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Teaching Secondary and Middle School Mathematics

✍ Scribed by Daniel J. Brahier;


Publisher
Routledge
Year
2024
Tongue
English
Leaves
540
Category
Library

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✦ Synopsis


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 seventh edition has been updated and expanded with particular emphasis on the latest technology, standards, and other resources. 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, Following on from the sixth edition, assessment takes a central role in planning and teaching. Unit 3 (of 5) addresses the use of summative and formative assessments to inform classroom teaching practices. A new appendix is included that lists websites that can be used in a methods class to view other teachers interacting with students for discussion of effective teaching practices. The feature entitled "Links and Resources" has been updated in each of the 13 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. Significant revisions have been made to Chapter 12, which now includes updated research and practices as well as a discussion on culturally responsive pedagogy. Likewise, Chapter 8 now includes a description of best and high-leverage teaching practices, and a discussion in Chapter 11 on alternative high school mathematics electives for students has been added. Chapter 9, on the practical use of classroom technology, has again been revised to reflect the latest tools available to classroom teachers, including apps that can be run on handheld personal devices, in light of changes in education resulting from the global pandemic. An updated Instructor's Manual features a test bank, sample classroom activities, PowerPoint slide content, chapter summaries, and learning outcomes for each chapter and can be accessed by instructors online at www.routledge.com/9781032472867.

✦ Table of Contents


Cover
Half Title
Title
Copyright
Dedication
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
Cognitive Objectives
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
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
Alternative 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 Tasks
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
Best Practices and Refection
Best Practices
High-Leverage Teaching Practices
Reflection on Practice
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
Virtual Teaching
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
Spotlight on Technology
The Teaching of Algebra
Classroom Dialogues
Conclusion
Glossary
Discussion Questions and Activities
Links and Resources
Chapter 11 Teaching Geometry, Statistics/Probability, and Discrete Mathematics
The Teaching of Geometry
How Would You React?
Spotlight on Technology
Statistics and Probability—Activities Sampler
The Teaching of Discrete Mathematics
Classroom Dialogues
Discrete Mathematics—Activities Sampler
A Word on Pre-Calculus, Mathematics Electives, and Calculus
Pre-Calculus
Other Electives
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 Differences
Spotlight on Technology
Ethnicity and Culture: Paving the Way to Equity
English Language Learners
Classroom Dialogues
Ideas for Meeting Diverse Student Needs
Differentiated Instruction
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
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
Appendix: Teaching Video Websites
Bibliography
Index


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