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Taylor & Francis
Teaching Secondary and Middle School Mathematics / Edition 5

Teaching Secondary and Middle School Mathematics / Edition 5

by Daniel J. Brahier


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Product Details

ISBN-13: 9781138922785
Publisher: Taylor & Francis
Publication date: 03/01/2016
Edition description: Revised
Pages: 490
Product dimensions: 8.50(w) x 10.90(h) x 1.10(d)

About the Author

Daniel Brahier is a Professor of Mathematics at Bowling Green State University in Ohio. In addition, he teaches an eighth grade mathematics class at St. Rose School in Perrysburg, Ohio. In his more than 30 years in education, he has been middle and high school mathematics and science teacher, a principal, a guidance counselor, a curriculum consultant, and a university professor. He is co-author of Today’s Mathematics, Twelfth Edition, a methods and content book for elementary teachers published by Wiley (2009), as well as the author of three other books on mathematics education. He is a Past-President of the Ohio Council of Teachers of Mathematics and has served in numerous capacities for the National Council of Teachers of Mathematics, such as the editorial panel of the journal of Mathematics Teaching in the Middle School. He has presented mini-courses and lectures throughout the United States as well as in Canada, Mexico, Australia, Singapore, and Germany.

Table of Contents

Unit IWhat Does It Mean to "Do," "Teach," and "Learn" Mathematics?1
Chapter 1Mathematics as a Process3
National and International Assessment Data6
The Need for Reform11
"Doing" Mathematics12
Problem Solving12
Reasoning and Proof16
Chapter 2Learning Theories and Psychology in Mathematics Education29
Research in Mathematics Education30
Quantitative and Qualitative Methods31
Experimental and Descriptive Research33
Learning Theories in Mathematics35
Bruner's Stages of Representation36
The van Hiele Model40
The Inquiry Approach and Constructivist Model43
Inductive versus Deductive Teaching47
Unit IIThe Mathematics Curriculum61
Chapter 3Curricular Models63
NCTM Curriculum Standards64
State Models67
The Core Curriculum68
Traditional versus Integrated Sequences75
Chapter 4Implementing a Course of Study88
The Course of Study89
Writing Goals and Objectives95
Classifying Objectives97
Affective Objectives97
Cognitive Objectives97
Selection and Organization of Resources104
Print Resources109
The Internet110
Organizing a Resource File112
Sample Recommended Resource Books117
COMAP "Hi-Map" (High School Mathematics) Teaching Modules117
NCTM Navigations Series118
NCTM Addenda Series Resource Books118
NSF-Funded Curricular Materials119
Unit IIITeaching Mathematics121
Chapter 5Planning for Instruction123
Unit Planning124
Lesson Planning130
General Considerations133
Goals and Objectives133
Materials and Resources134
Lesson Procedure135
Sample Lesson Plans138
Lesson Imaging versus Lesson Planning148
Reflecting on a Lesson150
Chapter 6Teaching Tools and Strategies156
Teaching Standards and Principles158
The NCTM Professional Teaching Standards158
The Teaching and Learning Principles160
Selecting Activities and Problems160
Classroom Tools164
Hands-On Manipulative Materials164
Use of Technology169
Diagrams, Graphs, and Other Discussion Starters172
Classroom Discourse174
Student and Teacher Roles174
Questioning Skills175
Cooperative Learning178
Learning Environment182
Reflective Practices188
Chapter 7Teaching Specific Mathematics Content194
The Teaching of Algebra196
Algebra--Sample Lesson Plan198
Algebra--Activities Sampler200
The Teaching of Geometry205
Geometry--Sample Lesson Plan207
Geometry--Activities Sampler210
The Teaching of Data Analysis and Probability214
Data Analysis and Probability--Sample Lesson Plan217
Data Analysis and Probability--Activities Sampler219
The Teaching of Discrete Mathematics226
Discrete Mathematics--Sample Lesson Plan228
Discrete Mathematics--Activities Sampler231
Unit IVAssessment in Mathematics241
Chapter 8The Role of Assessment243
What Is Assessment?244
Purposes for Assessment245
Test Construction248
Preparing Items248
Ensuring Validity and Reliability251
Scoring Student Work252
Including Review Items253
Limitations to Written Tests253
Alternate Strategies for Assessing Student Progress255
Open-Ended Questions and Rubrics258
Individual and Team Projects261
Observations and Checklists265
Chapter 9Principles of Assessment Practices278
NCTM Recommendations on Assessment279
The Assessment Standards279
The Assessment Principle284
Equity and Assessment284
Homework Assignments286
Homework Amount and Frequency287
Checking Homework Assignments291
Using Homework Assignments in Assessment293
Evaluation: Determining Final Grades296
Unit VMeeting Individual Student and Teacher Needs305
Chapter 10Meeting the Needs of All Students307
Defining and Achieving Equity309
Students with Special Needs310
Ethnic and Cultural Issues320
General Suggestions for Meeting Diverse Student Needs325
Chapter 11The Teacher of Mathematics in the School Community333
Working with Parents334
The Supervision and Evaluation of Teachers341
Functioning in a Department347
Ongoing Professional Development348
Making the Case for Long-Term Development348
Opportunities for Professional Development351
The Professional Development Plan354
Appendix ARecommended Web Sites359
Professional Organizations359
Curriculum Projects359
Activities and Lesson Plan Ideas360
General Mathematics Education Sites361
Appendix BCases362
Case 1The Marble Line (algebra)363
Case 2Chances Are (probability)375

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