STEM Project-Based Learning: An Integrated Science, Technology, Engineering, and Mathematics (STEM) Approach

 Robert M. Capraro, Mary Margaret Capraro e James R. Morgan

Sense Publishers |  2013 - 2ª edição | 198 páginas | rar - pdf | 5,3 Mb


link (password: matav)

pdf - 16 Mb - link

This second edition of Project-Based Learning (PBL) presents an original approach to Science, Technology, Engineering and Mathematics (STEM) centric PBL. We define STEM PBL as an "ill-defined task with a well-defined outcome," which is consistent with our engineering design philosophy and the accountability highlighted in a standards-based environment. This model emphasizes a backward design that is initiated by well-defined outcomes, tied to local, state, or national standard that provide teachers with a framework guiding students' design, solving, or completion of ill-defined tasks. This book was designed for middle and secondary teachers who want to improve engagement and provide contextualized learning for their students. However, the nature and scope of the content covered in the 14 chapters are appropriate for preservice teachers as well as for advanced graduate method courses. New to this edition is revised and expanded coverage of STEM PBL, including implementing STEM PBL with English Language Learners and the use of technology in PBL. The book also includes many new teacher-friendly forms, such as advanced organizers, team contracts for STEM PBL, and rubrics for assessing PBL in a larger format.

TABLE OF CONTENTS

Preface xi
Chapter 1 Why PBL? Why STEM? Why Now? An Introduction to STEM Project-Based Learning: An Integrated Science, Technology, Engineering, and Mathematics Approach 1
Robert M. Capraro and Scott W. Slough
Chapter 2 From the Project Method to STEM Project-Based Learning: The Historical Context 7
Lynn M. Burlbaw, Mark J. Ortwein and J. Kelton Williams
Chapter 3 Theoretical Framework for the Design of STEM Project-Based Learning 15
Scott W. Slough and John O. Milam
Chapter 4 Engineering Better Projects 29
James R. Morgan, April M. Moon and Luciana R. Barroso
Chapter 5 W3 of STEM Project-Based Learning 41
Serkan Özel
Chapter 6 Interdisciplinary STEM Project-Based Learning 47
Mary Margaret Capraro and Meredith Jones
Chapter 7 STEM Project-Based Learning: Specialized Form of Inquiry-Based Learning 55
Alpaslan Sahin
Chapter 8 Technology in STEM Project-Based Learning 65
Ozcan Erkan Akgun
Chapter 9 Affordances of Virtual Worlds to Support STEM Project-Based Learning 77
Trina Davis
Chapter 10 STEM Project-Based Learning and Teaching for Exceptional and Learners 85
Denise A. Soares and Kimberly J. Vannest
Chapter 11 Classroom Management Considerations: Implementing STEM Project-Based Learning 99
James R. Morgan and Scott W. Slough
Chapter 12 Changing Views on Assessment for STEM Project-Based Learning 109
Robert M. Capraro and M. Sencer Corlu
Chapter 13 English Language Learners and Project-Based Learning 119
Zohreh Eslami and Randall Garver
Chapter 14 Project-Based Learning: An Interdisciplinary Approach for Integrating Social Studies with STEM 129
Caroline R. Pryor and Rui Kang
Appendix A. Non-Newtonian Fluid Mechanics STEM PBL 139
Robert M. Capraro and Scott. W. Slough
Appendix B. Ideation Rubric 153
Appendix C. Oral Presentation Rubric 155
Appendix D. Presentation Rubric PT1 Individual 157
Appendix E. Presentation Rubric PT2 Group 159
Appendix F. STEM Project-Based Learning Storyboarding Guidelines 161
Appendix G. Crossing the Abyss: Popsicle Stick Bridge: WDO/IDT 163
Appendix H. Establishing Cooperative Group Behaviors and Norms for STEM PBL 171
Appendix I. Building High Quality Teams 173
Appendix J. Personal Responsibility and Time Management Report 175
Appendix K. Accountability Record 177
Appendix L. Peer Evaluation Handout 179
Appendix M. Leadership/Effort Bonus Worksheet 181
Appendix N. Simple Group Contract: Our Contract 183
Appendix O. Sample Group Contract 185
Appendix P. Team Contract 187
Appendix Q. Self Reflections 189
Appendix R. Reflection on Team Collaboration 191
Appendix S. Teacher Peer Evaluation of STEM PBL Project 193
Appendix T. Project-Based Learning Observation Record 195
Appendix U. Project Development Rubric 199
Appendix V. Who Killed Bob Krusty?: A Dynamic Problem-Solving Event 201

Appendix W. PBL Refresher: Quick Quiz – Project-Based Learning 203

Teaching and learning early number

Ian Thompson

Open University Press | 2008 - 2ª edição | 252 páginas | pdf | 1,9 Mb

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"This richly varied text offers generous support for every aspect of the teacher's role, while constantly reminding us that mathematical activity is not a de-contextualised skill that children possess, but part of their identity, their way of being in the world, engaged with the world, energetically - and playfully - trying to make sense of it."Mary Jane Drummond, formerly of the Faculty of Education, University of Cambridge, UK

Teaching and Learning Early Number is a bestselling guide for all trainee and practising Early Years teachers and classroom assistants. It provides an accessible guide to a wide range of research evidence about the teaching and learning of early number.

Major changes in the primary mathematics curriculum over the last decade - such as the National Numeracy Strategy, the Primary National Strategy, the Early Years Foundation Stage and the Williams Review - have greatly influenced the structure of this new edition. The book includes:

• A new introductory chapter to set the scene

• Six further new chapters - including Mathematics through play, Children's mathematical graphics and Interview-based assessment of early number knowledge

• Six completely re-written chapters and two updated chapters

• A new concluding chapter looking to the future

The chapters can be read in a standalone fashion and many are cross referenced to other parts of the book where specific ideas are dealt with in a different manner. Issues addressed include: new research on the complex process of counting and on children's written mathematical marks; counting in the home environment and play in the school setting; the importance of mathematical representations and of ICT in children's understanding of number; errors and misconceptions and the assessment of children’s number knowledge.

Contents
Notes on contributors ix
Editor’s preface xv
SECTION 1 - Setting the scene for teaching and learning early number 1
1 Still not getting it right from the start? 3
Carol Aubrey and Dondu Durmaz
SECTION 2 - The early stages of number acquisition 17
2 Children’s beliefs about counting 19
Penny Munn
3 Mathematics through play 34
Kate Tucker
4 The family counts 47
Rose Griffiths
SECTION 3 - The place of counting in number development 59
5 Development in oral counting, enumeration, and counting for cardinality 61
John Threlfall
6 Counting: what it is and why it matters 72
Effie Maclellan
7 Compressing the counting process: strength from the flexible interpretation of symbols 82
Eddie Gray
SECTION 4 - Extending counting to calculating 95
8 From counting to deriving number facts 97
Ian Thompson
9 Uses of counting in multiplication and division 110
Julia Anghileri
SECTION 5 - Representation and calculation 123
10 Children’s mathematical graphics: young children calculating for meaning 127
Elizabeth Carruthers and Maulfry Worthington
11 What do young children’s mathematical graphics tell us about the teaching of written calculation? 149
Ian Thompson
12 What’s in a picture? Understanding and representation in early mathematics 160
Tony Harries, Patrick Barmby and Jennifer Suggate
13 Mathematical learning and the use of information and communications technology in the early years 176
Steve Higgins
SECTION 6 - Assessing young children’s progress in number 189
14 Interview-based assessment of early number knowledge 193
Robert J. Wright
15 Addressing errors and misconceptions with young children 205
Ian Thompson
SECTION 7 - Towards an early years mathematics pedagogy 215
16 ‘How do you teach nursery children mathematics?’ In search of a mathematics pedagogy for the early years 217
Sue Gifford

Math and Logic Games: A Book of Puzzles and Problems

Facts on File | 1983 | 179 páginas | pdf | 7,5 Mb


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Discusses games with numbers, geometrical figures, logic, probability, and paradoxes, and looks at their mathematical basis

Contents

7 Introduction

9 Games with numbers

9 An historical note

11 A first criosity

12 Fibonacci numbers

14 A curious calculating dev ce: the abacus

20 The origins of algebra

21 Games with algebra

23 Odds and evens

24 The successor of a number

24 A shortcut in calculations

25 How much money is in your pocket?

25 How to guess a birth date

26 Guessing age and size of shoes

26 Where is the error?

27 Positional notation of numbers

28 One rotten apple can spoil the whole basket

29 Ordinary language and mathematical language

33 Games with geometrical figures

33 Geometry and optical illusions

41 Games with matches

42 Lo shu, an ancient Chinese figure

42 Magic squares: their history and mathematical features

44 More intricate magic squares

47 Diabolic squares

48 Magic stars

51 More about squares

51 An extraordinary surface

52 The bridges of Konigsberg

55 Elementary theory of graphs

57 Save the goat and the cabbage

58 The jealous husbands

61 Interchanging knights

62 A wide range of applications

63 Topology, or the geometry of distortion

70 Topological labyrinths

73 The Mobius ring

76 Games with topological knots

77 The four-colour theorem

84 Rubik's cube

91 Paradoxes and antinomies

91 The role of paradoxes in the development of mathematical thought

92 Pythagoras and Pythagoreanism

94 Geometrical representation of numbers

94 A tragic Pythagorean paradox: the odd equals the even

96 Unthinkable numbers

97 Zeno of Elea

98 Zeno's paradoxes

100 Theoretical significance and solution of Zeno's paradoxes

101 The part equals the whole

102 Sets: an antinomic concept

103 A postman and barber in trouble

104 Russell's paradox

105 A great game: mathematical logic

105 A special chessboard

105 What is a logical argument?

106 Logic and ordinary language

107 An ingenious idea of Leibniz

108 Logic: the science of correct reasoning

112 Logical variables

113 George Boole and the origins of propositional calculus

113 The logical calculus

114 Negation

115 Explanation of symbols

115 Conjunction and the empty set

116 The empty set

117 Disjunction

118 Implication

119 Who has drunk the brandy?

120 The multiplication tables of propositional calculus: truth-tables

125 Another solution to the problem of the brandy drinkers

126 Who is the liar?

129 How to argue by diagram

135 A practical application: logic circuits

143 Games with probability

143 The reality of chance and uncertainty

144 Cards, dice, games of chance and bets: historical origins of the calculus of probability

144 Chance phenomena

145 A clarification

146 Sample space

148 The measure of probability

148 Horse races

149 The concept of function

149 The algebra of events and probability games

150 The complementary event and its probability measure

150 The probability of the union of two events

151 The probability of the intersection of two events

152 The probability of a choice

153 Drawing a card from a pack

154 Joint throw of coin and die

154 Dependent events

156 Independent events

159 What is the probability that George and Bob speak the truth?

160 Probability and empirical science

160 Probability and statistics

160 Sample and population

161 Guess the vintage

161 Conclusion

163 Appendix: games with logic and probability

163 Note

164 Games with logic

167 Games with probability

177 List of main symbols used

179 Bibliography

181 Index

Symmetry: A Very Short Introduction

Ian Stewart

Oxford University Press | 2013 | 152 páginas | rar - epub | 5,9 Mb

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Symmetry is an immensely important concept in mathematics and throughout the sciences. In this Very Short Introduction, Ian Stewart demonstrates symmetry's deep implications, showing how it even plays a major role in the current search to unify relativity and quantum theory. Stewart, a respected mathematician as well as a widely known popular-science and science-fiction writer, brings to this volume his deep knowledge of the subject and his gift for conveying science to general readers with clarity and humor. He describes how symmetry's applications range across the entire field of mathematics and how symmetry governs the structure of crystals, innumerable types of pattern formation, and how systems change their state as parameters vary. Symmetry is also highly visual, with applications that include animal markings, locomotion, evolutionary biology, elastic buckling, waves, the shape of the Earth, and the form of galaxies. Fundamental physics is governed by symmetries in the laws of nature--Einstein's point that the laws should be the same at all locations and all times. 

Contents
List of illustrations
Introduction
1 What is symmetry?
2 Origins of symmetry
3 Types of symmetry
4 Structure of groups
5 Groups and games
6 Nature’s patterns
7 Nature’s laws
8 Atoms of symmetry
Further reading

Index

Examples and Problems in Mathematical Statistics

(Wiley Series in Probability and Statistics) 

Shelemyahu Zacks

 Wiley | 2014 | 654 páginas | rar - pdf |  2,8 Mb

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Provides the necessary skills to solve problems in mathematical statistics through theory, concrete examples, and exercises

With a clear and detailed approach to the fundamentals of statistical theory, Examples and Problems in Mathematical Statistics uniquely bridges the gap between theory andapplication and presents numerous problem-solving examples that illustrate the relatednotations and proven results.

Written by an established authority in probability and mathematical statistics, each chapter begins with a theoretical presentation to introduce both the topic and the important results in an effort to aid in overall comprehension. Examples are then provided, followed by problems, and finally, solutions to some of the earlier problems. In addition, Examples and Problems in Mathematical Statistics features:

• Over 160 practical and interesting real-world examples from a variety of fields including engineering, mathematics, and statistics to help readers become proficient in theoretical problem solving

• More than 430 unique exercises with select solutions

• Key statistical inference topics, such as probability theory, statistical distributions, sufficient statistics, information in samples, testing statistical hypotheses, statistical estimation, confidence and tolerance intervals, large sample theory, and Bayesian analysis

Recommended for graduate-level courses in probability and statistical inference, Examples and Problems in Mathematical Statistics is also an ideal reference for applied statisticians and researchers.

Table of Contents

Preface xv

List of Random Variables xvii

List of Abbreviations xix

1 Basic Probability Theory 1

PART I: THEORY, 1

1.1 Operations on Sets, 1

1.2 Algebra and σ-Fields, 2

1.3 Probability Spaces, 4

1.4 Conditional Probabilities and Independence, 6

1.5 Random Variables and Their Distributions, 8

1.6 The Lebesgue and Stieltjes Integrals, 12

1.7 Joint Distributions, Conditional Distributions and Independence, 21

1.8 Moments and Related Functionals, 26

1.9 Modes of Convergence, 35

1.10 Weak Convergence, 39

1.11 Laws of Large Numbers, 41

1.12 Central Limit Theorem, 44

1.13 Miscellaneous Results, 47

PART II: EXAMPLES, 56

PART III: PROBLEMS, 73

PART IV: SOLUTIONS TO SELECTED PROBLEMS, 93

2 Statistical Distributions 106

PART I: THEORY, 106

2.1 Introductory Remarks, 106

2.2 Families of Discrete Distributions, 106

2.3 Some Families of Continuous Distributions, 109

2.4 Transformations, 118

2.5 Variances and Covariances of Sample Moments, 120

2.6 Discrete Multivariate Distributions, 122

2.7 Multinormal Distributions, 125

2.8 Distributions of Symmetric Quadratic Forms of Normal Variables, 130

2.9 Independence of Linear and Quadratic Forms of Normal Variables, 132

2.10 The Order Statistics, 133

2.11 t-Distributions, 135

2.12 F-Distributions, 138

2.13 The Distribution of the Sample Correlation, 142

2.14 Exponential Type Families, 144

2.15 Approximating the Distribution of the Sample Mean: Edgeworth and Saddlepoint Approximations, 146

PART II: EXAMPLES, 150

PART III: PROBLEMS, 167

PART IV: SOLUTIONS TO SELECTED PROBLEMS, 181

3 Sufficient Statistics and the Information in Samples 191

PART I: THEORY, 191

3.1 Introduction, 191

3.2 Definition and Characterization of Sufficient Statistics, 192

3.3 Likelihood Functions and Minimal Sufficient Statistics, 200

3.4 Sufficient Statistics and Exponential Type Families, 202

3.5 Sufficiency and Completeness, 203

3.6 Sufficiency and Ancillarity, 205

3.7 Information Functions and Sufficiency, 206

3.8 The Fisher Information Matrix, 212

3.9 Sensitivity to Changes in Parameters, 214

PART II: EXAMPLES, 216

PART III: PROBLEMS, 230

PART IV: SOLUTIONS TO SELECTED PROBLEMS, 236

4 Testing Statistical Hypotheses 246

PART I: THEORY, 246

4.1 The General Framework, 246

4.2 The Neyman–Pearson Fundamental Lemma, 248

4.3 Testing One-Sided Composite Hypotheses in MLR Models, 251

4.4 Testing Two-Sided Hypotheses in One-Parameter Exponential Families, 254

4.5 Testing Composite Hypotheses with Nuisance Parameters—Unbiased Tests, 256

4.6 Likelihood Ratio Tests, 260

4.7 The Analysis of Contingency Tables, 271

4.8 Sequential Testing of Hypotheses, 275

PART II: EXAMPLES, 283

PART III: PROBLEMS, 298

PART IV: SOLUTIONS TO SELECTED PROBLEMS, 307

5 Statistical Estimation 321

PART I: THEORY, 321

5.1 General Discussion, 321

5.2 Unbiased Estimators, 322

5.3 The Efficiency of Unbiased Estimators in Regular Cases, 328

5.4 Best Linear Unbiased and Least-Squares Estimators, 331

5.5 Stabilizing the LSE: Ridge Regressions, 335

5.6 Maximum Likelihood Estimators, 337

5.7 Equivariant Estimators, 341

5.8 Estimating Equations, 346

5.9 Pretest Estimators, 349

5.10 Robust Estimation of the Location and Scale Parameters of Symmetric Distributions, 349

PART II: EXAMPLES, 353

PART III: PROBLEMS, 381

PART IV: SOLUTIONS OF SELECTED PROBLEMS, 393

6 Confidence and Tolerance Intervals 406

PART I: THEORY, 406

6.1 General Introduction, 406

6.2 The Construction of Confidence Intervals, 407

6.3 Optimal Confidence Intervals, 408

6.4 Tolerance Intervals, 410

6.5 Distribution Free Confidence and Tolerance Intervals, 412

6.6 Simultaneous Confidence Intervals, 414

6.7 Two-Stage and Sequential Sampling for Fixed Width Confidence Intervals, 417

PART II: EXAMPLES, 421

PART III: PROBLEMS, 429

PART IV: SOLUTION TO SELECTED PROBLEMS, 433

7 Large Sample Theory for Estimation and Testing 439

PART I: THEORY, 439

7.1 Consistency of Estimators and Tests, 439

7.2 Consistency of the MLE, 440

7.3 Asymptotic Normality and Efficiency of Consistent Estimators, 442

7.4 Second-Order Efficiency of BAN Estimators, 444

7.5 Large Sample Confidence Intervals, 445

7.6 Edgeworth and Saddlepoint Approximations to the Distribution of the MLE: One-Parameter Canonical Exponential Families, 446

7.7 Large Sample Tests, 448

7.8 Pitman’s Asymptotic Efficiency of Tests, 449

7.9 Asymptotic Properties of Sample Quantiles, 451

PART II: EXAMPLES, 454

PART III: PROBLEMS, 475

PART IV: SOLUTION OF SELECTED PROBLEMS, 479

8 Bayesian Analysis in Testing and Estimation 485

PART I: THEORY, 485

8.1 The Bayesian Framework, 486

8.2 Bayesian Testing of Hypothesis, 491

8.3 Bayesian Credibility and Prediction Intervals, 501

8.4 Bayesian Estimation, 502

8.5 Approximation Methods, 506

8.6 Empirical Bayes Estimators, 513

PART II: EXAMPLES, 514

PART III: PROBLEMS, 549

PART IV: SOLUTIONS OF SELECTED PROBLEMS, 557

9 Advanced Topics in Estimation Theory 563

PART I: THEORY, 563

9.1 Minimax Estimators, 563

9.2 Minimum Risk Equivariant, Bayes Equivariant, and Structural Estimators, 565

9.3 The Admissibility of Estimators, 570

PART II: EXAMPLES, 585

PART III: PROBLEMS, 592

PART IV: SOLUTIONS OF SELECTED PROBLEMS, 596

References 601

Author Index 613

Subject Index 617

A Mathematician's Apology

University of Alberta Mathematical Sciences Society | 2005 | 56 páginas | pdf | 174 kb

online: math.ualberta.ca

Cambridge University Press | 1967 | 80 páginas

online: archive.org

G. H. Hardy was one of this century's finest mathematical thinkers, renowned among his contemporaries as a 'real mathematician ... the purest of the pure'. He was also, as C. P. Snow recounts in his Foreword, 'unorthodox, eccentric, radical, ready to talk about anything'. This 'apology', written in 1940 as his mathematical powers were declining, offers a brilliant and engaging account of mathematics as very much more than a science; when it was first published, Graham Greene hailed it alongside Henry James's notebooks as 'the best account of what it was like to be a creative artist'. C. P. Snow's Foreword gives sympathetic and witty insights into Hardy's life, with its rich store of anecdotes concerning his collaboration with the brilliant Indian mathematician Ramanujan, his aphorisms and idiosyncrasies, and his passion for cricket. This is a unique account of the fascination of mathematics and of one of its most compelling exponents in modern times

Millions, Billions, & Trillions: Understanding Big Numbers

David A. Adler e Edward Miller

Holiday House | 2014 | páginas | rar - pdf | 30,9 Mb

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What does a million look like? A billion? A trillion? These huge numbers are hard to visualize. This book explains quantities in terms children can understand. For example, one million dollars could buy two full pizzas a day for more than sixty-eight years, it would take the heads of ten thousand people together to have one billion hairs.
This dynamic math duo explains the concepts of millions, billions, and trillions in a lighthearted way.