Designing Effective Mathematics Instruction : A Direct Instruction Math

by Stein, Marcy; Silbert, Jerry; Carnine, Douglas W.

• ISBN13: 9780135966518
• ISBN10: 0135966515
• Edition: 3rd
• Format: Paperback
• Copyright: 1997-01-01
• Publisher: Pearson College Div

Summary

An exciting edition of this practical math methods book that provides future teachers with practical procedures for increasing student success in math. Emphasizing specific, classroom-tested strategies, these authors provide techniques for teaching major math and needed prerequisite skills, as well as extensive background in diagnosing and correcting error patterns. In addition, they offer practical guidelines for curriculum evaluation and modification, recommendations for practice and review drills, and specific information on progress-monitoring.

Table of Contents

Formats for Teaching Major Skills	xiv
PART 1 Perspective	1	(36)
1 Direct Instruction	3	(12)
Instructional Design	4	(4)
Specify Long-and Short-term Objectives	4	(1)
Devise Procedural Strategies	4	(1)
Determine Necessary Preskills	4	(1)
Sequence Skills	4	(1)
Select a Teaching Procedure	5	(1)
Design Formats	6	(1)
Select Examples	7	(1)
Specify Practice and Review	7	(1)
Design Progress-Monitoring Procedures	7	(1)
Presentation Techniques	8	(6)
Maintaining Student Attention	8	(2)
Criterion Teaching	10	(4)
Organization of Instruction	14	(1)
2 Organizing Mathematics Instruction	15	(15)
Selecting Instructional Materials	15	(15)
Types of Mathematics programs	15	(2)
Program Evaluation	17	(2)
Modifying Commercial Programs	19	(3)
Initial Assessment	22	(1)
Grouping Students	23	(1)
Placing Students in a Program	24	(1)
Presenting a Unit	24	(1)
Presenting Daily Lessons	25	(2)
Progressing at an Optimal Rate	27	(3)
3 Relevant Research in Mathematics Instruction	30	(7)
Misconceptions in Mathematics	30	(1)
Instructional Research	31	(5)
Intial Instruction	31	(4)
Guided Practice	35	(1)
Independent Practice	36	(1)
Conclusion	36	(1)
PART II Skills and Concepts	37	(401)
4 Counting	38	(13)
Terms and Concepts	38	(1)
Skill Hierarchy	38	(2)
Introducing the Concept	40	(6)
Rote Counting by 1s to 30	40	(1)
Rational Counting: One Group	41	(1)
Rational Counting: Two Groups	42	(1)
Counting from Different Numbers	42	(1)
Oridnal Counting	43	(1)
Counting by 1s from 30 to 100	43	(1)
Counting Between 100 and 999	44	(1)
Skip Counting	44	(2)
Application Items: Counting	46	(1)
Teaching Formats	46	(5)
5 Symbol Identification and Place Value	51	(28)
Terms and Concepts	51	(1)
Skill Hierarchy	51	(3)
Introducing the Concept	54	(4)
Numeral Identification	54	(1)
Numeral Writing	55	(1)
Symbol Identification and writing	56	(1)
Equation Reading and Writing	56	(1)
Numeration Tasks: Numeral and Line Matching	57	(1)
Place Value Skills	58	(6)
Reading and Writing Teen Numbers	58	(1)
Reading and Writing Numbers 20-99	59	(1)
Reading and Writing Numbers 100-999	60	(1)
Reading and Writing Numbers 1,000-999,999	61	(1)
Reading and Writing Millions	62	(1)
Column Alignment	63	(1)
Expanded Notation	63	(1)
Application Items: Symbols and Place Value	64	(1)
Teaching Formats	65	(4)
6 Basic Facts	79	(20)
Teaching Procedures	79	(2)
Relationship Activities	81	(4)
Preskill	81	(1)
Series Saying	82	(1)
Three-Number Fact Families	82	(1)
Sequence for Introducing Facts	83	(1)
Coordinating Mastery and Relationship Activities	85	(2)
Exercises for Memorizing	87	(1)
Setting Up a Program to Promote Mastery	87	(1)
Two Fact Mastery Programs	87	(5)
Homogeneous Group Program	88	(1)
Heterogeneous Group Program	89	(2)
Parental Involvement	91	(1)
Additional Practice Activities	92	(1)
Remedial Students	92	(1)
Commercial Programs	93	(1)
Basic Facts	93
Application Items: Facts	94	(1)
Teaching Formats	95	(4)
7 Addition	99	(29)
Terms and Concepts	99	(1)
Skill Hierarchy	99	(2)
Introducing the Concept	101	(4)
Addition the Slow Way	102	(1)
Missing Addend Strategy	103	(1)
Addition the Fast Way	104	(1)
Diagnosis and Remediation	104	(1)
Direct Instruction Procedures for Multi-Digit Addition Problems	105	(7)
Problems Not Requiring Renaming	105	(1)
Problems Requiring Renaming	106	(2)
Three or More Addents	108	(1)
Diagnosis and Remediation	109	(3)
Commercial Programs	112	(2)
Addition: Regrouping	112	(2)
Application Items: Addition	114	(2)
Teaching Formats	116	(12)
8 Subtraction	128	(24)
Terms and Concepts	128	(1)
Skill Hierarchy	128	(2)
Introducing the Concept	130	(2)
Beginning Subtraction Strategy	131	(1)
Missing Subtrahend Problems	131	(1)
Diagnosis and Remediation	131	(1)
Fact Memorization	132	(1)
Multi-Digit Subtraction Problems	132	(5)
Teaching Procedure	133	(1)
Column Subtraction--No Renaming	133	(1)
Subtraction with Renaming	133	(2)
Complex Renaming Problems	135	(1)
Diagnosis and Remediation	136	(1)
Commercial Programs	137	(4)
Subtraction; Renaming	137	(4)
Application Items: Subtraction	141	(2)
Teaching Formats	143	(9)
9 Multiplication	152	(27)
Terms and Concepts	152	(2)
Skill Hierarchy	154	(1)
Introducing the Concept	155	(1)
Beginning Multiplication	155	(3)
Single-Digit Multiplication	155	(2)
Missing-Factor Multiplication	157	(1)
Diagnosis and Remediation	157	(1)
Multi-Digit Multiplication	158	(6)
Single-Digit Factor and Multi-Digit Factor	159	(2)
Two Multi-Digit Factors	161	(1)
Diagnosis and Remediation	162	(2)
Commercial Programs	164	(3)
Multiplication: Multiplying by Two or More Digits	164	(1)
Practice and Review	164	(3)
Application Items: Multiplication	167	(1)
Teaching Formats	168	(11)
10 Division	179	(37)
Terms and Concepts	179	(1)
Skill Hierarchy	180	(1)
Introducing the Concept	181	(4)
Problems Without Remainders	181	(1)
Division Facts	182	(1)
Problems with Remainders	182	(1)
Remainder Facts	183	(1)
Diagnosis and Remediation	184	(1)
Multi-Digit Problems	185
One-Digit Divisors	186	(2)
Two-Digit Divisors	188	(4)
Diagnosis and Remediation	192	(1)
Commercial Programs	192	(3)
Division: Renaming with Single-and Double-Digit Divisors	192	(3)
Application Items: Division	195	(2)
Teaching Formats	197	(19)
11 Problem Solving	216	(39)
Addition and Subtraction Problems	220	(8)
Introducing the Concept	220	(1)
A Number-Family Problem-Solving Strategy	221	(7)
Multiplication and Division Problems	228	(1)
Multi-Step Word Problems	229	(1)
Distractors	230	(1)
Diagnosis and Remediation	230	(1)
Commercial Programs	231	(1)
Practice	232	(1)
Strategy	232	(1)
Application Items; Story Problems	232	(1)
Teaching Formats	233	(22)
12 Fractions	255	(69)
Terms and Concepts	255	(1)
Skill Hierarchy	255	(9)
Fraction Analysis	264	(4)
Part-Whole Discrimination	265	(1)
Writing Numerical Fractions to Represent Diagrams	266	(1)
Drawing Diagrams to Represent Fractions	266	(1)
Decoding Fractions	267	(1)
Determining if a Fraction Is More, Less, or Equal to One	267	(1)
Reading and Writing Mixed Numbers	268	(1)
Rewriting Fractions	268	(7)
Completing Equivalent Fractions	269	(1)
Reducing Fractions	270	(3)
Converting Mixed Numbers and Improper Fractions	273	(2)
Operations--Adding and Subracting Fractions	275	(4)
Fractions with Like Denominators	275	(1)
Problems with Mixed Numbers	276	(1)
Fractions with Unlike Denominators	276	(1)
Reducing and Rewriting Answers as Mixed Numbers	277	(1)
More Complex Problems with Mixed Numbers	278	(1)
Comparing Fractions	278	(1)
Word Problems	278	(1)
Operations--Multiplying Fractions	279	(2)
Multiplying Proper Fractions	279	(1)
Multiplying Fractions and Whole Numbers	279	(1)
Multiplying Mixed Numbers	280	(1)
Operation--Dividing Fractions	281	(1)
Story Problems--Multiplication and Division	282	(1)
Diagnosis and Remediation	282	(1)
Reading and Writing Fractions and Mixed Numbers	282	(1)
Adding and Subtracting Fractions	282	(1)
Commercial Programs	283	(3)
Fractions: Adding and Subtracting Fractions with Unlike Denominators	283	(3)
Application Items: Fractions	286	(2)
Teaching Formats	288	(36)
13 Decimals	324	(30)
Terms and Concepts	324	(4)
Reading and Writing Decimals and Mixed Decimals	328	(2)
Reading Decimals Representing Tenths and Hundredths	328	(1)
Writing Decimals Representing Tenths and Hundredths	329	(1)
Reading and Writing Mixed Deciamls: Tenths and Hundredths	329	(1)
Reading and Writing Decimals Representing Thousandths	329	(1)
Equivalent Decimals	330	(1)
Adding and Subtracting Decimals and Mixed Decimals	330	(1)
Decimals Having the Same Number of Places	330	(1)
Decimals with Different Number of Places	331	(1)
Rounding Off Decimals	331	(1)
Multiplying Decimals	332	(1)
Dividing Decimals	332	(3)
Decimal or Mixed Decimal Divided by a Whole Number	333	(2)
Dividing by a Decimal or Mixed Decimal	335	(1)
Converting Fractions and Decimals	335	(2)
Converting a Fraction to a Decimals	336	(1)
Converting a Decimal to a Fraction	336	(1)
Diagnosis and Remediation	337	(1)
Application Items: Decimals	338	(1)
Teaching Formats	339	(15)
14 Percent and Ratio	354	(16)
Terms and Concepts	354	(1)
Percentage Problems	354	(4)
Converting Percent to Decimal	356	(1)
Simple Percentage Problems	356	(1)
Simple Percentage Story Problems	357	(1)
Complex Percentage Problems	357	(1)
Ratio Problems	358	(2)
Converting a Fraction to a Percent	358	(1)
Simple Ratio Story Problems	359	(1)
Complex Ratio Story Problems	360	(1)
Application Items: Percent and Ratio	360	(1)
Teaching Formats	361	(9)
15 Telling Time	370	(13)
Minutes After the Hour	370	(4)
Preskills	370	(3)
Units of 5 Minutes	373	(1)
Units of Single Minutes	374	(1)
Alternate Ways of expressing Time	374	(1)
Quarter After and Half Past	374	(1)
Using a Colon	375	(1)
Minutes Before the Hour	375	(1)
Diagnosis and Remediation	376	(1)
Application Items: Telling Time	376	(1)
Teaching Formats	377	(6)
16 Money	383	(12)
Determining the Value of a Group of Coins	383	(4)
Counting Change	387	(1)
Making Equivalent Change	387	(1)
Verifying Change	388	(1)
Decimal Notation in Money	388	(1)
Consumer Skills	389	(1)
Making Purchases with Coins	389	(1)
Counting Change	389	(1)
Reading Price Lists and Menus	389	(1)
Unit Pricing	390	(1)
Application Items: Money	390	(1)
Teaching Formats	390	(5)
17 Measurement	395	(21)
Customary and Metric Units	395	(3)
Introducing the Concept	398	(1)
Primary Grades	399	(2)
Common Units Equivalencies	399	(1)
Measuring Tools	399	(2)
Intermediate Grades	401	(7)
Metric Equivalencies	402	(1)
Conversion Problems	402	(3)
Operations	405	(1)
Story Problems	406	(1)
Measuring Tools	406	(2)
Application Items: Measurement	408	(1)
Teaching Formats	408	(8)
18 Mathematics Study Skills: Graphs, Charts, Maps, and Statistics	416	(13)
Graphs	416	(7)
Tables or Charts	423	(1)
Maps	423	(1)
Statistics	424	(1)
Teaching Procedure	424	(1)
Application Items: Study Skills	425	(1)
Teaching Formats	426	(3)
19 Geometry	429	(9)
Identifying and Defining Geometric Figures and Concepts	429	(6)
Measuring a Figure	435	(1)
Constructing Figures	436	(1)
Summary	437	(1)
Teaching Formats	437	(1)
Appendix A Direct Instruction Mathematics: A Longitudinal Evaluation of Low-Income Elementary School Students	438	(11)
Appendix B Frequently Asked Questions about Direct Instruction Mathematics	449	(4)
References	453	(3)
Index	456