Designing And Implementing Mathematics Instruction for Students With Diverse Learning Needs

by Hudson, Pamela P; Miller, Susan Peterson

• ISBN13: 9780205442065
• ISBN10: 0205442064
• Edition: 1st
• Format: Paperback
• Copyright: 2005-12-15
• Publisher: Pearson

Summary

This exciting new book integrates the explicit teaching practices that have proven effective for students with disabilities with the NCTM math standards that dominant current mathematics practices in theUnited States. In Part 1 of the book, teachers learn the fundamentals of mathematics assessment and instructional design for conceptual, declarative knowledge, procedural, and problem-solving lessons. In Part 2, the detailed scope and sequence charts, along with instructional guidelines keyed to the objectives, provide teachers with specific guidelines for assessment and design. The curriculum-based assessment chapter (Ch. 2) helps teachers group students for instruction, place in curriculum, monitor performance, and make data based decisions. Content coverage of all five NCTM content standards provides teachers the support needed to access the general education curriculum and help their students meet annual yearly progress expectations (Chapters 7 - 15). Detailed scope and sequence charts provide a valuable resource for assessing, planning,and designing instruction (Chapters 7-15). Instructional design discussion includes four domains: concepts, declarative knowledge, problem solving, and procedural knowledge. When teachers understand the function of the instruction, their effectiveness and efficiency are enhanced (Chapters 3-15). Integration of explicit teaching practices with NCTM approach helps teachers maintain practices that work for students with diverse needs while integrating reformed-based mathematics practices (in Chapters 1, 7-15). Detailed guidelines, including scripted lessons, on HOW to design and deliver effective instruction. These sample lessons illustrate how to apply the explicit teaching sequence to various content areas and provide examples for preservice and inservice teachers to use when developing their own lessons.

Table of Contents

Preface	ix
PART I Foundation For Planning and Implementing Mathematics Instruction	1	(162)
Designing a Balanced Curriculum and Meaningful Instruction	3	(28)
Making Curriculum Decisions	6	(5)
Balancing Instruction across Four Domains	11	(2)
Integrating Explicit Teaching Principles into an Instructional Cycle	13	(16)
Summary	29	(2)
Planning Instruction Using Curriculum-Based Assessment	31	(32)
Curriculum-Based Assessment	31	(18)
Planning Instruction	49	(13)
Summary	62	(1)
Promoting Conceptual Understanding	63	(23)
Characteristics of Instruction Designed to Promote Conceptual Understanding	65	(3)
Rationale for Promoting Conceptual Understanding	68	(2)
Guidelines for Planning Instruction That Promote Conceptual Understanding	70	(6)
Guidelines for Implementing Instruction That Promote Conceptual Understanding	76	(9)
Summary	85	(1)
Developing Procedural Knowledge	86	(20)
Rationale for Teaching Procedural Strategies	87	(1)
Characteristics of a Procedural Strategy	88	(4)
Guidelines for Planning Procedural Strategy Instruction	92	(5)
Guidelines for Implementing Procedural Strategy Instruction	97	(8)
Summary	105	(1)
Developing Declarative Knowledge	106	(24)
Characteristics of Instruction Designed to Develop Declarative Knowledge	107	(1)
Rationale for Developing Declarative Knowledge	107	(4)
Guidelines for Planning Instruction That Promote the Acquisition of Declarative Knowledge	111	(2)
Guidelines for Implementing Declarative Knowledge Instruction	113	(16)
Summary	129	(1)
Enhancing Problem-Solving Abilities	130	(33)
Characteristics of Instruction Designed to Enhance Problem-Solving Abilities	130	(1)
Rationale for Enhancing Problem-Solving Abilities	131	(3)
Guidelines for Planning Problem-Solving Instruction	134	(9)
Guidelines for Implementing Problem-Solving Instruction	143	(19)
Summary	162	(1)
PART II Teaching the Mathematics Curriculum	163	(424)
Developing Number Sense	165	(35)
Scope and Sequence Chart	165	(6)
Counting Skills	171	(6)
Reading and Writing Number Symbols and Words	177	(7)
Relationships among Whole Numbers	184	(4)
Place Value	188	(7)
Estimation	195	(3)
Summary	198	(2)
Teaching Whole Number Operations: Addition and Subtraction	200	(44)
Scope and Sequence Chart	200	(7)
Basic Addition and Subtraction Facts	207	(8)
Advanced Addition and Subtraction Computation	215	(24)
Integration of Technology When Teaching Whole Number Operations	239	(2)
Summary	241	(3)
Teaching Whole Number Operations: Multiplication and Division	244	(40)
Scope and Sequence Chart	244	(6)
Basic Multiplication and Division Facts	250	(12)
Advanced Multiplication and Division Computation	262	(20)
Summary	282	(2)
Teaching Rational Numbers	284	(56)
Scope and Sequence Chart	284	(15)
Fraction Foundation	299	(10)
Basic Fraction Computation	309	(4)
Fraction Equivalence	313	(4)
Decimal and Percent Foundation	317	(6)
Decimal Computation and Problem Solving	323	(5)
Fraction Computation and Problem Solving	328	(8)
Percent Computation and Problem Solving	336	(1)
Summary	337	(3)
Developing Basic Measurement Concepts and Skills	340	(41)
Scope and Sequence Chart	340	(10)
Curriculum and Instructional Framework	350	(5)
Length Foundation	355	(4)
Weight Foundation	359	(3)
Capacity Foundation	362	(3)
Value (Money) Foundation	365	(3)
Time Foundation	368	(5)
Perimeter Foundation	373	(2)
Area Foundation	375	(1)
Volume Foundation	376	(1)
Temperature Foundation	377	(1)
Summary	378	(3)
Teaching Advanced Measurement Skills	381	(51)
Scope and Sequence Chart	381	(14)
Curriculum and Instructional Framework	395	(5)
Advanced Skills in Measuring Length	400	(5)
Advanced Skills in Measuring Weight	405	(4)
Advanced Skills in Measuring Capacity	409	(5)
Advanced Skills in Measuring Value (Money)	414	(3)
Advanced Skills in Measuring Time	417	(2)
Advanced Skills in Measuring Temperature	419	(3)
Advanced Skills in Measuring Area, Perimeter, and Volume	422	(4)
Advanced Computation and Conversion of Standard Customary Units	426	(1)
Summary	427	(5)
Teaching Algebraic Thinking	432	(57)
Scope and Sequence Chart	432	(7)
Teaching Strategies to Enhance the Development of Algebraic Thinking	439	(4)
Patterns	443	(15)
Variables and Equality	458	(16)
Relations, Functions, and Representations	474	(10)
Summary	484	(5)
Teaching Geometry Concepts and Skills	489	(47)
Scope and Sequence Chart	489	(13)
Shape Identification	502	(12)
Circle Measurement	514	(2)
Shape Properties	516	(4)
Lines and Angles	520	(5)
Spatial Relationships	525	(4)
Transformations	529	(4)
Summary	533	(3)
Teaching Data Analysis, Statistics, and Probability	536	(51)
Scope and Sequence Chart	536	(11)
Data Collection and Probability Foundation	547	(10)
Data Display Formats	557	(13)
Simple Statistics	570	(3)
Expanded Probability and Data Analysis Skills	573	(8)
Summary	581	(6)
References	587	(10)
Index	597