Navigating through Data Analysis and Probability in Prekindergarten-Grade 2

Linda Jensen Sheffield, Mary Cavanagh, Linda Dacey, Carol R. Findell, Carole Greenes, and Marian Small

National Council of Teachers of Mathematics |  2002  | 100 páginas | PDF | 2,9 Mb

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This book demonstrates how some fundamental ideas about data analysis and probability can be introduced to build a strong foundation in young students. Activities designed to introduce and promote familiarity with essential concepts develop and extend students' ideas about data analysis and simple probability through the use of bar graphs, tallies, frequency tables, and Venn diagrams. Helpful margin notes provide teaching tips, anticipated student responses to questions, samples of students' work, and ways to modify the activities for students experiencing difficulty or needing enrichment. The supplemental CD-ROM features interactive electronic activities, master copies of activity pages for students, and additional readings for teachers.

Índice

Table of Contents

About This Book  . vii

Introduction . 1 (falta)

Chapter 1 - Data Collection, Organization, and Display . 11

Build a Graph . 15

What’s Your Favorite?  . 18

Junk Sort  . 22

All about Shoes  . 25

Chain It . 27

Families. 30

Row Your Boat  . 33

Morley Most and Lutie Least  . 36

Chapter 2 - Question Posing and Data Analysis .  41 (falta)

Back and Forth . 44 (falta)

Mystery Graphs . 50

Conducting a Survey . 53 (falta)

What a Difference a Day Makes . 55

Whom Do You Believe? . 58

Travel Agent . 61 (falta)

Chapter 3 - Probability . 63 (falta)

Possible or Impossible . 65

Spin It . 67

Which Bag Is Which?  . 70

Some Sums . 73 (falta)

Looking Back and Looking Ahead . 77 (falta)

Appendix - Blackline Masters and Solutions  . 79 (falta)

Vertical Graph Mat . 80

Horizontal Graph Mat . 81

Mary Had a Little Lamb . 82

Mystery Graphs . 83

Which Is Which? . 84

More than One Story. 85

Our Survey . 86

About Students . 87

More about Students  . 88

Favorite Colors  . 89

Children in a Class . 90

Class Trip . 91 (falta)

Spin It  . 93

Color Predictions  . 95

Color Splits  . 96

Solutions  . 97 (falta)

References  . 98 (falta)

Introduction
Table of Standards and Expectations, Data Analysis and Probability, Pre-K–12 (faltam)
Applet Activities
Get Organized
Shape Sorter
Guess the Rule
Make the Rule
Probability Games
Preset Spinner
Make Your Own Spinner
Dice Sums
Blackline Masters and Templates (faltam)
Blackline Masters
Ages of Students
Number of Students’ Pets
Number of Students’ Siblings
Students’ Favorite Sport
One-Half-Inch Grid Paper
One-Inch Grid Paper
Two-Centimeter Grid Paper

Readings from Publications of the National Council of Teachers of Mathematics

Collecting Data Outdoors: Making Connections to the Real World
Carole Basile
Teaching Children Mathematics

Describes a process of data collection with young children using the outdoors as a mathematical context. The process of data collection and processing introduces children to more abstract mathematics as they sort and classify data, create graphs, compare datasets, examine patterns, and interpret graphical representations.

 

Exploring Data: Kindergarten Children Do It Their Way
Frances R. Curcio e Susan Folkson
Teaching Children Mathematics

Describes situations in which children developed mathematical concepts through processes of sorting and classifying, comparing, measuring, matching with one-to-one correspondence, and enumerating. Data were gathered while observing informal discourse, during sharing sessions, and in a reading session.

Young Students Investigate Number Cubes
Alex Friedlander
Teaching Children Mathematics

Describes a series of learning activities built around number cubes. Sample activities introduce elementary properties of the cube, the magic rule of seven, and basic concepts related to graphs in the plane coordinate system.

Making Sense of Graphs: Critical Factors Influencing Comprehension and Instructional Implications
Susan N. Friel, Frances R. Curcio, e George W. Bright
Journal for Research in Mathematics Education

This article outlines critical factors that appear to influence graph comprehension and identifies instructional implications. The factors identified are purpose, task characteristics, discipline characteristics and reader characteristics. A sequence for ordering the introduction of graphs is proposed and ways instruction may be modified to promote graph sense making.

Pictures, Tables, Graphs, and Questions: Statistical Processes
Andrew C. Isaacs e Catherine Randall Kelso
Teaching Children Mathematics

Outlines an approach to the problem of over- or underquantification for students by teaching science as a process of collecting, organizing, and analyzing data that naturally integrates with mathematics. 

Students’ Probabilistic Thinking in Instruction 
Graham A. Jones, Cynthia W. Langrall, Carol A. Thornton, e A. Timothy Mogill
Journal for Research in Mathematics Education

Evaluates the thinking of third grade students in relation to an instructional program in probability which was informed by a research-based framework that included a description of students' probabilistic thinking. Reveals that overcoming misconceptions in sample space, applying both part-part and part-whole reasoning, and using invented language to describe probabilities were key patterns in producing growth in probabilistic thinking.

Hamster Math: Authentic Experiences in Data Collection

Beth Jorgensen

Teaching Children Mathematics

Describes the data collection and interpretation project of primary grade students involving predicting, graphing, estimating, measuring, number problem construction, problem solving, and probability.

Classification and Logical Reasoning 

Melfried Olson e Judith Olson

Teaching Children Mathematics

These activities explore classification and logical reasoning by providing students with opportunities to generate multiple answers and engage in multiple classifications of the same item. No solutions are suggested so that students will look to themselves as the mathematical authorities. Sample items for classification include birthday months, toys, holidays, and geometric figures. Numbers are classified by skip counting and factoring.

The Shape of Fairness 

Elizabeth Penner e Richard Lehrer

Teaching Children Mathematics

Describes how young children used geometric shapes to model a fair playing space for "Mother, may I?"

Take Two: Fair or Unfair? 

Lynae Sakshaug

Teaching Children Mathematics

Problem Solvers poses a problem for classroom use and gives a solution to a previously published problem.

Responses to the Take Two: Fair or Unfair? Problem

Lynae Sakshaug

Teaching Children Mathematics

Presents answers to the problem appearing in the January, 1999 Problem Solvers section of this journal, which was a strategy game called "Take Two" in which two players played by placing seven chips in a row and removing one or two chips each turn.

Which Graph Is Which?

Lynae Sakshaug

Teaching Children Mathematics

Introduces a problem that can be used to help children develop graph sense. Involves two graphs of which students must determine which one applies to which situation.

Young Children Deal with Data 

Judith V. Taylor

Teaching Children Mathematics

Presents activities having to do with data generation, organization, interpretation, representation, drawing conclusions, and making predictions on the basis of data which students have collected. 

Navigating through Data Analysis and Probability in Grades 3–5

Suzanne Chapin, Alice Koziol, Jennifer MacPherson, e Carol Rezba
National Council of Teachers of Mathematics | | 120 páginas | PDF | 3,89 Mb

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Investigations involving data give students opportunities to depict the shape of data sets and use statistical characteristics of the data to describe similarities and differences among related sets. An assortment of discussions, activities, and investigations emphasize the collection and analysis of data and develop the idea of probability as a measure of the likelihood of events that are meaningful and real to students. The accompanying CD-ROM features applets for students to manipulate and resources for teachers' professional development. It also features interactive electronic activities, master copies of activity pages for students, and additional readings for teachers.

Índice

Table of Contents

About This Book . vii

Introduction . 1 (falta)

Chapter 1 - From Questions to Method: Beginning the Process . 11 (falta)

Questions, Please?  . 13

What’s My Method? . 17

Chapter 2 - Using Data Analysis Methods . 21 (falta)

Long Jump  . 23

How Many Stars Can You Draw in One Minute? . 29

Do You Get Enough Sleep?. 34

Exploring the Mean  .39

Chapter 3 - Inferences and Predictions . 45 (falta)

The Foot, the Whole Foot, and Nothing but the Foot! . 47

Can You Catch Up? . .. 51

Chores—How Many Hours a Week Are Typical? . 56

Chapter 4 - What Are the Chances? . 61 (falta)

How Likely Is It to Land in the Trash Can? . 62

Is There Such a Thing as a Lucky Coin? . 68

Spin City . 73

Is It Fair? . 79

Looking Back and Looking Ahead .83

Appendix - Blackline Masters and Solutions  . 87 (falta)

Determining a Purpose for a Data Investigation . 88 (falta)

Getting Ready . 92

A Question to Investigate  . 94

Data Sets . 96

What’s My Method?—Descriptions  .98

What’s My Method?—Explorations .100

Summer Olympics 2000 . 101

How Long Is One Minute?  . 102

How Many Stars?—Another Class . 103

How Much Sleep Do You Get? . 104

How Much Sleep Do Children Typically Get? . 105

Women’s Soccer Results  . 106

The Foot, the Whole Foot, and Nothing but the Foot—Group Data  . 108

The Foot, the Whole Foot, and Nothing but the Foot—Class Data . 109

Can You Catch Up?. 110

Chores—How Many Hours a Week Are Typical? . 111

Stem-and-Leaf Plot of the Group’s Sample Data  . 112

Sample versus Population—How Do They Compare? . 113

Paper Toss Recording Sheet . 114

Spin It . 115

Matching Line Plots with Spinners . 116

Number Cards . 117

Rule Cards  . 118

Answer Key for Women’s Soccer Results . 119 (falta)

References . 120 (falta)

Contents of CD-ROM

Introduction

Table of Standards and Expectations, Data Analysis and Probability,

Pre-K–12

Applet Activities (falta)

  Probability Games

  Preset Spinner (on-line: illuminations.nctm)

  Make Your Own Spinner (on-line: illuminations.nctm)

  Dice Sums

  Coin Toss 

Blackline Masters and Templates

Readings from Publications of the National Council of Teachers of Mathematics

Problem Solving: Dealing with Data in the Elementary School

Harry Bohan, Beverly Irby, and Dolly Vogel

Teaching Children Mathematics

Describes the Elementary Mathematics Research Model, which furnishes a vehicle for problem solving through real data collection and analysis.

Using Probability Experiments to Foster Discourse

Thomas G. Edwards and Sarah M. Hensien

Teaching Children Mathematics

Describes how three experiments suitable for upper-elementary students can be used to foster classroom discourse in which students begin to explore probability.

Making Charts: Do Your Students Really Understand the Data?

Louis Feicht

Mathematics Teaching in the Middle School

Presents an activity in which students learn how to label graphs in order to make them meaningful.

Teaching Statistics: What’s Average?

Susan N. Friel

The Teaching and Learning of Algorithms in School Mathematics

Daily Activities for Data Analysis

Chris Hitch and Georganna Armstrong

Arithmetic Teacher

Presents four sets of activities to develop the concepts of data analysis and graphing. Students estimate sample populations using beans, examine graphs from newspapers and magazines, predict the most popular color of cars, and simulate quality control in a manufacturing process.

Understanding Students’ Probabilistic Reasoning  (falta)

Graham A. Jones, Carol A. Thornton, Cynthia W. Langrall, and James E. Tarr

Developing Mathematical Reasoning in Grades K–12

The Lunch-Wheel Spin

Julia A. Mason and Graham A. Jones

Arithmetic Teacher

Describes a problem formulated by fourth-grade students about having more pizza for lunch, and the clarifying, predicting, modeling, simulating, comparing, and extending activities that occurred in addressing the problem from a probabilistic perspective.

Children’s Concepts of Average and Representativeness

Jan Mokros and Susan J. Russell

Journal for Research in Mathematics Education

Interviews with (n=21) fourth, sixth, and eighth graders, who were asked to construct their own notion of average and representativeness in open-ended problems, identified five basic constructions of average as mode, an algorithmic procedure, what is reasonable, midpoint, and a mathematical point of balance. 

Teaching Mathematics with Technology: Statistics and Graphing

Janet Parker and Connie C. Widner

Arithmetic Teacher

Presents a series of four steps used in data analysis processes that help students investigate and interpret real world situations. Gives activities that employ computer software to create representative graphs of the data in the analysis process.

What Do Children Understand about Average?

Susan J. Russell and Jan Mokros

Teaching Children Mathematics

Interviews with fourth, fifth, and sixth graders found that they thought about the concept of average as mode, median, and/or a procedure. Presents approaches to develop the concept of average

Exploring Probability through an Evens-Odds Dice Game

Lynda R. Wiest and Robert J. Quinn

Mathematics Teaching in the Middle School

Presents a dice game that students can use as a basis for exploring mathematical probabilities and making decisions while they also exercise skills in multiplication, pattern identification, proportional thinking, and communication. 

Mean and Median: Are They Really So Easy?

Judith S. Zawojewski and J. Michael Shaughnessy

Teaching Mathematics in the Middle School

Analyzes National Assessment of Education Progress (NAEP) items to assess student understanding of spread as well as center, such as mean and median. Discusses implications for teaching statistics in 5th and 6th grade mathematics.

California Math Triumphs: Fractions and Decimals, Volume 2A

Basich Whintey

Mcgraw-hill | 2008 | 87 páginas | PDF | 8,97 Mb

link
link1

Site do Manual

glencoe.mcgraw-hill.com

California Math Triumphs is an intensive intervention resource for students who are two or more years below grade level. The series provides step-by-step intervention, vocabulary support, and data-driven decision making to help students succeed in high school mathematics.

Designed to support students needing the most intensive intervention, Math Triumphs: Fractions and Decimals helps build mastery of the foundational skills and concepts from prior grades that are prerequisites to the current grade level. Uniquely scaffolded practice problems provide support by breaking down each skill into the simplest understanding.

CONTENTS

Volume 2A - Chapter 1: Parts of a Whole
Volume 2A - Chapter 2: Equivalence of Fractions

Solve That Problem! Middle Primary: Skills and Strategies for Practical Problem Solving

Sharon Shapiro

Blake Education | 2001 | 88 páginas | PDF | 1,7 Mb

docs.google.com

Each unit in Solve That Problem! Middle Primary introduces a new problem-solving skill, following a structured sequence. Teaching notes on the specific skill the unit covers are followed by teaching examples that enable the easy introduction of these skills to students. The blackline master provided sets out a sequence for students to work through when implementing the new skill. Task cards give students the opportunity to put the new skill to use on problems of increasing complexity.

This book contains the following units:
- Drawing a Diagram
- Drawing a Table
- Acting it Out or Using Concrete Material
- Guessing and Checking
- Creating an Organised List
- Looking for a Pattern (incompleto)

Semiotics in Mathematics Education: Epistemology, History, Classroom and Culture

Sense Publishers | 2008 | 284 páginas

Estão disponíveis 6 dos 15 capítulos do livro.

Indice

The Ubiquitousness of Signs: By Way of Introduction (pdf)
Luis Radford, Gert Schubring e Falk Seeger

Intentionality and Sign (pdf)
Falk Seeger

On the Semiotics of Gestures (pdf)
Cristina Sabena

Eight Problems for a Semiotic Approach in Mathematics
Raymond Duval

Metaphor and Contingency
Michael Otte

The Dawning of Signs in Graph Interpretation
Wolff-Michael Roth

Trigometric Connections through a Semiotic Lens
Norma Presmeg

Between Public and Private: Where Students' Mathematical Selves Reside
Michael N. Fried (pdf)

Processes of Algebraization in the History of Mathematics: The Impact of Signs
Gert Schubring

From Representations to Onto-Semiotic Configurations in Analysing Mathematics Teaching and Learning Processes (pdf)
Vicenc Font, Juan D. Godino e Angel Contreras

Analyzing the Impact of Dynamic Representations and Classroom Connectivity on Participation, Speech and Learning
Stephen Hegedus e Luis Moreno-Armella

The GSP, as a Technical-Symbolic Tool, Mediating Both Geometric Conceptualizations and Communication
Adalira Saenz-Ludlow e Anna Athanasopoulou

The Ethics of Being and Knowing: Towards a Cultural Theory of Learning (pdf)
Luis Radford

An Attempt to Achieve Reification in Functions—A Study Based on Several Semiotic Registers
Tania M. M. Campos, Vera Helena Guisti de Souza e Rosana Nogueira de Lima

Symbolic Language Versus Understanding in Mathematics Education: A Brief Archaeological Investigation of Mathematics Education Discourse
Mircea Radu

Index

About the Contributors

The Big Idea: Pythagoras & His Theorem

Paul Strathern

Arrow Books Ltd | 1997 | 96 páginas | PDF | 19 Mb

Faltam as páginas 30 e 31

4shared.com
depositfiles.com
link
link1

djvu - 392 kb
link
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Modern Geometries

(Essays in Public Policy)

James R. Smart

Thomson Brooks/Cole | 1973 | 371 páginas | pdf | 10 Mb

Faltam páginas 146, 147, 148, 149, 158, 159, 160, 161.

link
link1

Descrição: This comprehensive, best-selling text focuses on the study of many different geometries -- rather than a single geometry -- and is thoroughly modern in its approach. Each chapter is essentially a short course on one aspect of modern geometry, including finite geometries, the geometry of transformations, convexity, advanced Euclidian geometry, inversion, projective geometry, geometric aspects of topology, and non-Euclidean geometries. This edition reflects the recommendations of the COMAP proceedings on Geometry's Future, the NCTM standards, and the Professional Standards for Teaching Mathematics. References to a new companion text, Active Geometry by David A. Thomas encourage students to explore the geometry of motion through the use of computer software. Using Active Geometry at the beginning of various sections allows professors to give students a somewhat more intuitive introduction using current technology before moving on to more abstract concepts and theorems.

Matemática para os primeiros anos

Mathematics in the early years
Juanita V. Copley (Editor)

National Council of Teachers of Mathematics | 1999 | 230 páginas

De momento, só estão disponíveis 8 dos 26 capítulos do livro.

Capítulos:
Preface
Juanita V. Copley
(pdf | 293 kb | 4shared.com)
Part 1. The historical, theoretical, and social aspects of early childhood mathematics
1- Why Do We Teach Young Children So Little Mathematics? Some Historical Considerations (falta)
Robert Balfanz
2- Children's Ways of Knowing: Lessons from Cognitive Development Research
Catherine Sophian
(pdf | 3,11 Mb | 4shared.com)
3 - The Sociology of Day Care (falta)
Edward L. McDill e Gary Natriello
4 - Cultural Aspects of Young Children's Mathematics Knowledge
Steven R. Guberman
(html | on-line: spot.colorado.edu)

Part 2. Mathematics for the young child
5 - Ready To Learn: Developing Young Children's Mathematical Powers
Carole Greenes
(pdf | on-line: fdlrs-south.dade.k12.fl.us)
6 - The Development of Informal Counting, Number, and Arithmetic Skills and Concepts Arthur J. Baroody, Jesse L.M. Wilkins
(falta)
7 - Geometric and Spatial Thinking in Young Children
Douglas H. Clements
(pdf |1,02 Mb | on-line: eric.ed.gov)
8 - Rational-Number Learning in the Early Years: What Is Possible?
Robert P. Hunting
(pdf | 1,01 Mb | on-line: eric.ed.gov)
9 - Young Children Doing Mathematics: Observations of Everyday Activities
Herbert P. Ginsburg, Noriyuki Inoue, Kyoung-Hye Seo
(pdf | 2,63 Mb | 4shared.com)

Part 3. The implementation of mathematics programs
10 - Cognitively Guided Instruction in One Kindergarten Classroom (falta)
Janet Warfield, Mary Jo Yttri
11 - Supporting Students' Ways of Reasoning about Patterns and Partitions (falta)
Kay McClain, Paul Cobb
12 - The Effective Use of Computers with Young Children
Douglas H. Clements
(html | on-line: spot.colorado.edu)
13 - Making Connections: A 'Number Curriculum' for Preschoolers
Ruth Shane
(pdf | 304 kb | on-line: eric.ed.gov)
14 - Within Easy Reach: Using a Shelf-Based Curriculum To Increase the Range of Mathematical Concepts Accessible to Young Children (falta)
Gregory D. Nelson
15 - Teaching Mathematics through Musical Activities (falta)
Sang Lim Kim
16 - The Boston University-Chelsea Project (falta)
Carole Greenes
17 - The Outdoors as a Context for Mathematics in the Early Years (falta)
Carole G. Basile
18 - Using Storybooks To Help Young Children Make Sense of Mathematics (falta)
Haekyung Hong
19 - Movement, Mathematics, and Learning: Experiences Using a Family Learning (falta)
Grace Davila Coates, Jose Franco
20 - Math in Motion (falta)
Mary E. Rudisill, Michelle L. Hamilton, Melanie A. Hart
21 - Assessing the Mathematical Understanding of the Young Child (falta)
Juanita V. Copley

Part 4. Mathematics for everyone
22 - Improving Opportunities and Access to Mathematics Learning in the Early Years
Yolanda N. Padron
(falta)
23 - What To Do When They Don't Speak English: Teaching Mathematics to English-Language Learners in the Early Childhood Classroom (falta)
Laurie R. Weaver, Catherine Gaines
24 - Involving Parents of Four- and Five-Year-Olds in Their Children's Mathematics Education: The FAMILY MATH Experience (falta)
Grace Davila Coates, Virginia Thompson
25 - Perspectives on Mathematics Education and Professional Development through the Eyes of Early Childhood Administrators (falta)
Marianne Weber
26 - Early Childhood Mathematics in Japan (falta)
Giyoo Hatano, Kayoko Inagaki

Research Ideas for the Classroom: High School Mathematics

Research Ideas for the Classroom: High School Mathematics
Patricia S. Wilson (Editor)

MacMillan | 1993 | 350 páginas

De momento, só estão disponíveis 2 dos 16 capítulos do livro.

Series Foreword
Sigrid Wagner
Introduction: Becoming Involved with Research
Patricia S. Wilson

PART I - Learning
1 - Cognitive Issues in Mathematics Education
Lee V. Stiff, Janet L. Johnson, e Mary R. Johnson
2 - Affective Issues in Mathematics Education
Douglas B. McLeod e Michele Ortega

PART II - Processes and Content
3 - Critical Thinking, Mathematical Reasoning, and Proof
Phares C. O'Daffer e Bruce A. Thornqulst
4 - Mathematical Problem Solving
James W. Wilson, Maria L. Fernandez, e Nelda Hadaway
on-line: jwilson.coe.uga.edu (html)
5 - Mathematical Symbols and Representations
Claude Janvier, Catherine Cirardon, e Jean-Charles Morand
6 - Improving the General Mathematics Experience
Harold L. Schocn e David Hallas
7 - Advancing Algebra
Sigrid Wagner e Sheila Parker
8 - Restructuring Geometry
William F. Burger e Barbara Culpepper
9 - Teaching and Learning Calculus
Joan Ferrini-Mundy e Darien Lauten
10 - Thinking about Uncertainty: Probability and Statistics
J. Michael Shaughnessy e Barry Bergman
11 - Computing Technology
M. Kathleen Heid e Terry Baylor
(pdf | 808 kb | 4share.com)

PART III - Teaching
12 - Instructional Activities and Decisions
Kim Prichard e Sue Bingaman
13 - Planning and Organizing Curriculum
Karen Brooks e Marilyn Suydam
14 - Inside the Teacher: Knowledge, Beliefs, and Attitudes
Catherine A. Brown e Jayne Baird
15 - Evaluation Issues
Elizabeth Badger, Thomas J. Cooney, e Timothy Kanold

PART IV - Classroom Research
16 - Teacher as Researcher: What Does It Really Mean?
Nina Kay Lankfor

A research companion to principles and standards for school mathematics

Jeremy Kilpatrick, W. Gary Martin, e Deborah Schifter (Editores)

National Council of Teachers of Mathmatics | 2003 | 413 páginas

O livro pode ser adquirido on-line em:

http://www.nctm.org/catalog/product.aspx?id=12341

De momento, estão disponíveis online, 16 dos capítulos do livro .

PDF - RAR - 12,4 Mb

Nenhum link disponível

Capítulos:
Contents (on-line: nctm.org)
Preface (on-line: nctm.org)
1 - Introdution
Jeremy Kilpatrick, W. Gary Martin e Deborah Schifter
2 - What research says about the NCTM standards
James Hiebert
3 - Making mathematics reasonable in school
Deborah Loewenberg Ball, Hyman Bass
(pdf | 1,83 Mb | on-line: personal.umich.edu)
ou (PDF | online: 393methods1)
4 - Teaching, teachers' knowledge, and their professional development
Denise S. Mewborn
5 - Classroom and large-scale assessment
Linda Dager Wilson, Patricia Ann Kenney
(PDF | online:393methods1)
6 - Developing mathematical power in whole number operations
Karen C. Fuson
(Parte do capítulo - pp. 78 - 94: PDF | online: math.wvu.edu)
7 - Fractions and multiplicative reasoning
Patrick W. Thompson, Luis A. Saldanha
(pdf | 100 kb | on-line: ite.sc.eduf)
8 - Facts and algorithms as products of students' own mathematical activity
Koeno Gravemeijer, Frans van Galen
(PDF | online : 393methods)
9 - On appreciating the cognitive complexity of school algebra: research on algebra learning and directions of curricular change
Daniel Chazan, Michal Yerushalmy
(online : PDF | 393methods1)
10 - Statis and change: integrating patterns, functions, and algebra throughout the K-12 curriculum
Erick Smith
11 - Teaching and learning geometry
Douglas H. Clements
(PDF | online: 393methods1)
12 - Developing understanding of measurement
Richard Lehrer
PDF | online: geometryandmeasurement)
13 - Reasoning about data
Clifford Konold, Traci L. Higgins
(PDF | online: 393methods1)
14 - Research on students' understanding of probability
J. Michael Shaughnessy
(PDF | online: 393methods1)
15 - Reasoning and proof
Erna Yackel, Gila Hanna
(PDF | online : 393methods1)
16 - Communication and language
Magdalene Lampert, Paul Cobb
(PDF | online: 393methods1)
17 - Representation in school mathematics: learning to graph and graphing to learn
Stephen Monk
(PDF | online : 393methods1)
18 -Representation in school mathematics: childrens' representations of problems
Stephen P. Smith
(PDF | online: 393methods1)
19 - Representation in school mathematics: a unifying research perspective
Gerald A. Goldin
20 - Implications of cognitive science research for mathematics education
Robert S. Siegler
(pdf | 330 Kb | on-line: psy.cmu.edu)
ou (PDF | online: 393methods1)
21 -  Situative research relevant to standards for school mathematics
James G. Greeno
(PDF | online: 393methods1)
22 - A sociocultural approach to mathematics reform: speaking, inscribing, and doing mathematics within communities of practice
Ellice Ann Forman
(PDF | online: 393methods1)
23 - Balancing the unbalanceable: the NCTM standards in light of theories of learning mathematics
Anna Sfard
24 - Using research in policy development: the case of the National Council of Teachers of Mathematics' Principles and standards for school mathematics
Joan Ferrini-Mundy, W. Gary Martin.

The development of mathematical skills

Chris Donlan (Editor)

Psychology Press | 2000 | 338 páginas

De momento apenas um dos capítulos do livro está disponível.

Capítulos
Section 1: Pre-school mathematical understanding
Numerical competence in infants
Karen Wynn
A developmental perspective on children's countingCatherine Sophian
Symbolic function in pre-schoolersPenny Munn
Section 2: Mathematical understanding and mathematical performance.
The relationship between conceptual and procedural knowledge in learning mathematics: A review
B. Rittle-Johnson e R. S. Siegler
( pdf | 2,1 M | on-line: psy.cmu.edu)
Doing mathematics as situated practiceNaoki Ueno
Mathematics across national boundaries: Cultural and linguistic perspectives on numerical competenceJohn Towse e Matthew Saxton
Section 3: Working memory and mental calculation: Effects of age and anxiety
Children's mental arithmetic and working memoryJohn W. Adams e Graham J. Hitch
On the cognitive consequences of mathematics anxietyMark H. Ashcraft, Elizabeth P. Kirk, e Derek Hopko
Section 4: Sources of individual difference in mathematical development
Cognitive neuropyschology and developmental dyscalculiaPaul Macaruso e Scott M. Sokol
Is hearing impairment a cause of difficulties in learning mathematics?Terezinha Nunes e Constanza Moreno
Number without language? Studies of children with specific language impairmentsChris Donlan
Individual differences in normal arithmetical developmentAnn Dowker

Descrição: Current research into the psychology of children's mathematics is extremely diverse. The present volume reflects this diversity; it is unique in its breadth, bringing together accounts of cutting-edge research from widely differing, sometimes opposing viewpoints. The reader with a grounding in developmental psychology but no knowledge of mathematical development will enjoy a wide ranging and challenging summary of current trends. Those already familiar with some of the work may take the opportunity to broaden their knowledge base and to evaluate new methodologies and the insights they offer.
The opening chapters describe studies of number awareness and numerical knowledge in infancy and early childhood. Contrasting nativist and socially-oriented accounts are presented. The second section of the book examines the broad principles underlying the acquisition of mathematical knowledge, the intricate effects of cultural context and the reflexive relation between mathematical activities and the situations within which they occur. A central section examines the working memory system, its role in arithmetical development and its vulnerability to effects of anxiety. Finally, individual differences in mathematical skills are explored through novel and contrasting perspectives including case studies in cognitive neuropsychology, and group studies of hearing-impaired children and children with specific language impairments. The final chapter gives a salutary reminder of the tremendous variation in patterns of mathematical learning to be found in unselected samples of children in mainstream education.
The book is an invitation to explore a complex set of phenomena for which no unitary explanation can be offered. It aims to show that apparently disparate research perspectives may be complementary to each other, and to suggest that progress towards a comprehensive account of mathematical skills may require a broad-based understanding of research from more than one viewpoint.

Second International Handbook of Mathematics Education

Second International Handbook of Mathematics EducationA.J. Bishop; M.A. Clements; C. Keitel; J. Kilpatrick; FY.S. Leung (Eds.)

Só estão disponíveis alguns textos

PART ONE

Introduction (on-line: pdf)
Alan J. Bishop

SECTION 1: POLICY DIMENSIONS OF MATHEMATICS EDUCATION

Introduction
Christine Keitel

1- Mathematics, mathematics education and economic conditions (on-line: pdf)
Derek Woodrow

2- Is mathematics for all? (on-line: pdf)
Peter Gates e Catherine Vistro- Yu

3- Mathematical literacy (on-line: pdf)
Eva Jablonka

4- Lifelong mathematics education
Gail FitzSimons, Diana Coben e John O'Donoghue

5- International comparative research in mathematics education
David Clarke

6- Mathematics education in international and global contexts (falta)
Bill Atweh, Phil Clarkson e Benvenido Nebres

SECTION 2: RESPONSES IN MATHEMATICS EDUCATION TO TECHNOLOGICAL DEVELOPMENTS

Introduction
Frederick Leung

7- Technology and mathematics education: a multidimensional overview of recent research and innovation (falta)
Jean-Baptiste Lagrange, Michele Artigue, Colette Laborde e Luc Trouche

8- Influence of technology on the mathematics curriculum (falta)
Ngai- Ying Wong

9- What can digital technologies take from and bring to research in mathematics education (on-line: pdf)
Celia Hoyles e Richard Noss

10- Technology as a tool for teaching undergraduate mathematics (falta)
Mike Thomas e Derek Holton

11- Mathematics teacher education and technology (falta)
Judith Mousley, Diana Lambdin e Yusuf Koc
PART TWO

SECTION 3: ISSUES IN RESEARCH IN MATHEMATICS EDUCATION

Introduction
Jeremy Kilpatrick

12- Getting the description right and making it count
Jill Adler e Steve Lerman

13- The impact of educational research on mathematics education
Dylan Wiliam

14- Preparing mathematics education researchers for disciplined inquiry
Jo Boaler, Deborah Ball e Ruhama Even

15- Mathematics teachers as researchers
Chris Breen

16- Researching mathematics education in situations of social and political conflict
Renuka Vithal e Paola Valero

17- Obstacles to the dissemination of mathematics education research
Andy Begg

SECTION 4: PROFESSIONAL PRACTICE IN MATHEMATICS EDUCATION

Introduction (falta)
Ken Clements

18- Challenging and changing mathematics teaching classroom practices
Dina Tirosh e Anna Graeber

19- Towards a didactic model for assessment design in mathematics education (on-line: fi.uu.nl)
Marja van den Heuvel-Panhuizen e Jerry Becker

20- Values in mathematics teaching - The hidden persuaders? (falta)
Alan Bishop, Wee Tiong Seah e Chien Chin

21- Regulating the entry of teachers of mathematics into the profession: Challenges, new models, and glimpses into the future 
Max Stephens

22- Examining the mathematics in mathematics teacher education (falta)
Thomas Cooney e Heide Wiegel

23- Educating new mathematics teachers: Integrating theory and practice, and the roles of practising teachers (falta)
Barbara Jaworski e Uwe Gellert

24- Professional development in mathematics education: Trends and tasks (falta)
Orit Zaslavsky, Olive Chapman e Roza Leikin