Making Sense of Mathematics Teacher Education

Fou-Lai Lin e Thomas Cooney

Springer | 2001 | 329 páginas | pdf |10,9 Mb

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This is a research-based book that deals with a broad range of issues about mathematics teacher education. It examines teacher education programs from different societies and cultures as it develops an international perspective on mathematics teacher education. Practical situations that are associated with related theories are studied critically. It is intended for teacher educators, mathematics educators, graduate students in mathematics education, and mathematics teachers.

Contents
SECTION I: PERSPECTIVES ON TEACHER EDUCATION
THOMAS 1. COONEY / Considering the Paradoxes, Perils, and Purposes of Conceptualizing Teacher Development 9
STEPHEN LERMAN / A Review of Research Perspectives on Mathematics Teacher Education 33
SECTION II: MAKING SENSE OF MATHEMATICS
JOAo PEDRO DA PONTE / Investigating Mathematics and Learning to Teach Mathematics 53
DINA TIROSH, RUTH STAVY, and PESSIA TSAMIR / Using the Intuitive- Rules Theory as a Basis for Educating Teachers 73
COLETTE LABORDE / The Use of New Technologies as a Vehicle for Restructuring Teachers' Mathematics 87
SECTION III: MAKING SENSE OF TEACHING
FRED GOFFREE and WIL OONK / Digitizing Real Teaching Practice for Teacher Education Programmes: The MILE Approach 111
PETER SULLIVAN and JUDY MOUSLEY / Thinking Teaching: Seeing Mathematics Teachers as Active Decision Makers 147
KENNETH RUTHVEN / Mathematics Teaching, Teacher Education, and Educational Research: Developing "Practical Theorising" in Initial Teacher Education 165
ANNA SFARD and CAROLYN KIERAN / Preparing Teachers for Handling Students' Mathematical Communication: Gathering Knowledge and Building Tools 185
SECTION IV: MAKING SENSE OF THE CONTEXT OF TEACHING
PAUL COBB and KAY MCCLAIN / An Approach for Supporting Teachers' Learning in Social Context 207
ALAN J. BISHOP / Educating Student Teachers About Values in Mathematics Education 233
CHIEN CHIN, YUH-CHYN LEU, and FOU-LAI LIN / Pedagogical Values, Mathematics Teaching, and Teacher Education: Case Studies of Two Experienced Teachers 247
SECTION V: MAKING SENSE OF THE COMPLEXITY OF TEACHER EDUCATION
KONRAD KRAINER / Teachers' Growth is More Than the Growth of Individual Teachers: The Case of Gisela 271
BARBARA JAWORSKI/Developing Mathematics Teaching: Teachers, Teacher Educators, and Researchers as Co-Learners 295

Learning from Computers: Mathematics Education and Technology

 Christine Keitel-Kreidt e Kenneth Ruthven

Springer | 2011 - reprint of the original 1st ed. 1993 edition | páginas | rar - pdf |10,3 Mb

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This study offers a re-examination of the mathematics curriculum and the teaching of mathematics in the light of changing technological possibilities. Recent developments in cognitive technologies and the impact of technology on mathematics teaching are amongst the topics explored.

Contents
1. Microworlds/Schoolworlds: The Transformation of an Innovation.
1.1 The story of microworlds.
1.2 The genesis.
1.3 From designers to mathematics educators.
1.4 Generating mathematics through microworlds: some illustrations.
1.5 Evocative computational objects and situated abstractions.
1.6 Microworlds in school mathematics.
1.7 Microworlds in the curriculum.
1.8 Reflections and implications.
2. Computer Algebra Systems as Cognitive Technologies: Implication for the Practice of Mathematics Education.
2.1 CAS: Some examples of symbol manipulations.
2.2 Computers and computer algebras in relation to pure mathematics.
2.3 Computer Algebra Systems in relation to mathematics education.
2.4 Opposition to instructional uses of Computer Algebra Systems.
2.5 Strengths of Computer Algebra Systems as learning tools.
2.6 Computer algebra in an educational context: One example.
2.7 CAS: From amplifiers to reorganisers.
3. The Computer as Part of the Learning Environment: The Case of Geometry.
3.1 The dual nature of geometrical figures.
3.2 Difficulties of students.
3.3 The notion of geometric figure as mediated by the computer.
3.4 Changes brought by computers to the relationship to the figure.
3.5 Interactions between student and software.
4. Software Tools and Mathematics Education: The Case of Statistics.
4.1 Didactical transposition and software tools.
4.2 The revolution in statistics.
4.3 Graphical and interactive data analysis: an example.
4.4 Making sense of statistical software tools.
4.5 Statistics education.
4.6 Statistics and a re-defined school mathematics
5. Didactic Design of Computer-based Learning Environments.
5.1 Understanding mathematics and the use of computers.
5.2 Designing QuadFun - A case description.
5.3 Interlude: Experimental aspects of mathematics.
5.4 Design issues.
5.5 A systemic view of didactic design.
6. Artificial Intelligence and Real Teaching.
6.1 Didactical interaction revisited.
6.2 The input of artificial intelligence.
6.3 Student-computer interaction, an overview.
6.4 Educational software in the classroom, a new complexity.
6.5 Open questions for future practice.
7. Computer Use and Views of the Mind.
7.1 The notion of cognition.
7.2 Cognitive reorganization by using tools.
7.3 Cognitive models and concreteness of thinking.- 7.4 Situated thinking and distributed cognition
7.5 The computer as a medium for prototypes.
7.6 Modularity of thought.
7.7 Conclusion.
8. Technology and the Rationalisation of Teaching.
8.1 The rationalisation of social practice.
8.2 The elusive rationality of teaching.
8.3 The marginal impact of machines on teaching.
8.4 The dynamics of pedagogical change.
8.5 The programming microworld.
8.6 The tutoring system.
8.7 The computer and the rationalisation of teaching.
9. Computers and Curriculum Change in Mathematics.
9.1 Locating the curriculum.-
9.2 Curriculum change as institutional change.
9.3 Redefining school mathematics.
9.4 Planning curriculum change.
9.5 Alternative scenarios.
10. On Determining New Goals for Mathematical Education.
10.1 Goals for mathematics education.
10.2 Goals for mathematics learners.
10.3 Role of the teacher and the educational institution.
10.4 Needed research on goals in mathematics education.
11. Beyond the Tunnel Vision: Analysing the Relationship Between Mathematics, Society and Technology.
11.1 Setting the stage.
11.2 Technology in society.
11.3 Mathematics shaping society?.
11.4 Living (together) with abstractions.
11.5 Mathematical technology as social structures.
11.6 Structural problems in an abstraction society.
11.7 Mathematics education as a social enterprise.
11.8 Mathematics education as a democratic forum.
11.9 Reflecting on computers in the classroom: Hardware-software-be(a)ware.
12. Towards a Social Theory of Mathematical Knowledge.
12.1 The Mechanistic Age - a historical introduction.
12.2 Mathematical and social individuation.
12.3 How can we master technology?.
12.4 Engineers versus mathematicians since the turn of the century.
References
Software.

Proceedings of the Fifth International Congress on Mathematical Education

ICME-5    1984      Adelaide (Australia)

Marjorie Carss

Birkhäuser | 1986 | 410 páginas | rar - pdf | 8,3 Mb

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Most of the presentations and papers prepared for ICME 5 are not included in the proceedings.

CONTENTS
Foreword vii
Plenary Sessions
Socio-Cultural Bases for Mathematical Education - Ubiratan D'Ambrosio 1
Reflection and Recursion - Jeremy Kilpatrick 7
Discrete Mathematics - Renjrey Potts 31
Action Groups
1. Early Childhood Years 49
2. Elementary School (Ages 7-12) 57
3. Junior Secondary School (Ages 11-16) 73
4. Senior Secondary School (Ages 15-19) 84
5. Tertiary (Post-Secondary) Institutions (18 + ) 95
6. Pre-Service Teacher Education III
7. Mathematics in Adult, Technical and Vocational Education 124
Theme Groups
1. Mathematics For All 133
2. The Professional Life of Teachers 146
3. The Role of Technology 159
4. Theory, Research and Practice in Mathematical Education 177
5. Curriculum Development 187
6. Applications and Modelling 197
7. Problem Solving 212
Topic Areas
1. Evaluation, Examinations and Assessment 227
2. Competitions 243
3. The Teaching of Geometry 254
4. Relationship Between the History and Pedagogy of Mathematics 256
5. Language and Mathematics 261
6. Psychology of Mathematics Education 273
7. Research and Teaching 284
8. Theory of Mathematics Education 293
9. Teaching of Statistics 300
10. Women and Mathematics 306
Invited Addresses
Presidential Address - Jean-Pierre Kahane 315
Public Forum 328
The Effects of Technology on Mathematics Education 346
The Nature of Proof 352
Debate: The Microcomputer: Miracle or Menace in Mathematics Education? 359
Specially Invited Presentations 373
The Work of ICMI 380
List of Participants 382

Using lCT in Primary Mathematics Practice and Possibilities

 

Bob Fox, Ann Montague-Smith e Sarah Wilkes

David Fulton Publishers | 2000 | 161 páginas | rar - pdf | 4,66 Mb

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This work explores the development and classroom application of hardware and software for primary mathematics. It reviews available software, considers pedagogy and best practice in mathematics and provides examples of ICT in mathematics.

Contents

Acknowledgements and notes about the authors IV

Introduction V

1 Background to ICT in the primary school

Bob Fox 1

2 Mathematics teaching and learning: past, present and future

Ann Montague-Smith 24

3 Mathematics software and its use

Bob Fox, Ann Montague-Smith and Sarah Wilkes 52

4 Mathematics on-line

Bob Fox 107

5 ICT in the daily mathematics lesson

Bob Fox and Sarah Wilkes 112

6 Conclusion

Bob Fox 139

Resources: software and hardware 143

Bibliography 144

Index 150

30 Mathematics Lessons Using the TI-15

Christine Dugan 

Shell Education | 2009 | 258 páginas | rar- pdf | Mb

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This book is designed for grades 3-5 instruction and provides step-by-step mathematics lessons that incorporate the use of the TI-15 calculator throughout the learning process. The 30 lessons included present mathematics in a real-world context and cover each of the five strands: number and operations, geometry, algebra, measurement, and data analysis and probability.

Table of contents

Young Mathematicians at Work: Constructing Algebra

Catherine Twomey Fosnot e William Jacob 

 Heinemann | 2010 | 220 páginas | pdf | 3,4 Mb

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The first three volumes of this popular series help teachers support children's development in number sense and operation, from addition and subtraction through fractions, decimals, and percents. Catherine Twomey Fosnot and Maarten Dolk's signature approach uses classroom vignettes to illustrate the investigations and minilessons students engage in as they build their mathematical knowledge.

The hallmarks of their approach include:

• Supporting children as they construct mathematical strategies and big ideas

• Creating realistic contexts and representational models that develop children's capacity to mathematize their world

• Building a collaborative community of mathematical thinkers engaged in inquiry

For the fourth volume Catherine teams up with Bill Jacob to offer a comfortably familiar and characteristically rich extension to the earlier work. In Constructing Algebra Catherine and Bill provide a landscape of learning that helps teachers recognize, support, and celebrate their students' capacity to structure their worlds algebraically. They identify for teachers the models, contexts, and landmarks that facilitate algebraic thinking in young students.

This volume will be a welcome resource for classroom teachers, math supervisors, and curriculum coordinators alike. Preparing young children for success in algebra is a crucial topic. Constructing Algebra provides the insightful and practical methods from the most trusted source for teaching mathematics to young students from Kindergarten through grade 8.

CONTENTS

CHAPTER 1: ALGEBRA: STRUCTURES OR STRUCTURING? 3

CHAPTER 2: THE LANDSCAPE OF LEARNING 23

CHAPTER 3: EARLY STRUCTURING OF THE NUMBER SYSTEM 37

CHAPTER 4: CONTINUING THE JOURNEY: THE ROLE OF CONTEXTS AND MODELS 55

CHAPTER 5: EQUIVALENCE ON THE HORIZON 77

CHAPTER 6: VARIATION VERSUS VARIABLES 93

CHAPTER 7: FURTHER HORIZONS: INTEGERS AND EQUIVALENCE 111

CHAPTER 8: COMPARING QUANTITIES AND RELATIONS 129

CHAPTER 9: DEVELOPING ALGEBRAIC STRATEGIES WITH MINILESSONS 155

CHAPTER 10: PROOF 171

Outros livros da mesma série:

Young mathematicians at work. Constructing number sense, addition, and subtraction por Catherine Twomey Fosnot; Maarten Ludovicus Antonius Marie Dolk Idioma: Inglês   Editora: Portsmouth, NH : Heinemann, ©2001.

Young mathematicians at work. Constructing multiplication and division por Catherine Twomey Fosnot; Maarten Ludovicus Antonius Marie Dolk Idioma: Inglês   Editora: Portsmouth, NH : Heinemann, ©2001.

Young mathematicians at work : constructing fractions, decimals, and percents por Catherine Twomey Fosnot; Maarten Ludovicus Antonius Marie Dolk Idioma: Inglês   Editora: Portsmouth, NH : Heinemann, ©2002.

Karl Pearson: The Scientific Life in a Statistical Age

Theodore M. Porter

Princeton University Press | 2006 | 353 páginas | rar - pdf |2,8 Mb

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Karl Pearson, founder of modern statistics, came to this field by way of passionate early studies of philosophy and cultural history as well as ether physics and graphical geometry. His faith in science grew out of a deeply moral quest, reflected also in his socialism and his efforts to find a new basis for relations between men and women. This biography recounts Pearson's extraordinary intellectual adventure and sheds new light on the inner life of science.
Theodore Porter's intensely personal portrait of Pearson extends from religious crisis and sexual tensions to metaphysical and even mathematical anxieties. Pearson sought to reconcile reason with enthusiasm and to achieve the impersonal perspective of science without sacrificing complex individuality. Even as he longed to experience nature directly and intimately, he identified science with renunciation and positivistic detachment. Porter finds a turning point in Pearson's career, where his humanistic interests gave way to statistical ones, in his Grammar of Science(1892), in which he attempted to establish scientific method as the moral educational basis for a refashioned culture.
In this original and engaging book, a leading historian of modern science investigates the interior experience of one man's scientific life while placing it in a rich tapestry of social, political, and intellectual movements.

Contents
Preface and Acknowledgments vii
CHAPTER ONE Introduction: An Improbable Personage 1
CHAPTER TWO Lehrjahre of a Poetic Wrangler 13
CHAPTER THREE Apostle of Renunciation: A New Werther 43
CHAPTER FOUR Pearson’s Progress: A Nineteenth-Century Passion Play 69
CHAPTER FIVE Cultural Historian in a Political Age 91
CHAPTER SIX Intellectual Love and the Woman Question 125
CHAPTER SEVEN Ether Squirts and the Inaccessibility of Nature 178
CHAPTER EIGHT Scientific Education and Graphical Statistics 215
CHAPTER NINE The Statistical Reformation 249
CHAPTER TEN Epilogue: Composing a Life 297
Bibliography 315
Index 329

Outro livro do mesmo autor:

Trust in numbers : the pursuit of objectivity in science and public life por Theodore M Porter Idioma: Inglês   Editora: Princeton, N.J. : Princeton University Press, ©1995.