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Teaching Secondary and Middle School Mathematics,9780205286140
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Teaching Secondary and Middle School Mathematics

by
Edition:
1st
ISBN13:

9780205286140

ISBN10:
0205286143
Format:
Hardcover
Pub. Date:
1/1/2000
Publisher(s):
Allyn & Bacon
List Price: $88.40
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Summary

Designed for pre-service or in-service teachers, Teaching Secondary and Middle School Mathematics offers succinct, current, and meaningful descriptions of what it takes to be an effective teacher of mathematics. This practical resource offers an effective balance of theory and practice, including a wealth of examples and descriptions of classroom situations. The units of the book include the nature of mathematics, the curriculum, lesson and unit planning (including a chapter on how technology influences planning), assessment, and the teaching profession. Appendices include reprints of selected NCTM Standards, sample State-level outcomes, case studies, a descriptive list of recommended Internet websites on mathematics education, and over 40 sample lessons and activities from various areas of mathematics. The 10-chapter format was designed with the professor in-mind. Most colleges and universities are on 10-week quarters or 15-week semesters, so it is practical to assign roughly one chapter per week. Each chapter contains specific outcomes for the reader, a glossary of relevant terms, several discussion questions and an extensive bibliography that contains references and suggested readings.

Author Biography

Daniel Brahier is Associate Professor of Mathematics Education at Bowling Green State University in Ohio and a current eighth-grade teacher

Table of Contents

Preface xv
UNIT I WHAT DOES IT MEAN TO ``DO,'' ``TEACH,'' AND ``LEARN'' MATHEMATICS? 1(54)
Mathematics as a Process
3(24)
National and International Assessment Data
6(3)
The Need for Reform
9(1)
``Doing'' Mathematics
10(13)
Problem Solving
10(5)
Reasoning
15(2)
Communication
17(2)
Connections
19(3)
Representation
22(1)
Conclusion
23(1)
Glossary
24(1)
Discussion Questions
25(1)
Bibliographic References and Resources
25(2)
Learning Theories and Psychology in Mathematics Education
27(28)
Research in Mathematics Education
28(4)
Learning Theories in Mathematics
32(16)
Bruner's Stages of Representation
32(4)
The van Hiele Model
36(1)
The Inquiry Approach and Constructivist Model
37(4)
Inductive versus Deductive Teaching
41(4)
Motivation
45(3)
Conclusion
48(1)
Glossary
49(2)
Discussion Questions
51(1)
Bibliographic References and Resources
52(3)
UNIT II THE MATHEMATICS CURRICULUM 55(54)
Curricular Models
57(23)
NCTM Curriculum Standards
58(4)
State Models
62(1)
The Core Curriculum
63(7)
Traditional versus Integrated Sequences
70(6)
Conclusion
76(1)
Glossary
77(1)
Discussion Questions
78(1)
Bibliographic References and Resources
79(1)
Implementing a Course of Study
80(29)
The Course of Study
81(5)
Writing Goals and Objectives
86(8)
Classifying Objectives
88(1)
Affective Objectives
88(1)
Cognitive Objectives
88(6)
Selection and Organization of Resources
94(8)
Textbooks
94(3)
Print Resources
97(1)
The Internet
98(2)
Organizing a Resource File
100(2)
Conclusion
102(1)
Glossary
103(1)
Discussion Questions
104(1)
Bibliographic References and Resources
105(1)
NCTM Addenda Series Resources Books
105(1)
Sample Recommended Resource Books
106(1)
Comap ``Hi-Map'' (High School Mathematics) Teaching Modules
106(1)
NSF-Funded Curricular Materials
107(2)
UNIT III TEACHING MATHEMATICS 109(100)
Planning for Instruction
111(26)
Unit Planning
112(5)
Lesson Planning
117(14)
Goals and Objectives
121(1)
Materials
121(1)
Motivation
122(1)
Lesson Procedure
123(1)
Transition Statements
123(1)
Closure
123(1)
Sample Lesson Plans
124(7)
Lesson Imaging versus Lesson Planning
131(1)
Reflecting on a Lesson
132(1)
Conclusion
133(1)
Glossary
134(1)
Discussion Questions
135(1)
Bibliographic References and Resources
135(2)
Responsibilities of the Professional Teacher
137(34)
Teaching Standards and Guiding Principles
139(2)
The NCTM Professional Teaching Standards
139(2)
Guiding Principles
141(1)
Selecting Activities and Problems
141(4)
Classroom Tools
145(8)
Hands-on Manipulative Materials
145(4)
Use of Technology
149(1)
Diagrams, Graphs, and Other Discussion Starters
150(3)
Classroom Discourse
153(7)
Studnet and Teacher Roels
153(1)
Questioning Skills
154(3)
Cooperative Learning
157(3)
Learning Environment
160(6)
Reflective Practices
166(1)
Conclusion
167(1)
Glossary
168(1)
Discussion Questions
168(1)
Bibliographic References and Resources
169(2)
Integrating Technology in Mathematics Instruction
171(38)
Computer Technology
173(7)
Graphing Calculators
180(8)
Laser Discs, CD-ROMs, and Videos
188(3)
The Internet and the World Wide Web
191(10)
Teacher Resources
191(8)
Student Research Tools and Projects
199(2)
Choosing between Paper and Pencil and Technology
201(2)
Conclusion
203(2)
Glossary
205(1)
Discussion Questions
205(1)
Bibliographic References and Resources
206(3)
UNIT IV ASSESSMENT IN MATHEMATICS 209(62)
The Role of Assessment
211(33)
What is Assessment?
212(1)
Purposes for Assessment
213(3)
Test Construction
216(6)
Preparing Items
216(3)
Ensuring Validity and Reliability
219(1)
Scoring Student Work
219(2)
Including Review Items
221(1)
Alternate Strategies for Assessing Student Progress
222(16)
Journals
222(2)
Open-Ended Questions and Rubrics
224(3)
Individual and Team Projects
227(4)
Observations and Checklists
231(3)
Interviews
234(2)
Portfolios
236(2)
Conclusion
238(1)
Glossary
239(2)
Discussion Questions
241(1)
Bibliographic References and Resources
242(2)
Standards and Equity in Assessment
244(27)
NCTM Recommendations on Assessment
245(5)
The Assessment Standards
245(4)
The Assessment Principle
249(1)
Equity through Assessment
250(2)
Homework Assignments
252(10)
Homework Amount and Frequency
253(1)
Laying the Groundwork for the Next Day
253(1)
Completing a Classroom Problem
254(2)
Practicing a Skill Developed in Class
256(1)
Checking Homework Assignments
257(2)
Using Homework Assignments in Assessment
259(3)
Evaluation: Determining Final Grades
262(4)
Conclusion
266(1)
Glossary
267(1)
Discussion Questions
267(1)
Bibliographic References and Resources
268(3)
UNIT V THE TEACHING PROFESSION AND APPENDICES 271(26)
The Teacher of Mathematics in the School Community
273(24)
Working with Parents
274(6)
The Supervision and Evaluation of Teachers
280(6)
Functioning in a Department
286(1)
Ongoing Professional Development
287(6)
Making the Case for Long-Term Development
287(2)
Opportunities for Professional Development
289(2)
The Professional Development Plan
291(2)
Conclusion
293(1)
Discussion Questions
293(1)
Bibliographic References and Additional Resources
294(3)
Appendix A Curriculum 297(22)
NCTM Curriculum Standard 2, Grades 6--8: Patterns, Functions, and Algebra
298(5)
NCTM Curriculum Standard 3, Grades 9--12: Geometry and Spatial Sense
303(10)
Sample State Model Strand, Grades K--12: Data Analysis and Probability
313(6)
Appendix B Teaching 319(14)
NCTM Professional Teaching Standard 1: Worthwhile Mathematical Tasks
320(6)
NCTM Guiding Principle: The Equity Principle
326(7)
Appendix C Assessment 333(4)
NCTM Assessment Standard: The Inferences Standard
334(3)
Appendix D Cases 337(20)
Case 1: The Marble Line (algebra)
338(11)
Case 2: Chances Are (probability)
349(8)
Appendix E Suggested Websites 357(10)
Professional Organizations
357(1)
Activities and Lesson Plan Ideas
358(4)
General Mathematics Education Sites
362(2)
Mathematics History and Miscellaneous
364(1)
On-Line Catalogs of Mathematics Education Materials and Supplies
365(1)
Sample Search Engines for the Internet
366(1)
Appendix F Sample Lessons and Activities 367(30)
Algebra---Sample Lesson Plan
367(2)
Algebra---Activities Sampler
369(4)
Geometry---Sample Lesson Plan
373(3)
Geometry---Activities Sampler
376(4)
Statistics and Probability---Sample Lesson Plan
380(2)
Statistics and Probability---Activities Sampler
382(6)
Discrete Mathematics---Sample Lesson Plan
388(3)
Discrete Mathematics---Activities Sampler
391(6)
Index 397


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