Teaching Today's Mathematics in the Middle Grades Book

All Chapters contain at the end:

Summary.

Student performances on International and National Assessments.

Exercises.

Portfolio Question.

Scenes from a Classroom.

Preparing for Praxis.

Mathematics-Literature Connection.

Teacher's Bookcase.

For Further Reading.

Resources.

Links.

References.

Preface.

1. Mathematics for the 21st Century.

Society's View of Mathematics.

Recent History of Mathematics Learning in the United States.

The New Math.

Back to Basics.

National Initiatives.

Curriculum and Evaluation Standards for School Mathematics.

Principles and Standards of School Mathematics.

Reasoning and proof.

Communication.

Connections.

Representation.

High-Stakes Testing.

NAEP.

TIMSS.

No Child Left Behind.

Technology.

2. The Challenge of Middle School Learners.

Middle School: a Time of Change.

Learning Styles.

Gardner's Eight Intelligences.

McCarthy's 4MAT Inventory of learning Styles.

Equity in Mathematics.

Gender Equity.

English Language Learners.

The Teacher.

Class Design.

Assessment.

Multicultural Aspects.

Special Needs Students.

Gifted and Talented Students.

Technology.

3. The Practice of Effective Instruction.

Teaching Styles.

Teacher-Centered Learning.

Student-Centered learning.

Determining the Mathematics Content for Your Class.

Standards-Based Programs.

Connected mathematics.

Mathematics in context.

MathScape.

Math Thematics.

Planning for High Stakes Tests.

Mathematical Proficiency.

Daily Planning.

Lesson Plans.

Objective.

Materials.

Prior Knowledge.

New Terms & Knowledge.

Time.

Class Organization.

Procedure.

Evaluation.

Pacing.

Sample Plans.

Organizing Students for Effective learning.

Using Small Groups.

Rationale.

Characteristics of Effective Groups.

Composition of Vooperative Groups.

Classroom climate.

General Social Norms.

Sociomathematical Norms.

Status Issues.

Other Instructional Formats.

Manipulatives.

Using Manipulatives in the Classroom.

Virtual Manipulatives.

4. Effective Assessment.

Assessment Standards.

Goals for Assessment.

Formative Assessments.

Journals.

Challenges of the Week.

Notebooks.

Observations.

Interviews.

Homework and Classwork.

Do Nows.

Summative Assessments.

Portfolios.

Implementation Strategies.

Unit Tests.

Creating Tests.

Open-Ended Questions.

Closed Questions.

Length of Test.

Recording Answers.

Grading.

Team Quizzes.

Performance Assessments.

Example from Data Analysis Unit.

Self Assessment.

Student-led Parent Conferences.

Standardized Tests.

Criterion Referenced and Norm Referenced Tests.

Dilemma Regarding State Tests.

NAEP.

TIMSS.

Standardized Tests for Teachers.

Implementing an Assessment Program.

5. Problem Solving: An Approach to Teaching and Learning Mathematics.

What Is Problem Solving?

Understanding.

What Problem Solving Looks Like in Classrooms.

Teacher’s Role: Before, During and After the Lesson.

Before.

During.

After.

From the Students’ Perspective.

Students’ Disposition.

Habits of Mind.

Problem Solving Strategies.

Heuristic: General Problem Solving Plan.

Find a Pattern.

Make a Picture.

Make a Chart/Graph.

Make a Model.

Work Backwards.

Use Intelligent Guessing and Checking.

Act It Out.

Use an Equation.

Solve a Simpler Problem.

Account for All Possibilities.

Adopt a Different Point of View.

Use Unit Analysis.

Discrete Mathematics.

Counting Techniques.

Sets.

Patterns.

Networks and Graphs.

Changed Emphasis on Problem Solving.

6. Making Sense of Number and Operations.

Role of Algorithms.

Using Manipulatives.

More Than One Algorithm.

Base 10 Number system.

Mental Math and Estimation.

Front-end Estimation.

Rounding as an Estimation Strategy.

Implementation Strategies.

Rational Numbers.

Part-Whole Interpretation.

Quotient Interpretation.

Ratio Interpretation.

Operator Interpretation.

Measure Meaning.

Fractions, Decimals and percents.

Linking Fractions, Decimals and Percents.

Operational Sense.

Addition and Subtraction.

Using the Fraction Strips.

Internet Lesson: Comparing Fractions.

Multiplication and Division.

Using Fraction Strips.

Using Area Models.

Using Question Strings.

Proportional Reasoning.

Using Rates.

Missing Term Proportional Problems.

Using Cross-Products.

Working with Percents.

Integers.

Using a Story Context.

Using Physical Models.

Using Question Strings.

7. Algebra: The Gateway.

What is Algebra?

Foundational concepts.

Understanding the Equal Sign.

Varying Roles of Variables.

Developing an Understanding of Proof.

Graphing.

Guides to Graphing.

Three Types of Algebraic Activities.

Representational and Generalizing Activities- The Rule of 5 at Work.

Seeing Change in Context.

Nonlinear Relationships.

Finite Differences.

Making Predictions.

Correlation and the Line of Best Fit.

Transformational Activities.

Solving Linear Equations.

Algebra Tiles.

Backtracking.

Technology.

Graphing Calculator.

Spreadsheets.

8. Geometry: Moving Beyond Formulas.

NCTM Geometry Standards.

Van Hiele Levels of Geometry Thinking.

Level 0 Visualization.

Level 1 Analysis.

Level 2 Abstraction.

Level 3 Deduction.

Level 4 Rigor.

Spatial Sense.

In two dimensions.

In three dimensions.

Symmetry.

Line symmetry.

Three dimensional symmetry.

The Pythagorean Theorem.

The Distance Formula.

Converse of the Pythagorean Theorem.

Hierarchy of Quadrilaterals.

Tessellations.

Tilings.

Internet lesson plan.

Creating tessellations.

Similarity.

Dilations.

Areas and volume relationships.

9. Measurement: Behind the Units.

NCTM Measurement Standards.

Benchmarks.

Measurement Systems.

The Metric System.

Customary system.

Angle Measure.

Area and perimeter.

Polygons.

Area-Perimeter Relationships.

Circles.

Internet Lesson Plan.

Volume.

Similar Solids.

10. Data Analysis: The Process.

Overview of Graphical Representations.

Line Plot.

Stem-and-Leaf Plot.

Bar Graph.

Histogram.

Box and Whisker Plot.

Line Graph.

Scatter Plot.

Measures of Central Tendency.

Measures of Dispersion.

Engaging Middle School Students in the Data Analysis Process.

Defining the Question.

Collecting the Data.

Analyzing the Data.

Misleading Graphs and Statistics.

Technology.

11. Probability; Measures of Uncertainty.

An Overview.

NCTM Probability Standards.

Probability in Middle School.

Experimental Probably.

Law of Large Numbers.

Internet lesson plan.

Simulations.

Technology.

Theoretical Probability.

Expected Value.

Gambler's Fallacy.

Compound Probability.

Geometric Probability.

Odds.

12. Teaching as a Career: The Journey Begins.

Professionalism of Teaching.

Beginning the Professional Journey.

Finding the Right Match.

Those First Few Weeks.

Professional Development Opportunities.

Join the National Council of Teachers of Mathematics.

Take a Course.

Volunteer for Work with a Coach.

Solicit Student Feedback.

Participate in a Lesson Study Group.

Volunteer for Committees.

Grants and Awards.