The Ambitious Horse - Ancient Chinese Mathematics Problems

Lawrence Swienciki

Key Curriculum | 2000 | 135 páginas | pdf (no OCR) | 7,94 Mb

online: math.utep.edu


pdf (OCR) - 5,72 Mb - link

• Numbers and Arithmetic includes subjects such as Chinese writing; The Calculating Rods of Ancient China: and ancient Chinese multiplication.

• Geometry and Dissection problems includes subjects such as tangrams, the Measure of Heaven and Ancient Chinese Philosophy.

• Algebra Integrated with Geometry includes subjects such as Square Roots; Quadratic Equations; and mathematical treats such as the "Pillar of Delightful Contemplation", the "Exalted Treasure of Jade" and the "Precious Golden Rope".

On the one hand this book is far beyond what many 7th and 8th grader students are capable of. On the other hand, it is so interesting and so well done that it might just be that this is the book that helps transforms your child from a grudging math student to an enthusiastic one!

Filled with stories, puzzles and plenty of hands-on problems, this book is a treasure. It is divided into three sections:

Answers and solutions included.

Note: The problems get more difficult as the book progresses and so can be used for several years. Suitable for a very math-able 7th grader, a solid 8th grader and to enthuse and inspire high school students

Math challenges : puzzles, tricks & games

Glen Vecchione e Nina Zottoli

Sterling | 1998 | 98 páginas | pdf |1,6 Mb

link

djvu - 1 Mb - link

Can quantum operations, recombinant shapes, and concealed distribution actually lead to fun? Sure they can! Just try these optical illusions, mechanical aptitude puzzles, maps and mazes. 

Contents1 Grid & Dot Games
2 Sum of the Parts
3 Vanishing Tricks
4 Stretchy Shapes & Squiggly Lines
5 Mechanical Aptitude
6 Logic Puzzles
7 Amazing Maps & Mazes
8 Fancy Figuring
9 Lewis Carroll, Puzzlemaker
Answers
Index

Mathematics for Secondary School Teachers

Elizabeth G. Bremigan, Ralph J. Bremigan e John D. Lorch

Mathematical Association of America | 2011 | páginas | rar - pdf | 3,9 Mb

link (password : matav)

Mathematics for Secondary School Teachers, which is intended for prospective educators in middle and high school, balances discovery learning with direct instruction.
Written to develop a deeper understanding of the mathematics that will be taught, the book presents topics of central importance in the secondary school mathematics curriculum, notably, functions, polynomials, trigonometry, exponential and logarithmic functions, numbers and operations, and measurements.
Beyond the goals of conceptual understanding and computational fluency, readers of the book can devise their own mathematical explanations and arguments; create examples and visual representations; remediate typical student errors and misconceptions; and analyze students’ work.
A broad collection of exercises of varying degrees of difficulty is integrated with the text. Instructors are able to emphasize the following:
Basics: The exploration of key precollege topics from intuitive and rigorous points of view;
Connections: The exploration of relationships among topics, using tools from college-level mathematics;
Extensions: The exploration of college-level mathematical topics that have a compelling relationship to precollege mathematics.
By taking into account the diverse mathematical backgrounds of preservice teachers and the varied goals of teacher preparation programs, the authors have written a textbook whose subject matter addresses a wide range of learning objectives appropriate for future teachers.
Mathematics for Secondary School Teachers can also be used in licensing programs; as a supplement to mathematics methods courses; as a text for graduate courses for in-service teachers; and as a resource for faculty development.

Table of ContentsPreface
To the Student
To the Instructor
1. Functions
2. Lines in the Plane
3. Quadratic Polynomials
4. Trigonometry
5. Hyperbolic Trigonometry
6. Numbers
7. Operations in Number Theory
8. Topics in Number Theory
9. Exponentiation
10. Exponential and Logarithmic Functions: History, Computation, and Application
11. Transcendental Functions and Complex Numbers
12. Beyond Quadratics: Higher Degree Polynomials
13. Measurement
Appendix A: Log Tables
Index

Writing Projects for Mathematics Courses: Crushed Clowns, Cars & Coffee to Go

Annalisa Crannell, Gavin LaRose e Thomas Ratliff

The Mathematical Association of America | 2004 | 128 páginas | rar - pdf | 621 kb


link (password: matav)


This volume is a collection of writing projects suitable in a wide range of undergraduate mathematics courses, from a survey of mathematics to differential equations. The projects vary in their level of difficulty and in the mathematics that they require, but are similar in the mode of presentation and use of applications. Students see these problems as real in a way that textbooks problems are not, even though many of the characters involved (dime–store detectives and CEOs) are obviously fictional. The stories are sometimes fanciful and sometimes grounded in standard scientific applications, but the mere existence of the story draws the students in and makes the problem relevant.

The book is the combined effort of four instructors who have used writing projects in their own courses. They provide an easy-to-use, widely applicable set of course materials that instructors can adopt and adapt to their own courses.

An extensive set of class-tested projects is included along with:

• implementation notes which highlight student difficulties,
• information about project solutions, and
• advice for grading writing projects.

Contents

1 Introduction and Supporting Information 1

1.1 Introduction 1

1.2 Motivation 2

1.3Use and Implementation of Projects 3

1.4 Grading Project Solutions 5

2 Projects 9

The Case of the Dough for the Greenhouse 10

The Case of the New Leaf 13

The Case of the Dropped Baton 15

The Case of the Falling Grapefruit 17

The Case of the Lead Poisoning 20

The Case of Darlene’s Rose 23

The Case of the Set-Up Cyclist 25

The Case of the Crushed Clown 27

A Bit of Caustic Rain 30

A Bit More Caustic Rain 33

Profitable Production 36

The Legality of the Stock Market 39

An Oily Mess 42

An Illuminating Project 44

A Question of Law 46

A Little Farming of Sorts 48
Defending Freedom, or Something Like That 51
A Jump and a Jerk 54
Fire Swamps and Rodents and Snakes (Oh, My) 58
Coffee to Go 61
A Dorm Room’s a Dorm Room, No Matter How Small 63
The Broad Side of the Barn 65
A Question of Carpeting 67
The Great Escape 69
I Guess Leonardo DiCaprio Was Booked 72
While Visions of Emus Danced in His Head 75
A Matter of Utmost Gravity 78
The X-Files Makes Me So Angry 80
The Company Picnic 82
The Restaurant 84
The Commute 86
The Raise 88
The Car 90
The Square Meal Deal 92
Stuck in Traffic in Chicago 94
3 Sample Solutions 97
3.1 Solution Paper and Checklist—Annalisa Crannell 97
3.2 Solution Paper and Rubric—Gavin LaRose 105
4 Additional Sample Checklists and Rubrics 113
5 Index by Course 117

Tricks, Games, and Puzzles With Matches

Maxey Brooke

Dover Pubns | 1973 | 64 páginas | pdf | 267 kb

online: arvindguptatoys.com

link

With a handful of matches you can challenge yourself and your friends to match hundreds of match tricks, games and puzzles. The quipment is simple and can easily be carried with you. The tricks, games and puzzles range from the simple to the advanced. No matter how many match tricks and puzzles you have previously done you are sure to find new twists, new challenges in the puzzles in this collection.
There are classic match problems, problems by foremost puzzlers, and a number of Makey Brooke's own creations. There is match-arithmetic, where you are required to balance equations by removing or adding matches, including a few that require advanced mathematical notation. There are match spellings, match story games, tricks that involve kitchen matches, paper match books and match boxes, and simple mathematical games you can play with matches. A rich selection of match constructions, in which you are required to build, unbuild, or reconstruct squares and other geometrical units by simply moving matches, is made even richer by the inclusion of a special selection from T.R. Dawson's works. The solutions section gives complete information for solving the puzzles plus material on winning games and working the tricks.

Outro livro de Maxey Brooke: 

150 puzzles in crypt-arithmetic. por Maxey Brooke Idioma: Inglês   Editora: New York, Dover Publications [1963]

Thinking and Problem Solving

Robert J. Sternberg

Academic Press | 1998 -2ª edição |482 páginas | pdf | 7,2 Mb

link

Thinking and Problem-Solving presents a comprehensive and up-to-date review of literature on cognition, reasoning, intelligence, and other formative areas specific to this field. Written for advanced undergraduates, researchers, and academics, this volume is a necessary reference for beginning and established investigators in cognitive and educational psychology. Thinking and Problem-Solving provides insight into questions such as: how do people solve complex problems in mathematics and everyday life? How do we generate new ideas? How do we piece together clues to solve a mystery, categorize novel events, and teach others to do the same? 
Key Features* Provides a comprehensive literature review* Covers both historical and contemporary approaches* Organized for ease of use and reference* Chapters authored by leading scholars

Contents

Contributors xiii
Foreword xv
Preface xvii
1 History of Research on Thinking and Problem Solving
Roger L. Dominowski and Lyle E. Bourne, Jr.
2 Contemporary Approaches to the Study of Thinking and Problem Solving
K. Anders Ericsson and Reid Hastie
3 Knowledge Representation
Timothy P. McNamara
4 Concepts and Categories
Brian H. Ross and Thomas L. Spalding
5 Deduction and Its Cognitive Basis
Lance J. Rips
6 Inductive Reasoning
Jeffery Bisanz, Gay L. Bisanz, and Connie A. Korpan
7 Problem Solving
Earl Hunt
8 Language and Thought
Richard J. Gerrig and Mahzarin R. Banaji
9 Intelligence
Robert J. Sternberg
10 Creativity
Todd I. Lubart
11 Development of Problem Solving
Shari Ellis and Robert S. Siegler
12 Cultural Dimensions of Cognition: A Multiplex, Dynamic System of Constraints and Possibilities
Robert Serpell and A. Wade Boykin
13 The Teaching of Thinking and Problem Solving
Raymond S. Nickerson

Outros livros do mesmo autor:

Understanding and teaching the intuitive mind : student and teacher learning por Bruce Torff; Robert J Sternberg; Idioma: Inglês   Editora: Mahwah, N.J. : Lawrence Erlbaum Associates, 2000.

The nature of mathematical thinking por Robert J Sternberg; Talia Ben-Zeev;   Idioma: Inglês   Editora: Mahwah, NJ : L. Erlbaum Associates, 1996.

The Practice of Mathematics

Yvette Solomon

Routledge | 1989 | 211 páginas | rar - pdf | 6 Mb

link (password: matav)

The psychological description and explanation of how children learn to work with numbers is dominated by the theories of Piaget. Yvette Solomon suggests an alternative approach to the child's conception of number.

Contents

Acknowledgements

1. The development of the number concept as a field of psychological investigation

2. Why does Piaget's theory take its particular form? 9

The background to Piaget's explanation: the status and nature of mathematical propositions 10

Mathematics and genetic epistemology: the relation between logic and psychology 18

3. The child's conception of number 28

Piaget's criticisms of intuitionism and logicism 28

Piaget's synthesis of order and class 36

4. Piaget's account of the growth of understanding 43

Piaget's criticisms of empiricism and rationalism 43

Growth as a synthesis of genesis and structure 48

5. Does Piaget give an adequate account of growth? 66

The transition from weaker to stronger logics 67

Reflective abstraction and the growth of knowledge 70

'The individual constructs his world': Piaget's account of objective knowledge 75

6. Do number theorists give adequate accounts of knowing? 79

Piaget's essentialism 80

Bryant's work 89

Gelman and Gallistel' s work 99

7. Can a Piagetian perspective be defended? 109

Socio-cognitive conflict and the growth of knowledge 110

Information-processing theory and Piagetian theory: Case's 'neo-Piagetian' analysis 119

8. Knowing how and when to use numbers 131

Linguistic, non-linguistic and social contexts, and psychological experiments 131

The context of doing arithmetic 147

Understanding the context of doing arithmetic 150

9. 'The development of mathematical thinking ': entering into the social practices of number use 160

Analysing social practices 161

Entering into social practices 179

Notes 188

References 193

Index 200

Outros livros da mesma autora:

Mathematical literacy : developing identities of inclusion por Yvette Solomon Idioma: Inglês   Editora: New York : Routledge, 2009.

Mathematical relationships in education : identities and participation por Laura Black; Heather Mendick; Yvette Solomon;  Publicação de conferência Idioma: Inglês   Editora: New York : Routledge, 2009.