Foundations of Mathematics: An Active Approach to Number, Shape and Measures in the Early Years

Carole Skinner, Judith Stevens

Featherstone Education | 2013 | 137 páginas | rar - pdf | 12 Mb

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Foundations of Mathematics outlines seven strands of practice which underpin successful mathematical development inchildren aged 3-7. Early years mathematics specialists, Carole and Judith, draw on their experience of working with early years practitioners, including consultants and advisers, across the UK and internationally. The book is completely up-to-date and embeds the Revised Early Years Foundation Stage throughout the book. The book brims with multi-sensory ideas that will trigger children's curiosity, measuring using sand mousse, hunting for buried treasure and building secret dens outdoors.

There are:
- activities that involve playing and exploring,
- games to make learning active, and
- experiences to develop creative and critical thinking.

Alongside these practical experiences and activities are clear explanations of the reasoning behind the ideas with clear guidance on the role of the practitioner and 'Home Challenges' to promote the engagement of families. The authors provide straightforward advice to support the development of a mathematically-enriched learning environment and ideas to help children transfer learning into their own child-initiated play, to build a genuine and solid foundation for mathematics.

Contents
Chapter 1: All about number....7.
Numbers in order; Counting; Recognising numerals; Mathematical mark-making;
The role of the adult; Maths home challenges
Chapter 2: Doing calculations....25.
Adding; Subtracting; Multiplying and dividing ; The role of the adult; Maths home challenges
Chapter 3: Working with shapes...41.
3D shapes; 2D shapes.; Position, direction and movement.; Pattern and symmetry; The role of the adult; Maths home challenges
Chapter 4: Learning to measure....59.
Length; Weight; Capacity; Time; The role of the adult; Maths home challenges
Chapter 5: Solving problems...77
Problem solving on a maths trail; Problem solving using number; Problems involving doubling, halving and sharing; The role of the adult; Maths home challenges
Chapter 6: Collecting and sorting ...89.
Collecting; Sorting; Collections; The role of the adult; Maths home challenges
Chapter 7: Stories and rhymes...103.
Traditional stories; Core rhymes; Contemporary stories; The role of the adult; Maths home challenges ;Books and rhyme lists
Chapter 8: Maths outdoors...121
Extending indoor learning experiences outdoors.; Extending indoor role play to include
outdoor role play; Outdoor learning zones and resources.; Games to play outdoors; Tallying and scoring; The role of the adult
Aide memoire....133.
References and further reading...135

Play's the Thing : Mathematical Games for the Classroom and Beyond

 Alan Lipp

Anthem Press | 2011 | 147 páginas | rar - pdf | 238 kb

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The book presents 18 games and develops the concepts of game analysis and winning strategies. Students are encouraged to play these mathematical games together, collect data developed through their play, and analyze the data to develop a winning strategy. Through the exploration of mathematical games, ‘The Play’s the Thing’ introduces teachers and students to the fun of play and to the mathematics behind the fun.

ContentsAcknowledgments xi
Prologue To the Teacher xiii
Act 0 To the Student xv
Act 1 Blockers 1
Act 1 Exercises 2
Act 2 Nimble 5
Act 2 Exercises 6
Act 3 More Variations 9
Act 3 Exercises 10
Act 4 Take Away 1, 2, 3 13
Looking for a Strategy 13
Act 4 Exercises 14
Act 5 Two Piles: A Hidden Game 17
Act 6 Two Piles 1, 2, 3 21
Act 7 Nim 29
Act 8 Flit 37
Act 8 Exercises 38
Act 9 Mr Flit 41
Act 10 Landis 47
Act 10 Exercises 48
Act 11 Add’em Up 51
Act 11 Exercises 52
Act 12 Connect-the-Dots 55
Act 12 Exercises 55
Act 13 Boxes 59
Act 13 Exercises 60
Act 14 Hold That Line 65
Act 14 Exercises 66
Act 15 The Fifteen Game 69
Act 15 Exercises 70
Act 16 Sliders 73
Act 16 Exercises 75
Act 17 Lynch 76
Act 17 Exercises 78
Act 18 Progression: Down and Up 81
Act 19 Harder Stuff 87
Answers 97

Mathematics Teaching Practice: Guide for University and College Lecturers

John H. Mason

Woodhead Publishing | 2002 | 231 páginas | rar - pdf | 11,6 Mb

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Mathematics; Clarifying the distinction between mathematical research and mathematics education, this book offers hundreds of suggestions for making small and medium sized changes for lectures, tutorials, task design, or problem solving. Here is guidance and inspiration for effective mathematics teaching in a modern technological environment, directed to teachers who are unhappy with results or experience, or those now in teacher training or new to the profession. Commencing with a range of student behaviours and attitudes that have struck and amazed tutors and lecturers, Proffessor Mason offers a wealth of partial diagnoses, followed by specific advice and suggestions for remedial actions. 

Contents: 
Student difficulties with mathematics; 
Lecturing; 
Tutoring; 
Constructing tasks; 
Marking and commenting; 
Making use of history; 
Issues and concerns in teaching mathematics; 
Appendix A Exploratory tasks; 
Appendix B Convergence case study; 
Bibliography

Puzzles From Penrose the Mathematical Cat

Theoni Pappas

Wide World Publishing, Tetra | 2013 | 158 páginas | rar - pdf | 8,4 Mb

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The famous mathematical cat Penrose takes us on a trip though puzzleland, while sharing fascinating and challenging puzzles in this uniquely designed mini book. Each page's puzzle is introduced by our star Penrose or one of his quirky friends. Readers are treated to page after page of Penrose antics and problems, while the over 100 mind teasers stimulate and engage its readers gray cells, This book's mini format and fun graphics makes it hard to resist picking up, and its characters and puzzles are sure to entertain both kids or adults.

A Survey of the Almagest: With Annotation and New Commentary by Alexander Jones

Olaf Pedersen e Alexander Jones

Springer | 2011 | 481 páginas 

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The Almagest, by the Greek astronomer and mathematician Ptolemy, is the most important surviving treatise on early mathematical astronomy, offering historians valuable insight into the astronomy and mathematics of the ancient world.Pedersen's 1974 publication, A Survey of the Almagest, is the most recent in a long tradition of companions to the Almagest. Part paraphrase and part commentary, Pedersen's work has earned the universal praise of historians and serves as the definitive introductory text for students interested in studying the Almagest.In this revised edition, Alexander Jones, a distinguished authority on the history of early astronomy, provides supplementary information and commentary to the original text to account for scholarship that has appeared since 1974. This revision also incorporates various corrections to Pedersen's original text that have been identified since its publication.This volume is intended to provide students of the history of astronomy with a self-contained introduction to the Almagest, helping them to understand and appreciate Ptolemy's great and classical work.

Pacific CRYSTAL Centre for Science, Mathematics, and Technology Literacy: Lessons Learned

Larry D. Yore, Eileen Van Der Flier-Keller e David W. Blades

Sense Publishers | 2011 | 278 páginas | pdf | 2,2 Mb 

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The University of Victoria Pacifi c Centre for Scientifi c and Technological Literacy is one of fi ve Centres for Research into Youth, Science Teaching and Learning (CRYSTAL) funded for 5 years (2005-2010) by the Natural Sciences and Engineering Research Council Canada (NSERC). Pacifi c CRYSTAL intended to promote scientifi c, mathematical, and technological literacy for responsible citizenship through research partnerships with university and educational communities. Pacifi c CRYSTAL's functional structure consisted of 3 research and development nodes connected to a leadership and administrative node, which was charged with facilitating the activities of 19 projects and 42 principal investigators, partners, and research associates. Node 1, an incubation centre, involved extracurricular authentic science, mathematics, and technology experiences; Node 2, a classroom testing environment, fi eld-tested instructional ideas and strategies to develop evidence-based practices; and Node 3, lighthouse schools, involved systemic change and leadership opportunities that adapted, demonstrated, and disseminated tested ideas, resources, and strategies to a much broader education community and attempted to infl uence public policy. This book provides descriptions of the target goals, research and development projects, and lessons learned.

TABLE OF CONTENTS
List of Pacific CRYSTAL Project Leaders (2005–2011) ....... vii
Acknowledgements ........ ix
I. Overview, Common Themes, and Theoretical Frameworks
1. Pacific CRYSTAL Centre for Science, Mathematics, and Technology Literacy: Lessons Learned: Overview ......... 3
Larry D. Yore and Eileen Van der Flier-Keller
2. Foundations of Scientific, Mathematical, and Technological Literacies— Common Themes and Theoretical Frameworks ...... 23
Larry D. Yore
II. Authentic Learning—Informal Environments and Extracurricular Science, Mathematics, and Technology Opportunities: Anchoring and Bridging Real-world, Cultural, and School Experiences
3. Adolescents’ Science Career Aspirations Explored through Identity and Possible Selves ....... 47
E. Anne Marshall, Francis L. Guenette, Tanya Ward, Tara Morley, Breanna Lawrence and Kate Fisher
4. Giving Voice to Science from Two Perspectives: A Case Study ......... 67
Nikki Wright, Earl Claxton, Jr., Lewis Williams and Tammy Paul
5. Seaquaria in Schools: Participatory Approaches in the Evaluation of an Exemplary Environmental Education Program......... 83
David B. Zandvliet, Mary Holmes and Matthias Starzner
6. Teaching Problem Solving and Computer Science in the Schools: Concepts and Assessment .......... 99
Sarah Carruthers, Todd M. Milford, Yvonne Coady, Celina Gibbs, Katherine Gunion and Ulrike Stege
7. Outreach Workshops, Applications, and Resources: Helping Teachers to Climb Over the Science, Mathematics, and Technology Threshold by Engaging their Classes ... 113
Leslee Francis Pelton and Timothy W. Pelton
III. Moving Tested Ideas into Classrooms
8. Explicit Literacy Instruction Embedded in Middle School Science Classrooms: A Community-based Professional Development Project to Enhance Scientific Literacy ..... 133
Christine D. Tippett and Robert J. Anthony
9. Enhancing Science Education through an Online Repository of Controversial, Socioscientific News Stories  149
Susan M. Teed, David B. Zandvliet and Carlos Gustavo A. Ormond
10. Promoting Earth Science Teaching and Learning: Inquiry-based Activities and Resources Anchoring Teacher Professional Development and Education ... 165
Eileen Van der Flier-Keller, David W. Blades and Todd M. Milford
IV. Knowledge Transfer, Systemic Implementation, and Building Leadership Capacity
11. Modelling of Large-scale PISA Assessment Data: Science and Mathematics Literacy .. 187
Todd M. Milford, John O. Anderson and Jiesu Luo
12. Time and Teacher Control in Curriculum Adoption: Lessons from the Lighthouse Schools Project ..... 203
David W. Blades
13. The Development of a Place-based Learning Environment at the Bowen Island Community School .... 217
Carlos Gustavo A. Ormond, Susan M. Teed, Laura Piersol and David B. Zandvliet
V. Closing Remarks and Implications for the Future
14. Epilogue of Pacific CRYSTAL—Lessons Learned about Science, Mathematics, and Technology Literacy, Teaching and Learning ..... 237
Larry D. Yore and Eileen Van der Flier-Keller
Appendix: Pacific CRYSTAL Project: Highly Qualified Personnel .... 253
Index .... 265

Pythagoras His Life, Teaching, and Influence

Christoph Riedweg e Steven Rendall

Cornell University Press | 2011 . 2ª edição | 198 páginas | rar - epub | 1 Mb

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One of the most important mathematical theorems is named after Pythagoras of Samos, but this semi-mythical Greek sage has more to offer than formulas. He is said to have discovered the numerical nature of the basic consonances and transposed the musical proportions to the cosmos, postulating a "harmony of the spheres." He may have coined the words "cosmos" and "philosophy." He is also believed to have taught the doctrine of transmigration of souls and therefore to have advised a vegetarian diet.

Ancient legends have Pythagoras conversing with dogs, bears, and bulls. A distinctly Pythagorean way of life, including detailed ritual regulations, was observed by his disciples, who were organized as a secret society. Later, Pythagorean and Platonic teachings became fused. In this Platonized form, Pythagoreanism has remained influential through medieval Christianity and the Renaissance down to the present.

Christoph Riedweg's book is an engaging introduction to the fundamental contributions of Pythagoras to the establishment of European culture. To penetrate the intricate maze of lore and ascertain what history can tell us about the philosopher, Riedweg not only examines the written record but also considers Pythagoras within the cultural, intellectual, and spiritual context of his times. The result is a vivid overview of the life and teachings of a crucial Greek thinker and his most important followers.

Contents
Preface
1. Fiction and Truth: Ancient Stories about Pythagoras
Pythagoras’ Appearance
Biographical Information
Pythagoras as a Teacher
2. In Search of the Historical Pythagoras
The Cultural-Historical and Intellectual Environment
The Oldest Testimonies
Guru and Scholar
Did Pythagoras Invent the Word Philosophy?
3. The Pythagorean Secret Society
Were the Pythagoreans an Ancient “Sect”?
The Pythagoreans in the Fifth and Fourth Centuries B.C.E.
4. Thinkers Influenced by Pythagoras and His Pupils
Pre-Platonic Thinkers
Plato and the Old Academy
Hellenistic “Forgeries” and Neo-Pythagoreanism
Pythagoras as an Idea in the Middle Ages and Modernity—A Prospect
Chronology