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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 Today’s Mathematics in the Middle Grades focuses 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.
All Chapters contain at the end:
Student performances on International and National Assessments.
Scenes from a Classroom.
Preparing for Praxis.
For Further Reading.
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.
Curriculum and Evaluation Standards for School Mathematics.
Principles and Standards of School Mathematics.
Reasoning and proof.
No Child Left Behind.
2. The Challenge of Middle School Learners.
Middle School: a Time of Change.
Gardner's Eight Intelligences.
McCarthy's 4MAT Inventory of learning Styles.
Equity in Mathematics.
English Language Learners.
Special Needs Students.
Gifted and Talented Students.
3. The Practice of Effective Instruction.
Determining the Mathematics Content for Your Class.
Mathematics in context.
Planning for High Stakes Tests.
New Terms & Knowledge.
Organizing Students for Effective learning.
Using Small Groups.
Characteristics of Effective Groups.
Composition of Vooperative Groups.
General Social Norms.
Other Instructional Formats.
Using Manipulatives in the Classroom.
4. Effective Assessment.
Goals for Assessment.
Challenges of the Week.
Homework and Classwork.
Length of Test.
Example from Data Analysis Unit.
Student-led Parent Conferences.
Criterion Referenced and Norm Referenced Tests.
Dilemma Regarding State Tests.
Standardized Tests for Teachers.
Implementing an Assessment Program.
5. Problem Solving: An Approach to Teaching and Learning Mathematics.
What Is Problem Solving?
What Problem Solving Looks Like in Classrooms.
Teacher’s Role: Before, During and After the Lesson.
From the Students’ Perspective.
Habits of Mind.
Problem Solving Strategies.
Heuristic: General Problem Solving Plan.
Find a Pattern.
Make a Picture.
Make a Chart/Graph.
Make a Model.
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.
Networks and Graphs.
Changed Emphasis on Problem Solving.
6. Making Sense of Number and Operations.
Role of Algorithms.
More Than One Algorithm.
Base 10 Number system.
Mental Math and Estimation.
Rounding as an Estimation Strategy.
Fractions, Decimals and percents.
Linking Fractions, Decimals and Percents.
Addition and Subtraction.
Using the Fraction Strips.
Internet Lesson: Comparing Fractions.
Multiplication and Division.
Using Fraction Strips.
Using Area Models.
Using Question Strings.
Missing Term Proportional Problems.
Working with Percents.
Using a Story Context.
Using Physical Models.
Using Question Strings.
7. Algebra: The Gateway.
What is Algebra?
Understanding the Equal Sign.
Varying Roles of Variables.
Developing an Understanding of Proof.
Guides to Graphing.
Three Types of Algebraic Activities.
Representational and Generalizing Activities- The Rule of 5 at Work.
Seeing Change in Context.
Correlation and the Line of Best Fit.
Solving Linear Equations.
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.
In two dimensions.
In three dimensions.
Three dimensional symmetry.
The Pythagorean Theorem.
The Distance Formula.
Converse of the Pythagorean Theorem.
Hierarchy of Quadrilaterals.
Internet lesson plan.
Areas and volume relationships.
9. Measurement: Behind the Units.
NCTM Measurement Standards.
The Metric System.
Area and perimeter.
Internet Lesson Plan.
10. Data Analysis: The Process.
Overview of Graphical Representations.
Box and Whisker 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.
11. Probability; Measures of Uncertainty.
NCTM Probability Standards.
Probability in Middle School.
Law of Large Numbers.
Internet lesson plan.
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.