Designing Effective Mathematics Instruction : A Direct Instruction Math,9780135966518

Designing Effective Mathematics Instruction : A Direct Instruction Math

by ; ;
Edition: 3rd
ISBN13: 9780135966518
ISBN10: 0135966515
Format: Paperback
Pub. Date: 1997-01-01
Publisher(s): Pearson College Div
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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

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