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The SEND Code of Practice (2015) reinforced the requirement that all teachers must meet the needs of all learners. This topical book provides practical, tried and tested strategies and resources that will support teachers in making maths lessons accessible and interesting for all pupils, including those with special needs. The author draws on a wealth of experience to share his understanding of special educational needs and disabilities and show how the maths teacher can reduce or remove any barriers to learning. Offering strategies that are specific to the context of maths teaching, this book will enable teachers to: adopt a ‘problem solving’ approach to ensure students use and apply mathematics at all times during their learning develop students’ understanding of mathematical ideas structure lessons to empower and actively engage students create a mutually supportive classroom which maximises learning opportunities plan the classroom layout and display to enhance learning, for example displaying number lines, vocabulary lists and pupils’ work successfully train and fully use the support of their teaching assistants. An invaluable tool for continuing professional development, this text will be essential for secondary maths teachers (and their teaching assistants) seeking guidance specific to teaching maths to all pupils, regardless of their individual needs. This book will also be of interest to secondary SENCOs, senior management teams and ITT providers. In addition to free online resources, a range of appendices provide maths teachers with a variety of pro forma and activity sheets to support effective teaching. This is an essential tool for maths teachers and teaching assistants, and will help to deliver successful, inclusive lessons for all pupils.
First Published in 2003. Routledge is an imprint of Taylor & Francis, an informa company.
Between the pressure to meet standards and the overwhelming number of different learning needs that students have, planning lessons has become more complex. Judy Storeygard provides proven approaches to understanding the behaviors of children with special needs and effectively teaching all students.
Title Page 1 Dedication 2 About the Authors 3 Table of Contents 4 Introduction 10 Purposes of Mathematics 10 Perspective 11 The What and When of Mathematics Programming 12 A Primary Purpose 13 A Basic Understanding for Teachers 15 Section 1: Problem Solving Precedes Computation 19 Framework for Alternative Representations 20 Utilizing Alternative Representations in Problem Solving 26 What is a Problem? 27 Information Processing in Word Problem Activities 30 Word Problems and Conjunctive/Disjunctive Relationship 31 Selecting the Best Question for a Word Problem 34 Word Problems Using Cloze Procedure 35 Views of Mathematics 38 Problem Solving Precedes Computation 39 Semantics 41 Active and Passive Problem Solving 45 Problem to Match the Question 46 Information Sets to Complete a Problem Activity 46 Display Activities for Problem Creation 46 Developing Vocabulary 47 Teaching Vocabulary 49 Instruction in Vocabulary 50 Syntax 53 The Elements of a Word Problem 54 Classifying Word Problems by Mathematical Constructs 56 Section 2: Developing Word Problems for Diagnostic Feedback 59 Problem Solving, Cognition and Language Complexity 59 Word Problem Solving Activities 60 Problem Characteristics 62 Direct Word Problems 63 Indirect Word Problems 65 Two Step Problems 67 Word Problems Made From Nonsense Words 68 Problem Formats 69 Script/display/picture format 69 Write format 72 Story format 73 Sentence format 74 Nominal Numbers 76 Organizing Quantitative Information 77 Section 3: Connections to Other Subjects 79 Arithmetic Activities and Word Problems Related to Community Concerns 79 Addition 79 Subtraction 80 Multiplication 81 Division 83 Quantitative and Qualitative Distractors 84 Contiguity and Non-Contiguity 85 Definite and Indefinite Quantifiers 86 Word Problems to Address Emotions 86 Formula Types of Word Problems 88 Machines and formulas 88 Work and simple machines 89 Effort and resistance 93 Pre-Algebra Thinking 94 Extended Problem Activities 94 Related Problems 95 Solving a Problem 95 Being a Problem Solver 95 Long-Term Problem Solving 96 Executive Processes 99 Summary 101 Section 4: Arithmetic Computation 102 Preparing to Compute 105 Patterns 105 Pattern Traits - Identify a Pattern and Original Learning 106 Pattern Traits - Identify a Pattern and Intradimensional Shift 107 Pattern Traits - Identify a Pattern and Extradimensional Shift 107 Pattern Traits - Copy a Pattern and Extradimensional Shift 108 Pattern Traits - Extend a Pattern and Extradimensional Shift 108 Sequences 110 Counting 111 Counting Forward and Backward 111 Cardinal Property 113 Skip Counting 113 Naming the Numbers 114 Section 5: Knowing About and Being Able To Do 117 Curricula Choices 119 Alternative Representations 121 Background for the Operations 122 Relations 123 Counting 123 A Pendulum 125 A Balance Scale 125 Counting the 10's and Accounting for the 10's 126 Unusual Combinations of 10's 129 Place Value 130 Estimation 131 Expanded Notation 133 Representations of Quantity 134 Section 6: Communicating Mathematics 137 Knowing About and Doing Addition 140 Addition - Things to Know About Addition 141 Addition - Things to Know When Doing Addition 146 A + H: Memorization of Basic Facts 148 Subtraction - Things to Know About Subtraction 150 Subtraction - Things to Know When Doing Subtraction 152 YAP and YAN 155 Multiplication - Things to Know About Multiplication 156 Multiplication - Things to Know When Doing Multiplication 158 Division - Things to Know About Division 162 Division - Things to Know When Doing Division 163 Section 7: Teaching the Operations Using Whole Numbers 168 Probability Control 171 Controlled Repetition 172 Active versus Passive Activities 172 Error Detection Activities 173 Teaching Addition 173 Teaching Subtraction 180 Alternative Algorithms 184 Left-to-right 184 Without renaming 184 Teaching Multiplication 185 Alternative Representations 189 Array multiplication 194 Two or more digit combinations 192 Estimation 195 Algorithmic Variations 196 Teaching Division 196 Remainders 202 Moving Over 203 Regrouping Partial Dividends 204 Alternative Algorithms 207 Section 8: Hand-Held Calculators 209 Activity-Based Computer Participation 209 Evaluation 216 Section 9: Concluding Comments 218 Appendix 219 References 233.
This book provides prospective and practicing teachers with research insights into the mathematical difficulties of students with learning disabilities and classroom practices that address these difficulties. This linkage between research and practice celebrates teachers as learners of their own students’ mathematical thinking, thus contributing an alternative view of mathematical progression in which students are taught conceptually. The research-based volume presents a unique collaboration among researchers in special education, psychology, and mathematics education from around the world. It reflects an ongoing work by members of the International Group for the Psychology of Mathematics Education (PME) and the North American Chapter of the PME Working Groups. The authors of chapters in this book, who have been collaborating extensively over the past 7 years, are from Australia, Canada, the United Kingdom, and the United States.
Math Instruction for Students with Learning Problems, Second Edition provides a research-based approach to mathematics instruction designed to build confidence and competence in pre- and in-service PreK–12 teachers. This core textbook addresses teacher and student attitudes toward mathematics, as well as language issues, specific mathematics disabilities, prior experiences, and cognitive and metacognitive factors. The material is rich with opportunities for class activities and field extensions, and the second edition has been fully updated to reference both NCTM and CCSSM standards throughout the text and includes an entirely new chapter on measurement and data analysis.
This resource is a guiding perspective emphasizing techniques and strategies designed to address specific difficulties or weaknesses to help the challenged student conquer math.
For years the text of choice for developing excellence as a teacher of K–12 students with moderate and severe disabilities, this clearly written work has now been revised and updated. Chapters provide step-by-step procedures for designing standards-based individualized education plans and evaluating and enhancing student progress. Methods and materials for teaching literacy, mathematics, science, and social studies are described in depth. The book also describes effective ways to build functional daily living skills. User-friendly features include extensive vignettes and classroom examples, end-of-chapter application exercises, and reproducible planning and assessment tools. Purchasers get access to a Web page where they can download and print the reproducible materials in a convenient 8 1/2" x 11" size. New to This Edition *Reflects important advances in research and evidence-based practice. *Chapter on collaborating with culturally diverse families, plus a stronger multicultural focus throughout. *Chapter on writing instruction. *Two additional chapters on reading and math, ensuring coverage of both foundational and grade-aligned skills. *Increased attention to students with autism spectrum disorder and to uses of technology.
Is it a learning disability or a teaching disability?"" Achieving Fluency presents the understandings that all teachers need to play a role in the education of students who struggle: those with disabilities and those who simply lack essential foundational knowledge. This book serves teachers and supervisors by sharing increasingly intensive instructional interventions for struggling students on essential topics aligned with NCTM's Curriculum Focal Points, the new Common Core State Standards for Mathematics, and the practises and processes that overlap the content. These approaches are useful for both overcoming ineffective approaches and implementing preventive approaches.
The purpose of Making Math Accessible to Students With Special Needs is to support everyone involved in mathematics education to become confident and competent with mathematics instruction and assessment so that 99% of students will be able to access enrolled grade-level mathematics. Six chapters address topics critical to effective mathematical instruction such as federal and state legislation, research-based instructional best practices in mathematics, and the selection, administration, and evaluation of accommodations for instruction and assessment. These topics are combined to offer teachers understandable, practical instructional procedures. The resource guides readers through the 5E instructional model, which provides an array of choices and strategies for providing high-quality instruction to all students. This resource actively engages readers through reflections and tasks in each chapter and can be used as a self-study professional development or as a group book study. Sample answers to tasks and reflections are found in the appendix, along with additional supports. Making Math Accessible to Students With Special Needs is designed for all teachers involved with mathematics instruction and is a unique resource for alternatively certified teachers and adjunct professionals.