81
How Much Ribbon? 85
Match or No Match 89
Math from the Ceiling 93
Cutting the Cake 97
Making Generalizations 99
The Firehouse Problem 101
The Largest Square Problem 105
A Statistical Experiment 109
Anno’s Magic Hat Tricks 111
Mathematics and Poetry 115
A Long Division Activity 117
Assessing Understanding of Fractions 121
Comparing Fractions 125
A Measurement Problem 129
Acrobats, Grandmas, and Ivan 133
Tiles in the Bag 137
Writing Questions from Graphs 139
From the Ceiling to Algebra 141
The Budgie Problem 143
Probability Tile Games 147
Penticubes 151
Multiplication and Division 155
Guess Our Number 157
What Is a Polygon?—A Geoboard Lesson 159
When Is the Cup Half Full? 161
Blackline Masters 165

Problems with patterns and numbers

Malcolm Swan

Shell Centre team:

Alan Bell, Barbara Binns, Hugh Burkhardt, Rosemary Fraser, John Gillespie,

David Pimm, Jim Ridgway, Malcolm Swan, Clare Trott,

co-ordinated by Jim Ridgway and Clare Trott, and directed by Hugh Burkhardt.

Joint Matriculation Board | 1984 | PDF

nationalstemcentre.org.uk (link direto)

primas-project.eu (link direto)

Problems with Patterns and Numbers has become an influential book on the teaching of problem solving. It focuses on non-routine problem solving in mathematics, and the teaching strategies needed to handle it in the classroom.

Many teachers find it difficult to know how to enable students to work independently on non-routine problems. This resource has been designed to help teachers introduce students to problem solving strategies and gradually, lesson-by-lesson, allow students more opportunities to apply these strategies to an ever-increasing range of problems.

Pedagogical issues

These materials focus particularly on the 'scaffolding' issue in problem solving: How might we remove some of the structure, so typical of textbooks, how can we support students without 'taking over' the problem. How can we assess problem solving? Analysing and representing problems by trying special cases, collecting data systematically, searching for patterns and making hypotheses, testing hypotheses on further examples, explaining and justifying results.

How We Think: A Theory of Goal-Oriented Decision Making and its Educational Applications

Alan H. Schoenfeld

Routledge | 2010 | 264 páginas | PDF | 2,72 Mb

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Teachers try to help their students learn. But why do they make the particular teaching choices they do? What resources do they draw upon? What accounts for the success or failure of their efforts? In How We Think, esteemed scholar and mathematician, Alan H. Schoenfeld, proposes a groundbreaking theory and model for how we think and act in the classroom and beyond. Based on thirty years of research on problem solving and teaching, Schoenfeld provides compelling evidence for a concrete approach that describes how teachers, and individuals more generally, navigate their way through in-the-moment decision-making in well-practiced domains. Applying his theoretical model to detailed representations and analyses of teachers at work as well as of professionals outside education, Schoenfeld argues that understanding and recognizing the goal-oriented patterns of our day to day decisions can help identify what makes effective or ineffective behavior in the classroom and beyond.

Math Word Problems Demystified

Allan G. Bluman

2.ª edição

McGraw-Hill Professional | 2004 | 317 páginas | PDF | 3,9 Mb

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With Math Word Problems Demystified, you master the subject one simple step at a time -- at your own speed. This unique self-teaching guide offers practice problems, a quiz at the end of each chapter to pinpoint weaknesses, and a 40 question final exam to reinforce the methods and material presented in the book.

CONTENTS

Preface ix

LESSON 1 Introduction to Solving Word Problems 1

LESSON 2 Solving Word Problems Using

Whole Numbers 6

REFRESHER I Decimals 11

LESSON 3 Solving Word Problems Using Decimals 14

REFRESHER II Fractions 18

LESSON 4 Solving Word Problems Using Fractions 27

Quiz 1 31

REFRESHER III Percents 35

LESSON 5 Solving Word Problems Using Percents 43

LESSON 6 Solving Word Problems Using Proportions 51

LESSON 7 Solving Word Problems Using Formulas 60

Quiz 2 66

REFRESHER IV Equations 69

LESSON 8 Algebraic Representation 82

LESSON 9 Solving Number Problems 88

LESSON 10 Solving Digit Problems 98

LESSON 11 Solving Coin Problems 108
Quiz 3 118
LESSON 12 Solving Age Problems 121
LESSON 13 Solving Distance Problems 131
LESSON 14 Solving Mixture Problems 147
LESSON 15 Solving Finance Problems 160
LESSON 16 Solving Lever Problems 172
LESSON 17 Solving Work Problems 181
Quiz 4 194
REFRESHER V Systems of Equations 197
LESSON 18 Solving Word Problems Using
Two Equations 207
REFRESHER VI Quadratic Equations 226
LESSON 19 Solving Word Problems Using Quadratic
Equations 232
LESSON 20 Solving Word Problems in Geometry 240
Quiz 5 252
LESSON 21 Solving Word Problems Using Other
Strategies 255
LESSON 22 Solving Word Problems in Probability 267
LESSON 23 Solving Word Problems in Statistics 276
Quiz 6 283
Final Exam 285
Answers to Quizzes and Final Exam 293
Supplement: Suggestions for
Success in Mathematics 295
Index 299

Livros do mesmo autor, disponíveis no blog:

- Pre-Algebra Demystified (2004)
- Probability Demystified (2005) 

Techniques of Problem Solving

Steven G. Krantz

American Mathematical Society | 1997 | 465 páginas | DJVU | 3 Mb

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The purpose of this book is to teach the basic principles of problem solving, including both mathematical and nonmathematical problems. This book will help students to ...translate verbal discussions into analytical data.
learn problem-solving methods for attacking collections of analytical questions or data.build a personal arsenal of internalized problem-solving techniques and solutions.
become "armed problem solvers", ready to do battle with a variety of puzzles in different areas of life.
Taking a direct and practical approach to the subject matter, Krantz's book stands apart from others like it in that it incorporates exercises throughout the text. After many solved problems are given, a "Challenge Problem" is presented. Additional problems are included for readers to tackle at the end of each chapter. There are more than 350 problems in all.

Problem Solving: Just for the Fun of It!

Dave Youngs, Michelle Pauls

AIMS Education Foundation | 2004 | 146 páginas | PDF | 3,6 Mb

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Grades 4-9

21 activities—144 pages

Nurture a positive attitude toward math while improving your students’ problem-solving skills. Problem Solving: Just for the Fun of It! will give students problems beyond the usual math exercises and will challenge them to think in different ways.

Students will gain confidence and build their thinking skills as they explore the possibilities in each activity. For example, in “The Fascinating Triangle,” students arrange the numbers one through six in a triangular array so that the sum of the numbers on every side is the same. Watch as students initially approach the problem cautiously, but soon gain confidence as they unlock multiple possibilities and patterns.

The activities are designed to foster positive feelings about mathematics by providing a wide selection of motivating problem-solving investigations. Topics include math patterns, paradoxes, palindromes, and mathematical microworlds.

A major goal of Problem Solving: Just for the Fun of It! is to introduce students to the wonderful world of recreational mathematics. This long-standing tradition is absent from many modern classrooms where mathematics is viewed as necessary and utilitarian, but certainly not recreational. With the proper care and nurturing, a positive, “just for the fun of it” attitude can be kindled in students using the investigations in this book.

Solve That Problem! Upper Primary: Skills and Strategies for Practical Problem Solving

Sharon Shapiro

Blake Education | 2001 | 88 páginas | PDF | 1,6 Mb

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Each unit in Solve That Problem! Upper Primary introduces a new problem-solving skill, following a structured sequence. Teaching notes on the specific skill the unit covers are followed by teaching examples that enable the easy introduction of these skills to students. The blackline master provided sets out a sequence for students to work through when implementing the new skill. Task cards give students the opportunity to put the new skill to use on problems of increasing complexity.

This book contains the following units:
- Creating a Tree Diagram
- Working Backwards
- Using Simpler Numbers
- Open-Ended Problem Solving
- Analysing and Investigating
- Using Logical Reasoning.

Solve That Problem! Middle Primary: Skills and Strategies for Practical Problem Solving

Sharon Shapiro

Blake Education | 2001 | 88 páginas | PDF | 1,7 Mb

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Each unit in Solve That Problem! Middle Primary introduces a new problem-solving skill, following a structured sequence. Teaching notes on the specific skill the unit covers are followed by teaching examples that enable the easy introduction of these skills to students. The blackline master provided sets out a sequence for students to work through when implementing the new skill. Task cards give students the opportunity to put the new skill to use on problems of increasing complexity.

This book contains the following units:
- Drawing a Diagram
- Drawing a Table
- Acting it Out or Using Concrete Material
- Guessing and Checking
- Creating an Organised List
- Looking for a Pattern (incompleto)

Mathematical Problem Solving

Alan Schoenfeld

Academic Press | 409 páginas | 1985 |  PDF | 3 Mb (no OCR)

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djvu | 3,49 Mb (OCR)
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Schoenfeld outlines four categories needed to characterize someones problem solving skills. They are resources, heuristics, control and beliefs. Discussion and examples are given in detail about these categories. It has been very thorough and useful to me.

Real-World Problems for Secondary School Mathematics Students

Juergen Maasz, John O'Donoghue

Sense Publishers | 2011 | 292 páginas | PDF | 17,92 Mb

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This is a book full of ideas for introducing real world problems into mathematics classrooms and assisting teachers and students to benefit from the experience. Taken as a whole these contributions provide a rich resource for mathematics teachers and their students that is readily available in a single volume. Nowadays there is a universal emphasis on teaching for understanding, motivating students to learn mathematics and using real world problems to improve the mathematics experience of school students. However, using real world problems in mathematics classrooms places extra demands on teachers in terms of extra-mathematical knowledge e.g. knowledge of the area of applications, and pedagogical knowledge. Care must also be taken to avoid overly complex situations and applications. Papers in this collection offer a practical perspective on these issues, and more. While many papers offer specific well worked out lesson type ideas, others concentrate on the teacher knowledge needed to introduce real world applications of mathematics into the classroom. We are confident that mathematics teachers who read the book will find a myriad of ways to introduce the material into their classrooms whether in ways suggested by the contributing authors or in their own ways, perhaps through mini-projects or extended projects or practical sessions or enquiry based learning. We are happy if they do! This book is written for mathematics classroom teachers and their students, mathematics teacher educators, and mathematics teachers in training at pre-service and in-service phases of their careers.

Use of Representations in Reasoning and Problem Solving: Analysis and Improvement

Lieven Verschaffel

Routledge | 2010  | 272 páginas  | PDF | 2,1 Mb

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Within an increasingly multimedia focused society, the use of external representations in learning, teaching and communication has increased dramatically. Whether in the classroom, university or workplace, there is a growing requirement to use and interpret a large variety of external representational forms and tools for knowledge acquisition, problem solving, and to communicate with others.
Use of Representations in Reasoning and Problem Solving brings together contributions from some of the world’s leading researchers in educational and instructional psychology, instructional design, and mathematics and science education to document the role which external representations play in our understanding, learning and communication. Traditional research has focused on the distinction between verbal and non-verbal representations, and the way they are processed, encoded and stored by different cognitive systems. The contributions here challenge these research findings and address the ambiguity about how these two cognitive systems interact, arguing that the classical distinction between textual and pictorial representations has become less prominent. The contributions in this book explore:
* how we can theorise the relationship between processing internal and external representations
* what perceptual and cognitive restraints can affect the use of external representations
* how individual differences affect the use of external representations
* how we can combine external representations to maximise their impact
* how we can adapt representational tools for individual differences.
Using empirical research findings to take a fresh look at the processes which take place when learning via external representations, this book is essential reading for all those undertaking postgraduate study and research in the fields of educational and instructional psychology, instructional design and mathematics and science education.

Problem Solving in Mathematics, Grades 3-6: Powerful Strategies to Deepen Understanding

Alfred S. Posamentier, Stephen Krulik

Corwin Press | 2009 | 152 páginas | PDF | 705 kb

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“A wonderful collection of problems that were thoroughly researched and presented.” (Timothy J. McNamara, National K-12 Consultant/Professional Developer )

“Helps fill a gap in the field of mathematics education-a specific explication with appropriate examples of the variety of problem solving approaches.” (Pearl Solomon, Author )

“Demonstrates problem solving strategies with solutions and teaching notes and allows the teacher to create a collection of problems to fit a particular grade level.” (Janice L. Richardson, Associate Professor and Education Coordinator, Department of Mathematics )


Contents
Preface vii
Publisher’s Acknowledgments ix
About the Authors x
1. An Introduction to Problem Solving 1
Problem Solving on Assessment Tests 3
The Heuristics of Problem Solving 4
How to Use This Book 4
Problem Decks 5
The Strategies of Problem Solving 6
2. Organizing Data 7
Applying the Organizing Data Strategy 7
Chapter Teaching Notes 8
Problems for Students 9
3. Intelligent Guessing and Testing 24
Applying the Intelligent Guessing and Testing Strategy 25
Chapter Teaching Notes 26
Problems for Students 27
4. Solving a Simpler Equivalent Problem 36
Applying the Solving a Simpler Equivalent Problem Strategy 36
Chapter Teaching Notes 37
Problems for Students 38
5. Acting It Out or Simulation 48
Applying the Acting It Out or Simulation Strategy 48
Chapter Teaching Notes 50
Problems for Students 51
6. Working Backwards 60
Applying the Working Backwards Strategy 61
Chapter Teaching Notes 62
Problems for Students 63
7. Finding a Pattern 71
Applying the Finding a Pattern Strategy 72
Chapter Teaching Notes 73
Problems for Students 74
8. Logical Reasoning 88
Applying the Logical Reasoning Strategy 88
Chapter Teaching Notes 89
Problems for Students 90
9. Making a Drawing 99
Applying the Making a Drawing Strategy 99
Chapter Teaching Notes 100
Problems for Students 101
10. Adopting a Different Point of View 116
Applying the Adopting a Different Point of View Strategy 117
Chapter Teaching Notes 117
Problems for Students 118
Readings on Problem Solving 134