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Teaching Mathematics in Elementary and Middle School: Developing Mathematical Thinking / Edition 1
     

Teaching Mathematics in Elementary and Middle School: Developing Mathematical Thinking / Edition 1

by Joseph G.R. Martinez, Nancy C. Martinez, Nancy C. Martinez, Nancy C. Martinez
 

ISBN-10: 0130549789

ISBN-13: 9780130549785

Pub. Date: 08/22/2006

Publisher: Prentice Hall

For courses in undergraduate Elementary and Middle School Mathematics Education

With an emphasis on inquiry and process, Teaching Mathematics in Elementary and Middle School embraces active mathematics instruction and the development of mathematical thinking through problem solving. The text challenges future teachers to prepare their K-8

Overview

For courses in undergraduate Elementary and Middle School Mathematics Education

With an emphasis on inquiry and process, Teaching Mathematics in Elementary and Middle School embraces active mathematics instruction and the development of mathematical thinking through problem solving. The text challenges future teachers to prepare their K-8 students for a world that requires a higher level of mathematical literacy and enables them to compete in a global society. Teachers will develop their own mathematical abilities allowing them to help students discover a rich combination of thinking processes and problem-solving strategies, raising the learning expectations for all.

Product Details

ISBN-13:
9780130549785
Publisher:
Prentice Hall
Publication date:
08/22/2006
Edition description:
BK&CD-ROM
Pages:
432
Product dimensions:
8.90(w) x 11.20(h) x 0.80(d)

Table of Contents

CHAPTER 1 Teaching Mathematics in the 21st Century

Being a Teacher in the 21st Century

Beyond Shop-and-Yard Mathematics

In Step with the New Mathematical Literacy

Changing Views About Who should Learn Mathematics

Tradition and Myths

Equity Reforms

Changing Views About What Should Be Learned

Tying the Curriculum to Mental Age and Social Utility

Responding to a Bigger World

Building Consensus and Setting Standards

National Standards for Mathematics Education

State and Local Standards

Meeting the Challenges of the 21st Century

Meeting the Challenges as a Nation

Meeting the Challenges in the Classroom

Questions for Discussion, Thought, and Further Research

CHAPTER 2 Empowering Children to Learn Mathematics

Teaching Important Mathematics to All Students

Legislation for Equity and Excellence

Important Mathematics

Understanding How Students Learn Mathematics

Changing Perspectives of Learning

Matching Teaching to Learning: Modesl for Diversity

Mastery Learning

Inquiry-based Learning

Universal Design for Learning Mathematics

Questions for Thought, Discussion, and Further Research

CHAPTER 3 Preparing Students to Think Mathematically

Learning to Think and Reason Mathematically

The Importance of Mathematical Thinking

The Processes of Mathematical Thinking

Understanding Interactions That Affect Mathematical Thinking and Learning

The Cognitive Domain

The Affective Domain

Interactions

Applying Mathematical Thinking in Problem Solving

Polya's Four Steps to Problem Solving

Problem-Solving Approach to Learning

Multiple Solutions/New Beginning

Developing a Mathematical World View

Diversity in Learning and Thinking Mathematically

Questions for Further Thought, Discussion, Research

CHAPTER 4 Enhancing Mathematics Learning Through Instruction and Assessment

Flexible Mathematics Instruction

Multiple Means of Engagement

Multiple Means of Representation

Multiple Means of Expression

Multiple Means of Assessment

Diversity in Learning and Thinking Mathematically

Questions for Further Thought, Discussion, and Research

CHAPTER 5 Understanding Numbers

Understanding the Mathematics of Young Children

Learning the Language of Numbers

Developing Verbal and Nonverbal Mathematical Skills

Concrete Mathematics and Nonverbal Skills

Spoken and Written Mathematics and Verbal Skills

Discovering Number in Patterns and Relationships

What is more, less, or the same?

Why is something more, less, the same?

Counting and Number Sense

Understanding Number Systems

What is a number system?

Why do we need number systems?

Number Systems and Time

Number Systems and Measurement

Number Systems and Money

The Decimal Number System

Diversity in Learning and Thinking Mathematically

Questions for Further Thought, Discussions, and Research

CHAPTER 6 Working with Whole Numbers: Addition and Subtraction

The Changing Faces of Whole Numbers: Cardinal, Ordinal, Measurement

Cardinal Numbers

Ordinal Numbers

Measurement

Single-Digit Addition and Subtraction

Children's Strategies for Adding

Children's Strategies for Subtracting

Fingermath

Mental Addition and Subtraction

Multi-digit Addition and Subtraction

Building Concepts for Working with Multi-digit Numbers

Adding and Subtracting Multi-digit Numbers

Understanding Standard Algorithms

Understanding Alternative Algorithms

Diversity in Learning and Thinking Mathematically

Questions for Further Thought, Discussion, and Research

Chapter 7 Working with Whole Numbers: Multiplying and Dividing

Discovering Multiplication and Division in Early Grades

Understanding Multiplication

What is a multiplication algorithm?

What kinds of multiplication algorithms do students invent?

How might teachers introduce other multiplication algorithms?

Understanding Division

What kinds of division algorithms do students invent?

How do students handle division problems with remainders?

How can teachers help students understand other division algorithms?

Diversity in Learning and Thinking Mathematically

Questions for Further Thought, Discussion and Research

CHAPTER 8 Geometric Thinking Across the Grades

Geometry as the Mathematicas of Living Space and the Living World

The Four Faces of Geometry

Geometric Thinking from Level to Level

Early Experiences with Shapes and Space

Later Experiences with Shapes and Space

Symmetry

Transformations

Symmetry, Transformations, and NCTM Standards

Explorations in Two and Three Dimensions: Plane and Solid Geometry

The Early Grades

The Middle Grades

The Upper Grades

Diversity in Learning and Thinking Mathematically

Questions for Further Thought, Discussion, and Research

CHAPTER 9 Understanding and Using Measurement Concepts

Measurement Sense

Early Stages in Understanding Measurement

The Three Knowledge Bases of Measurement

The Mental Tools of Measurement

Measurement Systems

Teaching the Metric System

Measuring Time and Temperature

Measurement and Geometry

Plane Geometry

Solid Geometry

Diversity in Learning and Thinking Mathematically

Questions for Further Thought, Discussion, and Research

Chapter 10 Algabraic Thinking Across the Grades

Changing "Algebra for Some" to "Algebra for All"

Understanding Algebraic Thinking

Identifying Patterns in Algebraic Thinking

Fostering Algebraic Thinking

Problem Solving and Algebraic Thinking

Understanding the Big Ideas of Algebra

Equality/Balance

Variable

Functions

Representation

Proportion

Building Bridges from Arithmetic to Algebra

Hands-on Algebra

Real-life and Imaginative Contexts

Connections

Diversity in Learning and Thinking Mathematically

Questions for Further Thought, Discussion, and Research

CHAPTER 11 Working with Data

Worlds of Data

The Processes of Working with Data

Collecting and Organizing Data

Analyzing Data

Displaying and Interpreting Data

Understanding and Using Data

Probability

Talking about Probability

Calculating Probability

The Process Plus Probability: The M&Ms Project

Diversity in Learning and Thinking Mathematically

Questions for Further Thought, Discussion, and Research

CHAPTER 12 Exploring Part-Whole Relationships: Fractions

Students, Teachers, and Fractions--Complex Topic, Complex Relationship

A Hands-on Pedagogy for Teaching Fractions: Connecting Constructed Knowledge and Instructed Knowledge

Real-life Contexts

Hands-on Explorations

Multiple Representations

Language Connections

Big Ideas of Fractions

Properties of Fractions

Operations with Fractions

Diversity in Learning and Thinking Mathematically

Questions for Further Thought, Discussion, and Research

CHAPTER 13 Exploring Part-Whole Relationships: Decimals, Percents, Ratio, and Proportion

Understanding Decimals and Percents

Connecting Fractons, Decimals, and Percents

Exploring Decimals and Percents as Mathematical Concepts

Decimals

Percents

Converting Percents, Decimals, and Fractions

Performing Operations with Decimals and Percents

Addition and Subtraction

Multiplication and Division

Understanding Decimals and Percents in Practical Applications

Understanding Ratio and Proportion

Ratio

Proportion

Strategies for Developing Proportional Reasoning

Diversity in Learning and Thinking Mathematically

Questions for Further Thought, Discussion, and Research

CHAPTER 14 Building Bridges

Making the Transition

Reviewing the Research

Identifying the Gaps

Building Affective and Conceptual Bridges

Affective Bridges

Cognitive Bridges

Diversity in Learning and Thinking Mathematically

Questions for Further Thought, Discussion, and Research

APPENDIX A: Make Your Own Manipulatives and Blackline Masters

Make Your Own Manipulatives

Fraction Strips

Fraction Squares

Fraction Circles

Pattern Shapes

Tangrams

Geoboard

Base-10 Blocks

Counters

Decimal Squares

Multiplication Arrays

Polygon Cut-outs

Blackline Masters

Modified Cartesian Coordinate Grid

Geoboard Dot Paper

One-Centimeter Grid Paper

Triangular Grid Paper

Classroom Observation Form

Learning/Teaching Plan Form

APPENDIX B: Resources, Mathematics in Literature For Elementary and Middle School

NCTM Standard: Number and Operations

Number Sense

Counting

Addition

Subtraction

Multiplication

Decimals/Percentages

Division/Fractions

Ratio and/or Proportion

Place Value

Time

Money

Classification

Order

NCTM Standard: Algebra

NCTM Standard: Geometry

Geometric Progression

Tangrams

Geometric Shapes

Area

Perimeter

Dimensionality

NCTM Standard: Measurement

NCTM Standard: Data Analysis and Probability

Other Topics

Multicultural

Cartesian Coordinate System

Code-Breaking (Problem Solving Involving Codes)

Classic Literature

Geography and Reading Maps

Spanish Language

Prime Numbers

Multiples/Factors

References/Readings

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