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

Cases of Assessment in Mathematics Education: An ICMI Study

Mogens Niss

Springer | 1993 ; edição de 2013 | 215 páginas | pdf | 5,9 Mb

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This book is one of the first to present a variety of carefully selected cases to describe and analyze in depth and considerable detail assessment in mathematics education in various interesting places in the world. The book is based on work presented at an invited international ICMI seminar and includes contributions from first rate scholars from Europe, North America, the Caribbean, Asia and Oceania, and the Middle East.
The cases presented range from thorough reviews of the state of assessment in mathematics education in selected countries, each possessing `archetypical' characteristics of assessment, to innovative or experimental small or large scale assessment initiatives. All the cases presented have been implemented in actual practice.
The book will be particularly stimulating reading for mathematics educators -- at all levels -- who are concerned with the innovation of assessment modes in mathematics education, as well as everybody working in the field of mathematics education: in research and development, in curriculum planning, assessment institutions and agencies, mathematics specialists in ministries, teacher trainers, textbook authors, frontline teachers.

TABLE OF CONTENTS
MOGENS NISS
Introduction 1
LUIS RICO
Mathematics Assessment in the Spanish Educational System 9
DESMOND R. BROOMES & JAMES A. HALLIDAY
Major Issues in Assessing Mathematics Performance at 16+ Level: A Caribbean Perspective 21
MURAD JURDAK
Assessment in Mathematics Education in the Arab Countries 35
JOHN A. DOSSEY & JANE O. SWAFFORD
Issues in Mathematics Assessment in the United States 43
EDWARD A. SILVER & SUZANNE LANE
Assessment in the Context of Mathematics Instruction Reform: the Design of Assessment in the QUASAR Project 59
MARGARET BROWN
Assessment in Mathematics Education: Developments in Philosophy and Practice in the United Kingdom 71
CHRIS LITTLE
The School Mathematics Project: Some Secondary School Assessment Initiatives in England 85
LUCIANA BAZZINI
The Teaching/Learning Process and Assessment Practice: Two Intertwined Sides of Mathematics Education 99
GUNNAR GJONE
Types of Problems and How Students in Norway Solve Them 107
HANS NYGAARD JENSEN
Assessment of Primary and Lower Secondary Mathematics in Denmark 119
KIRSTEN HERMANN & BENT HIRSBERG
Assessment in Upper Secondary Mathematics in Denmark 129
WIM KLEUNE & HENK SCHURING
Assessment of Examinations in the Netherlands 139
MAX STEPHENS & ROBERT MONEY
New Developments in Senior Secondary Assessment in Australia 155
LEONOR CUNHA LEAL & PAULO ABRANTES
Assessment in an Innovative Curriculum Project for Mathematics in Grades 7-9 in Portugal
WEI CHAO-QUN & ZHANG HUI
Educational Assessment in Mathematics Teaching: Applied Research in China
CHENG ZEMIN & LV SHAOZHENG
The Practice and Study of Evaluating Mathematics Teaching in China
RUTH K. SWEETNAM
Assessment in Mathematics Within the International Baccalaureate 203
Index 213

The Place of mathematics in modern education

NCTM Yearbooks, 11.º

NCTM | 1936 | 284 páginas | pdf |

online: ERIC

Contents
Attacks on mathematics and how to meet them / W.D. Reeve
The reorganization of secondary education / William Betz
The meaning of mathematics / E.T. Bell
The contribution of mathematics to civilization / David Eugene Smith
The contribution of mathematics to education / Cyril Ashford
Mathematics in general education / W. Leitzmann
Mathematics as related to other great fields of knowledge / Georg Wolff
Form and appreciation / Griffith C. Evans

Mathematical Modelling Education, Engineering And Economics

ICTMA 12

Christopher Haines, Peter Galbraith, Werner Blum e Sanowar Khan

Woodhead Publishing | 2007 | 511 páginas | rar - pdf | 63,6 Mb

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This book continues the ICTMA tradition of influencing teaching and learning in the application of mathematical modelling. Each chapter shows how real life problems can be discussed during university lectures, in school classrooms and industrial research. International experts contribute their knowledge and experience by providing analysis, insight and comment whilst tackling large and complex problems by applying mathematical modelling. This book covers the proceedings from the Twelfth International Conference on the Teaching of Mathematical Modelling and Applications.

• Covers the proceedings from the Twelfth International Conference on the Teaching of Mathematical Modelling and Applications
• Continues the ICTMA tradition of influencing teaching and learning in the application of mathematical modelling
• Shows how real life problems can be discussed during university lectures, in school classrooms and industrial research

TABLE OF CONTENTS

Preface v

MODEL TRANSITIONS IN A REAL WORLD v

ICTMA12 - THE CONFERENCE vii

ICTMA xi

ICTMA Books xii

Acknowledgements xiii

Section 1: Models and Modelling in Reality 1

1.1 Communicating big themes in applied mathematics 2

Julian Hunt FRS, University College, London, UK

1.2 Economic modelling: Theory, reality, uncertainty and 25

decision-making

Kate Barker, Bank of England, UK

Section 2: Modelling Constructs in Education 43

2.1 Dreaming a 'possible dream': More windmills to conquer 44

Peter Galbraith, University of Queensland, Australia

2.2 Modelling in class: What do we want the students 63

to learn?

Katja Maaß, University of Education, Freiburg, Germany

2.3 Learning by constructing and sharing models 79

Celia Hoyles and Richard Noss, Institute of Education, University of London, UK

Section 3: Recognising Modelling Competencies 89

3.1 Exemplar models: Expert-novice student behaviours 90

Rosalind Crouch, University of Hertfordshire

and Christopher Haines, City University, London, UK

3.2 A teaching experiment in mathematical modelling 101

Toshikazu Ikeda, Yokohama National University, Japan

Max Stephens, University of Melbourne, Australia

and Akio Matsuzaki, Tsukuba University, Japan

3.3 Modelling and modelling competencies in school 110

Gabriele Kaiser, University of Hamburg, Germany

3.4    Exploring university students' competencies in modelling 120

France Caron and Jacques Bélair, Université de Montréal, Canada

3.5 Facilitating middle secondary modelling competencies 130

Peter Galbraith, University of Queensland, Australia

Gloria Stillman and Jill Brown, University of Melbourne

and Ian Edwards, Luther College, Melbourne, Australia

3.6 Assessing mathematical modelling competency 141

Tomas Højgaard Jensen, The Danish University of Education, Denmark

3.7 A stochastic model for the modelling process 149

Michael Voskoglou, Higher Technological Educational Institute, Patras, Greece

3.8 Assessing progress in mathematical modelling 158

John Izard, RMIT University, Melbourne, Australia

3.9 An introduction to CUMCM

Qiyuan Jiang and Jinxing Xie, Tsinghua University, China 168

and Qixiao Ye, Beijing Institute of Technology, China

Section 4: Everyday Aspects of Modelling 'Literacy' 176

4.1 Functional mathematics and teaching modelling 177

Hugh Burkhardt, University of Nottingham, UK

4.2 Modelling and the critical use of mathematics 187

Jussara de Loiola Araújo, Universidade Federal de Minas Gerais (UFMG), Brazil

4.3 Learners’ context preferences and mathematical literacy 195

Cyril Julie, University of the Western Cape, South Africa

4.4 ‘Real world’ interactions for adult basic numeracy tutors 203

Yvonne Hillier, City University, London, UK

4.5 Math modelling: What skills do employers want in industry? 212

ManMohan Sodhi and Byung-Gak Son, City University, London, UK

Section 5: Cognitive Perspectives on Modelling 221

5.1 How do students and teachers deal with modelling problems? 222

Werner Blum and Dominik Leiß, University of Kassel, Germany

5.2    Teacher-student interactions in mathematical modelling 232

Jonei Cerqueira Barbosa, State University of Feira de Santana, Brazil

5.3 Mathematical modelling: A teachers' training study 241

José Ortiz, University of Carabobo, Venezuela,

Luis Rico and Enrique Castro, University of Granada, Spain

5.4 Mathematics in the physical sciences: Multiple perspectives 250

Geoff Wake and Graham Hardy, University of Manchester, UK

5.5 Modelling problems from a cognitive perspective 260

Rita Borromeo Ferri, University of Hamburg, Germany

5.6 An explorative study on realistic mathematical modelling 271

Cinzia Bonotto, University of Padova, Italy

5.7 Student reasoning when models and reality conflict 281

Jerry Legé, California State University, Fullerton, USA

5.8 The concept of the derivative in modelling and applications 288

Gerrit Roorda, Pauline Vos and Martin Goedhart,        University of Groningen, The Netherlands

5.9 Inequalities as modelling tools in computing applications 294

Sergei Abramovich, State University of New York at Potsdam, USA

Section 6: The Practice of Modelling 303

6.1 Integration of energy issues in mathematics classrooms 304

Astrid Brinkmann, Berufskolleg Iserlohn, University of Dortmund

and Klaus Brinkmann, University of Trier, Umwelt Campus, Birkenfeld, Germany

6.2   Models of ecology in teaching engineering mathematics 314

Norbert Gruenwald and Gabriele Sauerbier,

Wismar University of Technology, Germany,

Tatyana Zverkova, Odessa National University, Ukraine

and Sergiy Klymchuk, Auckland University of Technology, New Zealand

6.3 Modelling as an integrated part of the class on calculus 323

Adolf Johannes Riede, Ruprecht-Karls-Universität, Heidelberg, Germany

6.4 Case study: Leak detection in a pipeline 332

Andrei Kolyshkin, Riga Technical University, Latvia

6.5 Discrete and continuous models for the evolution of 340

lizard populations

Michael Jones and Arup Mukherjee, Montclair State University, New Jersey, USA

6.6 Modelling and problem solving in billiards 349

Burkhard Alpers,  Aalen University of Applied Sciences: Germany

6.7 The lottery of Casanova 359

Hans-Wolfgang Henn and Andreas Büchter, University of Dortmund, Germany

6.8 Model transitions in the real world: The Catwalk problem 368

Thomas Lingefjärd and Mikael Holmquist, Gothenburg University, Sweden

6.9 Fractal image compression 377

Franceso Leonetti, University of L’Aquila, Italy

6.10 Modelling heat flow in work rolls 386

Leticia Corral, Instituto Tecnológico de Cd. Cuauhtémoc, Chihuahua, Mexico,

Rafael Colás, UANL, San Nicolás de los Garza, Mexico and Antonino Hernández,
        Centro de Investigación en Materiales

Avanzados, Chihuahua, México

6.11 Applications of modelling in engineering and technology 395

Sanowar Khan, Kenneth Grattan and Ludwik Finkelstein,  City University, London, UK

Section 7: Behaviours in Engineering and Applications 405

7.1 Mathematics in architecture education 406

Igor Verner and Sarah Maor,  Technion – Israel Institute of Technology

7.2 Modelling in Engineering: Advantages and difficulties 415

Maria Salett Biembengut and Nelson Hein, Universidade Regional de Blumenau, Brazil

7.3 Modelling: Difficulties for novice engineering students 424

Marta Anaya, María Inés Cavallaro and María Cristina Domínguez,

University of Buenos Aires, Argentina

7.4 Integration of applications in the Technion calculus course 433

Shuki Aroshas, Igor Verner and Abraham Berman,        Technion – Israel Institute of Technology

7.5 Mathematical modelling modules for calculus teaching 443

Qiyuan Jiang and Jinxing Xie, Tsinghua University, China

and Qixiao Ye, Beijing Institute of Technology, China

7.6 An experimental approach to teaching modelling 451

Ken Houston and Mark McCartney, University of Ulster, UK

7.7 Modelling for pre-service teachers 458

Susann Mathews and Michelle Reed, Wright State University, Dayton, Ohio, USA

7.8 The Finnish Network for mathematical modelling 465

          Robert Piché, Seppo Pohjolainen, Kari Suomela, Kirsi Silius and
         Anne-Maritta  Tervakari, Tampere University of Technology, Finland

7.9 Learning environment through modelling and computing 473

Regina Lino Franchi, Methodist University of Piracicaba, Brazil

7.10 Modelling is for reasoning 480

Luís Soares Barbosa and Maria Helena Martinho, Minho University, Braga, Portugal

Authors’ contact email addresses 490

Teaching Fractions Through Situations : A Fundamental Experiment

 

(Mathematics Education Library) 

Guy Brousseau e Virginia McShane Warfield 

Springer | 2014 | 226 páginas | rar - pdf |1,8 Mb

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2,2 Mb - link

This work presents one of the original and fundamental experiments of Didactique, a research program whose underlying tenet is that Mathematics Education research should be solidly based on scientific observation. Here the observations are of a series of adventures that were astonishing for both the students and the teachers: the reinvention of fractions and of decimal numbers in a sequence of lessons and situations that permitted the students to construct the concepts for themselves. The book leads the reader through the highlights of the sequence's structure and some of the reasoning behind the lesson choices. It then presents explanations of some of the principal concepts of the Theory of Situations. In the process, it offers the reader the opportunity to join a lively set of fifth graders as they experience a particularly attractive set of lessons and master a topic that baffles many of their contemporaries.

Linguistic and Cultural Influences on Learning Mathematics

(Psychology of Education and Instruction Series)

Rodney R. Cocking e Jose P. Mestre 

Routledge | 1988 | 329 páginas | rar- pdf | 16,1 Mb

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The combined impact of linguistic, cultural, educational and cognitive factors on mathematics learning is considered in this unique book. By uniting the diverse research models and perspectives of these fields, the contributors describe how language and cognitive factors can influence mathematical learning, thinking and problem solving. The authors contend that cognitive skills are heavily dependent upon linguistic skills and both are critical to the representational knowledge intimately linked to school achievement in mathematics.

Contents
Contributors/ ix
Foreword xi
Chapter 1 Introduction: Considerations of Language Mediators of Mathematics Learning
Rodney R. Cocking, Jose P. Mestre
Chapter 2 Conceptual Issues Related to Mathematics Achievement of Language Minority Children 
Rodney R. Cocking, Susan Chipman
Chapter 3 Linking Language with Mathematics Achievement: Problems and Prospects
Geoffrey B. Saxe
Chapter 4 Intention and Convention in Mathematics Instruction: Reflections on the Learning of Deaf Students 63
Joan B. Stone
Chapter 5 Why Should Developmental Psychologists Be Interested in Studying the Acquisition of Arithmetic? 73
Ellin Kofsky Scholnick
Chapter 6 Patterns of Experience and the Language of Mathematics 91
Manon P. Charbonneau, Vera John-Steiner
Chapter 7 Bilingualism, Cognitive Function, and Language Minority Group Membership 101
Edward A. De A vila
Chapter 8 the Mathematics Achievement Characteristics of Asian-American Students 123
Sau-Lim Tsang
Chapter 9 Mexican-American Women and Mathematics: Participation, Aspirations, and Achievement 137
Patricia MacCorquodale
Chapter 10 Assumptions and Strategies Guiding Mathematics Problem Solving by Ute Indian Students 161
William L. Leap
Chapter 11 Opportunity to Learn Mathematics in Eighth-Grade Classrooms in the United States: Some Findings from the Second International Mathematics Study 187
Kenneth J. Travers
Chapter 12 the Role of Language Comprehension in Mathematics and Problem Solving 201
Jose P. Mestre
Chapter 13 Linguistic Features of Mathematical Problem Solving: Insights and Applications 221
George Spanos, Nancy C. Rhodes, Theresa Corasaniti Dale, Joann Crandall
Chapter 14 Bilinguals' Logical Reasoning Aptitude: a Construct Validity Study 241
Richard P. Duran
Chapter 15 Effects of Home Language and Primary Language on Mathematics Achievement: a Model and Results for Secondary Analysis 259
David E. Myers, Ann M. Milne
A Final Note... 294
Epilogue: And Then I Went to School 295
Joseph H. Suina
Author Index 301
Subject Index 309

Investigations into Assessment in Mathematics Education: An ICMI Study

(New ICMI Study Series)

Mogens Niss

Springer |1993; edição de 2010 | 272 páginas | rar - pdf | 24,5 Mb

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This book is one of the first to attempt a systematic in-depth analysis of assessment in mathematics education in most of its important aspects: it deals with assessment in mathematics education from historical, psychological, sociological, epistmological, ideological, and political perspectives. The book is based on work presented at an invited international ICMI seminar and includes chapters by a team of outstanding and prominent scholars in the field of mathematics education. Based on the observation of an increasing mismatch between the goals and accomplishments of mathematics education and prevalent assessment modes, the book assesses assessment in mathematics education and its effects. In so doing it pays particular attention to the need for and possibilities of assessing a much wider range of abilities than before, including understanding, problem solving and posing, modelling, and creativity. The book will be of particular interest to mathematics educators who are concerned with the role of assessment in mathematics education, especially as regards innovation, and to everybody working within the field of mathematics education and related areas: in R&D, curriculum planning, assessment institutions and agencies, teacher trainers, etc. 

TABLE OF CONTENTS
MOGENS NISS
Assessment in Mathematics Education and its Effects: An Introduction 1
JEREMY KILPATRICK
The Chain and the Arrow: From the History of Mathematics Assessment 31
GEOFFREY HOWSON
The Relationship Between Assessment, Curriculum and Society 47
JIM RIDGWAY & DON PASSEY
An International View of Mathematics Assessment - Through a Class, Darkly
PETER GALBRAITH
Paradigms, Problems and Assessment: Some Ideological Implications
DAVID WHEELER
Epistemological Issues and Challenges to Assessment: What is Mathematical Knowledge?
THOMAS A. ROMBERG
How One Comes to Know:
Models and Theories of the Learning of Mathematics
ANTOINE BODIN
What Does to Assess Mean? The Case of Assessing Mathematical Knowledge
STIEG MELLIN-OLSEN
A Critical View of Assessment in Mathematics Education: Where is the Student as a Subject? 143
HERBERT P. GINSBURG & SUSAN F. JACOBS & LUZ S. LOPEZ
Assessing Mathematical Thinking and Learning Potential in Primary Grade Children 157
BENGT JOHANSSON
Diagnostic Assessment in Arithmetic 169
JOHN IZARD
Challenges to the Improvement of Assessment Practice 185
MALCOLM SWAN
Improving the Design and Balance of Mathematical Assessment 195
DEREK FOXMAN
The Assessment of Performance Unit's Monitoring Surveys 1978-1987 217
DAVID F. ROBITAILLE & J. STUART DONN
TIMSS: The Third International Mathematics and Science Study 229
GIlA HANNA
The Validity of International Performance Comparisons 245
NORMAN L. WEBB
Visualizing a Theory of the Assessment of Students' Knowledge of Mathematics 253
Index 265