Today's Mathematics, 10th Edition, Part 2, Activities and Instructional Ideas, 10th Edition

by James W. Heddens (Emeritus, Kent State Univ.); William R. Speer (Univ. of Nevada Las Vegas)

• ISBN13: 9780471387930
• ISBN10: 0471387932
• Edition: 10th
• Format: Paperback
• Copyright: 2000-08-01
• Publisher: Wiley

Summary

This classic allows readers to easily build a valuable set of ideas and reference materials for actual classroom use. Designed to aid the teacher in understanding mathematical concepts and relationships, the authors reflect recent recommendations from the National Council of Teachers of Mathematics Standards 2000.

Table of Contents

Learning Mathematics	1	(19)
Teaching Competencies	1	(1)
Calls for Change	2	(1)
National and International Achievement	3	(1)
The Identification of Standards	4	(1)
Principles and Standards for School Mathematics	5	(2)
Implementing the Process Standards	7	(2)
Describing a Contemporary Elementary Mathematics Program	9	(1)
Levels of Abstraction	10	(1)
Research Snapshot	11	(1)
Theoretical Foundations for a Contemporary Mathematics Program	11	(4)
Theory into Practice	15	(1)
Closure	16	(1)
Terminology, Symbols, and Procedures	16	(1)
Teaching Competencies and Self-Assessment Tasks	17	(1)
References	17	(1)
Related Readings	18	(1)
Teaching Mathematics	19	(12)
Teaching Competencies	19	(1)
The NCTM Professional Teaching Standards	20	(1)
The NCTM Principles and Standards for School Mathematics	20	(2)
Designing Mathematics Lessons	22	(2)
Creating Mathematics Objectives	24	(1)
The Role of Motivation and Follow-Up	25	(1)
Research Snapshot	25	(1)
The Evaluation of Learning and Teaching	26	(1)
Adjusting Instruction to Meet Needs	27	(1)
Classroom Instructional Aids	27	(2)
Closure	29	(1)
Terminology, Symbols, and Procedures	29	(1)
Teaching Competencies and Self-Assessment Tasks	30	(1)
References	30	(1)
Related Readings and Teacher Resources	30	(1)
Assessing Mathematics	31	(14)
Teaching Competencies	31	(1)
The NCTM Principles and Standards for School Mathematics	32	(1)
Assessment Standards	32	(2)
Purposes for Assessment	34	(2)
Research Snapshot	36	(1)
Assessment Techniques	36	(6)
Closure	42	(1)
Terminology, Symbols, and Procedures	42	(1)
Teaching Competencies and Self-Assessment Tasks	43	(1)
References	43	(1)
Related Readings and Teacher Resources	43	(2)
Technology Tools for Enhancing Teaching, Learning, and Assessing Mathematics	45	(16)
Teaching Competencies	45	(1)
Calculators in Mathematics	46	(1)
Research Snapshot	46	(1)
Calculators and the Education of Youth	47	(1)
Calculator Features and Functions	48	(1)
Tools for Measuring Motion	48	(1)
Computers in Mathematics	49	(1)
The Use of Technology in the Learning and Teaching of Mathematics	49	(1)
Instructional Software in the Mathematics Classroom	50	(1)
Application Software in the Mathematics Classroom	51	(1)
Multimedia in the Mathematics Classroom	52	(1)
Telecommunications in the Mathematics Classroom	53	(2)
Computers in the Program Mode: HTML	55	(1)
Computers in the Program Mode: Logo	56	(1)
Some Logo Computer Terms	57	(1)
Closure	58	(1)
Terminology, Symbols, and Procedures	58	(2)
Practice Exercises for Teachers	60	(1)
Teaching Competencies and Self-Assessment Tasks	60	(1)
Related Readings and Teacher Resources	60	(1)
Problem Solving, Decision Making, and Communicating in Mathematics	61	(22)
Teaching Competencies	61	(1)
The Nature of Problem Solving	62	(3)
Research Snapshot	65	(1)
Problem-Solving Strategies	65	(4)
Approaching Word Problems Effectively	69	(2)
Logic and Reasoning	71	(1)
The Language of Logic	71	(2)
The Language of Mathematics	73	(3)
Closure	76	(1)
Terminology, Symbols, and Procedures	77	(1)
Practice Exercises for Teachers	78	(3)
Teaching Competencies and Self-Assessment Tasks	81	(1)
Related Readings and Teacher Resources	81	(2)
Number Sense, Numeration, and Place Value	83	(30)
Teaching Competencies	83	(1)
A Foundation for Mathematics Development	84	(1)
Patterns and Other Relationships in the Primary Curriculum	85	(1)
Number Sense	86	(5)
Number Relations	91	(1)
Extending Numberness Concepts	92	(1)
Place-Value Numeration	93	(1)
Decimal Numeration	93	(5)
Ancient Numeration Systems	98	(2)
Research Snapshot	100	(1)
Number Bases Other than Ten	101	(3)
Closure	104	(1)
Terminology, Symbols, and Procedures	104	(4)
Practice Exercises for Teachers	108	(3)
Teaching Competencies and Self-Assessment Tasks	111	(1)
Related Readings and Teacher Resources	112	(1)
Addition and Subtraction of Whole Numbers	113	(22)
Teaching Competencies	113	(2)
Meaning and Models for Addition	115	(1)
Developing Basic Addition Facts	116	(1)
Memorizing Basic Addition Facts Using Structures	116	(5)
Extending Basic Addition Facts Using Place Value	121	(1)
Regrouping in the Addition Process	122	(1)
Meaning and Models for Subtraction	123	(1)
Research Snapshot	124	(2)
Developing Basic Subtraction Facts	126	(1)
Memorizing Basic Subtraction Facts Using Structures	127	(1)
Extending Basic Subtraction Facts Using Place Value	128	(1)
Regrouping in the Subtraction Process	129	(1)
Closure	130	(1)
Terminology, Symbols, and Procedures	131	(1)
Practice Exercises for Teachers	132	(1)
Teaching Competencies and Self-Assessment Tasks	133	(1)
Related Readings and Teacher Resources	133	(2)
Multiplication and Division of Whole Numbers	135	(22)
Teaching Competencies	135	(1)
Meaning and Models for Multiplication	136	(2)
Developing and Memorizing Basic Multiplication Facts	138	(3)
Expanding Basic Multiplication Facts through Place Value	141	(1)
Research Snapshot	142	(3)
Regrouping in Multiplication	145	(1)
Meaning and Models for Division	146	(2)
Developing and Memorizing Basic Division Facts	148	(1)
Remainders in Division	149	(1)
Expanding Basic Division Facts through Place Value	149	(3)
Closure	152	(1)
Terminology, Symbols, and Procedures	152	(2)
Practice Exercises for Teachers	154	(1)
Teaching Competencies and Self-Assessment Tasks	155	(1)
Related Readings and Teacher Resources	156	(1)
Number Theory and Number Systems	157	(184)
Teaching Competencies	157	(1)
The Language of Number Theory	158	(2)
The Sieve of Eratosthenes	160	(1)
Factor Trees	161	(2)
Prime Factorization	163	(2)
Divisibility ``Rules''	165	(1)
Research Snapshot	166	(1)
Least Common Multiples and Greatest Common Factors	167	(1)
Number Systems	168	(8)
Closure	176	(1)
Terminology, Symbols, and Procedures	176	(1)
Practice Exercises for Teachers	177	(2)
Teaching Competencies and Self-Assessment Tasks	179	(1)
Related Readings and Teacher Resources	180	(1)
Algebraic Reasoning: Generalizing Patterns and Relationships	181	(14)
Teaching Competencies	181	(1)
The Content of Algebra	182	(1)
Research Snapshot	183	(1)
Algebra in Problem Solving	183	(2)
Promoting Algebraic Thinking in the Lower Elementary Grades	185	(2)
Enhancing Algebraic Thinking in the Upper Elementary and Middle Grades	187	(4)
Closure	191	(1)
Terminology, Symbols, and Procedures	191	(1)
Practices Exercises for Teachers	192	(2)
Teaching Competencies and Self-Assessment Tasks	194	(1)
Related Readings and Teacher Resources	194	(1)
Rational Numbers Expressed as Fractions: Concepts	195	(16)
Teaching Competencies	195	(1)
A Fractional Part of the History of Fractional Numbers	196	(1)
Rational Numbers--A Definition and Description	196	(1)
Research Snapshot	197	(1)
The ``Regions'' Model for Fractional Numbers	198	(2)
The ``Groups of Objects'' Model for Rational Numbers	200	(1)
The ``Number Line'' Model for Rational Numbers	201	(1)
Knowledge and Understandings Prior to Operations	202	(4)
Closure	206	(1)
Terminology, Symbols, and Procedures	207	(1)
Practice Exercises for Teachers	207	(2)
Teaching Competencies and Self-Assessment Tasks	209	(1)
Related Readings and Teacher Resources	209	(2)
Rational Numbers Expressed as Fractions: Operations	211	(20)
Teaching Competencies	211	(1)
Research Snapshot	212	(1)
Addition of Fractional Numbers	213	(4)
Subtraction of Fractional Numbers	217	(3)
Multiplication of Fractional Numbers	220	(4)
Division of Fractional Numbers	224	(2)
Closure	226	(1)
Terminology, Symbols, and Procedures	226	(2)
Practice Exercises for Teachers	228	(2)
Teaching Competencies and Self-Assessment Tasks	230	(1)
Related Readings and Teacher Resources	230	(1)
Rational Numbers Expressed as Decimals: Concepts and Operations	231	(22)
Teaching Competencies	231	(1)
Models that Give Decimals Meaning	232	(1)
Place Value--A Foundation for Decimals	233	(2)
Exponential Notation	235	(1)
Addition with Decimal Numbers	236	(1)
Subtraction with Decimal Numbers	237	(1)
Multiplication with Decimal Numbers	238	(1)
Division with Decimal Numbers	239	(1)
Relating Decimals and Fractions	240	(2)
Scientific Notation	242	(1)
Ratio, Proportion, and Percent	243	(1)
Research Snapshot	244	(5)
Closure	249	(1)
Terminology, Symbols, and Procedures	249	(1)
Practice Exercises for Teachers	250	(1)
Teaching Competencies and Self-Assessment Tasks	251	(1)
Related Readings and Teacher Resources	252	(1)
Data Analysis: Graphs, Statistics, and Probability	253	(16)
Teaching Competencies	253	(1)
A Child's View of Statistics	254	(1)
Measures of Central Tendency in Data	255	(1)
Research Snapshot	256	(1)
Organizing and Interpreting Data	256	(4)
Taking a ``Chance''	260	(1)
Experimental Probability	260	(1)
Theoretical Probability	261	(1)
Permutations and Combinations	262	(1)
Models for Exploring Probability	263	(2)
Closure	265	(1)
Terminology, Symbols, and Procedures	265	(1)
Practice Exercises for Teachers	266	(2)
Teaching Competencies and Self-Assessment Tasks	268	(1)
Related Readings and Teacher Resources	268	(1)
Measurement	269	(18)
Teaching Competencies	269	(1)
The Historical Development of Measurement Systems	270	(1)
Contemporary Measurement Systems	271	(4)
The Process of Measurement	275	(3)
Computing with Denominate Numbers	278	(1)
Money and Time as Measures	279	(2)
Research Snapshot	281	(1)
Closure	282	(1)
Terminology, Symbols, and Procedures	283	(1)
Practice Exercises for Teachers	283	(2)
Teaching Competencies and Self-Assessment Tasks	285	(1)
Related Readings and Teacher Resources	285	(2)
Geometry: Basic Concepts and Structures	287	(22)
Teaching Competencies	287	(1)
Research Snapshot	288	(1)
Early Experiences in Geometry	289	(1)
The ``Building Blocks'' of Geometry	290	(2)
Extending the Basics--Curves, Regions, and Rays	292	(2)
Angles and Angle Measure	294	(3)
Exploring Geometric Constructions	297	(2)
Symmetry and Transformational Geometry	299	(2)
Other Devices for Exploring Geometric Concepts	301	(1)
Closure	302	(1)
Terminology, Symbols, and Procedures	302	(1)
Practice Exercises for Teachers	303	(3)
Teaching Competencies and Self-Assessment Tasks	306	(1)
Related Readings and Teacher Resources	307	(2)
Geometry: Polygons and Polyhedra	309	(30)
Teaching Competencies	309	(1)
Defining Polygons	310	(1)
Research Snapshot	310	(2)
A Closer Look at Triangles	312	(5)
A Closer Look at Quadrilaterals	317	(1)
A Closer Look at Circles	318	(1)
Area, Perimeter, and Circumference Measurement	319	(4)
Defining Polyhedra	323	(7)
Closure	330	(1)
Terminology, Symbols, and Procedures	330	(3)
Practice Exercises for Teachers	333	(4)
Teaching Competencies and Self-Assessment Tasks	337	(1)
Related Readings and Teacher Resources	337	(2)
A Look Back As You Move Ahead	339	(2)
Overview	339	(2)
Appendix Answers to Practice Exercises, Chapters 5-17	341	(36)
Index	377