A Practical Guide to Teaching Mathematics in the Secondary School

Clare Lee, Sue Johnston-Wilder e Robert Ward-Penny

(Routledge Teaching Guides)

Routledge | 2013 | 145 páginas | rar  - pdf | 6,5 Mb

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A Practical Guide to Teaching Mathematics in the Secondary School offers straightforward advice, inspiration and support for mathematics teachers whether in training or newly qualified. Based on the best research and practice available, it offers a wide range of tried and tested approaches that succeed in secondary classrooms. Each chapter contains a wealth of tasks and ideas that allow teachers to reflect on the approaches and make plans for using them in their own classrooms, and offers ideas for lesson plans, learning activities and suggested further reading and development.

Illustrated throughout with case studies and practical insights from classroom observations and experience, this book covers key aspects of mathematics teaching, including:

• managing the class and learning environment;

• teaching the topics of mathematics;

• encouraging mathematical thinking;

• choosing and using resources;

• using multi-media technology;

• assessing work in mathematics.

A Practical Guide to Teaching Mathematics in the Secondary School is an essential companion to the core textbook Learning to Teach Mathematics in the Secondary School. Written by expert professionals, it supports you in your development of imaginative and effective lessons on a variety of curriculum topics in different teaching situations.

Contents

List of illustrations vii

Notes on contributors ix

Series editors’ introduction xi

Acknowledgements xiii

Abbreviations used xiv

Introduction 1

1 Planning mathematics lessons 3

Robert Ward-Penny and Clare Lee

■ the process of constructing a lesson plan ■ the elements that can be used ■ planning for effective starters and plenaries ■ timing and signposting ■ interrogating, evaluating and improving your plan

2 Practical Assessment for Learning 13

Clare Lee

■ the principles of Assessment for Learning ■ how to decide what your pupils will learn ■ how your pupils can recognise success ■ providing feedback ■ flexible planning

3 ICT from the front of the class 21

Ian Boote

■ using ICT at the front of the classroom ■ encouraging greater participation and exploration ■ using presentation software effectively ■ using games ■ existing online resources and the internet ■ motivation

4 Pupil-led ICT 31

Dave Miller

■ pupils exploring mathematical ideas using ICT themselves ■ virtual manipulatives ■ using real-life data ■ graphing programs ■ geometry programs ■ practical concerns associated with ICT

5 Multimedia technology 41

Chris Chisholm

■ multimedia resources and equipment ■ making videos and podcasts ■ improving literacy and team-working skills ■ data loggers ■ graphical calculators

6 Working collaboratively 51

Andrea Pitt

■ the advantages and practicalities of working collaboratively ■ the types of activity that are suitable ■ how to make choices about the size and structure of groups ■ the teacher’s role

7 Discussion and communication 61

Jenni Ingram

■ developing communication and mathematical thinking ■ how whole-class discussions can be initiated ■ creating an environment for discussion ■ setting ground rules ■ using real-world communication

8 Enquiry as a vehicle for teaching and learning mathematics 69

Mike Ollerton

■ using enquiry as part of teaching mathematics ■ the importance of an accessible start ■ the role of the teacher ■ how enquiry enables students to work independently and collaboratively ■ how progress is assessed

9 Taking mathematics outside 83

Robert Ward-Penny

■ ideas to enable your pupils to learn mathematics outside the classroom ■ planning issues ■ the kinds of activities the pupils could use ■ how noticing mathematical situations encourages your pupils to learn mathematics

10 Active and creative mathematics 93

Nick McIvor

■ the use of games as part of teaching mathematics ■ practical aspects of using games ■ how every lesson can be a story ■ using mystery to focus the pupils ■ ways of maximising engagement

11 Developing subject knowledge 103

Robert Ward-Penny

■ developing your subject knowledge ■ extending ‘higher’ by challenging your mathematical thinking ■ ‘deeper’ using external sources and historical and cross-cultural roots ■ ‘wider’ to engage and interest your pupils

12 Action research: systematic reflective action to improve practice 113

Clare Lee

■ action research as a means of solving problems encountered in teaching ■ research methodology ■ designing a project ■ putting the ideas of action research into practice to aid professional development

Websites and resources 123

References 125

Index 127

Les jeux mathematiques d'Eureka

Eureka (Marie Berrondo)

Dunod | 1979 | 187 páginas | djvu | 2,6 Mb

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Marie Berrondo, qui a choisi le pseudonyme d'Eurêka, propose 253 récréations suivies de solutions détaillées. Les problèmes touchent aux probabilités, à la logique, aux relations entre vitesses, distance et temps, à la géométrie et à l'arithmétique.

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.

Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem

 Simon Singh

Fourth Estate | 1997 | 315 páginas | epub | 1,1 Mb

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mobi - 2 Mb - link

xn + yn = zn, where n represents 3, 4, 5, ...no solution

"I have discovered a truly marvelous demonstration of this proposition which this margin is too narrow to contain."
With these words, the seventeenth-century French mathematician Pierre de Fermat threw down the gauntlet to future generations.  What came to be known as Fermat's Last Theorem looked simple; proving it, however, became the Holy Grail of mathematics, baffling its finest minds for more than 350 years.  In Fermat's Enigma--based on the author's award-winning documentary film, which aired on PBS's "Nova"--Simon Singh tells the astonishingly entertaining story of the pursuit of that grail, and the lives that were devoted to, sacrificed for, and saved by it.  Here is a mesmerizing tale of heartbreak and mastery that will forever change your feelings about mathematics.


CONTENTS
Preface
1 ‘I Think I’ll Stop Here’
2 The Riddler
3 A Mathematical Disgrace
4 Into Abstraction
5 Proof by Contradiction
6 The Secret Calculation
7 A Slight Problem
Epilogue Grand Unified Mathematics
Appendices
Suggestions for Further Reading

Index

Statistics and Probability with Applications for Engineers and Scientists

Bhisham C. Gupta e Irwin Guttman 

Wiley | 2013 | 898 páginas | rar - pdf | 9,18 Mb

link (password: matav)

An understanding of statistical tools is essential for engineers and scientists who often need to deal with data analysis over the course of their work. Statistics and Probability with Applications for Engineers and Scientists walks readers through a wide range of popular statistical techniques, explaining step-by-step how to generate, analyze, and interpret data for diverse applications in engineering and the natural sciences.

Unique among books of this kind, Statistics and Probability with Applications for Engineers and Scientists covers descriptive statistics first, then goes on to discuss the fundamentals of probability theory. Along with case studies, examples, and real-world data sets, the book incorporates clear instructions on how to use the statistical packages Minitab® and Microsoft® Office Excel® to analyze various data sets. The book also features:

• Detailed discussions on sampling distributions, statistical estimation of population parameters, hypothesis testing, reliability theory, statistical quality control including Phase I and Phase II control charts, and process capability indices

• A clear presentation of nonparametric methods and simple and multiple linear regression methods, as well as a brief discussion on logistic regression method
• Comprehensive guidance on the design of experiments, including randomized block designs, one- and two-way layout designs, Latin square designs, random effects and mixed effects models, factorial and fractional factorial designs, and response surface methodology
• A companion website containing data sets for Minitab and Microsoft Office Excel, as well as JMP ® routines and results

Assuming no background in probability and statistics, Statistics and Probability with Applications for Engineers and Scientists features a unique, yet tried-and-true, approach that is ideal for all undergraduate students as well as statistical practitioners who analyze and illustrate real-world data in engineering and the natural sciences.

What successful math teachers do, grades 6-12 : 80 research-based strategies for the common core-aligned classroom

Alfred S. (Steven) Posamentier, Terri L. (Lynn) Germain-Williams e Daniel I. Jaye

Corwin | 2013 - 2.ª edição | 272 páginas | rar - epub |1,2  Mb

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What Successful Math Teachers Do is a powerful portal to what the best research looks like in practice, strategy by strategy-now aligned to both the Common Core and the NCTM Standards.

Contents
Prologue
Acknowledgments
About the Authors
Chapter 1. Make Sense of Problems and Persevere in Solving Them
Chapter 2. Reason Abstractly and Quantitatively
Chapter 3. Construct Viable Arguments and Critique the Reasoning of Others
Chapter 4. Model With Mathematics
Chapter 5. Use Appropriate Tools Strategically
Chapter 6. Attend to Precision
Chapter 7. Look for and Make Use of Structure
Chapter 8. Look for and Express Regularity in Repeated Reasoning
Chapter 9. Manage Your Classroom
Chapter 10. Assess Student Progress
Chapter 11. Consider Social Aspects in Teaching Mathematics
Epilogue
Resource: What the Authors Say
Index

Measurement

Paul Lockhart 

Belknap Press of Harvard University Press | 2012 | 416 páginas | rar - pdf | 1,44 Mb

link (password: matav)

For seven years, Paul Lockhart’s A Mathematician’s Lament enjoyed a samizdat-style popularity in the mathematics underground, before demand prompted its 2009 publication to even wider applause and debate. An impassioned critique of K–12 mathematics education, it outlined how we shortchange students by introducing them to math the wrong way. Here Lockhart offers the positive side of the math education story by showing us how math should be done. Measurement offers a permanent solution to math phobia by introducing us to mathematics as an artful way of thinking and living.

In conversational prose that conveys his passion for the subject, Lockhart makes mathematics accessible without oversimplifying. He makes no more attempt to hide the challenge of mathematics than he does to shield us from its beautiful intensity. Favoring plain English and pictures over jargon and formulas, he succeeds in making complex ideas about the mathematics of shape and motion intuitive and graspable. His elegant discussion of mathematical reasoning and themes in classical geometry offers proof of his conviction that mathematics illuminates art as much as science.

Lockhart leads us into a universe where beautiful designs and patterns float through our minds and do surprising, miraculous things. As we turn our thoughts to symmetry, circles, cylinders, and cones, we begin to see that almost anyone can “do the math” in a way that brings emotional and aesthetic rewards. Measurement is an invitation to summon curiosity, courage, and creativity in order to experience firsthand the playful excitement of mathematical work.

CONTENTS

Reality and Imagination…1

On Problems…5

Part One: Size and Shape…21

In which we begin our investigation of abstract geometrical figures.

Symmetrical tiling and angle measurement. Scaling and proportion. Length, area, and volume. The method of exhaustion and its consequences. Polygons and trigonometry. Conic sections and projective geometry. Mechanical curves.

Part Two: Time and Space…199

Containing some thoughts on mathematical motion. Coordinate systems and dimension. Motion as a numerical relationship. Vector representation and mechanical relativity. The measurement of velocity. The differential calculus and its myriad uses. Some final words of encouragement to the reader.

Acknowledgments…399

Index…401

Outro livro do mesmo autor:

A mathematician's lament por Paul Lockhart   Idioma: Inglês   Editora: New York, NY : Bellevue Literary Press, 2009.