Direct Instruction Mathematics 5th Edition by Marcy Stein,Diane Kinder,Jerry Silbert,Kristen Rolf,Douglas Carnine 013471122X 9780134711225

Part I Perspective

Chapter 1 Direct Instruction

Learning Outcomes

Mathematical Proficiency

Instructional Design

Sequence of Skills and Concepts

Explicit Instructional Strategies

Preskills

Example Selection

Practice and Review

Instructional Delivery

Progress Monitoring

Presentation Techniques

Signals

Pacing

Error-Correction Procedures

Diagnosis and Remediation

Instructional Language

Sequencing Guidelines Applied to Language Instruction

Teach Preskills of a Strategy Before the Strategy

Teach Easy Skills Before More Difficult Ones

Separate the Introduction of Information or Strategies that are Likely to be Confused

Apply What You Learned

Chapter 2 Research Support for Direct Instruction Mathematics

Learning Outcomes

The Need for Excellent Math Instruction

Current Performance of U.S. Math Students

Research on Direct Instruction

Research Recommendations for Math Instruction

Apply What You Learned

Chapter 3 Curriculum Evaluation and Modification

Learning Outcomes

The Curriculum Adoption Process

Time Allocation and Committee Responsibilities

Screening Process

Topics for Curriculum Evaluation

General Program Design

Does the program provide a logical sequence of skills and concepts?

Are Objectives Stated as Observable and Measurable Behaviors?

Does the Program Integrate Conceptual Understanding, Procedural Fluency, and Problem Solving in a Coherent Manner?

Specific Content Design

Strategy Instruction

Preskills

Example Selection

Practice and Review

Modifying Mathematics Curriculum

Apply What You Learned

Part II Basic Concepts and Skills

Chapter 4 Counting

Learning Outcomes

Skill Hierarchy

Conceptual Understanding

Instructional Procedures

Rote Counting by Ones to 30

Correcting Errors

Rational Counting: One Group

Correcting Errors

Practice and Review

Rational Counting: Two Groups

Correcting Errors

Practice and Review

Counting from Numbers Other Than One

Correcting Errors

Ordinal Counting

Counting by Ones from 30 to 100

Counting Backward

Counting Between 100 and 999

Practice and Review

Skip Counting

Practice and Review

Correcting Errors

Apply What You Learned

Chapter 5 Symbol Identification and Place Value

Learning Outcomes

Skill Hierarchy

Conceptual Understanding

Instructional Procedures: Symbol Identification

Numeral Identification

Numeral Writing

Correcting Errors

Symbol Identification and Writing

Equation Reading and Writing

Correcting Errors

Numeral/Object Correspondence

Identifying a Number and Drawing Lines

Counting Objects and Writing a Numeral

Practice and Review

Instructional Procedures: Place Value

Reading and Writing Teen Numerals

Reading Teen Numerals

Writing Teen Numerals

Practice and Review

Reading and Writing Tens Numerals

Reading Numerals 20–99

Writing Numerals 20–99

Reading and Writing Hundreds Numerals

Reading Numerals 100–999

Writing Numerals 100–999

Reading and Writing Thousands Numerals

Reading Numerals 1,000–9,999

Writing Numerals 1,000–9,999

Reading and Writing Millions Numerals

Expanded Notation

Column Alignment

Apply What You Learned

Chapter 6 Basic Facts

Learning Outcomes

Skill Hierarchy

Conceptual Understanding and Organization

Instructional Procedures: Relationship Activities

Plus-One Facts

Series Saying

Three-Number Fact Families

Instructional Procedures: Coordinating Mastery and Relationship Activities

Memorization Activities

Performance Criteria

Intensive Practice and Systematic Review

Record-Keeping Procedures

Instructional Procedures: Two Fact Mastery Programs

Homogenous Group Program

Materials

Pretesting

Daily Practice

Timed Test

Performance Criteria

Summary

Heterogeneous Group Program

Materials

Pretesting

Daily Practice

Student Record Form

Summary

Parental Involvement

Motivational Practice Activities

Commercial Programs

Apply What You Learned

Chapter 7 Addition

Learning Outcomes

Skill Hierarchy

Conceptual Understanding

Instructional Procedures: Beginning Addition

Addition the Slow Way

Missing Addend Strategy

Addition the Fast Way

Diagnosis and Remediation

Component-Skill Errors

Strategy Errors

Instructional Procedures: Multi-Digit Addition

Problems Not Requiring Renaming

Problems Requiring Renaming

Preskill

Introducing the Problems

Three or More Addends

Self-Checking

Diagnosis and Remediation

Fact Errors

Component-Skill Errors

Strategy Errors

Apply What You Learned

Chapter 8 Subtraction

Learning Outcomes

Skill Hierarchy

Conceptual Understanding

Instructional Procedures: Beginning Subtraction

Cross-out Strategy

Missing Subtrahend Strategy

Diagnosis and Remediation

Component-Skill Errors

Fact Memorization

Instructional Procedures: Multi-Digit Subtraction Problems

Column Subtraction—No Renaming

Subtraction with Renaming

Self-Checking

Complex Renaming Problems

Diagnosis and Remediation

Fact Errors

Strategy Errors

Component-Skill Errors

Apply What You Learned

Chapter 9 Multiplication

Learning Outcomes

Skill Hierarchy

Conceptual Understanding

Instructional Procedures: Beginning Multiplication

Single-Digit Multiplication

Missing-Factor Multiplication

Diagnosis and Remediation

Instructional Procedures: Multi-Digit Multiplication

Single-Digit Factor and Multi-Digit Factor

Preskills

Strategy

Example Selection

Self-Checking

Two Multi-Digit Factors

Diagnosis and Remediation

Fact Errors

Component-Skill Errors

Strategy Errors

Apply What You Learned

Chapter 10 Division

Learning Outcomes

Skill Hierarchy

Conceptual Understanding

Instructional Procedures: Beginning Division

Problems Without Remainders

Division Facts

Problems with Remainders

Remainder Facts

Diagnosis and Remediation

Fact Errors

Component-Skill Errors

Instructional Procedures: Multi-Digit Division

One-Digit Divisors

Problems with Two-Digit Quotient

Zero in the Quotient

Quotients of Three or More Digits

Self-Checking

Two-Digit Divisors

Preskills

Problems with Correct Estimated Quotients

Problems with Incorrect Estimated Quotients

Diagnosis and Remediation

Component-Skill Errors

Apply What You Learned

Chapter 11 Problem Solving

Learning Outcomes

Skill Hierarchy

Conceptual Understanding

Instructional Procedures: Addition and Subtraction Problems

Introducing the Concept

A Number-Family Problem-Solving Strategy

Preskill for the Number-Family Strategy

Temporal Sequence Problems

Comparison Problems

Classification Problems

Reading Tables

Distractors

Multi-step Word Problems

Instructional Procedures: Multiplication and Division Problems

Diagnosis and Remediation

Fact Errors

Calculation Errors

Decoding Errors

Vocabulary Errors

Translation Errors

Apply What You Learned

Chapter 12 Measurement, Time, and Money

Learning Outcomes

Skill Hierarchy

Conceptual Understanding

Measurement

Time

Money

Measurement: Customary and Metric Units

Common Units and Equivalencies

Measuring Tools

Conversion Problems

Converting Metric Units

Converting Customary Units

Operations

Word Problems

Time

Minutes After the Hour

Preskills

Units of 5 Minutes

Units of Single Minutes

Alternate Ways of Expressing Time

Digital Clocks

Quarter After and Half Past

Minutes Before the Hour

Money

Determining the Value of a Group of Coins

Consumer-Related Money Skills

Verifying Change Received

Counting Change

Decimal Notation in Money

Diagnosis and Remediation

Apply What You Learned

Part III Extended Concepts and Skills

Chapter 13 Fractions

Learning Outcomes

Skill Hierarchy

Conceptual Understanding

Part–Whole Discrimination

Writing Numerical Fractions to Represent Figures

Drawing Figures to Represent Fractions

Reading Fractions

Determining Whether a Fraction Equals, Exceeds, or is Less than One Whole

Reading and Writing Mixed Numerals

Instructional Procedures: Rewriting Fractions

Completing Equivalent Fractions

Preskills

Format

Example Selection

Reducing Fractions

Preskills

Determining the Greatest Common Factor

Reducing Fractions

Reducing Fractions with Larger Numbers

Converting Mixed Numerals and Improper Fractions

Converting Improper Fractions to Mixed Numerals

Converting Mixed Numbers to Improper Fractions

Instructional Procedures: Addition and Subtraction of Fractions

Fractions with Like Denominators

Problems with Mixed Numbers

Fractions with Unlike Denominators

Preskills

Format

Reducing and Rewriting Answers as Mixed Numerals

More Complex Problems with Mixed Numbers

Comparing Fractions

Word Problems

Instructional Procedures: Multiplication and Division of Fractions

Multiplying Fractions

Multiplying Proper Fractions

Multiplying Fractions and Whole Numbers

Multiplying Mixed Numbers

Dividing Fractions

Word Problems—Multiplication and Division

Diagnosis and Remediation of Common Fraction Errors

Errors in Reading and Writing Fractions and Mixed Numerals

Errors in Adding and Subtracting Fractions

Apply What You Learned

Chapter 14 Decimals

Learning Outcomes

Skill Hierarchy

Conceptual Understanding

Instructional Procedures: Reading and Writing Decimals

Reading and Writing Decimals and Mixed Decimals

Reading Decimals Representing Tenths and Hundredths

Writing Decimals Representing Tenths and Hundredths

Reading and Writing Mixed Decimals: Tenths and Hundredths

Reading and Writing Decimals Representing Thousandths

Equivalent Decimals

Instructional Procedures: Decimal Operations

Adding and Subtracting Decimals and Mixed Decimals

Decimals Having the Same Number of Places

Decimals Having Different Numbers of Places

Rounding Off Decimals

Multiplying Decimals

Dividing Decimals

Decimal or Mixed Decimal Divided by a Whole Number

Dividing by a Decimal or Mixed Decimal

Converting Fractions and Decimals

Converting a Fraction to a Decimal

Converting a Decimal to a Fraction

Diagnosis and Remediation

Apply What You Learned

Chapter 15 Percent, Ratio, and Probability

Learning Outcomes

Skill Hierarchy

Conceptual Understanding

Percentage Problems

Converting Percent to Decimal

Simple Percentage Problems

Simple Percentage Word Problems

Complex Percentage Problems

Ratio Problems

Converting a Fraction to a Percent

Simple Ratio Word Problems

Complex Ratio Word Problems

Probability Problems

Single-Event Probability

Compound Probability

Probability Word Problems

Diagnosis and Remediation

Apply What You Learned

Chapter 16 Data Analysis

Learning Outcomes

Skill Hierarchy

Conceptual Understanding

Graphs

Classifying, Representing, and Interpreting Data

Picture Graphs

Bar Graphs

Line Plots, Stem and Leaf Plots

Descriptive Statistics

Measures of Central Tendency

Measures of Variability

Diagnosis and Remediation

Apply What You Learned

Chapter 17 Geometry

Learning Outcomes

Skill Hierarchy

Conceptual Understanding

Identifying and Defining Geometric Figures and Concepts

Calculating Perimeter, Area, and Volume

Perimeter and Area

Volume

Measuring and Constructing Figures Using Tools

Using Logic in Working with Angles and Lines

Diagnosis and Remediation

Apply What You Learned

Chapter 18 Pre-algebra

Learning Outcomes

Skill Hierarchy

Conceptual Understanding

Coordinate System and Functions (CSF)

Other Types of Numbers: Primes, Factors, Integers, and Exponents

Primes and Factors

Integers

Exponents

Expressions and Equations

Solving for a Single Variable

Substitutions

Like Terms

Word Problems

Ratios and Proportions (R/P)

Using Ratio Tables to Solve Classification Problems

Using Ratio Tables with Fractions

Using Ratio Tables to Solve Comparison Problems

Using Ratio Tables with Percent Problems

Diagnosis and Remediation

Apply What You Learned

Appendix A Direct Instruction Mathematics and Common Core State Standards

Appendix B Frequently Asked Questions About Direct Instruction Mathematics

Instructional Questions and Issues

A. Doesn’t Direct Instruction Mathematics Promote Only Rote Learning?

B. How do You Know that Direct Instruction Mathematics Strategies are Effective?

C. What Role do Manipulatives Play in Mathematics Instruction Using a Direct Instruction Approach?

D. Should Teachers Spend Time Teaching Memorization of Math Facts?

E. Should Students be Allowed to Use Calculators in Math Class?

F. What Direct Instruction Mathematics Programs Are Commercially Aavailable?

Issues of Instructional Organization and Management

A. Is Direct Instruction for Only Struggling Students?

B. How Does a Direct Instruction Approach in Mathematics Work with Students with Special Needs?