Selected lectures from the Seventh International Congress on Mathematical Education

ICME-7    1992      Québec (Canada) 

David E Robitaille, David H. Wheeler, Carolyn Kieran

Presses de l'Universite Laval | 1994 | 380 páginas | pdf (OCR) | 16,3 Mb

link

pdf (no OCR) | 35,1 Mb
online:  mathematik.uni-bielefeld.de

djvu (OCR) | 19 Mb
online: mathematik.uni-bielefeld.de

Contents
Preface p. IX 
Contribution de l'apprentissage de la géométrie à la formation scientifique - Gérard Audibert p. 1 
Diagnostic Teaching - Alan Bell p. 19 
Reading, Writing and Mathematics: Rethinking -Raffaella Borasi and Marjorie Siegel p. 35 
Teachers Using Videotapes as Reference Points -John L. Clark p. 49 
The Transition to Secondary School Mathematics -David Clarke p. 59 
Mathematicians and Mathematical Education -Michael P. Closs p. 77 
Les mathématiques comme reflet d'une culture -Jean Dhombres p. 89 
Imagery and Reasoning in Mathematics and Mathematics Education - Tommy Dreyfus p. 107
Interweaving Numbers, Shapes, Statistics, and the Real World in Primary School and Primary Teacher Education - Andrejs Dunkels p. 123 
Teaching Mathematics and Problem Solving to Deaf and Hard-of-Hearing Students - Harvey Goodstein p. 137 
The Origin and Evolution of Mathematical Theories- Miguel de Guzmàn p. 147 
Le calcul infinitésimal - Bernard R. Hodgson p. 157 
Computer-Based Microworlds: a Radical Vision or a Trojan Mouse? - Celia Hoyles p. 171 
Different Ways of Knowing: Contrasting Styles of Argument in India and the West - George Gheverghese Joseph p. 183 
Mathematics Education in the Global Village : the Wedge and the Filter - Murad Jurdak p. 199 
Bonuses of Understanding Mathematical Understanding - Thomas E. Kieren p. 211 
Curriculum Change: An American-Dutch Perspective - Jan de Lange p. 229 
Training Teachers or Educating Professionals? What are the Issues and How Are They Being Resolved? - Glenda Lappan and Sarah Theule-Lubienski p. 249 
What is Discrete Mathematics and How Should We Teach It? - Jacobus H. van Lint p. 263 
Intuition and Logic in Mathematics - Michael Otte p. 271 
Vers une construction réaliste des nombres rationnels - Nicolas Rouche p. 285
Mathematics is a Language - Fritz Schweiger p. 297 
Mathematical Thinking and Reasoning for All Students - Moving from Rhetoric to Reality - Edward A. Silver p. 311 
Humanistic and Utilitarian Aspects of Mathematics - Thomas Tymoczko p. 327 
From "Mathematics for Some" to "Mathematics for All" - Zalman Usiskin p. 341 
On the Appreciation of Theorems by Students and Teachers - Hans-Joachim Vollrath p. 353 
Geometry as an Element of Culture - Alexandr D. Alexandrov p. 365 

Algebra for College Students

Jerome E. Kaufmann e Karen L. Schwitters

Cengage Learning | 2010 - 9ª edição | 831 páginas | rar - pdf | 9,7 Mb

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Kaufmann and Schwitters have built this text's reputation on clear and concise exposition, numerous examples, and plentiful problem sets. This traditional text consistently reinforces the following common thread: learn a skill; practice the skill to help solve equations; and then apply what you have learned to solve application problems. This simple, straightforward approach has helped many students grasp and apply fundamental problem solving skills necessary for future mathematics courses. Algebraic ideas are developed in a logical sequence, and in an easy-to-read manner, without excessive vocabulary and formalism. The open and uncluttered design helps keep students focused on the concepts while minimizing distractions. Problems and examples reference a broad range of topics, as well as career areas such as electronics, mechanics, and health, showing students that mathematics is part of everyday life. The text's resource package--anchored by Enhanced WebAssign, an online homework management tool--saves instructors time while also providing additional help and skill-building practice for students outside of class.

CONTENTS
1 Basic Concepts and Properties 1
1.1 Sets, Real Numbers, and Numerical Expressions 2
1.2 Operations with Real Numbers 10
1.3 Properties of Real Numbers and the Use of Exponents 20
1.4 Algebraic Expressions 27
Chapter 1 Summary 36
Chapter 1 Review Problem Set 38
Chapter 1 Test 40
2 Equations, Inequalities, and Problem Solving 41
2.1 Solving First-Degree Equations 42
2.2 Equations Involving Fractional Forms 49
2.3 Equations Involving Decimals and Problem Solving 57
2.4 Formulas 64
2.5 Inequalities 74
2.6 More on Inequalities and Problem Solving 81
2.7 Equations and Inequalities Involving Absolute Value 90
Chapter 2 Summary 97
Chapter 2 Review Problem Set 101
Chapter 2 Test 104
Chapters 1– 2 Cumulative Review Problem Set 105
3 Polynomials 107
3.1 Polynomials: Sums and Differences 108
3.2 Products and Quotients of Monomials 114
3.3 Multiplying Polynomials 119
3.4 Factoring: Greatest Common Factor and Common Binomial Factor 127
3.5 Factoring: Difference of Two Squares and Sum or Difference of Two Cubes 135
3.6 Factoring Trinomials 141
3.7 Equations and Problem Solving 149
Chapter 3 Summary 155
Chapter 3 Review Problem Set 158
Chapter 3 Test 161
4 Rational Expressions 163
4.1 Simplifying Rational Expressions 164
4.2 Multiplying and Dividing Rational Expressions 169
4.3 Adding and Subtracting Rational Expressions 175
4.4 More on Rational Expressions and Complex Fractions 182
4.5 Dividing Polynomials 190
4.6 Fractional Equations 196
4.7 More Fractional Equations and Applications 202
Chapter 4 Summary 211
Chapter 4 Review Problem Set 216
Chapter 4 Test 218
Chapters 1– 4 Cumulative Review Problem Set 219
5 Exponents and Radicals 221
5.1 Using Integers as Exponents 222
5.2 Roots and Radicals 229
5.3 Combining Radicals and Simplifying Radicals That Contain Variables 238
5.4 Products and Quotients Involving Radicals 243
5.5 Equations Involving Radicals 249
5.6 Merging Exponents and Roots 254
5.7 Scientific Notation 259
Chapter 5 Summary 265
Chapter 5 Review Problem Set 269
Chapter 5 Test 271
6 Quadratic Equations and Inequalities 273
6.1 Complex Numbers 274
6.2 Quadratic Equations 281
6.3 Completing the Square 289
6.4 Quadratic Formula 293
6.5 More Quadratic Equations and Applications 300
6.6 Quadratic and Other Nonlinear Inequalities 308
Chapter 6 Summary 314
Chapter 6 Review Problem Set 318
Chapter 6 Test 320
Chapters 1– 6 Cumulative Review Problem Set 321
7 Linear Equations and Inequalities in Two Variables 323
7.1 Rectangular Coordinate System and Linear Equations 324
7.2 Linear Inequalities in Two Variables 337
7.3 Distance and Slope 342
7.4 Determining the Equation of a Line 353
7.5 Graphing Nonlinear Equations 363
Chapter 7 Summary 371
Chapter 7 Review Problem Set 376
Chapter 7 Test 379
8 Functions 381
8.1 Concept of a Function 382
8.2 Linear Functions and Applications 391
8.3 Quadratic Functions 398
8.4 More Quadratic Functions and Applications 407
8.5 Transformations of Some Basic Curves 416
8.6 Combining Functions 425
8.7 Direct and Inverse Variation 432
Chapter 8 Summary 440
Chapter 8 Review Problem Set 447
Chapter 8 Test 449
Chapters 1– 8 Cumulative Review Problem Set 450
9 Polynomial and Rational Functions 453
9.1 Synthetic Division 454
9.2 Remainder and Factor Theorems 458
9.3 Polynomial Equations 463
9.4 Graphing Polynomial Functions 473
9.5 Graphing Rational Functions 483
9.6 More on Graphing Rational Functions 492
Chapter 9 Summary 499
Chapter 9 Review Problem Set 503
Chapter 9 Test 504
10 Exponential and Logarithmic Functions 505
10.1 Exponents and Exponential Functions 506
10.2 Applications of Exponential Functions 513
10.3 Inverse Functions 524
10.4 Logarithms 534
10.5 Logarithmic Functions 542
10.6 Exponential Equations, Logarithmic Equations, and Problem Solving 549
Chapter 10 Summary 559
Chapter 10 Review Problem Set 565
Chapter 10 Test 567
Chapters 1– 10 Cumulative Review Problem Set 568
11 Systems of Equations 571
11.1 Systems of Two Linear Equations in Two Variables 572
11.2 Systems of Three Linear Equations in Three Variables 582
11.3 Matrix Approach to Solving Linear Systems 589
11.4 Determinants 598
11.5 Cramer’s Rule 607
11.6 Partial Fractions (Optional) 613
Chapter 11 Summary 619
Chapter 11 Review Problem Set 623
Chapter 11 Test 625
12 Algebra of Matrices 627
12.1 Algebra of 2 2 Matrices 628
12.2 Multiplicative Inverses 634
12.3 m n Matrices 640
12.4 Systems of Linear Inequalities: Linear Programming 649
Chapter 12 Summary 658
Chapter 12 Review Problem Set 662
Chapter 12 Test 664
Chapters 1 – 12 Cumulative Review Problem Set 665
13 Conic Sections 669
13.1 Circles 670
13.2 Parabolas 676
13.3 Ellipses 684
13.4 Hyperbolas 693
13.5 Systems Involving Nonlinear Equations 702
Chapter 13 Summary 709
Chapter 13 Review Problem Set 714
Chapter 13 Test 715
14 Sequences and Mathematical Induction 717
14.1 Arithmetic Sequences 718
14.2 Geometric Sequences 725
14.3 Another Look at Problem Solving 733
14.4 Mathematical Induction 738
Chapter 14 Summary 744
Chapter 14 Review Problem Set 746
Chapter 14 Test 748
Appendix A Prime Numbers and Operations with Fractions 749
Appendix B Binomial Theorem 757
Answers to Odd-Numbered Problems and All Chapter Review, Chapter Test, Cumulative Review, and Appendix A Problems 761
Index I-1

More Language Arts, Math, and Science for Students with Severe Disabilities

Diane Browder, Fred Spooner, Martin Agran  e Lynn Ahlgrim-Delzell 

Brookes Publishing | 2014 | 326 páginas | rar - pdf | 2,8 Mb

link (password : matav)

How can today's educators teach academic content to students with moderate and severe developmental disabilities while helping all students meet Common Core State Standards? This text has answers for K-12 teachers, straight from 37 experts in special and general education. A followup to the landmark bestseller Teaching Language Arts, Math, and Science to Students with Significant Cognitive Disabilities, this important text prepares teachers to ensure more inclusion, more advanced academic content, and more meaningful learning for their students. Teachers will have the cutting-edge research and recommended practices they need to identify and deliver grade-aligned instructional content leading to more opportunities and better quality of life for students with severe disabilities.

PRACTICAL MATERIALS: Detailed vignettes based on the authors real-life experiences, teaching examples and guidelines that illustrate recommended practices, helpful figures and tables, resource lists, and suggestions for incorporating technology into teaching and learning.

PREPARE TEACHERS TO

• skillfully adapt lessons in language arts, math, and science for students with disabilities

• align instruction with Common Core State Standards

• select target skills and goals

• differentiate instruction using appropriate supports and assistive technologies

• balance academic goals and functional skills

• make the most of effective instructional procedures such as peer tutoring, cooperative learning, and co-teaching

• maintain high expectations for student achievement

• promote generalization by embedding instruction into ongoing classroom activities

• assess students progress and make adjustments to instruction

Contents
About the Reproducible Materials . vii
About the Editors. ix
About the Contributors. xi
Foreword
Martin Agran. xix
Preface. xxiii
Acknowledgments. xxv
I Greater Access to General Curriculum
1 More Content, More Learning, More Inclusion
Diane M. Browder and Fred Spooner. 3
2 Embedded Instruction in Inclusive Settings
John McDonnell, J. Mathew Jameson, Timothy Riesen, and Shamby Polychronis. 15
3 Common Core State Standards Primer for Special Educators
Shawnee Y. Wakeman and Angel Lee. 37
II Teaching Common Core Language Arts
4 Passage Comprehension and Read-Alouds
Leah Wood, Diane M. Browder, and Maryann Mraz. 63
5 Reading for Students Who Are Nonverbal
Lynn Ahlgrim-Delzell, Pamela J. Mims, and Jean Vintinner. 85
6 Comprehensive Beginning Reading
Jill Allor, Stephanie Al Otaiba, Miriam Ortiz, and Jessica Folsom. 109
7 Teaching Written Expression to Students with Moderate to Severe Disabilities
Robert Pennington and Monica Delano. 127
III Teaching Common Core Mathematics and Teaching Science
8 Beginning Numeracy Skills
Alicia F. Saunders, Ya-yu Lo, and Drew Polly. 149
9 Teaching Grade-Aligned Math Skills
Julie L. Thompson, Keri S. Bethune, Charles L. Wood, and David K. Pugalee. 169
10 Science as Inquiry
Bree A. Jimenez and Heidi B. Carlone . 195
11 Teaching Science Concepts
Fred Spooner, Bethany R. McKissick, Victoria Knight, and Ryan Walker. 215
IV Alignment of Curriculum, Instruction, and Assessment
12 The Curriculum, Instruction, and Assessment Pieces of the Student Achievement Puzzle
Rachel Quenemoen, Claudia Flowers, and Ellen Forte. 237
13 Promoting Learning in General Education for All Students
Cheryl M. Jorgensen, Jennifer Fischer-Mueller, and Holly Prud’homme . 255
14 What We Know and Need to Know About Teaching Academic Skills
Fred Spooner and Diane M. Browder. .275
Index . 287

Which way did the bicycle go: and other intriguing mathematical mysteries

Joseph D. E. Konhauser, Dan Velleman e Stan Wagon

The Mathematical Association of America | 1996 | 255 páginas | djvu | 4,2 Mb

link
link1

This book contains the best problems selected from over 25 years of the Problem of the Week at Macalester College. This collection will give students, teachers, and university professors a chance to experience the pleasure of wrestling with some beautiful problems of elementary mathematics. Readers can compare their sleuthing talents with those of Sherlock Holmes, who made a bad mistake regarding the first problem in the collection: Determine the direction of travel of a bicycle that has left its tracks in a patch of mud. The collection contains a variety of other unusual and interesting problems in geometry, algebra, combinatorics, and number theory. For example, if a pizza is sliced into eight 45-degree wedges meeting at a point other than the center of the pizza, and two people eat alternating wedges, will they get equal amounts of pizza? Or: Is an advertiser's claim that a certain unusual combination lock allows thousands of combinations justified? Complete solutions to the 191 problems are included with problem variations and topics for investigation.

Contents
Preface
Plane geometry
Number theory
Algebra
Combinatorics and graph theory
Three-dimensional geometry
Miscellaneous
Solutions

The Mathematical Traveler: Exploring The Grand History Of Numbers

Calvin C. Clawson

Springer | 1994 | 310 páginas | rar - pdf | 11,6 Mb

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This classic work by Calvin Clawson examines the remarkable co-evolution of numbers and human culture. From the early clay beads and ropes that our ancestors used as primitive counting tools to the influence of fractals and complex number systems on chaos theory, The Mathematical Traveler takes us on a journey over continents and through time to discover how mathematics has become an integral part of our world. We stop at ancient Sumeria, China, Greece, Italy, and England, where we learn about the discovery of our current counting system, the golden mean, pi, irrational numbers, and other mathematical innovations. More than just an overview of the history of numbers, The Mathematical Traveler explores how the understanding of mathematics helped humanity to create the underpinnings of art, technology, economics, and science that shaped the world we live in today.

Contents
INTRODUCTION 1
CHAPTER 1 How Do We Count? 5
CHAPTER 2 Early Counting 19
CHAPTER 3 Counting in Other Species 37
CHAPTER 4 Ancient Numbers 49
CHAPTER 5 Chinese and New World Numbers 77
CHAPTER 6 Problems in Paradise 95
CHAPTER 7 The Negative Numbers 121
CHAPTER 8 Dealing with the Infinite 135
CHAPTER 9 Dedekind's Cut: Irrational Numbers 161
CHAPTER 10 Story of 'IT: Transcendental Numbers 181
CHAPTER 11 Expanding the Kingdom: Complex Numbers 207
CHAPTER 12 Really Big: Transfinite Numbers 223
CHAPTER 13 The Genius Calculators 233
CHAPTER 14 What Does It All Mean? 247
CHAPTER 15 Numbers: Past, Present, and Future 263
End Notes 281
Glossary 289
Bibliography 299
Index 3

Outro livro do mesmo autor:

Mathematical sorcery : revealing the secrets of numbers por Calvin C Clawson Idioma: Inglês   Editora: New York : Plenum, ©1999.

Using and Applying Mathematics at Key Stage 1: A Guide to Teaching Problem Solving and Thinking Skills

Elaine Sellars e Sue Lowndes

David Fulton Publishers | 2003 | 63 páginas | rar - pdf | 3,1 Mb

link (password: matav)


All pupils - able children included - need to be taught strategies to enable their thinking skills to progress. They also need help with developing different approaches to problem solving. A sustained piece of work that requires perseverance, logical strategies, and refinement of method and extension of the original task is not the same as a straightforward quick-fix type problem. Both types of problem solving need to be taught. This book presents a series of activities that can be used with whole classes to provide a curriculum for the teaching of problem solving and the development of thinking skills. Each tried and tested investigation is clearly explained with ideas on how to introduce the task to a class, full solutions and resource sheets.
Activities include making 10p: a task to encourage systematic listing; tables and chairs: working systematically and spotting patterns; polygons and polyhedra: investigating diagonals, triangles, faces, edges and vertices; hidden faces: investigating different shapes and sizes of dice; and pond borders: investigating area and perimeter.

Proceedings of the Seventh International Congress on Mathematical Education

ICME-7    1992      Québec (Canada)

Claude Gaulin, Bernard R. Hodgson, David H. Wheeler, John C. Egsgard

Les Presses de l'Universite Laval | 1994 | 529 páginas | pdf (OCR) |33,4  Mb

link

pdf - 496,6 Mb (no OCR) 
link direto: mathematik.uni-bielefeld.de

djvu - 50,7 Mb (OCR)
link direto:  mathematik.uni-bielefeld.de

Contents 

Preface p. XIII 

Codes of countries p. XXI 

Schedule p. XXIV 

PRESIDENTIAL ADDRESS1

Plenary Lectures 

Teachers of Mathematics - Geoffrey Howson p. 9 

Bringing Mathematical Research to Life in the Schools - Maria M. Klawe p. 27 

Enseigner la géométrie: permanences et révolutions - Colette Laborde p. 47 

Fractals, the Computer, and Mathematics Education - Benoit B. Mandelbrot p. 77 

Working Groups 

WG 1: La formation de concepts mathématiques élémentaires au primaire (Helen Mansfield, AUS) p. 101 

WG 2: Students' Misconceptions and Inconsistencies of Thought (Shlomo Vinner, ISR) p. 109 

WG 3: Students' Difficulties in Calculus (Michèle Artigue, FRA) p. 114 

WG 4: Theories of Learning Mathematics (Pearla Nesher, ISR) p. 120 

WG 5: Improving Students' Attitudes and Motivation (Gilah Leder, AUS) p. 128 

WG 6: Preservice and Inservice Teacher Education (John Dossey, USA) p. 134 

WG 7: Language and Communication in the Mathematics Classroom (Heinz Steinbring) 

WG 8: Innovative Assessment of Students in the Mathematics (Jùlianna Szendrei, HUN) 

WG 9: [Not listed] 

WG 10: Multicultural and Multilingual Classrooms (Patrick Scott, USA) p. 154 

WG 11: The Role of Geometry in General Education (Rina Hershkowitz, ISR) p. 160 

WG 12: Probability and Statistics for the Future Citizen (Mary Rouncefield, GBR) p. 168 

WG 13: The Place of Algebra in Secondary and Tertiary Education (Carolyn Kieran, CAN) 

WG 14: Mathematical Modelling in the Classroom (Trygve Breitag, NOR) p. 180 

WG 15: Undergraduate Mathematics for Different Groups of Students (Daniel Alibert, FRA) 

WG 16: The Impact of the Calculator on the Elementary School (Hilary Shuard †, GBR) 

WG 17: Technology in the Service of the Mathematics Curriculum (Klaus-D. Graf, GER)  

WG 18: Methods of Implementing Curriculum Change (Hugh Burkhard, GBR) p. 202 

WG 19: Early School Leavers (Carlos Vasco, COL) p. 205 

WG 20: Mathematics in Distance Learning (Gordon Knight, NZL) p. 211 

WG 21: The Public Image of Mathematics and Mathematicians (Thomas Cooney, USA)

WG 22: Mathematics Education with Reduced Resources (Elfriede Wenzelburger †, MEX)

WG 23: Methodologies in Research in Mathematics Education (Norbert Knoche, GER)

Topic Groups 

TG 1: Mathematical Competitions (Edward J. Barbeau) p. 239 

TG 2: Ethnomathematics and Mathematics Education (Ubiratan D'Ambrosio, BRA) p. 242 

TG 3: Mathematics for Work: Vocational Education (Rudolf Straesser, GER) p. 244 

TG 4: Indigenous Peoples and Mathematics Education (Bill Barton, NZL) p. 247 

TG 5: The Social Context of Mathematics Education (Alan J. Bishop) p. 250 

TG 6: The Theory of Practice and Proof (Gila Hanna, CAN) p. 253 

TG 7: Mathematical Games and Puzzles (Tibor Szentivanyi, HUN) p. 257 

TG 8: Teaching Mathematics through Project Work (Jarkko Leino, FIN) p. 260 

TG 9: Mathematics in the Context of the Total Curriculum (John Mack, AUS) p. 264 

TG 10: Constructivist Interpretations of Teaching and Learning Mathematics (John A. Malone and Peter S. Taylor, AUS) p. 268 

TG 11: Art and Mathematics (Rafael Pérez Gòmez, ESP) p. 272 

TG 12: Graduate Programs and the Formation of Researchers in Mathematics Education (Hans-Georg Steiner, DEU) p. 274 

TG 13: Television in the Mathematics Classroom (David Roseveare, GBR) p. 278 

TG 14: Cooperation between Theory and Practice in Mathematics Education (Falk Seeger, DEU) p. 282 

TG 15: Statistics in the School and College Curriculum (Richard Schaeffer, USA) p. 286 

TG 16: The Philosophy of Mathematics Education (Paul Ernest, GBR) p. 289 

TG 17: La documentation professionnelle des enseignants de mathématiques (Jeanne Bolon, FRA) p. 293 

Study Groups 

HPM: An Historical Perspective on Learning, Teaching and Using Mathematics p. 299 

IOWME: Gender and Mathematics Education p. 304 

PME: Report of Activities p. 310 

ICMI Studies 

S1: The Influence of Computers and Informatics on Mathematics and its Teaching p. 315 

S2: The Popularization of Mathematics p. 319 

S3: Assessment in Mathematics Education and its Effects p. 323 

Miniconference on Calculators and Computers p. 331 

Abstracts of Lectures p. 341-382 

[contains the abstracts of the Selected Lectures of the second volume and the abstracts of the lectures by following authors: Philip J. Davis, Jean-Marc Deshouillers, Joaquin Giménez, Fred Goffree, Ronald L. Graham, Magdalene Lampert, Ronald Lancaster, Fernand Lemay, Charles Lovitt, , Seymour Papert, Nancy Shelley, Uri Treisman, Marion Walter] 

Short Presentations and Round Tables p. 385 

Projects and Workshops p. 389 

Special Exhibitions and Math Trail p. 399 

National Presentations p. 407 

Special Sessions 

Probe p. 413 

Crossfire: Mathematical Competitions - Do the Benefits Outweigh the Disadvantages? p. 417 

Awarding of Honorary Degrees to Jean-Pierre Kahane and Henry Pollak p. 421 

Tribute to H.S.M. Coxeter p. 423 

A Celebration in Memory of Caleb Gattegno p. 425 

Films and Videos p. 429 

Special Meetings p. 433 

Secretary's Closing Remarks - Mogens Niss p. 437 

Committees and Sponsors p. 451 

List of Participants p. 463 

Distribution by Country p. 494