Children's Logical and Mathematical Cognition Progress in Cognitive Development Research

 C.J. Brainerd

Springer | 2011 - reprint of the original 1st ed. 1982 edition | páginas | pdf | 6,6 Mb

link

Contents
Chapter 1 Conservation - Nonconservation: Alternative Explanations .. 1
Curt Acredolo
Conservation and the Appreciation of an Identity Rule ....
Operational and Nonoperational Conservation .. 2
Nonconservation and the Overreliance on Perceptual Cues .... 4
Pseudononconservation .... 5
Nonoperational Conservation .... 14
Conclusions ....... 21
Future Research: The Development of the Identity Rule ..... 24
Reference Notes ..... 27
References ...... 27
Chapter 2 The Acquisition and Elaboration of the Number Word Sequence .... 33
Karen C. Fuson, John Richards, and Diane J. Briars
Acquisition of the Sequence .... 35
Elaboration of the Sequence ... 55
Conclusion ......... 89
Reference Notes ...... 89
References ..... 91
Chapter 3 Children's Concepts of Chance and Probability
Harry W. Hoemann and Bruce M. Ross
Piagetian Theory ... 94
Subsequent Studies .... 99
Theoretical Implications ... 116
References .... 120
Chapter 4 The Development of Quantity Concepts: Perceptual and Linguistic Factors .. 123
Linda S. Siegel
Linguistic Factors and the Development of Quantity Concepts ..... 123
A Taxonomy of Quantity Concepts .... 124
The Relationship between Language and Thought in the Child .... 128
Study 1: Concept versus Language ....... 129
Study 2: Does Language Training Facilitate Concept Acquisition? ... 132
Study 3: Visual versus Verbal Functions .... 138
Study 4: Training of Cognitive and Language Abilities ...... 140
Study 5: Cognitive Development of Children with Impaired Language Development ... 141
Study 6: The Abstraction of the Concept of Number ....... 144
Conclusion ........ 152
Reference Notes... 153
References ..... 153
Chapter 5 Culture and the Development of Numerical Cognition: Studies among the Oksapmin of Papua New Guinea ... 157
Geoffrey B. Saxe
Methodology and Cross-Cultural Number Research .... 158
The Oksapmin Community ..... 159
Studies on Numerical Cognition among the Oksapmin ... 160
Concluding Remarks
Chapter 6 Children's Concept Learning as Rule-Sampling Systems with Markovian Properties . 177
Charles J. Brainerd
Concept Learning as Rule Sampling ....179
Some Questions about Concept Learning ... 185
Some Experimental Evidence ...192
Remark ......202
Appendix ... 203
References .. 208
Index ..... 213

Big ideas of early mathematics : what teachers of young children need to know

The Early Math Collaborative

Pearson | 2013 | 209 páginas | rar -pdf | 4,2 Mb


link (password: matav)

In this unique guide, classroom teachers, coaches, curriculum coordinators, college students, and teacher educators get a practical look at the foundational concepts and skills of early mathematics, and see how to implement them in their early childhood classrooms.

Big Ideas of Early Mathematics presents the skills educators need to organize for mathematics teaching and learning during the early years. For teachers of children ages three through six, the book provides foundations for further mathematics learning and helps facilitate long-term mathematical understanding.

Contents
About the Authors vii
Foreword ix
Preface x
INTRODUCTION 2
Chapter 1 SETS 12
Chapter 2 NUMBER SENSE 28
Chapter 3 COUNTING 46
Chapter 4 NUMBER OPERATIONS 64
Chapter 5 PATTERN 82
Chapter 6 MEASUREMENT 98
Chapter 7 DATA ANALYSIS 112
Chapter 8 SPATIAL RELATIONSHIPS 130
Chapter 9 SHAPE 146
CONCLUSION 168
Big Ideas Charts 174
Book Study Guide 184
Bibliography 190
Index 192

The Calendar: The 5000-year Struggle to Align the Clock and the Heavens - and What Happened to the Missing Ten Days

David Ewing Duncan

Fourth Estate Ltd | 1999 | 384 páginas | rar - epub | 1,51 Mb

link (password: matav)

The 5,000-year struggle to align the heavens with the clock and what happened to the missing ten days. Measuring the daily and yearly cycle of the cosmos has never been entirely straightforward.The year 2000 is alternatively the year 2544 (Buddhist), 6236 (Ancient Egyptian), 5761 (Jewish) or simply the year of the Dragon (Chinese). The story of the creation of the Western calendar is a story of emperors and popes, mathematicians and monks, and the growth of scientific calculation to the point where, bizarrely, our measurement of time by atomic pulses is now more acurate than Time itself: the Earth is an elderly lady and slightly eccentric - she loses half a second a century. Days have been invented (Julius Caesar needed an extra 80 days in 46BC), lost (Pope Gregory XIII ditched ten days in 1582) and moved (because Julius Caesar had thirty-one in his month, Augustus determined that he should have the same, so he pinched one from February). The Calendar links politics and religion, astronomy and mathematics, Cleopatra and Stephen Hawking. And it is published as millions of computer users wonder what will happen when, after 31 December 1999, their dates run out...

Contents
Prelude: A Net Cast Over Time
1 A Lone Genius Proclaims The Truth About Time
2 Luna: Temptress of Tim
3 Caesar Embraces Time
4 A Flaming Cross of Gold
5 Time Stands Still
6 Monks Dream While Counting on Their Fingers
7 Charlemagne’s Sandglass
8 The Strange Journey of 365.242199
9 From the House of Wisdom to Darkest Europe
10 Latinorum Penuria (The Poverty of the Latins)
11 The Battle Over Time
12 From the Black Death to Copernicus
13 Solving the Riddle of Time
14 Ten Days Lost Forever
15 Living on Atomic Time

The Improbability Principle: Why Coincidences, Miracles, and Rare Events Happen Every Day

David J. Hand

Scientific American | 2014 | 288 páginas | rar - epub | 376 kb

link (matav)

In The Improbability Principle, the renowned statistician David J. Hand argues that extraordinarily rare events are anything but. In fact, they’re commonplace. Not only that, we should all expect to experience a miracle roughly once every month.
But Hand is no believer in superstitions, prophecies, or the paranormal. His definition of “miracle” is thoroughly rational. No mystical or supernatural explanation is necessary to understand why someone is lucky enough to win the lottery twice, or is destined to be hit by lightning three times and still survive. All we need, Hand argues, is a firm grounding in a powerful set of laws: the laws of inevitability, of truly large numbers, of selection, of the probability lever, and of near enough.
Together, these constitute Hand’s groundbreaking Improbability Principle. And together, they explain why we should not be so surprised to bump into a friend in a foreign country, or to come across the same unfamiliar word four times in one day. Hand wrestles with seemingly less explicable questions as well: what the Bible and Shakespeare have in common, why financial crashes are par for the course, and why lightning does strike the same place (and the same person) twice. Along the way, he teaches us how to use the Improbability Principle in our own lives—including how to cash in at a casino and how to recognize when a medicine is truly effective.
An irresistible adventure into the laws behind “chance” moments and a trusty guide for understanding the world and universe we live in, The Improbability Principle will transform how you think about serendipity and luck, whether it’s in the world of business and finance or you’re merely sitting in your backyard, tossing a ball into the air and wondering where it will land.

Contents
Title Page
Dedication
Epigraph
Preface
1. The Mystery
2. A Capricious Universe
3. What Is Chance?
4. The Law of Inevitability
5. The Law of Truly Large Numbers
6. The Law of Selection
7. The Law of the Probability Lever
8. The Law of Near Enough
9. The Human Mind
10. Life, the Universe, and Everything
11. How to Use the Improbability Principle
Epilogue
Appendix A: Mind-Numbingly Large and Mind-Bogglingly Small
Appendix B: Rules of Chance
Notes
Index
Also by David J. Hand
A Note About the Author

Outro livro do mesmo autor:

Statistics : a very short introduction por D J Hand Idioma: Inglês   Editora: Oxford ; New York : Oxford University Press, 2008.

Cognitive Activation in the Mathematics Classroom and Professional Competence of Teachers: Results from the COACTIV Project

(Mathematics Teacher Education, 8)

Mareike Kunter; Jürgen Baumert; Werner Blum; Uta Klusmann; Stefan Krauss; Michael Neubrand

Springer | 2013 |374  páginas | rar - pdf | 2,24 Mb

link (password: matav)

This work reports the findings of the Professional Competence of Teachers, Cognitively Activating Instruction, and Development of Students´ Mathematical Literacy project (COACTIV). COACTIV applies a broad, innovative conceptualization of teacher competence to examine how mathematics teachers’ knowledge, beliefs, motivational orientations, and self-regulation skills influence their instructional practice and teaching outcomes In this project data was collected on various aspects of teacher competence and classroom instruction from the perspective of both the teachers themselves and their students. Moreover, it gauges the effects of these teacher characteristics on student learning, as indexed by the progress students in each class. Questions addressed in the study which are reported in this volume include: What are the characteristics of successful teaching? What distinguishes teachers who succeed in their profession? How can the quality of instruction be improved?

Contents
1 Professional Competence of Teachers, Cognitively Activating Instruction, and the Development of Students’ Mathematical Literacy (COACTIV): A Research Program ... 1
Jürgen Baumert, Mareike Kunter, Werner Blum, Uta Klusmann, Stefan Krauss, and Michael Neubrand
Part I Theoretical and Empirical Foundations
2 The COACTIV Model of Teachers’ Professional Competence ...... 25
Jürgen Baumert and Mareike Kunter
3 Teacher Education in Germany .... 49
Kai S. Cortina and Mark Hoover Thames
4 The Development of Teachers’ Professional Competence .... 63
Mareike Kunter, Thilo Kleickmann, Uta Klusmann, and Dirk Richter
5 The COACTIV Research Program: Methodological Framework ..... 79
Katrin Löwen, Jürgen Baumert, Mareike Kunter, Stefan Krauss, and Martin Brunner
6 The Model of Instructional Quality in COACTIV: A Multicriteria Analysis .... 97
Mareike Kunter and Thamar Voss
7 Task Analysis in COACTIV: Examining the Potential for Cognitive Activation in German Mathematics Classrooms ..... 125
Michael Neubrand, Alexander Jordan, Stefan Krauss, Werner Blum, and Katrin Löwen
Part II Aspects of Professional Competence
8 Mathematics Teachers’ Domain-Specifi c Professional Knowledge: Conceptualization and Test Construction in COACTIV ...... 147
Stefan Krauss, Werner Blum, Martin Brunner, Michael Neubrand, Jürgen Baumert, Mareike Kunter, Michael Besser, and Jürgen Elsner
9 The Effect of Content Knowledge and Pedagogical Content Knowledge on Instructional Quality and Student Achievement .. 175
Jürgen Baumert and Mareike Kunter
10 Teachers’ General Pedagogical/Psychological Knowledge .. 207
Thamar Voss and Mareike Kunter
11 The Diagnostic Skills of Mathematics Teachers ... 229
Martin Brunner, Yvonne Anders, Axinja Hachfeld, and Stefan Krauss
12 Mathematics Teachers’ Beliefs .... 249
Thamar Voss, Thilo Kleickmann, Mareike Kunter, and Axinja Hachfeld
13 Motivation as an Aspect of Professional Competence: Research Findings on Teacher Enthusiasm .... 273
Mareike Kunter
14 Occupational Self-Regulation ..... 291
Uta Klusmann
Part III The Development of Professional Competence
15 Individual Characteristics of Prospective Teachers ..... 311
Uta Klusmann
16 Learning at University ...... 321
Thilo Kleickmann and Yvonne Anders
17 Professional Development Across the Teaching Career .... 333
Dirk Richter
Part IV Discussion
18 The COACTIV Research Program on Teachers’ Professional Competence: Summary and Discussion .... 345
Mareike Kunter and Jürgen Baumert
19 Publications from the COACTIV Research Program (January 2013) ...... 369
Mareike Kunter, Jürgen Baumert, Werner Blum, Uta Klusmann, Stefan Krauss, and Michael Neubrand
Index ....... 375

Prospective Mathematics Teachers’ Knowledge of Algebra A Comparative Study in China and the United States of America

Rongjin Huang

Springer Spektrum | 2014 | 196 páginas | rar - pdf |1,76 Mb

link (password: matav)

Rongjin Huang examines teachers’ knowledge of algebra for teaching, with a particular focus on teaching the concept of function and quadratic relations in China and the United States. 376 Chinese and 115 U.S.A. prospective middle and high school mathematics teachers participated in this survey. Based on an extensive quantitative and qualitative data analysis the author comes to the following conclusions: The Chinese participants demonstrate a stronger knowledge of algebra for teaching and their structure of knowledge of algebra for teaching is much more interconnected. They show flexibility in choosing appropriate perspectives of the function concept and in selecting multiple representations. Finally, the number of college mathematics and mathematics education courses taken impacts the teachers’ knowledge of algebra for teaching.

Contents

·        Knowledge Needed for Teaching

·        Mathematics Teacher Education in China and the U.S.A.

·        Instrumentation, Data Collection, and Data Analysis

·        Comparison of Knowledge of Algebra for Teaching (KAT) between China and the U.S.A.

·        Relationship among Different Components of KAT

·        Comparison of KTCF between China and the U.S.A.

Target Groups

·        Researchers, academics, and scholars of mathematics and didactics

·        Teachers

Mathematics Education: A Numerical Landscape

Robert Adjiage e Francois Pluvinage

Nova Science Pub Inc | 2009 | 92 páginas | rar - pdf | 492 kb

link (password: matav)

This book concerns the field of mathematics education. Today, for almost any technology, attaining the most advanced level relies on using digital systems. Therefore, the authors focus on number acquisition and use, emphasise major discussions about related topics, and introduce our personal contribution. They consider three areas: numbers in society, at school, and in the field of education. Modern society needs two kinds of number users: the first has to deal with numbers, the second has to work with numbers. According to the framework for PISA assessment, dealing with numbers concerns every citizen facing situations in which the use of a quantitative... reasoning... would help clarify, formulate or solve a problem. Working with numbers is what a professional (marketing specialist, engineer, physician, artist...) does when he has to cope with numerical theoretical frameworks, or when he collaborates with a mathematician. This brings two types of questioning: what does competence in mathematics mean? What level of achievement is desirable in number-learning to meet either numerical need? The authors examine what is proposed for teaching such a broad subject to 7-to-18-year-olds. They first observe and question the educational system, the designer of curricula, scenarios for teaching, training programmes, and national assessments. Secondly, they question the notions of problem solving and modelling as mere responses to mathematics-teaching issues. The authors then focus on what really happens in a standard classroom, particularly how teachers apply recommendations and directives, and how the generalisation of assessments affects their practice. Three aspects are considered: epistemological, cognitive, and didactical. The authors distinguish four related levels which they have named: numeracy (competence linked to whole numbers), rationacy (competence linked to ratios and rational numbers), algebracy (competence linked to algebra), and functionacy (competence linked to calculus). The cognitive aspect evokes the essential issue of semiotic registers for representing and processing numerical objects, considers the discipline-of-expression aspect of mathematics, and other issues taken into account by numerous researchers, such as process and object. The didactical is devoted to exposing our conceptual framework for teaching numbers and understanding their learning. An experiment in ratio teaching is described and analysed.

CONTENTS
Preface vii
Chapter 1 Introduction 1
Chapter 2 Numbers in Society 5
Chapter 3 Curricula and Assessment; the Case of Modelling 13
Chapter 4 Studying Numbers: How Long and up to Which Degree
of Accuracy? 23
Chapter 5 Cognitive Aspects 31
Chapter 6 Mathematical Competence 39
Chapter 7 The Four Competences 47
Chapter 8 Conclusion 69
References 71
Index 77