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9780205433599

Teaching Today's Mathematics In The Middle Grades

by ;
  • ISBN13:

    9780205433599

  • ISBN10:

    0205433596

  • Edition: 1st
  • Format: Paperback
  • Copyright: 2005-09-14
  • Publisher: Pearson
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List Price: $151.00

Summary

This text provides current and future middle school teachers with the mathematics content, essential concepts, methodology, activities, and resources to both learn and teach mathematics in grades 6 - 8. Teaching Todayrs"s Mathematics in the Middle Gradesfocuses exclusively on the middle school learner and the middle school mathematics curriculum. Although each chapter discusses foundational mathematics concepts from earlier grades and previews topics that will follow the middle grades, the emphasis is on the middle school. This selective focus allows for proper development of critical topics in the middle school such as proportionality and algebraic thinking, and the integral role of manipulatives. Assessment practices and problem-solving are emphasized, again, from the viewpoint of effective practices for middle grades students.

Table of Contents

Preface xvii
About the Authors xxiii
Section One Teaching Mathematics in the Middle Grades
Mathematics for the Twenty-First Century
1(15)
Society's View of Mathematics
1(2)
Recent History of Mathematics Learning in the United States
3(7)
The New Math
4(1)
Back to Basics
4(1)
National Initiatives
4(1)
Curriculum and Evaluation Standards for School Mathematics
5(2)
Principles and Standards of School Mathematics
7(3)
High-Stakes Testing
10(2)
NAEP
10(1)
TIMSS
10(1)
No Child Left Behind
11(1)
Technology
12(2)
Summary
14(1)
Exercises
14(1)
Resources
14(1)
References
15(1)
The Challenge of Middle School Learners
16(18)
Middle School: A Time of Change
16(2)
Learning Styles
18(2)
Gardner's Multiple Intelligences
18(1)
McCarthy's 4MAT Inventory of Learning Styles
19(1)
Equity in Mathematics
20(9)
Gender Equity
21(2)
English-Language Learners
23(3)
Special Needs Students
26(1)
Gifted and Talented Students
27(2)
Technology
29(1)
Summary
29(1)
Exercises
30(1)
Resources
31(2)
References
33(1)
Section Two Effective Instruction in the Mathematics Classroom
The Practice of Effective Instruction
34(31)
Teaching Styles
34(2)
Teacher-Centered Learning
34(1)
Student-Centered Learning
35(1)
Determining the Mathematics Content for Your Class
36(2)
Standards-Based Programs
36(2)
Planning for High-Stakes Tests
38(1)
Mathematical Proficiency
38(2)
Daily Planning
40(1)
Lesson Plans
41(7)
Objective
41(1)
Materials
41(1)
Prior Knowledge
41(1)
New Terms and Knowledge
42(1)
Time
42(1)
Class Organization
43(1)
Procedure
43(1)
Evaluation
43(1)
Pacing
43(1)
Sample Lesson Plans
43(5)
Organizing Students for Effective Learning
48(8)
Using Small Groups
48(1)
Characteristics of Effective Groups
48(3)
Composition of Cooperative Groups
51(2)
Classroom Climate
53(2)
Other Instructional Formats
55(1)
Manipulatives
56(4)
Using Manipulatives in the Classroom
56(2)
Virtual Manipulatives
58(2)
Summary
60(1)
Exercises
60(2)
Resources
62(1)
References
62(2)
Blackline Master 3.1 Consecutive Sums
64(1)
Assessment: Balanced and Varied
65(29)
NCTM Standards
65(2)
Goals of Assessment
67(1)
Formative Assessments
68(6)
Journals
68(1)
Challenges of the Week
69(2)
Notebooks
71(1)
Observations
71(2)
Interviews
73(1)
Homework and Classwork
74(1)
Do Nows
74(1)
Summative Assessments
74(7)
Portfolios
75(1)
Unit Tests
75(3)
Grading
78(1)
Team Quizzes
79(2)
Performance Assessments
81(3)
Example from a Data Analysis Unit
81(1)
Self-Assessment
82(1)
Student-Led Parent Conferences
82(2)
Standardized Tests
84(6)
Criterion-Referenced and Norm-Referenced Tests
84(1)
The Dilemma Regarding State Tests
84(2)
NAEP
86(1)
TIMSS
87(2)
Standardized Tests for Teachers
89(1)
Implementing an Assessment Program
90(1)
Summary
91(1)
Exercises
91(2)
Resources
93(1)
References
93(1)
Problem Solving: An Approach to Teaching and Learning Mathematics
94(33)
NCTM Standards
94(1)
What Is Problem Solving?
95(1)
Understanding
95(1)
What Problem Solving Looks Like in Classrooms
96(1)
Teacher's Role: Before, during, and after the Lesson
96(4)
Before
96(3)
During
99(1)
After
99(1)
From the Students' Perspective
100(1)
Students' Disposition
100(1)
Habits of Mind
100(1)
Problem-Solving Strategies
101(12)
Heuristic
101(2)
Find a Pattern
103(1)
Make a Picture
103(1)
Make a Chart
104(1)
Make a Physical Model
104(2)
Work Backwards
106(1)
Use Intelligent Guessing and Checking
106(1)
Act It Out
107(1)
Use an Equation or Number Sentence
108(1)
Solve a Simpler Problem
108(1)
Account for All Possibilities
109(1)
Adopt a Different Point of View
110(2)
Use Unit Analysis
112(1)
Discrete Mathematics
113(6)
Counting Techniques
113(3)
Sets
116(1)
Patterns
116(2)
Networks and Graphs
118(1)
Changed Emphasis on Problem Solving
119(1)
Summary
120(1)
Student Performance on International and National Assessments
121(1)
Exercises
121(1)
Resources
122(1)
References
123(2)
Blackline Master 5.1 Attitude Survey
125(1)
Blackline Master 5.2 Network Exploration
126(1)
Section Three Mathematics Topics
Making Sense of Number and Operations
127(46)
NCTM Standards
128(1)
Role of Algorithms
129(2)
Using Manipulatives
129(1)
More Than One Algorithm
130(1)
Base-Ten Number System
131(4)
Mental Math and Estimation
135(5)
Front-End Estimation
136(1)
Rounding as an Estimation Strategy
137(1)
Implementation Strategies
138(1)
Number Facts
138(2)
Rational Numbers
140(5)
Part/Whole Interpretation
140(3)
Quotient Interpretation
143(1)
Ratio Interpretation
143(1)
Operator Interpretation
144(1)
Measure Interpretation
144(1)
Fractions, Decimals, and Percents
145(6)
Linking Fractions, Decimals, and Percents
145(1)
Operational Sense
146(1)
Addition and Subtraction
146(3)
Multiplication and Division
149(2)
Proportional Reasoning
151(8)
Using Rates
152(2)
Missing-Term Proportional Problems
154(1)
Using Cross-Products
155(2)
Working with Percents
157(2)
Integers
159(3)
Using a Story Context
160(1)
Using Physical Models
160(1)
Using Question Strings
161(1)
Summary
162(1)
Student Performance on International and National Assessments
163(1)
Exercises
163(2)
Resources
165(1)
References
165(2)
Blackline Master 6.1 Number Line Equivalences
167(1)
Blackline Master 6.2 Operational Relationships
168(1)
Blackline Master 6.3 Making One!
169(1)
Blackline Master 6.4 Fraction Strips at Work!
170(1)
Blackline Master 6.5 Can You See It?
171(2)
Algebra: The Gateway
173(39)
What Is Algebra?
173(2)
Foundational Concepts
175(4)
Understanding the Equal Sign
175(1)
Varying Roles of Variables
175(3)
Graphing
178(1)
Three Types of Algebraic Activities
179(19)
Representational and Generalizing Activities---The Rule of 5 at Work
180(10)
Transformational Activities
190(3)
Technology
193(5)
Summary
198(1)
Student Performance on International and National Assessments
199(1)
Exercises
199(2)
Resources
201(1)
References
202(2)
Blackline Master 7.1 Magic Tricks
204(1)
Blackline Master 7.2 Messy Mathematics
205(1)
Blackline Master 7.3 Building Blocks
206(1)
Blackline Master 7.4 Up and Down Staircases
207(1)
Blackline Master 7.5 Pick a Deal!
208(1)
Blackline Master 7.6 Do the Wave
209(1)
Blackline Master 7.7 The Choice Is Yours!
210(1)
Blackline Master 7.8 The Crickets' Chorus
211(1)
Geometry: Moving beyond Formulas
212(47)
NCTM Standards
212(1)
Van Hiele Levels of Geometry Thinking
213(6)
Level 0: Visualization
214(1)
Level 1: Analysis
214(1)
Level 2: Abstraction
214(1)
Level 3: Deduction
215(1)
Level 4: Rigor
216(3)
Spatial Sense
219(7)
In Two Dimensions
219(2)
In Three Dimensions
221(3)
Technology
224(2)
Symmetry
226(3)
Line Symmetry
226(2)
Three-Dimensional Symmetry
228(1)
The Pythagorean Theorem
229(4)
Converse of the Pythagorean Theorem
232(1)
Hierarchy of Quadrilaterals
233(3)
Tessellations
236(4)
Tilings
236(1)
Internet Lesson Plan
237(2)
Creating Tessellations
239(1)
Similarity
240(6)
Dilations
241(2)
Areas and Volume Relationships
243(3)
Summary
246(1)
Student Performance on International and National Assessments
247(1)
Exercises
247(1)
Resources
248(2)
References
250(1)
Blackline Master 8.1 How Many Triangles?
251(1)
Blackline Master 8.2 Cross Sections of a Cube
252(1)
Blackline Master 8.3 Block Structures
253(1)
Blackline Master 8.4 Pythagorean Puzzle 1
254(1)
Blackline Master 8.5 Pythagorean Puzzle 2
255(1)
Blackline Master 8.6 Pythagorean Puzzle 3
256(1)
Blackline Master 8.7 Pythagorean Puzzle 4
257(1)
Blackline Master 8.8 Pythagorean Puzzle 5
258(1)
Measurement: Behind the Units
259(37)
NCTM Standards
259(1)
Benchmarks
260(2)
Measurement Systems
262(4)
The Metric System
262(1)
The Customary System
263(3)
Angle Measure
266(3)
Area and Perimeter
269(12)
Polygons
269(7)
Circles
276(5)
Volume
281(2)
Similar Solids
283(2)
Summary
285(1)
Student Performance on International and National Assessments
285(1)
Exercises
286(1)
Resources
287(1)
References
288(1)
Blackline Master 9.1 How Close Is Close?
289(1)
Blackline Master 9.2 The Angle Wheel
290(1)
Blackline Master 9.3 Flipping for π
291(1)
Blackline Master 9.4 Curve and Straight
292(1)
Blackline Master 9.5 Minimum Perimeter
293(2)
Blackline Master 9.6 Cube and Pyramid Templates
295(1)
Data Analysis: The Process
296(31)
NCTM Standards
297(1)
Overview of Graphical Representations
298(8)
Line Plot
298(1)
Stem-and-Leaf Plot
299(1)
Bar Graph
300(1)
Histogram
301(2)
Box-and-Whisker Plot
303(1)
Line Graph
304(1)
Scatter Plot
305(1)
Circle Graph
306(1)
Measures of Central Tendency
306(3)
Measures of Dispersion
309(1)
Engaging Middle School Students in the Data Analysis Process
310(7)
Defining the Question
310(1)
Collecting the Data
311(1)
Analyzing the Data
312(1)
Internet Lesson Plan
313(1)
Misleading Graphs and Statistics
314(3)
Technology
317(1)
Summary
317(1)
Student Performance on International and National Assessments
318(1)
Exercises
318(1)
Resources
319(1)
References
320(1)
Blackline Master 10.1 Histogram or Bar graph: The Choice Is Yours
321(1)
Blackline Master 10.2 Meaning of the Mean: Data
322(1)
Blackline Master 10.3 Meaning of the Mean: Reflection
323(1)
Blackline Master 10.4 Can This Be True?
324(1)
Blackline Master 10.5 Minutes Spent Studying
325(1)
Blackline Master 10.6 Grades Earned
326(1)
Probability: Measures of Uncertainty
327(33)
An Overview
328(1)
NCTM Standards
328(1)
Probability in Middle School
328(22)
Experimental Probability
330(4)
Simulations
334(3)
Theoretical Probability
337(4)
Expected Value
341(1)
Compound Probability
341(7)
Geometric Probability
348(2)
Odds
350(1)
Summary
351(1)
Student Performance on International and National Assessments
352(1)
Exercises
352(1)
Resources
353(1)
References
354(1)
Blackline Master 11.1 Collect Them All
355(1)
Blackline Master 11.2 A Happy Family
356(1)
Blackline Master 11.3 Let It Roll
357(1)
Blackline Master 11.4 Wheel of Money
358(1)
Blackline Master 11.5 Stay or Switch?
359(1)
Teaching as a Career: The Journey Begins
360(5)
Professionalism of Teaching
360(1)
Beginning the Professional Journey
361(1)
Finding the Right Match
361(1)
Those First Few Weeks
361(1)
Professional Development Opportunities
362(2)
Join the National Council of Teachers of Mathematics
362(1)
Take a Course
362(1)
Volunteer for Work with a Coach
362(1)
Solicit Student Feedback
363(1)
Participate in a Lesson Study Group
363(1)
Volunteer for Committees
363(1)
Grants and Awards
363(1)
Exercises
364(1)
References
364(1)
Index 365

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