Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades Pre K-2

John A. Van de Walle, Lou Ann H. Lovin, Karen H Karp and Jennifer M. Bay Williams

Pearson | 2013 - 2ª edição | 417 páginas | rar-pdf | 9,3 Mb

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Initially adapted from Van de Walle’s market-leading textbook, Elementary and Middle School Mathematics, the Van de Walle Professional Mathematics Series are practical guides for developmentally appropriate, student-centered mathematics instruction from best selling mathematics methods authors John Van de Walle, LouAnn Lovin, Karen Karp, and Jennifer Bay-Williams. Specially designed for in-service teachers, each volume of the series focuses on the content relevant to a specific grade band and provides additional information on creating an effective classroom environment, engaging families, and aligning teaching to the Common Core State Standards. Additional activities and expanded lessons are also included.

The series has three objectives:
1. To illustrate what it means to teach student-centered, problem-based mathematics
2. To serve as a reference for the mathematics content and research-based instructional strategies suggested for pre-kindergarten to grade two, grades three to five, and grades six to eight
3. To present a large collection of high quality tasks and activities that can engage children in the mathematics that is important for them to learn

Volume I is tailored specifically to pre-kindergarten to grade 2, allowing teachers to quickly and easily locate information to implement in their classes. The student-centered approach will result in children who are successful in learning mathematics, making these books indispensable for Pre-K-2 classroom teachers!

Table of Contents
Part 1: Establishing a Student-Centered Environment
Chapter 1: Teaching Mathematics for Understanding
Chapter 2: Teaching Mathematics Through Problem Solving
Chapter 3: Assessing for Learning
Chapter 4: Differentiating Instruction
Chapter 5: Planning, Teaching, and Assessing Culturally and Linguistically Diverse Children
Chapter 6: Planning, Teaching, and Assessing Children with Exceptionalities
Chapter 7: Collaborating with Families, Community, and Principals
Part 2: Teaching Student-Centered Mathematics
Chapter 8: Developing Early Number Concepts and Number Sense
Chapter 9: Developing Meaning for the Operations
Chapter 10: Helping Children Master the Basic Facts
Chapter 11: Developing Whole Number Place Value Concepts
Chapter 12: Building Strategies for Whole-Number Computation
Chapter 13: Promoting Algebraic Reasoning
Chapter 14: Exploring Early Fraction Concepts
Chapter 15: Building Measurement Concepts
Chapter 16: Developing Geometric Thinking and Geometric Concepts
Chapter 17: Helping Children Use Data

The Adventure of Reason: Interplay Between Philosophy of Mathematics and Mathematical Logic, 1900-1940

Paolo Mancosu

Oxford University Press | 2011 | 631 páginas | rar - pdf | 2,68 Mb

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Paolo Mancosu presents a series of innovative studies in the history and the philosophy of logic and mathematics in the first half of the twentieth century. The Adventure of Reason is divided into five main sections: history of logic (from Russell to Tarski); foundational issues (Hilbert's program, constructivity, Wittgenstein, Godel); mathematics and phenomenology (Weyl, Becker, Mahnke); nominalism (Quine, Tarski); semantics (Tarski, Carnap, Neurath). Mancosu exploits extensive untapped archival sources to make available a wealth of new material that deepens in significant ways our understanding of these fascinating areas of modern intellectual history. At the same time, the book is a contribution to recent philosophical debates, in particular on the prospects for a successful nominalist reconstruction of mathematics, the nature of finitist intuition, the viability of alternative definitions of logical consequence, and the extent to which phenomenology can hope to account for the exact sciences. 

CONTENTS

PART I. MATHEMATICAL LOGIC, 1900–1935

Introduction 2

1. The Development of Mathematical Logic from Russell to Tarski, 1900–1935 (with Richard Zach and Calixto Badesa) 5

PART II. FOUNDATIONS OF MATHEMATICS

Introduction 122

2. Hilbert and Bernays on Metamathematics 125

Addendum 155

3. Between Russell and Hilbert: Behmann on the Foundations of Mathematics 159

4. The Russellian Influence on Hilbert and His School 176

5. On the Constructivity of Proofs: A Debate among Behmann, Bernays, Godel, and Kaufmann 199

6. Wittgenstein’s Constructivization of Euler’s Proof of the Infinity of Primes (with Mathieu Marion) 217

7. Between Vienna and Berlin: The Immediate Reception of Godel’s Incompleteness Theorems 232

8. Review of Godel’s CollectedWorks, Vols. IV and V 240

PART III. PHENOMENOLOGY AND THE EXACT SCIENCES

Introduction 256

9. HermannWeyl: Predicativity and an Intuitionistic Excursion 259

10. Mathematics and Phenomenology: The Correspondence

between O. Becker and H.Weyl (with T. Ryckman) 277

11. Geometry, Physics, and Phenomenology: Four Letters of O. Becker to H.Weyl (with T. Ryckman) 308

12. “Das Abenteuer der Vernunft”: O. Becker and D. Mahnke on the Phenomenological Foundations of the Exact Sciences 346

PART IV. TARSKI AND QUINE ON NOMINALISM

Introduction 358

13. Harvard 1940–1941: Tarski, Carnap, and Quine on a Finitistic Language of Mathematics for Science 361

14. Quine and Tarski on Nominalism 387

PART V. TARSKI AND THE VIENNA CIRCLE ON TRUTH AND LOGICAL CONSEQUENCE

Introduction 412

15. Tarski, Neurath, and Kokoszy´nska on the Semantic Conception of Truth 415

16. Tarski on Models and Logical Consequence 440

Addendum 463

17. Tarski on Categoricity and Completeness: An Unpublished Lecture from 1940 469

18. Appendix: “On the Completeness and Categoricity of Deductive Systems” (1940) 485

Notes 493

Bibliography 571

Index 611

Outros livros do mesmo autor:

The philosophy of mathematical practice por Paolo Mancosu; Idioma: Inglês   Editora: Oxford : Oxford University Press, 2010.

Visualization, explanation and reasoning styles in mathematics por Paolo Mancosu; Klaus Frovin Jørgensen; Stig Andur Pedersen; Idioma: Inglês   Editora: Dordrecht ; Norwell, MA : Springer, ©2005.

Philosophy of mathematics and mathematical practice in the seventeenth century por Paolo Mancosu Idioma: Inglês   Editora: New York [u.a.] Oxford Univ. Press 1996

Mathematical Modelling in Education and Culture: ICTMA 10

(Mathematics & Applications)

Q.X. Ye, Werner Blum, S.K. Houston e Q.Y. Jiang

Woodhead Publishing |2003 | 341 páginas | pdf

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The mathematical modelling movement in mathematics education at school and university level has been influencing curricula for about 25 years. Lecturers will find useful material to enhance their teaching and extracurricular activities and educators will find innovative ideas to inform their course design and focus their research, while students will find interesting problems to explore.

Table of Contents
Preface X
Section A - Research in Teaching, Learning and Assessment
1 Context in application and modelling - an empirical approach
Andreas Busse' and Gabriele Kaise
2 Mathematical modelling as pedagogy: Impact of an immersion programme
Trudy Dunne' and Peter Galbraith2
3 Using ideas from physics in teaching mathematical proofs
Gila Hanna' and Hans Niels Jahnke
4 Deconstructing mathematical modelling: Approaches to problem solving
Christopher Haines’, Rosalind Crouch’ and Andrew Fitzharris’
5 Investigating students’ modelling skills
Ken Houston and Neville Neil
6 “How to model mathematically” table and its applications
Wang Geng
Section B - Mathematical Modelling Competitions
7 New applications of the mathematics A-lympiad
Dkdk de Haan
8 Mathematics contest in modelling: Problems from practice
Shang Shouting, Zheng Tong and Shang Wei
Section C - Using Technology in the Teaching of Modelling
9 Modelling and spreadsheet calculation 101
Mike Keune’ and Herbert Henning’
10 Technology-enriched classrooms: Some implications for teaching applications and modelling
Peter Galbraith, Peter Renshaw, Merrilyn Goos and Vince Geiger
11 Choosing and using technology for secondary mathematical modelling tasks: Choosing the right peg for the right hole
Vince Geiger, Peter Galbraith, Peter Renshaw and Merrilyn Goos
Section D - Models for Use in Teaching
12 Groups, symmetry and symmetry breaking
Albert Fassler
13 The rainbow: f'rom myth to model
Hans- Wolfgang Henn
14 Teaching inverse problems in undergraduate level mathematics, modelling and applied mathematics courses
Fengshan Liu
15 Bezier curves and surfaces in the classroom
Baoswan Dzung Wong
Section E - Teacher Education
16 A mathematical modelling course for pre-service secondary school mathematics teachers
Zhonghong Jiang, Edwin McClintock and George 0 'Brien
17 Mathematical modelling in teacher education
Mikael Holmquist and Thomas LingeJard
18 Two modelling topics in teacher education and training 209
Ado y Riede
Section F - Innovative Modelling Courses
19 The knowledge and implementation for the course of mathematical experiment
Zhao Jing, Jiang Jihong, Dan Qi and Fu Shilu
20 Teaching patterns of mathematical application and modelling in high school
Tang Anhua, Sui Lili and Wang Xiaodan
21 Mathematical experiment course: Teaching mode and its practice
Qiongsun Liu, Shanqiang Ren, Li Fu and Qu Gong
22 The mathematical modelling - orientated teaching method of elicitation
Ruiping Hu and Shuxia Zhang
23 Teaching and assessment of mathematical modelling in community colleges
Lu Xiuyan, Mo Jingiing and Lu Keqiang
24 The role of mathematical experiment in mathematics teaching
Jinyuan-Li
25 Theory and practice in teaching of mathematical modelling at high school level
Qiu Jinjia

Working with Foucault in Education

M. Walshaw

Sense Publishers | 2007 | 205 páginas | pdf |3,3 Mb
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Education has a long tradition of opening itself up to new ideas and new ideas are what Working with Foucault in Education is all about. The book introduces readers to the scholarly work of Michel Foucault at a level that it neither too demanding not too superficial. It demonstrates to students, educators, scholars and policy makers, alike, how those ideas might be useful in understanding people and processes in education. This new line of investigation creates an awareness of the merits and weaknesses of contemporary theoretical frameworks and the impact these have on the production of educational knowledge. Working with Foucault in Education engages readers in selected aspects of education. Its ten chapters take a thematic approach and include vignettes that explore issues relating to curriculum development, learning to teach, classroom learning and teaching, as well as research in contemporary society. These explorations allow readers to develop a new attitude towards education. The reason this is possible is that Foucault provides a language and the tools to deconstruct as well as shift thinking about familiar concepts. They also provide the means for readers to participate in educational criticism and to play a role in educational change.

CONTENTS
Acknowledgments ix
Foreword xi
1 Getting to grips with Foucault 1
The importance of theory 1
A context for Foucault’s ideas 3
Foucault and poststructuralism 5
A brief history of Foucault’s counter-history 6
Early work 8
From archaeology to genealogy to ethics 9
Key concepts 17
Conclusion 25
2 An archaeology of learning 27
Behaviourism 28
Cognitivism 29
Constructivism 31
Sociocultural formulations 32
Activity/Situativity/Social practice theory 34
Conclusion 37
3 Discourse analysis 39
Discourse 40
Discourse analysis 44
Subject positions and texts 45
The policy text in context 46
Conclusion 62
4 The subjectivity of the learner 65
Subjectivity as constituted in discourses 66
Power 67
Knowledge 69
Donna’s mathematical performance 71
Conclusion 77
5 Students’ identity at the cultural crossroads 79
Identity 80
Colliding discourses 82
Mothers and daughters and low socio-economic status 85
Mothers and daughters and high socio-economic status 89
Reflections on identity 93
6 Learning to teach in context 95
Teachers’ identities’ explained 95
Dividing practices 99
Exploring context in identity construction 102
Three moments of identity 103
Reflections on context in identity construction 109
7 Subjectivity and regulatory practices 111
Disciplinary power 112
Subjectification 114
An exploration into the constitution of teaching 115
Transitory positions 116
Regulatory practices 119
Technologies of surveillance and normalisation 124
Concluding thoughts on the constitution of teaching 127
8 Girls disciplining others 129
Normalisation 129
Stories about girls (and boys) in schooling 131
The study 133
Girls monitoring boys in the classroom 134
Girls monitoring other girls in the classroom 137
Closing comments about disciplining practices 140
9 Research 143
Knowing others 144
Research traditions 144
Rethinking research 146
Constructing reality 149
Breaking away from convention 152
Rachel’s story 155
Reflections on research 163
10 Endings marking new beginnings 165
Looking back 166
Looking forward 168
Bibliography 171
Suggestions for further reading 177
Foucault’s work: A selection 177
Index 181

Scientists, Mathematicians, and Inventors: An Encyclopedia of People Who Changed the World

Doris Simonis

Greenwood | 1998 | 256 páginas | epub | 4,4 Mb

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The first of four volumes in the landmark Lives and LegacieS Oryx Press series, Scientists, Mathematicians, and Inventors profiles approximately 200 men and women who changed the world by leaving lasting legacies in their fields. It fills a gap in the biographical reference shelf by offering far more than basic facts about a scientist's life and work—each entry describes not only the immediate effects of the individual's discoveries, but their impact on later scientific findings as well. Each entry contains a timeline listing important dates in the biographee's life as well as a bibliography of the most important works on the subject. A master timeline chronicling major events in scientific exploration and an annotated general bibliography are also included.

Mathematical Excursions

Richard N. Aufmann, Joanne Lockwood, Richard D. Nation and Daniel K. Clegg

Cengage Learning | 2012 - 3ª edição |1010 páginas | PDF | 25 Mb

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MATHEMATICAL EXCURSIONS, Third Edition, teaches students that mathematics is a system of knowing and understanding our surroundings. For example, sending information across the Internet is better understood when one understands prime numbers; the perils of radioactive waste take on new meaning when one understands exponential functions; and the efficiency of the flow of traffic through an intersection is more interesting after seeing the system of traffic lights represented in a mathematical form. Students will learn those facets of mathematics that strengthen their quantitative understanding and expand the way they know, perceive, and comprehend their world. We hope you enjoy the journey.

Contents
1. PROBLEM SOLVING. 
Inductive and Deductive Reasoning. Excursion: KenKen Puzzles: An Introduction. Problem Solving with Patterns. Excursion: Polygonal Numbers. Problem-Solving Strategies. Excursion: Routes on a Probability Demonstrator. Chapter 1 Summary. Chapter 1 Review. Chapter 1 Test. 
2. SETS. 
Basic Properties of Sets. Excursion: Fuzzy Sets. Complements, Subsets, and Venn Diagrams. Excursion: Subsets and Complements of Fuzzy Sets. Set Operations. Excursion: Union and Intersection of Fuzzy Sets. Applications of Sets. Excursion: Voting Systems. Infinite Sets. Excursion: Transfinite Arithmetic. Chapter 2 Summary. Chapter 2 Review Exercises. Chapter 2 Test. 
3. LOGIC. 
Logic Statements and Quantifiers. Excursion: Switching Networks. Truth Tables, Equivalent Statements, and Tautologies. Excursion: Switching Networks--Part II. The Conditional and the Biconditional. Excursion: Logic Gates. The Conditional and Related Statements. Excursion: Sheffer's Stroke and the NAND Gate. Symbolic Arguments. Excursion: Fallacies. Arguments and Euler Diagrams. Excursion: Using Logic to Solve Crypterithms. Chapter 3 Summary. Chapter 3 Review Exercises. Chapter 3 Test. 
4. APPORTIONMENT AND VOTING. 
Introduction to Apportionment. Excursion: Apportioning the 1790 House of Representatives. Introduction to Voting. Excursion: Variations of the Borda Count Method. Weighted Voting Systems. Excursion: Blocking Coalitions and the Banzhaf Power Index. Chapter 4 Summary. Chapter 4 Review Exercises. Chapter 4 Test. 
5. THE MATHEMATICS OF GRAPHS. 
Graphs and Euler Circuits. Excursion: Pen-Tracing Puzzles. Weighted Graphs. Excursion: Extending the Greedy Algorithm. Planarity and Euler's Formula. Excursion: The Five Regular Convex Polyhedra. Graph Coloring. Excursion: Modeling Traffic Lights with Graphs. Chapter 5 Summary. Chapter 5 Review Exercises. Chapter 5 Test. 
6. NUMERATION SYSTEMS AND NUMBER THEORY. 
Early Numeration Systems. Excursion: A Rosetta Tablet for the Traditional Chinese Numeration System. Place-Value Systems. Excursion: Subtraction via the Nines Complement and the End-Around Carry. Different Base Systems. Excursion: Information Retrieval via a Binary Search. Arithmetic in Different Bases. Excursion: Subtraction in Base Two via the Ones Complement and the End-Around Carry. Prime Numbers. Excursion: The Distribution of the Primes. Topics from Number Theory. Excursion: A Sum of the Divisors Formula. Chapter 6 Summary. Chapter 6 Review Exercises. Chapter 6 Test. 
7. GEOMETRY. 
Basic Concepts of Euclidean Geometry. Excursion: Preparing a Circle Graph. Perimeter and Area of Plane Figures. Excursion: Perimeter and Area of a Rectangle with Changing Dimensions. Properties of Triangles. Excursion: Topology: A Brief Introduction. Volume and Surface Area. Excursion: Water Displacement. Right Triangle Trigonometry. Excursion: Approximating the Value of Trigonometric Ratios. Non-Euclidean Geometry. Excursion: Finding Geodesics. Fractals. Excursion: The Heighway Dragon Fractal. Chapter 7 Summary. Chapter 7 Review Exercises. Chapter 7 Test. 
8. MATHEMATICAL SYSTEMS. 
Modular Arithmetic. Excursion: Computing the Day of the Week. Applications of Modular Arithmetic. Excursion: Public Key Cryptography. Introduction to Group Theory. Excursion: Wallpaper Groups. Chapter 8 Summary. Chapter 8 Review Exercises. Chapter 8 Test. 
9. APPLICATIONS OF EQUATIONS. 
First-Degree Equations and Formulas. Excursion: Body Mass Index. Rate, Ratio, and Proportion. Excursion: Earned Run Average. Percent. Excursion: Federal Income Tax. Second-Degree Equations. Excursion: The Sum and Product of the Solutions of a Quadratic Equation. Chapter 9 Summary. Chapter 9 Review Exercises. Chapter 9 Test. 
10. APPLICATIONS OF FUNCTIONS. 
Rectangular Coordinates and Functions. Excursion: Dilations of a Geometric Figure. Properties of Linear Functions. Excursion: Negative Velocity. Finding Linear Models. Excursion: A Linear Business Model. Quadratic Functions. Excursion: Reflective Properties of a Parabola. Exponential Functions. Excursion: Chess and Exponential Functions. Logarithmic Functions. Excursion: Benford's Law. Chapter 10 Summary. Chapter 10 Review Exercises. Chapter 10 Test. 
11. THE MATHEMATICS OF FINANCE. 
Simple Interest. Excursion: Day-of-the-Year Table. Compound Interest. Excursion: Consumer Price Index. Credit Cards and Consumer Loans. Excursion: Car Leases. Stocks, Bonds, and Mutual Funds. Excursion: Treasury Bills. Home Ownership. Excursion: Home Ownership Issues. Chapter 11 Summary. Chapter 11 Review Exercises. Chapter 11 Test. 
12. COMBINATORICS AND PROBABILITY. 
The Counting Principle. Excursion: Decision Trees. Permutations and Combinations. Excursion: Choosing Numbers in Keno. Probability and Odds. Excursion: The Value of Pi by Simulation. Addition and Complement Rules. Excursion: Keno Revisited. Conditional Probability. Excursion: Sharing Birthdays. 12.6 Expectation. Excursion: Chuck-a-luck. Chapter 12 Summary. Chapter 12 Review Exercises. Chapter 12 Test. 
13. STATISTICS. 

Measures of Central Tendency. Excursion: Linear Interpolation and Animation. Measures of Dispersion. Excursion: Geometric View of Variance and Standard Deviation. Measures of Relative Position. Excursion: Stem-and-Leaf Diagrams. Normal Distribution. Excursion: Cut-Off Scores. Linear Regression and Correlation. Excursion: An Application of Linear Regression. Chapter 13 Summary. Chapter 13 Review Exercises. Chapter 13 Test.

Success with STEM: Ideas for the classroom, STEM clubs and beyond

 Sue Howarth e Linda Scott 

Routledge | 2014 | 188 páginas | rar - pdf | 1,33 Mb

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Success with STEM is an essential resource, packed with advice and ideas to support and enthuse all those involved in the planning and delivery of STEM in the secondary school. It offers guidance on current issues and priority areas to help you make informed judgements about your own practice and argue for further support for your subject in school. It explains current initiatives to enhance STEM teaching and offers a wide range of practical activities to support exciting teaching and learning in and beyond the classroom.

Illustrated with examples of successful projects in real schools, this friendly, inspiring book explores:

• Innovative teaching ideas to make lessons buzz

• Activities for successful practical work

• Sourcing additional funding

• Finding and making the most of the best resources

• STEM outside the classroom

• Setting-up and enhancing your own STEM club

• Getting involved in STEM competitions, fairs and festivals

• Promoting STEM careers and tackling stereotypes

• Health, safety and legal issues

• Examples of international projects

• An wide-ranging list of project and activity titles

Enriched by the authors’ extensive experience and work with schools, Success with STEM is a rich compendium for all those who want to develop outstanding lessons and infuse a life-long interest in STEM learning in their students. The advice and guidance will be invaluable for all teachers, subject leaders, trainee teachers and NQTs.