Teaching Secondary and Middle School Mathematics combines the latest developments in research, standards, and technology with a vibrant writing style to help teachers prepare for the excitement and challenges of teaching secondary and middle school mathematics today. In the fully revised fifth edition, scholar and mathematics educator Daniel Brahier invites teachers to investigate the nature of the mathematics curriculum and reflect on research-based "best practices" as they define and sharpen their own personal teaching styles.
The fifth edition has been updated and expanded with a particular emphasis on the continued impact of the Common Core State Standards for Mathematics and NCTM's just-released Principles to Actions, as well as increased attention to teaching with technology, classroom management, and differentiated instruction.
A full new Chapter 7 on selection and use of specific tools and technology combined with "Spotlight on Technology" features throughout clearly illustrate the practical aspects of how technology can be used for teaching or professional development.
Foundational Chapters 1 and 2 on the practices and principles of mathematics education have been revised to build directly on Common Core State Standards for Mathematics and Principles to Actions, with additional references to both documents throughout all chapters.
A new Chapter 4 focuses on the use of standards in writing objectives and organizing lesson plan resources while an updated Chapter 5 details each step of the lesson planning process.
A fully revised Chapter 12 provides new information on teaching diverse populations and outlines specific details and suggestions for classroom management for mathematics teachers.
Classroom Dialogues" features draws on the author's 35-year experience as an educator to present real-world teacher-student conversations about specific mathematical problems or ideas
"How Would You React?" features prepares future teachers for real-life scenarios by engaging them in common classroom situations and offering tried-and-true solutions.
With more than 60 practical, classroom-tested teaching ideas, sample lesson and activities, Teaching Secondary and Middle School Mathematics combines the best of theory and practice to provide clear descriptions of what it takes to be an effective teacher of mathematics.
Daniel 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 also teaches junior high (Grades 7 and 8) mathematics at St. Rose School in Perrysburg, Ohio.
Contents Preface Acknowledgements Meet the Author UniT 1 What Does It Mean to "Do," "Teach," and "Learn" Mathematics? Chapter 1 Mathematics as a Process National and International Assessment Data? ? ? ? How Would You React? The Need for Reform? ? ? "Doing" Mathematics? ? ? Problem Solving? ? ? ? Mathematical Reasoning? Spotlight on Technology Communication? ? ? Connections? and Structure Representation? Classroom Dialogues Conclusion Glossary Discussion Questions and Activities 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 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? 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 Conclusion Glossary? ? Discussion Questions and Activities 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? ? Spotlight on Technology Goals and Objectives in the Mathematics Classroom Classifying Objectives Affective Objectives Cognitive Objectives Selection and Organization of Resources Print Resources ? ? Classroom Dialogues The Internet Organizing a Resource File Conclusion Glossary Discussion Questions and Activities 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 Unit 3 Mathematics TEACHING Chapter 6 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 Reflective Practices? ? ? Conclusion Glossary? Discussion Questions and Activities Chapter 7 Teaching and Learning: Tools and Technology How Would You React? Classroom Tools Hand-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 Chapter 8 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 Chapter 9 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 Unit 4 Assessment in MathematicS Chapter 10 The Role of Assessment 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 Chapter 11 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? ? ? Classroom Dialogues Evaluation: Maintaining and Determining Final Grades Conclusion Glossary? ? ? ? Discussion Questions and Activities 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 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 Bibliographic References and Resources Index