Teaching Secondary and Middle School Mathematics
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Teaching Secondary and Middle School Mathematics
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Teaching Secondary and Middle School Mathematics combines the latest developments in research, technology, and standards with a vibrant writing style to help teachers prepare for the excitement and challenges of teaching secondary and middle school mathematics.
The book explores the mathematics teaching profession by examining the processes of planning, teaching, and assessing student progress through practical examples and recommendations. Beginning with an examination of what it means to teach and learn mathematics, the reader is led through the essential components of teaching, concluding with an examination of how teachers continue with professional development throughout their careers. Hundreds of citations are used to support the ideas presented in the text, and specific websites and other resources are presented for future study by the reader. Classroom scenarios are presented to engage the reader in thinking through specific challenges that are common in mathematics classrooms.
The sixth edition has been updated and expanded with particular emphasis on the latest technology, resources, and standards. The reader is introduced to the ways that students think and how to best meet their needs through planning that involves attention to differentiation, as well as how to manage a classroom for success.
Features include:
- The entire text has been reorganized so that assessment takes a more central role in planning and teaching. Unit 3 (of 5) now addresses the use of summative and formative assessments to inform classroom teaching practices.
● A new feature, "Links and Resources," has been added to each of the 13 chapters. While the book includes a substantial listing of citations and resources after the chapters, five strongly recommended and practical resources are spotlighted at the end of each chapter as an easy reference to some of the most important materials on the topic.
● Approximately 150 new citations have either replaced or been added to the text to reflect the latest in research, materials, and resources that support the teaching of mathematics.
● A Quick Reference Guide has been added to the front of the book to assist the reader in identifying the most useful chapter features by topic.
● A significant revision to Chapter 13 now includes discussions of common teaching assessments used for field experiences and licensure, as well as a discussion of practical suggestions for success in methods and student teaching experiences.
● Chapter 9 on the practical use of classroom technology has been revised to reflect the latest tools available to classroom teachers, including apps that can be run on handheld, personal devices.
An updated Instructor’s Manual features a test bank, sample classroom activities, Powerpoint slides, chapter summaries, and learning outcomes for each chapter, and can be accessed by instructors online at www.routledge.com/9780367146511
Table of Contents
Preface
Acknowledgments
About the Author
Quick Reference Guide
UNIT 1 What Does It Mean to "Do," "Teach," and "Learn" Mathematics?
■ CHAPTER 1 Mathematics as a Process
National and International Assessment Data
Trends in Mathematics and Science Study (TIMSS)
Program for International Student Assessment (PISA)
National Assessment of Educational Progress (NAEP)
How Would You React?
The Need for Reform
21st Century Skills
"Doing" Mathematics
Problem Solving
Mathematical Reasoning
Spotlight on Technology
Communication
Connections and Structure
Representation
Classroom Dialogues
Conclusion
Glossary
Discussion Questions and Activities
Links and Resources
■ CHAPTER 2 Principles of Mathematics Education
The Six Principles
Teaching and Learning
How Would You React?
Access and Equity
Curriculum
Tools and Technology
Spotlight on Technology
Assessment
Professionalism
Classroom Dialogues
Connecting the Principles
Conclusion
Glossary
Discussion Questions and Activities
Links and Resources
■ CHAPTER 3 Learning Theories and Psychology in
Mathematics Education
Research in Mathematics Education
Quantitative and Qualitative Methods
How Would You React?
Experimental and Descriptive Research
Learning Theories in Mathematics
Development of Learning Theory
Behaviorist Theory
Zone of Proximal Development
Communities of Practice
Multiple Intelligences
Mindsets
Bruner’s Stages of Representation
The van Hiele Model
The Inquiry Approach and Constructivist Model
Spotlight on Technology
Inductive versus Deductive Teaching
Classroom Dialogues
Motivation
Ego Versus Mastery Goals
Emotions – Interest and Curiosity
Self-Confidence (Self-Efficacy)
Disposition and Math Anxiety
Conclusion
Glossary
Discussion Questions and Activities
Links and Resources
UNIT 2 Mathematics Curriculum and Planning
■ CHAPTER 4 Standards, Objectives, and Resources
Developing Curriculum Standards—Historical Perspective
How Would You React?
The Common Core State Standards for Mathematics
The Core Curriculum
Traditional versus Integrated Sequences
Tracking
Reasons Why Schools Choose (or Reject) an Integrated Curriculum
Spotlight on Technology
Goals and Objectives in the Mathematics Classroom
Classifying Objectives
Affective Objectives
Cognitive Objectives
Knowledge and Skill
Concept
Application
Selection and Organization of Resources
Textbooks
Print Resources
Classroom Dialogues
Organizing a Resource File
Conclusion
Glossary
Discussion Questions and Activities
Links and Resources
■ CHAPTER 5 Planning for Instruction
Unit Planning
How Would You React?
Lesson Planning
General Information
Standards and Objectives
Materials and Resources
Motivation
Lesson Procedure
Closure
Extension
Assessment
Spotlight on Technology
Sample Lesson Plans
Analysis of Sample Lesson Plan 1
Analysis of Sample Lesson Plan 2
Classroom Dialogues
Lesson Imaging versus Lesson Planning
Reflecting on a Lesson
Conclusion
Glossary
Discussion Questions and Activities
Links and Resources
UNIT 3 Assessment in Mathematics
■ CHAPTER 6 Assessment: Purposes and Strategies
What Is Assessment?
Purposes for Assessment
Test Construction
Preparing Items
Ensuring Validity and Reliability
Scoring Student Work
How Would You React?
Including Review Items
Limitations to Written Tests
Alternate Strategies for Assessing Student Progress
Journals
Open-Ended Questions and Rubrics
Spotlight on Technology
Individual and Team Projects
Observations and Checklists
Interviews
Self-Assessment
Classroom Dialogues
Portfolios
Conclusion
Glossary
Discussion Questions and Activities
Links and Resources
■ CHAPTER 7 Assessment: Standards, Homework, and Grading
NCTM Recommendations on Assessment
The Assessment Standards
How Would You React?
The Assessment Principle
Equity and Assessment
Homework Assignments
Homework Amount and Frequency
Checking Homework Assignments
Spotlight on Technology
Using Homework Assignments in Assessment
Data-Driven Decision Making
Classroom Dialogues
Evaluation: Maintaining and Determining Final Grades
Conclusion
Glossary
Discussion Questions and Activities
Links and Resources
UNIT 4 Mathematics Teaching
■ CHAPTER 8 Teaching and Learning: Tasks, Learning
Environment, and Discourse
Teaching Standards and Related Principles
The NCTM Standards for Teaching and Learning Mathematics
Knowledge Standards
The Teaching and Learning Principle
Selecting Activities and Problems
How Would You React?
Learning Environment
Spotlight on Technology
Classroom Discourse
The Role of Discourse
Questioning Skills
Reading and Literacy
Classroom Dialogues
Cooperative Learning
Structures of Cooperative Learning
Reflective Practices
Conclusion
Glossary
Discussion Questions and Activities
Links and Resources
■ CHAPTER 9 Teaching and Learning: Tools and Technology
How Would You React?
Classroom Tools
Hands-on Manipulative Materials
Spotlight on Technology
Diagrams, Graphs, and Other Discussion Starters
Classroom Technology
Calculators
CAS Technology
Interactive Whiteboards
Mobile Devices
Classroom Dialogues
Dynamic Geometry Software
Document Cameras
Blended Classes and Flipped Classrooms
Conclusion
Glossary
Discussion Questions and Activities
Links and Resources
■ CHAPTER 10 Teaching Number Sense and Algebra
Reasoning and Sense Making
How Would You React?
The Teaching of Number Sense
Sample Lesson Plan: Number Sense
Number Sense—Activities Sampler
Spotlight on Technology
The Teaching of Algebra
Sample Lesson Plan: Algebra
Classroom Dialogues
Algebra—Activities Sampler
Conclusion
Glossary
Discussion Questions and Activities
Links and Resources
■ CHAPTER 11 Teaching Geometry, Statistics/Probability,
and Discrete Mathematics
The Teaching of Geometry
Sample Lesson Plan: Geometry
How Would You React?
Geometry—Activities Sampler
Spotlight on Technology
The Teaching of Statistics and Probability
Sample Lesson Plan: Statistics and Probability
Statistics and Probability—Activities Sampler
The Teaching of Discrete Mathematics
Sample Lesson Plan: Discrete Mathematics
Classroom Dialogues
Discrete Mathematics—Activities Sampler
A Word on Pre-Calculus and Calculus
Conclusion
Glossary
Discussion Questions and Activities
Links and Resources
UNIT 5 Meeting Individual Student and Teacher Needs
■ CHAPTER 12 Managing a Mathematics Classroom
Defining and Achieving Equity
Students with Special Needs
How Would You React?
Gender
Spotlight on Technology
Ethnic and Cultural Issues
English Language Learners
Classroom Dialogues
Ideas for Meeting Diverse Student Needs
Differentiated Instruction
General Suggestions for Differentiating in the Classroom
Classroom Management Tips
Conclusion
Glossary
Discussion Questions and Activities
Links and Resources
■ CHAPTER 13 The Teacher of Mathematics in the School Community
Working with Parents
Hints for Helping Your Child in Mathematics
How Would You React?
The Supervision and Evaluation of Teachers
Spotlight on Technology
Functioning in a Department
Ongoing Professional Development
Making the Case for Long-Term Development
Classroom Dialogues
Opportunities for Professional Development
The Professional Development Plan
Conclusion
Discussion Questions and Activities
Links and Resources
Bibliography
Index
Author(s)
Biography
Daniel J. Brahier is a Professor of Mathematics Education at Bowling Green State University in Ohio and Director of the Science and Math Education in ACTION scholarship program at BGSU. He taught middle and high school mathematics for 38 years, and has served as an administrator and consultant.