The Ambitious Horse - Ancient Chinese Mathematics Problems

Lawrence Swienciki

Key Curriculum | 2000 | 135 páginas | pdf | 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

Tricks, Games, and Puzzles With Matches

Maxey Brooke

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

online: arvindguptatoys.com

Para mais livros sobre matemática recreativa veja em: 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.

Mathematics and Measurement

 Oswald Ashton Wentworth Dilke

University of California Press | 1987 | 66 páginas

online: google books

pdf - 9,27 Mb - link

Para mais livros sobre medida procure em: link
This fully illustrated book outlines the ancient systems of mathematics and measurement and describes how they were used in mapping, surveying, telling time, trade and commerce, as well as in leisure pursuits such as games and puzzles, and in the occult.

Contents
The Background 
2 Numbering by Letters 
1 Mathematical Education in the Greek World 
4. Measurement
5 Mathematics (or the Surveyor and Architect)
6 Mapping and the Concept of Scale 
7 Telling the Time
8. Calculatioos for Trade and Commerce
9. Mathematics in Leisure Pursuits and the Occult 
10 The Sequel 
Bibliography 62
Index 

Diophantos of Alexandria: A Study in the History of Greek Algebra

Thomas Little Heath

Cambridge, University press | 1985 | 298 páginas

online: ualberta.ca
archive.org
hathitrust.org
forgottenbooks.org

pdf - link (google books)

The Greek mathematician Diophantos of Alexandria lived during the third century CE. Apart from his age (he reached eighty-four), very little else is known about his life. Even the exact form of his name is uncertain, and only a few incomplete manuscripts of his greatest work, Arithmetica, have survived. In this impressive scholarly investigation, first published in 1885, Thomas Little Heath (1861-1940) meticulously presents what can be gleaned from Greek, Latin and Arabic sources, and guides the reader through the algebraist's idiosyncratic style of mathematics, discussing his notation and originality. This was the first thorough survey of Diophantos' work to appear in English. Also reissued in this series are Heath's two-volume History of Greek Mathematics, his treatment of Greek astronomy through the work of Aristarchus of Samos, and his edition in modern notation of the Treatise on Conic Sections by Apollonius of Perga.

Soviet studies in the psychology of learning and teaching mathematics - Volumes 7 - 14

This is one of a series that is a collection of translations from the extensive Soviet literature of the past 25 years on research in the psychology of mathematics instruction. It also includes works on methods of teaching mathematics directly influenced by the psychological research. Selected papers and books considered to be of value to the American mathematics educator have been translated from the Russian and appear in this series for the first time in English. The aim of this series is to acquaint mathematics educators and teachers with directions, ideas, and accomplishments in the psychology of mathematical instruction in the Soviet Union. 

Volume VII - Children's Capacity for Learning Mathematics
Steffe, Leslie P., Ed.; And Others 
1975 | 276 páginas | pdf 
online: ERIC

The work of El'konin, Davydov, and Minskaya reported in this volume represents a start toward the alleviation of the lack of theory-based experimental investigations of mathematics learning and teaching. 
TABLE OF CONTENTS
Introduction, Leslie Steffe
Learning Capacity and Age Level, D. B. El'konin and V. V..Davydov
Primary Schoolchildren's Intellectual Capabilities and the Content of Instruction, D. B. El'konin
Logical and Psychological Problems of Elementary Mathematics as an Academic Subject, V. V. Davydov
The Psychological Characteristics of the "Prenumerical" Period of Mathematics Instruction, V. V. Davydov 
Developing the Concept of Number by Means of the Relationship of Quantities, G. I. Minskaya 

Volume VIII - Methods of Teaching Mathematics
Steffe, Leslie P., Ed.; And Others 
1975 | 290 páginas | pdf 
online: ERIC

This volume contains four articles: Principles, Forms, and Methods of Mathematics Instruction; ; ; and Independent Work for Pupils in Arithmetic Lessons in the Early Grades
TABLE OF CONTENTS 
Introduction, Leslie  P. Steffe
Principles, Forms, and Methods of Mathematics Instruction, I. A. Gibsh 
The Relation Between Mathematics Instruction and Life, G. G. Maslova and. A. D. Semushin 
The Pupil's Activity as a Necessary Condition for Improving the Quality of Instruction, I. A. Gibsh 
Independent Work for Pupils in Arithmetic Lessons in the Early Grades, M. I. More

Volume IX - Problem Solving Processes of Mentally Retarded Children
Clarkson, Sandra P., Ed.; And Others
1975 | 184 páginas | pdf
online: ERIC

The articles in this volume are concerned with the instruction in problem solving of mentally retarded pupils in the auxiliary schools of the Soviet Union. Both articles in this volume describe research in problem solving and also provide concrete suggestions for improving instruction. The literature reviews contained in these articles provide us with much information on the state of research in the Soviet Union on problem solving in mathematics.
TABLE OF CONTENTS
The Solution of Complex Arithmetic Problems in Auxiliary School, K. A. Mikhal'skii 
Basic Difficulties Encountered in Auxiliary School Pupils in Solving Arithmetic Problems, M. I. Ku'mitskaya 

Volume X - Teaching Mathematics to Mentally Retarded Children
Clarkson, Sandra P., Ed.; And Others
1975 | 184 páginas | pdf
online: ERIC

The articles in this volume deal with the instruction in geometry and arithmetic of mentally retarded pupils in the Soviet Union. These pupils attend special schools, called auxiliary schools, where they are trained in content that can later be related to specific job skills. Authors of the articles have attempted to identify the specific knowledge that the pupils possess and to design more effective instructional methods for increasing that knowledge. 
TABLE OF CONTENTS
Introduction
Instructing Auxiliary School Pupils in Visual Geometry, P. G. Tishini
Visual.and Verbal Means in Pregaratory Exercises in Teaching Arithmetic Problem Solving, N. F. Kuimina-Syromyatnikova
Some Features of Elementary Arithmetic Instruction for Auxiliary School Pupils, T. V. Khanutina 

Volume XI - Analysis and Synthesis as Problem Solving Methods
Kantowski, Mary Grace, Ed.; And Others
1975 | 186 páginas | pdf
online: ERIC

This volume differs from the others in the series in that the entire volume records the search for a method of problem-solving instruction based on the analytic-synthetic nature of the problem-solving process. In this work, Kalmykova traces the history of the use of the analytic and synthetic methods in her country, explores elementary classroom situations involving teachers who had various degrees of success in problem-solving instruction, makes hypotheses regarding the use of certain techniques, and concludes with suggestions for "productive" methods to be used in the classroom
TABLE OF CONTENTS
Introduction, Mary C. Kantowski
Chapter I. Overview
Chapter II. Substantiation of the Problem of Analysis end Synthesis
Chapter III. Experimental Investigations of the Use of the Method of Analysis in School 
Chapter IV. Experimental Investigations of Analysis as a Method of Searching for a Solution
Chapter V. Productive Method of Analysis and Synthesis

Volume XII - Problems of Instruction
Wilson, James W., Ed.; And Others
1975 | 185 páginas | pdf
online: ERIC

The seven studies found in this volume are: ;; ;;; ; and Psychological Characteristics of Pupils' Assimilation of the Concept of a Function.
TABLE OF CONTENTS
Introduction
An Experiment in the Psychological Analysis of Algebraic Errors, P. A. Shevarev
Pupils' Comprehension of Geometric Proofs, F. N. Gonoboldn
Elements of the Historical Approach in Teaching Mathematics, I. N. Shevchenko
Overcoming Students' Errors in the Independent Solution of Arithmetic Problems, 0. T. Yochkovskaya
Stimulating Student Activity in the Study of Functional Relationships, Yu. I. Goldberg
Psychological Grounds for Extensive Use of Unsolvable Problems, Ya.  I.  Grudenov
Psychological Characteristics of Pupils' Assimilation of the Concept of a Function, I. A. Marnyanskii

Volume XIII - Analysis of Reasoning Processes
Wilson, James W., Ed.; And Others
1975 | 244 páginas | pdf
online: ERIC

The analysis of reasoning processes in the learning of concepts or the solving of problems is the theme common to the ten articles in this volume. These articles, except for the first one by Ushakova, were published between 1960 and 1967 and were part of the available literature during a revision of the Soviet school mathematics curriculum. The articles are interesting because of the topics they treat and because of the research styles they illustrate
TABLE OF CONTENTS
Introduction, James Wilson and Jeremy Kilpatrick
The Role of Comparison in-the Formation of Concepts do by Third-Grade Pupils,  M. N. Ushakova
On the Formation of an Elementary Concept of Number by the Child, V. V. Davydov
The Generalized Conception in Problem Solving, A. V. Brushlinskii
An Analysis of the Process of Solving Simple Arithmetic Problem, G. P. Shchedrovitskii and S. G. Yak'obson 
An Attempt at an Experimental Investigation of Psychological Regularity in Learning, B. B. Kopov
The Formation of Generalized Operations as a Method for Preparing Pupils to Solve Geometry Problems Independently, E. I. Mashbits
An Experimental Investigation of Problem Solving and Modeling the Thought Processes, D. N.Zavalishin and V. N. Pushkin 
The Composition of Pupils' Geometry Skills, A. K. Artemov
On the Process of Searching for an Unknown-While Solving a Mental Problem,  A. V. Brushlinskii
The Mechanisms of Solving Arithmetic Problems, L. M. Fridman

Volume XIV - Teaching Arithmetic in the Elementary School
Hooten, Joseph R., Ed.; And Others
1975 | 214 páginas | pdf
online: ERIC

The six chapter titles are: 
The Psychological and Didactic Principles of Teaching Arithmetic; 
The Introduction of Numbers, Counting, and the Arithmetical Operations;
Instruction in Mental and Written Calculation; Teaching Problem Solving; 
Geometry in the Primary Grades; 
Different Kinds of Pupils and How to Approach Them in Arithmetic Instruction.

Research on mathematical thinking of young children : six empirical studies

Leslie P. Steffe 

 National Council of Teachers of Mathematics | 1975 | 207 páginas | pdf | 3,2 Mb

online: ERIC

Para outros livros relacionados procure em: link

This volume includes reports of six studies of the thought processes of children aged four through eight. In the first paper Steffe and Smock outline a model for learning and teaching mathematics. Six reports on empirical studies are then presented in five areas of mathematics learning: (1) equivalence and order relations; (2) classification and seriation; (3) interdependence of classification, seriation, and number concepts; (4) Boolean Algebra; and (5) conservation and measurement. In a final chapter, the main findings of these papers are summarized and implications are discussed, with suggestions for further research.

Table of Contents
Introduction, Leslie P. Sleffe 1
I.On a Model for Learning and Teaching Mathematics, Leslie P. Sleffe and Charles D. Smock 4
II.Learning of Equivalence and Order Relations by Four- and Five-Year-Old Children, Leslie P. Sleffe and Russell L. Carey,19
III.Learning of Equivalence and Order Relations byDisadvantaged Five- and Six-Year-Old Children, Douglas T. Owens 47
IV.Learning of Classification and Seriation by Young Children, R Marlin L. Johnson 73
V.The Generalization of Piagetian Operations as It Relates to the Hypothesized Functional Interdependence between Classification, Seriation, and Number Concepts, Richard A. Lesh 94
VI.Learning of Selected Parts of a Boolean Algebra by Young Children, David C. Johnson 123
VII.The Performance of Mist- and Second -Grade Children on Liquid Conservation and Measurement Problems Employing Equivalence and Order Relations, Thomas P. Carpenter 145
Summary and Implications, Kennelh Lovell 171
References 191