More Language Arts, Math, and Science for Students with Severe Disabilities

Diane Browder, Fred Spooner, Martin Agran  e Lynn Ahlgrim-Delzell 

Brookes Publishing | 2014 | 326 páginas | rar - pdf | 2,8 Mb

link (password : matav)

How can today's educators teach academic content to students with moderate and severe developmental disabilities while helping all students meet Common Core State Standards? This text has answers for K-12 teachers, straight from 37 experts in special and general education. A followup to the landmark bestseller Teaching Language Arts, Math, and Science to Students with Significant Cognitive Disabilities, this important text prepares teachers to ensure more inclusion, more advanced academic content, and more meaningful learning for their students. Teachers will have the cutting-edge research and recommended practices they need to identify and deliver grade-aligned instructional content leading to more opportunities and better quality of life for students with severe disabilities.

PRACTICAL MATERIALS: Detailed vignettes based on the authors real-life experiences, teaching examples and guidelines that illustrate recommended practices, helpful figures and tables, resource lists, and suggestions for incorporating technology into teaching and learning.

PREPARE TEACHERS TO

• skillfully adapt lessons in language arts, math, and science for students with disabilities

• align instruction with Common Core State Standards

• select target skills and goals

• differentiate instruction using appropriate supports and assistive technologies

• balance academic goals and functional skills

• make the most of effective instructional procedures such as peer tutoring, cooperative learning, and co-teaching

• maintain high expectations for student achievement

• promote generalization by embedding instruction into ongoing classroom activities

• assess students progress and make adjustments to instruction

Contents
About the Reproducible Materials . vii
About the Editors. ix
About the Contributors. xi
Foreword
Martin Agran. xix
Preface. xxiii
Acknowledgments. xxv
I Greater Access to General Curriculum
1 More Content, More Learning, More Inclusion
Diane M. Browder and Fred Spooner. 3
2 Embedded Instruction in Inclusive Settings
John McDonnell, J. Mathew Jameson, Timothy Riesen, and Shamby Polychronis. 15
3 Common Core State Standards Primer for Special Educators
Shawnee Y. Wakeman and Angel Lee. 37
II Teaching Common Core Language Arts
4 Passage Comprehension and Read-Alouds
Leah Wood, Diane M. Browder, and Maryann Mraz. 63
5 Reading for Students Who Are Nonverbal
Lynn Ahlgrim-Delzell, Pamela J. Mims, and Jean Vintinner. 85
6 Comprehensive Beginning Reading
Jill Allor, Stephanie Al Otaiba, Miriam Ortiz, and Jessica Folsom. 109
7 Teaching Written Expression to Students with Moderate to Severe Disabilities
Robert Pennington and Monica Delano. 127
III Teaching Common Core Mathematics and Teaching Science
8 Beginning Numeracy Skills
Alicia F. Saunders, Ya-yu Lo, and Drew Polly. 149
9 Teaching Grade-Aligned Math Skills
Julie L. Thompson, Keri S. Bethune, Charles L. Wood, and David K. Pugalee. 169
10 Science as Inquiry
Bree A. Jimenez and Heidi B. Carlone . 195
11 Teaching Science Concepts
Fred Spooner, Bethany R. McKissick, Victoria Knight, and Ryan Walker. 215
IV Alignment of Curriculum, Instruction, and Assessment
12 The Curriculum, Instruction, and Assessment Pieces of the Student Achievement Puzzle
Rachel Quenemoen, Claudia Flowers, and Ellen Forte. 237
13 Promoting Learning in General Education for All Students
Cheryl M. Jorgensen, Jennifer Fischer-Mueller, and Holly Prud’homme . 255
14 What We Know and Need to Know About Teaching Academic Skills
Fred Spooner and Diane M. Browder. .275
Index . 287

Dyscalculia: Action plans for successful learning in mathematics

Glynis Hannell

Routledge | 2013 - 2ª edição | 137 páginas | rar -pdf | 682 kb

link
password: matav

Based on expert observations of children who experience difficulties with maths this book gives a comprehensive overview of dyscalculia, providing a wealth of information and useful guidance for any practitioner. With a wide range of appropriate and proven intervention strategies it guides readers through the cognitive processes that underpin success in mathematics and gives fascinating insights into why individual students struggle with maths. Readers are taken step-by-step through each aspect of the maths curriculum and each section includes:

• Examples which illustrate why particular maths difficulties occur

• Practical ‘action plans’ which help teachers optimise children’s progress in mathematics

This fully revised second edition will bring the new research findings into the practical realm of the classroom. Reflecting current knowledge, Glynis Hannell gives increased emphasis to the importance of training ‘number sense’ before teaching formalities, the role of concentration difficulties and the importance of teaching children to use strategic thinking. Recognising that mathematical learning has a neurological basis will continue to underpin the text, as this has significant practical implications for the teacher.

Contents

Section 1: Introduction to dyscalculia 1
1 Understanding dyscalculia 3
Section 2: Effective teaching, effective learning 15
2 The biological basis of learning 17
3 Making mathematical connections 22
4 Assessment 30
5 Individual differences and mathematics 34
6 Confidence and mathematics 40
Section 3: Understanding the number system 45
7 Introduction to understanding the number system 47
8 Number sense 50
9 Counting 56
10 Using number patterns 62
11 Understanding place value 65
12 Composition and decomposition of numbers 69
Section 4: Understanding operations 73
13 Dyscalculia and operations 75
14 Understanding algorithms 77
15 Addition 81
16 Subtraction 88
17 Multiplication 92
18 Division 95
19 Learning number facts 98
Section 5: Measurement and rational numbers 101
21 Rational numbers 106
Section 6: Teacher resources 111
22 Parent information sheets 113
References 123
Index 125

Math Misconceptions, PreK-Grade 5: From Misunderstanding to Deep Understanding

Christine Oberdorf, Karren Schultz-Ferrell

Heinemann | 2010 | 200 páginas | mobi | 4,3 Mb

link (password: matav)

"In this wonderfully insightful book, Honi, Christine, and Karren not only describe a vast array of perfectly understandable mathematical misconceptions that students have across the elementary curriculum, they also provide numerous practical instructional strategies and activities for helping remediate and "undo" the misconceptions. The classroom vignettes they describe will ring true to everyone who has tried to teach mathematics to young, and not-so-young, children."

-Steven Leinwand

• identifying the most common errors relative to the five NCTM content strands (number and operations, algebra, geometry, measurement, and data analysis and probability)

• investigating the source of these misunderstandings

• proposing ways to avoid as well as "undo" misconceptions.

Children enter school filled with all kinds of ideas about numbers, shapes, measuring tools, time, and money-ideas formed from the expressions they hear...the things they see on television...the computer screen...in children's books...all around them. It's no wonder some children develop very interesting and perhaps incorrect ideas about mathematical concepts.

"How can we connect the informal knowledge that students bring to our classrooms with the mathematics program adopted by our school system? Just as important, how do we ensure that the mathematics we are introducing and reinforcing is accurate and will not need to be re-taught in later years?"

Math Misconceptions answers these questions by:

Using classroom vignettes that highlight common misconceptions in each content area, followed by applicable research about the root causes of the confusion, the authors offer numerous instructional ideas and interventions designed to prevent or correct the misconception.

Untangle your students' math misconceptions. This practical resource will help make it all make sense, and raise math achievement in your classroom.

Contents

Foreword  .v

Acknowledgments . .ix

Introduction . . .xi

CHAPTER 1 Number and Operations ..1

Counting with Number Words 2

Thinking Addition Means “Join Together” and Subtraction Means “Take Away” 7

Renaming and Regrouping When Adding and Subtracting Two-Digit Numbers 13

Misapplying Addition and Subtraction Strategies to Multiplication and Division 20

Multiplying Two-Digit Factors by Two-Digit Factors 24

Understanding the Division Algorithm 29

Understanding Fractions 34

Adding and Subtracting Fractions 40

Representing, Ordering, and Adding/Subtracting Decimals 43

CHAPTER 2 Algebra .. .49

Understanding Patterns 50

Meaning of Equals 55

Identifying Functional Relationships 61

Interpreting Variables 66

Algebraic Representations 71

CHAPTER 3 Geometry . . .78

Categorizing Two-Dimensional Shapes 78

Naming Three-Dimensional Figures 84

Navigating Coordinate Geometry 88

Applying Reflection 95

Solving Spatial Problems 100

CHAPTER 4 Measurement .108

Reading an Analog Clock 108

Determining the Value of Coins 116

Units Versus Numbers 121

Distinguishing Between Area and Perimeter 127

Overgeneralizing Base-Ten Renaming 132

CHAPTER 5 Data Analysis and Probability . . .137

Sorting and Classifying 137

Choosing an Appropriate Display 142

Understanding Terms for Measures of Central Tendency 148

Analyzing Data 152

Probability 158

CHAPTER 6 Assessing Children’s Mathematical Progress . . .164

Assessment: The Received View 164

Assessment from a Better Angle 165

Types of Formative Assessments 166

Why Assess? 170

Final Thoughts 171

References 173

Index ..179

The Math Gene: How Mathematical Thinking Evolved And Why Numbers Are Like Gossip

Keith Devlin

Basic Books| 2001 | 352 Páginas| EPUB | 0,9 Mb

filepost.com
link

Why is math so hard? And why, despite this difficulty, are some people so good at it? If there’s some inborn capacity for mathematical thinking—which there must be, otherwise no one could do it —why can’t we all do it well? Keith Devlin has answers to all these difficult questions, and in giving them shows us how mathematical ability evolved, why it’s a part of language ability, and how we can make better use of this innate talent. He also offers a breathtakingly new theory of language development—that language evolved in two stages, and its main purpose was not communication—to show that the ability to think mathematically arose out of the same symbol-manipulating ability that was so crucial to the emergence of true language. Why, then, can’t we do math as well as we can speak? The answer, says Devlin, is that we can and do—we just don’t recognize when we’re using mathematical reasoning.

Outros livros do mesmo autor, disponíveis no blog:

Mathematics: The New Golden Age, Penguin (1988)
Life by the Numbers, John Wiley & Sons (1998)

The Language of Mathematics: Making the Invisible Visible, W.H. Freeman & Company (1998)

Sets, Functions, and Logic: An Introduction to Abstract Mathematics , CRC (2003)
The Numbers Behind NUMB3RS: Solving Crime with Mathematics, Plume (2007)
The Unfinished Game: Pascal, Fermat, and the Seventeenth-Century Letter that Made the World Modern, Basic Books (2008)
Mathematics Education for a New Era: Video Games as a Medium for Learning, A K Peters (2011)

Errors and Misconceptions in Maths at Key Stage 2

Mike Spooner

David Fulton Publishers | 2002 | 60 páginas | RAR - PDF | 1 Mb

link
password : matav

The activities in this book are designed both to help children to learn and to understand math concepts, and also to prepare them for taking SATS papers at KS2. There is plenty of research evidence to suggest that children are helped in their understanding of math problems if teachers focus on common misconceptions, and if children are given opportunities for discussion and explanation of their own understanding. Children can also feel stigmatized by being made to focus on their own errors.

Mike Spooner has developed activities that present already completed work which children then assess, correct and discuss - in this way they can analyze mistakes without damage to their own self-esteem. The activities are presented in the same format as the SATS papers, to give children practice in coping with that format. The book also contains writing frames that children can use to structure their discussions of math problems.

Contents
Introduction: Error correction exercises
How do the exercises work?
What does this approach offer?
A rationale for this approach
Errors and misconceptions
How to use the exercises
Writing frames
Further outcomes of the trials
Appendix 1.1: The place value or Gattegno chart
Appendix 1.2: Place value chart
Appendix 1.3: Decimal number line
Using the exercises
The exercises
Numbers and the number system
Rounding numbers
Decimals
Calculation
Multiplying and dividing by 10 and 100
Solving numerical problems
Interpreting calculator displays
Co-ordinates
Using protractors and rulers
Reading scales
Appendix A: Briefing sheet
Appendix B: Writing frame
Appendix C: Writing frame
Bibliography

Livros relacionados, disponíveis no blog:

Ryan, J. & Williams, J. (2007). Children's mathematics 4-15: learning from errors and misconceptions. Open University Press

Cockburn, A. e Littler, G. (eds) (2008). Mathematical Misconceptions: A Guide for Primary Teachers. Sage Publications

The Trouble with Maths: A Practical Guide to Helping Learners with Numeracy Difficulties

Steve Chinn

Routledge | 2011 - 2.ª edição | 185 páginas | RAR - PDF | 1 Mb

link
password: matav

Now in a second edition, the award-winning The Trouble with Maths offers important insights into the often confusing world of numeracy. By looking at learning difficulties in maths from several perspectives, including the language of mathematics, thinking styles and the demands of individual topics, this book offers a complete overview of the most common problems associated with mathematics teaching and learning. It draws on tried-and-tested methods based on research and the author’s many years of classroom experience to provide an authoritative yet highly accessible one-stop classroom resource.

Combining advice, guidance and practical activities, this user-friendly guide will enable you to:

• develop flexible thinking skills;
• use alternative strategies for pupils to access basic facts;
• understand the implications of pre-requisite skills, such as working memory, on learning;
• implement effective preventative measures before disaffection sets in;
• recognise maths anxiety and tackle self-esteem problems;
• tackle the difficulties with word problems that many pupils may have;
• select appropriate materials to enhance understanding.

With useful features such as checklists for the evaluation of books, an outline for setting up an inclusive Maths Department policy and a brand new chapter on materials, manipulatives and communication, this book will equip you with the essential skills to tackle your pupils’ maths difficulties and improve standards. This book will be useful for all teachers, classroom assistants, learning support assistants and parents who have pupils who underachieve with maths.

Contents

List of illustrations viii

Preface to the second edition x

1 Introduction: learning difficulties in maths and dyscalculia 1

2 Factors that affect learning 19

3 What the curriculum asks pupils to do and where difficulties may occur 40

4 Thinking style and mathematics 61

5 Developmental perspectives 79

6 The vocabulary and language of maths 98

7 Anxiety and attributions 110

8 The inconsistencies of maths 119

9 Manipulatives and materials: multisensory learning 125

10 The nasties: long division and fractions 142

Appendix 1 Further reading 154

Appendix 2 Checklists and resources 155

Appendix 3 ‘Jog your memory cards’ for multiplication facts 157

Appendix 4 Setting an inclusive maths department policy 161

Notes 166

Index 168

The Trouble with Maths: A Practical Guide to Helping Learners with Numeracy Difficulties (2004)

1.ª edição 

Obstacles épistémologiques relatifs à la notion de limite

Anka Sierpinska

Recherches en Didactique des Mathematiques, Vol. 6, n°1, pp. 5-67, 1985

PDF - 2,4 Mb


Nenhum link disponível

Résumé

La recherche dont il est question dans le présent article se place dans la voie des recherches indiquée par Guy Brousseau dans son article (1983). Découvrir les obstacles épistémologiques lié aux mathématiques à enseigner à l’école et trouver les moyens didactiques pour aider les élèves à les surmonter - voilà, brièvement, deux principaux problèmes de ce programme de recherche. Ici, il s’agit du cas particulier de la notion de limite et l’article ne touche qu’au premier de ces problèmes : on propose une liste d’obstacles épistémologiques relatifs à la notion de limite présents encore chez des élèves d’aujourd’hui ; on ne propose pas les situations didactiques qui permettraient aux élèves de franchir ces obstacles.

Abstract

The present paper is concerned with a research the direction of which was indicated by Guy Brousseau in his 1983. To discover the epistemological obstacles connected with mathematics to be taught at school and to.elaborate didactical means to help the students to overcome them- these are, briefly, two main problems of this research programme. In this paper, the particular case of the notion of limit is considered and only the first of the two above mentionned problems is dealt with : a list of epistemological obstacles relative to the notion of limit is proposed ; there are no proposals of didactical situations enabling the students to overcome these.

Resumen

La investigación que trata este artículo se situa dentro de la línea de investigaciones indicadas por Guy Brousseau (1983). Descubrir los obstáculos epistemológicos ligados a las matemáticas que se enseñan en la escuela y encontrar los medios didácticos para ayudar los alumnos a superarlos. Brevemente presentamos aqui dos problemas principales de ese programa de investigación. Se trata del caso particular de la noción de limite y el artículo toca solamente el primero de esos problemas : se propone una lista de obstáculos epistemológicos relativos a la noción de límite presentes todavía en los alumnos de hoy en dia ; no se proponen situaciones didácticas que permitirian a los alumnos de superar esos obstáculos.

Artigo digitalizado por William (Obrigado!)

Multiple Perspectives on Difficulties in Learning Literacy and Numeracy

Claire Wyatt-Smith, John Elkins e Stephanie Gunn

Springer | 2010 | : 422 Páginas | PDF | 2,89 Mb

link
link1

• Features coverage at the intersection of literacy education, numeracy education and learning disabilities, which traditionally have tended to be addressed separately by researchers and policy makers
• Draws upon diverse theoretical perspectives in the common goal of improved learning especially for students who are struggling to achieve expected standards
• Includes contributions by international experts

This book advances understandings of the difficulties in learning that students experience in the key areas of literacy and numeracy and the interventions that have been used to improve outcomes. By including authors drawn from several countries and with expertise in a variety of research traditions, the book addresses the sometimes complementary and sometimes contradictory results, and generates new approaches to understanding and serving students with difficulties in literacy and numeracy. A distinctive feature of the book is its focus at the intersection of literacy education, numeracy education and learning difficulties. Traditionally these have tended to be addressed separately by researchers and policy makers, leading to compartmentalised thinking and often demonstrates lack of awareness of developments in the other domains. In short, to date there has been limited exchange across these fields. Further, the published research and indeed policy attention indicates a relative imbalance given to literacy and numeracy education and learning difficulties relative to these more generally. The authors in this book respond to this by providing a more balanced coverage of these fields and extend the discussion into the contribution of information and communication technologies. This book brings together for the first time internationally recognised scholars from a diverse range of countries whose contributions provide an opening for new insights into difficulties in learning literacy and numeracy from a range of educational policy and practice contexts.

Índice

Contents Acknowledgements About the contributors List of figures List of tables Chapter 1 Theoretical frameworks and ways of seeing: Operating at the intersection—literacy, numeracy and learning difficulties Claire Wyatt-Smith & John Elkins, Griffith University, Australia Chapter 2 Learning difficulties, literacy and numeracy: Conversations across the fields Stephanie Gunn & Claire Wyatt-Smith, Griffith University, Australia Chapter 3 Researching the opportunities for learning for students with learning difficulties in classrooms: An ethnographic perspective Judith Green & Beth Yeager, University of California, Santa Barbara, United States, & Maria Lucia Castanheira, Federal University of Minas Gerais, Brazil Chapter 4 The new literacies of online reading comprehension: New opportunities and challenges for students with learning difficulties Jill Castek, University of California, Berkeley, Lisa Zawilinski, J. Greg McVerry, W. Ian O’Byrne & Donald J. Leu, University of Connecticut, United States Chapter 5 Literacy, technology and the Internet: What are the challenges and opportunities for learners with reading difficulties, and how do we support them in meeting those challenges and grasping those opportunities? Colin Harrison, University of Nottingham, United Kingdom Chapter 6 Essential provisions for quality learning support: Connecting literacy, numeracy and learning needs Peta Colbert, Griffith University, Australia Chapter 7 Reading the home and reading in school: Framing deficit constructions as learning difficulties in Singapore English classrooms Anneliese Kramer-Dahl & Dennis Kwek, National Institute of Education/Nanyang Technological University, Singapore Chapter 8 Parent, family and community support for addressing difficulties in literacy Janice Wearmouth, University of Bedfordshire, Bedford, United Kingdom & Mere Berryman, Poutama Pounamu Education Research and Development Centre, New Zealand Chapter 9 Enhancing reading comprehension through explicit comprehending strategy teaching John Munro, The University of Melbourne, Australia Chapter 10 The writing achievement, metacognitive knowledge of writing and motivation of middle-school students with learning difficulties Christina E. van Kraayenoord, Karen B. Moni, Anne Jobling & Robyn Miller, The University of Queensland, Australia; John Elkins, Griffith University, Australia & David Koppenhaver, Appalachian State University, Boone, North Carolina, United States Chapter 11 The role of self-monitoring in initial word recognition learning Robert M. Schwartz, Oakland University, Michigan & Patricia A. Gallant, University of Michigan-Flint, Michigan, United States Chapter 12 Effective instruction for older, low-progress readers: Meeting the needs of Indigenous students Kevin Wheldall & Robyn Beaman, Macquarie University, Australia Chapter 13 Actualising potential in the classroom: Moving from practising to be numerate towards engaging in the literate practice of mathematics Raymond Brown, Griffith University, Australia Chapter 14 Effective instruction in mathematics for students with learning difficulties Marjorie Montague, University of Miami, Florida, United States Chapter 15 Language, culture and learning mathematics: A Bourdieuian analysis of Indigenous learning Robyn Jorgensen (Zevenbergen), Griffith University, Australia and Nyangatjatjara Aboriginal Corporation, Yulara, Northern Territory, Australia Chapter 16 ‘She’s not in my head or in my body’: Developing identities of exclusion and inclusion in whole-class discussions Laura Black, University of Manchester, United Kingdom Chapter 17 Breaking down the silos: The search for an evidentiary base John Elkins & Claire Wyatt-Smith, Griffith University, Australia Index

Dyscalculia Assessment

Jane Emerson, Brian Butterworth, Patricia Babtie

Continuum | 2010 | 224 páginas | PDF | 1 Mb

link
link1

A complete assessment tool for investigating maths difficulties in children, this book also provides advice for implementing the findings into teaching plans. Dyscalculia is a specific learning disability involving difficulty in acquiring numeracy skills. A significant group of children fail to progress beyond counting in ones; they cannot calculate efficiently or learn their tables. This assessment tool is designed to explore which aspects of numeracy the child is struggling to acquire. The evidence from the assessment can then be used to draw up a personalized teaching plan. With clear, step-by-step instructions alongside photocopiable or downloadable assessment sheets, "The Dyscalculia Assessment" contains what you need to pinpoint a child's difficulties with numeracy, and use that information to help the child progress. The Assessment is ideal for use with primary school children, but can easily be adapted for older or younger students, and is invaluable for SENCOs, TAs, educational psychologists and teacher's wishing to support students with maths difficulties in their class.

Table of Contents

Dedication and Acknowledgements \ Foreword \ Introduction: How To Use The Assessment \ 1. What Is Dyscalculia? \ 2. Numeracy, Dyscalculia and Co-Occurring Conditions \ 3. An Overview of The Dyscalculia Assessment \ 4. The Dyscalculia Assessment \ 5. Interpreting The Assessment \ 6. Games and Activities \ Appendices \ 1. Diagnosing Dyscalculia: The Dyscalculia Screener \ 2. The Wechsler Intelligence Scale For Children (WISC IV) \ 3. The Dyscalculia Assessment: Sample Report \ 4. The Dyscalculia Assessment: Summary Maths Profile \ 5. Group Grid \ 6. The Dyscalculia Assessment: Questionnaire For Teachers And Parents \ 7. Individual Teaching Plan \ 8. Resources \ Useful Websites \ Equipment Suppliers \ Useful Organizations \ Templates \ References And Further Reading \ Glossary \ Index

Fear of Math: How to Get over It and Get on With Your Life

Claudia Zaslavsky

Rutgers University Press | 1994 | 264 páginas | Djvu | 4 Mb

link
rapidgator.net

This book about mathematics anxiety focuses on many factors in society that bring about fear and avoidance of mathematics, and the influence of these factors on various groups in the population. The book begins with several stories of people who have suffered from or overcome mathematics anxiety, followed by a chapter giving reasons for overcoming it, including many real-life examples where an understanding of mathematics is necessary. The next chapter discusses myths of innate inferiority, including spatial ability, the Scholastic Aptitude Test, timed tests, intelligence tests, and needed research. In chapter 4 gender, race, ethnicity, and class are discussed. The next two chapters discuss mathematics in schools and school math versus real math. Chapter 7 includes strategies for overcoming fear and avoidance of mathematics and how to accommodate unique learning styles. The next chapter discusses how families and parents can help their children be more successful in mathematics. The last chapter is a call for a more humane mathematics that will serve all people. A list of intervention programs, organizations and government agencies, distributors of mathematics books and materials, and a select bibliography are included.

Mathematical Misconceptions: A Guide for Primary Teachers

Anne Cockburn, Paul Littler

Sage Publications | 2008 | 177 páginas | PDF | 

link
link1

With contributors comprised of teachers, teacher educators, mathematicians, and psychologists, Mathematical Misconceptions brings together information about pupils’ work from four different countries, and looks at how children, from the ages of 3 - 11, think about numbers and use them. It explores the reasons for their successes, misunderstandings, and misconceptions, while also broadening the reader’s own mathematical knowledge.

Contents

List of figures vi

List of pictures ix

List of tables x

Introduction 1

0 Zero: understanding an apparently paradoxical number 7

Anne D. Cockburn and Paul Parslow-Williams

1 Equality: getting the right balance 23

Paul Parslow-Williams and Anne D. Cockburn

2 Beginning to unravel misconceptions 39

Sara Hershkovitz, Dina Tirosh and Pessia Tsamir

3 Insights into children’s intuitions of addition, subtraction, multiplication and division 54

Dina Tirosh, Pessia Tsamir and Sara Hershkovitz

4 Right or wrong? Exploring misconceptions in division 71

Pessia Tsamir, Sarah Hershkovitz and Dina Tirosh

5 Developing an understanding of children’s acquisition of number concepts 86

Anne D. Cockburn

6 Highlighting the learning processes 101

Graham Littler and Darina Jirotková

7 Everyday numbers under a mathematical magnifying glass 123

Carlo Marchini and Paola Vighi

Appendix 152

Index 159

Outros livros de Anne Cockburn, disponíveis no blog:

Cockburn, A.D. (1999) Teaching Mathematics with Insight: the identification, diagnosis and remediation of young children's mathematical errors. London: Falmer Press

Cockburn, A.D. (ed. 2007) Mathematical Understanding 5-11. London: Sage Publications

Outros livros de Anne Cockburn, disponíveis na Internet:

Cockburn, A.D. (1996) Teaching Under Pressure. London: Falmer Press
Cockburn, A.D. e Haydn , T. (2004) Recruiting and Retaining Teachers: understanding why teachers teach. London: Routledge Falmer

Haylock, D.W. e Cockburn, A.D. (2008). Understanding Mathematics for Young Children. London: Sage Publications
Introduction
Capther 1 - Understanding Mathematics

Mind Bugs: The Origins of Procedural Misconceptions

(Learning, Development, and Conceptual Change)
Kurt VanLehn

The MIT Press | 1990 | 266 páginas | epub | 830 Kb

uploading.com
link


Descrição: As children acquire arithmetic skills, they often develop "bugs" - small, local misconceptions that cause systematic errors. Mind Bugs combines a novel cognitive simulation process with careful hypothesis testing to explore how mathematics students acquire procedural skills in instructional settings, focusing in particular on these procedural misconceptions and what they reveal about the learning process. VanLehn develops a theory of learning that explains how students develop procedural misconceptions that cause systematic errors. He describes a computer program, "Sierra," that simulates learning processes and predicts exactly what types of procedural errors should occur. These predictions are tested with error data from several thousand subjects from schools all over the world. Moreover, each hypothesis of the theory is tested individually by determining how the predictions would change if it were removed from the theory. Integrating ideas from research in machine learning, artificial intelligence, cognitive psychology, and linguistics, Mind Bugs specifically addresses error patterns on subtraction tests, showing, for example, why some students have an imperfect understanding of the rules for borrowing. Alternative explanatory hypotheses are explored by incorporating them in Sierra in place of the primary hypotheses, and seeing if the program still explains all the subtraction bugs that it explained before. Kurt VanLehn is Assistant Professor in the Department of Psychology at Carnegie Mellon University. Mind Bugs is included in the series Learning, Development, and Conceptual Change, edited by Lila Gleitman, Susan Carey, Elissa Newport, and Elizabeth Spelke.

On The Study And Difficulties of Mathematics

Augustus De Morgan

on-line: archive.org (The Open Court Publishing Company, 1910)

Kessinger Publishing | 2004 | 300 páginas

Descrição: 1910. Augustus De Morgan was an important innovator in the field of logic. In addition, he made many contributions to the field of mathematics and the chronicling of the history of mathematics. He writes in the Preface that his object has been to notice particularly several points in the principles of algebra and geometry, which have not obtained their due importance in our elementary works on these sciences. Contents: On Arithmetical Notation; Elementary Rules of Arithmetic; Arithmetical Fractions; Decimal Fractions; Algebraical Notation and Principles; Elementary Rules of Algebra; Equations of the First Degree; On the Negative Sign, etc.; Equations of the Second Degree; On Roots in General, and Logarithms; On the Study of Algebra; On the Definitions of Geometry; On Geometrical Reasoning; On Axioms; On Proportion; and Application of Algebra to the Measurement of Lines, Angles, Proportion of Figures and Surfaces. See other titles by this author available from Kessinger Publishing.

Childrens Mathematics 4-15: Learning from Errors and Misconceptions

Julie Ryan, Julian Williams

Open University Press | 2007 | 264 páginas |   PDF | 2,65 Mb

link

Descrição: The mistakes children make in mathematics are usually not just ‘mistakes’ - they are often intelligent generalizations from previous learning. Following several decades of academic study of such mistakes, the phrase ‘errors and misconceptions’ has recently entered the vocabulary of mathematics teacher education and has become prominent in the curriculum for initial teacher education. The popular view of children’s errors and misconceptions is that they should be corrected as soon as possible. The authors contest this, perceiving them as potential windows into children’s mathematics. Errors may diagnose significant ways of thinking and stages in learning that highlight important opportunities for new learning. This book uses extensive, original data from the authors’ own research on children’s performance, errors and misconceptions across the mathematics curriculum. It progressively develops concepts for teachers to use in organizing their understanding and knowledge of children’s mathematics, offers practical guidance for classroom teaching and concludes with theoretical accounts of learning and teaching. Children’s Mathematics 4-15 is a groundbreaking book, which transforms research on diagnostic errors into knowledge for teaching, teacher education and research on teaching. It is essential reading for teachers, students on undergraduate teacher training courses and graduate and PGCE mathematics teacher trainees, as well as teacher educators and researchers.

The Trouble with Maths: A Practical Guide to Helping Learners with Numeracy Difficulties

Steve Chinn

RoutledgeFalmer | 2004 | 192 páginas | PDF

link

Descrição: Written in a superb jargon-free style, this book offers important insights into the often confusing world of numeracy. By looking at learning difficulties in maths from several perspectives, including the language of mathematics, thinking styles and the demands of individual topics, Steve Chinn delivers a comprehensive yet succinct text which will become an essential classroom companion to anyone who uses it. Whilst considering every aspect concerning maths and learning, this book achieves a perfect balance of advice, guidance and practical activities, enabling the reader to: develop flexible thinking skills; use alternative strategies for pupils to access basic facts; implement effective preventative measures before disaffection sets in; recognise maths anxiety and tackle self-esteem problems; make accurate ongoing assessments of pupils' difficulties; design informal diagnostic procedures. With useful features such as checklists for evaluation of books, software and text materials, this book highlights essential skills that will allow teachers to diagnose and address maths difficulties and improve standards. It draws on tried and tested methods based on the author's years of classroom experience to provide an authoritative one-stop classroom resource for teachers, classroom assistants, Special Educational Needs Co-ordinators, student teachers, and learning support staff.

Índice

Contents
List of illustrations
Foreword
1 Introduction: learning difficulties in mathematics
2 Factors that affect learning
3 What the curriculum asks pupils to do and where difficulties may occur
4 Thinking styles in mathematics
5 Developmental perspectives
6 The language of maths
7 Anxiety and attributions
8 The inconsistencies of maths
9 Assessment and diagnosis
10 Thenasties… long division and fractions
Appendix 1 Further Reading
Appendix 2 Checklists and resources
Appendix 3 Jog Your Memory cards for multiplication facts
Appendix 4 Setting an inclusive maths department policy
Appendix 5 Criterion referenced tests
Notes
Index

The Trouble with Maths: A Practical Guide to Helping Learners with Numeracy Difficulties (2011)
2.ª edição

How Students (Mis-)Understand Science and Mathematics: Intuitive Rules

(Ways of Knowing in Science, 13)
Ruth Stavy, Dina Tirosh

Teachers College Press | 2000 | 127 páginas | chm | 788 kb


link

Referência em MathEdu

In this volume, the authors identify three "intuitive rules" and demonstrate how these rules can be used to interpret important misconceptions many students have about science and maths. By showing how learners react in similar ways to scientifically unrelated situations, the authors make a strong case for a theoretical framework that can explain these inconsistencies and predict students' responses to scientific and mathematical tasks. Provided are useful teaching strategies, grounded in this framework, that may be used to strengthen students' abilities to understand scientific and mathematics content.

Table of contents

Introduction

1. How Children and Adults Use the Intuitive Rule “More A-More B” 1

Equality Situations 3

Inequality Situations 31

Some Questions About the Use of This Rule 37

2. Learning About the Intuitive Rule “Same A-Same B” 42

Directly Given Equality 42

Logically Deduced Equality 50

Some Questions About the Use of This Rule 59

3. The Nature of the Intuitive Rule “Everything Can Be Divided” 64

Repeated Halving 65

Decreasing Series 74

Some Questions About the Use of This Rule 78

4. Toward a Theory of Intuitive Rules 82

Theoretical Approaches to Students' Alternative Reasoning and Conceptions 83

Some Questions About the Intuitive Rules Theory 85

5. Using Knowledge About Intuitive Rules: Educational Implications 89

Overcoming the Effects of the Intuitive Rules: General and Specific Teaching Strategies 89

Overcoming the Effects of the Intuitive Rules: Using Related Knowledge in Instruction 97

References 109

Index 119

About the Authors 127