The Simpsons and Their Mathematical Secrets

Bloomsbury USA | 2013 | 279 páginas | epub/mobi

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You may have watched hundreds of episodes of The Simpsons (and its sister show Futurama) without ever realizing that cleverly embedded in many plots are subtle references to mathematics, ranging from well-known equations to cutting-edge theorems and conjectures. That they exist, Simon Singh reveals, underscores the brilliance of the shows’ writers, many of whom have advanced degrees in mathematics in addition to their unparalleled sense of humor.
While recounting memorable episodes such as “Bart the Genius” and “Homer3,” Singh weaves in mathematical stories that explore everything from p to Mersenne primes, Euler’s equation to the unsolved riddle of P v. NP; from perfect numbers to narcissistic numbers, infinity to even bigger infinities, and much more. Along the way, Singh meets members of The Simpsons’ brilliant writing team—among them David X. Cohen, Al Jean, Jeff Westbrook, and Mike Reiss—whose love of arcane mathematics becomes clear as they reveal the stories behind the episodes.
With wit and clarity, displaying a true fan’s zeal, and replete with images from the shows, photographs of the writers, and diagrams and proofs, The Simpsons and Their Mathematical Secrets offers an entirely new insight into the most successful show in television history.

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Contents
CHAPTER 0 The Truth About The Simpsons
CHAPTER 1 Bart the Genius
CHAPTER 2 Are you π-Curious?
CHAPTER 3 Homer’s Last Theorem
CHAPTER 4 The Puzzle of Mathematical Humor
EXAMINATION I
CHAPTER 5 Six Degrees of Separation
CHAPTER 6 Lisa Simpson, Queen of Stats and Bats
CHAPTER 7 Galgebra and Galgorithms
EXAMINATION II
CHAPTER 8 A Prime-Time Show
CHAPTER 9 To Infinity and Beyond
CHAPTER 10 The Scarecrow Theorem
EXAMINATION III
CHAPTER 11 Freeze-Frame Mathematics
CHAPTER 12 Another Slice of π
CHAPTER 13 Homer3
EXAMINATION IV
CHAPTER 14 The Birth of Futurama
CHAPTER 15 1,729 and a Romantic Incident
CHAPTER 16 A One-Sided Story
CHAPTER 17 The Futurama Theorem
EXAMINATION V
EπLOGUE
APPENDIX 1 The Sabermetrics Approach in Soccer
APPENDIX 2 Making Sense of Euler’s Equation
APPENDIX 3 Dr. Keeler’s Recipe for the Sum of Squares
APPENDIX 4 Fractals and Fractional Dimensions
APPENDIX 5 Keeler’s Theorem
ACKNOWLEDGMENTS
ONLINE RESOURCES
PICTURE CREDITS
BY THE SAME AUTHOR

Numeracy and Beyond: Applying Mathematics in the Primary School

Martin Hughes, Charles Desforges, Christine Mitchell, Clive Carre

Open University Press | 2000 | 134 páginas | pdf |

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One of the fundamental problems in education is that of applying skills and knowledge which learners have gained in one context to problems they encounter in another. This is particularly so in mathematics, where the problems encountered by learners in applying mathematical knowledge are well documented. Using and applying mathematics has been a central component of the National Curriculum in mathematics. However, the National Numeracy Strategy has adopted a new approach, in which 'using and applying' is integrated throughout the mathematics curriculum. This book aims to help teachers develop their understanding and practice in this crucial area. It is based on the findings of a major research study, funded by the Nuffield Foundation, in which a group of primary teachers worked closely with the research team to develop their thinking and practice. The book provides a clear conceptual analysis of the problem of application, together with extensive examples of ways in which teachers can address it in their classrooms at Key Stages 1 and 2. A novel feature of the book is that it includes first-hand accounts of practice in Japanese classrooms, and outlines what teachers in the UK and elsewhere may learn from Japanese methods.

Number Theory in Mathematics Education: Perspectives and Prospects

(Studies in Mathematical Thinking and Learning)

Rina Zazkis, Stephen R. Campbell

Lawrence Erlbaum Associates | 2006 | 304 páginas | pdf | 2,8 Mb

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This book offers multiple interconnected perspectives on the largely untapped potential of elementary number theory for mathematics education: its formal and cognitive nature, its relation to arithmetic and algebra, its accessibility, its utility and intrinsic merits, to name just a few. Its purpose is to promote explication and critical dialogue about these issues within the international mathematics education community. The studies comprise a variety of pedagogical and research orientations by an international group of researchers that, collectively, make a compelling case for the relevance and importance of number theory in mathematics education in both pre K-16 settings and mathematics teacher education. Topics variously engaged include: • understanding particular concepts related to numerical structure and number theory; • elaborating on the historical and psychological relevance of number theory in concept development; • attaining a smooth transition and extension from pattern recognition to formative principles; • appreciating the aesthetics of number structure; • exploring its suitability in terms of making connections leading to aha! insights and reaching toward the learner's affective domain; • reexamining previously constructed knowledge from a novel angle; • investigating connections between technique and theory; • utilizing computers and calculators as pedagogical tools; and • generally illuminating the role number theory concepts could play in developing mathematical knowledge and reasoning in students and teachers. Overall, the chapters of this book highlight number theory-related topics as a stepping-stone from arithmetic toward generalization and algebraic formalism, and as a means for providing intuitively grounded meanings of numbers, variables, functions, and proofs. Number Theory in Mathematics Education: Perspectives and Prospects is of interest to researchers, teacher educators, and students in the field of mathematics education, and is well suited as a text for upper-level mathematics education courses.

Contents
List of Contributors vii
Preface ix
1 Number Theory in Mathematics Education Research: Perspectives and Prospects
Rina Zazkis and Stephen R. Campbell
2 Understanding Elementary Number Theory in Relation to Arithmetic and Algebra
Stephen R. Campbell
3 What Makes an Example Exemplary: Pedagogical and Didactical Issues in Appreciating Multiplicative Structures
John Mason
4 For the Beauty of Number Theory 69
Nathalie Sinclair
5 On the Path to Number Theory: Repeating Patterns as a Gateway
Rina Zazkis and Peter Liljedahl
6 Learning by Teaching: The Case of Sieve of Eratosthenes and One Elementary School Teacher
Roza Leikin
7 Learning Elementary Number Theory Through a Chain of Discovery: Preservice Teachers’ Encounter with Pentominoes
Peter Liljedahl
8 The Number-Theoretic Experience of 12- to 15-Year-Olds in a Calculator Environment: The Intertwining Coemergence of Technique and Theory
Carolyn Kieran and José Guzmán
9 Learning Number Theory Concepts Via Geometrical Interactive Computerized Setting
Ilana Lavy
10 Overlooking Number Patterns in Algorithmic Problem Solving
David Ginat
11 Revisiting Algebra in a Number Theoretical Setting 249
Jennifer Christian Smith

Outros livros da mesma autora, disponíveis no blog:

- Campbell. S. R., & Zazkis, R. (Eds.) (2002). Learning and teaching number theory: Research in cognition and instruction. Westport, CT: Ablex Publishing 
- Leikin, R. & Zazkis, R. (Eds.) (2010). Learning through Teaching Mathematics:  Developing teachers’ knowledge and expertise in practice. Springer.

- Zazkis, R. (2011). Relearning mathematics: A challenge for prospective elementary school teachers. Information Age Publishing. Charlotte, NC.

Capítulos em livros, da mesma autora, disponíveis no blog:

- Zazkis, R. & Gadowsky, K. (2001). Attending to transparent features of opaque representations of natural numbers. In A. Cuoco (Ed.), NCTM 2001 Yearbook: The roles of representation in school mathematics (pp. 41-52). Reston, VA: NCTM. 
-  Zazkis, R. (2008). Divisibility and transparency of number representations. In M. P. Carlson & C. Rasmussen (Eds.), Making the Connection: Research and practice in undergraduate mathematics (pp. 81-92). MAA notes. 

Essential Primary Mathematics

Caroline Rickard
Open University Press | 2013 | 339 páginas | rar-pdf | 12,1 Mb

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If you are teaching or learning to teach primary mathematics, this is the toolkit to support you! Not only does it cover the essential knowledge and understanding that you and your pupils need to know, it also offers 176 great ideas for teaching primary mathematics - adaptable for use within different areas of mathematics and for different ages and abilities. Tackling children's misconceptions in each topic area and differentiation through open-ended tasks and elements of choice, the book encourages you to think deeply about the teaching of the primary mathematics curriculum. The classroom activities, which are simple to resource and use, support you in meeting the Teachers' Standards securely and encourage children to: think deeply about mathematics and to challenge themselves; develop mathematical independence; engage in mathematical talk; and work collaboratively with others to further understanding. Whether you are just getting started in your teaching career or more experienced you will find a wealth of innovative activities to support you in teaching primary mathematics in effective and creative ways. "This book is an absolute must for every primary teacher. The perfect blend of subject knowledge, common misconceptions, pupil activities and self-assessment questions will support all those who are feeling slightly less than confident about teaching a mathematical topic. It will also be invaluable to experienced teachers and subject leaders who wish to think more deeply about how to teach mathematics effectively." (Sue Davis, Primary PGCE Course Leader and Lecturer in Mathematics Education, University of Leicester, UK). "This book has the conversational style of an excellent mentor and/or tutor of primary mathematics. It offers advice and guidance on how to be an effective teacher of mathematics whilst still drawing the reader's attention to the importance of developing good subject knowledge, and how this can be addressed. Mathematical concepts are explained with reference to their theoretical underpinning and are then set in the context of real learning opportunities that illustrate good pedagogy. There is a real emphasis on teaching for learning, and this is most evident in the introductory chapter which provides a brief discussion of the big issues currently being debated in the field of primary mathematics. The consistent format of the subject chapters supports the reader's ability to plan and teach a wide range of appropriate activities based on rich mathematics. These are all neatly illustrated by children's drawings which bring the book to life. This is an all encompassing text for any student or teacher of mathematics and will feature on my highly recommended reading list." (Paula Stone, Senior Lecturer Primary Education (Mathematics), Canterbury Christ Church University, UK). "This book is ideal for student and practicing teachers alike. The user-friendly format such as the overview of contents at the beginning of each chapter and the highlighting of key misconceptions in each area, make it easy to locate relevant information. Each chapter evolves logically through subject knowledge and progression in learning for children. This book stands out from other texts I have used as there is an extremely helpful section at the end of each chapter which provides suggested classroom activities with associated learning objectives for each area of mathematics. As a final year student, I only wish this book had been available to me at the beginning of my course!" (Shelley Rogers, Student Teacher, University of Chichester, UK). "This book approaches the teaching of primary mathematics with a clear ethos, which is explained in the first chapter and then pervades all the suggestions and discussions which follow. The author deals with issues such as turning children's misconceptions and 'mistakes' into learning opportunities, provoking the children into communicating their reasoning and differentiating lessons in ways that empower rather than categorise children. The author's experience of having taught and observed hundreds of mathematics lessons is distilled into the essence of primary mathematics teaching." (Dr Marcus Witt, Senior Lecturer in Primary and Early Years Mathematics Education, University of the West of England, UK). "The theory sections of the book are really detailed which helps to provide a secure knowledge base for teaching primary mathematics. I especially like the way that the book is laid out; it is really easy to navigate. I love how the common misconceptions are outlined and explained in boxes separate to the body of the text but are also re-listed at the end of a chapter so that you could revise the potential issues which may arise before you start to teach a particular topic. The activities are well organised and adaptable but it is useful to see which age range each activity is suggested for at a glance, alongside the learning objective." (Natalie Ridler, NQT).

Contents
Acknowledgements ix
1 Introduction 1
2 Counting and the number system 12
3 Addition and subtraction 47
4 Multiplication 85
5 Division 120
6 Algebra 151
7 Measures 175
8 Data 200
9 Probability 240
10 Shape 263
11 Space 290
12 Conclusion 313
References 315
Index 317

Fractals, Googols, and Other Mathematical Tales

Theoni Pappas

Wide World Publishing, Tetra | 1993 | 72 Páginas | rar - pdf| 3 Mb

link (novo ficheiro)
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A new treasure trove of stories that make mathematical ideas come to life with an unusual cast of characters. This book explores mathematical concepts and topics such as real numbers, exponents, dimensions, and geometry in both serious and humorous ways.

Outros livros da mesma autora, disponíveis no blog:

The Magic Of Mathematics - Discovering The Spell Of Mathematics (1994)
The Joy of Mathematics: Discovering Mathematics All Around You  (1993)