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Teaching Secondary and Middle School Mathematics,9780205412631
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Teaching Secondary and Middle School Mathematics

by
Edition:
2nd
ISBN13:

9780205412631

ISBN10:
0205412637
Format:
Hardcover
Pub. Date:
1/1/2005
Publisher(s):
Allyn & Bacon
List Price: $120.80
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Summary

Teaching Secondary and Middle School Mathematics combines up-to-date technology and research with a vibrant writing style to help preservice teachers grasp curriculum, teaching, and assessment issues as they relate to 6-12 mathematics.

Author Biography

Daniel Brahier is Associate Professor of Mathematics Education at Bowling Green State University in Ohio.

Table of Contents

Preface xiii
UNIT I WHAT DOES IT MEAN TO ``DO,'' ``TEACH,'' AND ``LEARN'' MATHEMATICS?
1(60)
Mathematics as a Process
3(26)
National and International Assessment Data
6(5)
The Need for Reform
11(1)
``Doing'' Mathematics
12(12)
Problem Solving
12(4)
Reasoning and Proof
16(3)
Communication
19(1)
Connections
20(3)
Representation
23(1)
Conclusion
24(1)
Glossary
25(1)
Discussion Questions and Activities
26(1)
Bibliographic References and Resources
26(3)
Learning Theories and Psychology in Mathematics Education
29(32)
Research in Mathematics Education
30(5)
Quantitative and Qualitative Methods
31(2)
Experimental and Descriptive Research
33(2)
Learning Theories in Mathematics
35(19)
Bruner's Stages of Representation
36(4)
The van Hiele Model
40(3)
The Inquiry Approach and Constructivist Model
43(4)
Inductive versus Deductive Teaching
47(4)
Motivation
51(3)
Conclusion
54(1)
Glossary
55(3)
Discussion Questions and Activities
58(1)
Bibliographic References and Resources
58(3)
UNIT II THE MATHEMATICS CURRICULUM
61(60)
Curricular Models
63(25)
NCTM Curriculum Standards
64(3)
State Models
67(1)
The Core Curriculum
68(7)
Traditional versus Integrated Sequences
75(8)
Conclusion
83(1)
Glossary
84(1)
Discussion Questions and Activities
84(1)
Bibliographic References and Resources
85(3)
Implementing a Course of Study
88(33)
The Course of Study
89(6)
Writing Goals and Objectives
95(9)
Classifying Objectives
97(1)
Affective Objectives
97(1)
Cognitive Objectives
97(7)
Selection and Organization of Resources
104(9)
Textbooks
104(5)
Print Resources
109(1)
The Internet
110(2)
Organizing a Resource File
112(1)
Conclusion
113(1)
Glossary
114(1)
Discussion Questions and Activities
115(1)
Bibliographic References and Resources
116(1)
Sample Recommended Resource Books
117(1)
Comap ``Hi-Map'' (High School Mathematics) Teaching Modules
117(1)
NCTM Navigations Series
118(1)
NCTM Addenda Series Resource Books
118(1)
NSF-Funded Curricular Materials
119(2)
UNIT III TEACHING MATHEMATICS
121(120)
Planning for Instruction
123(33)
Unit Planning
124(6)
Lesson Planning
130(18)
General Considerations
133(1)
Goals and Objectives
133(1)
Materials and Resources
134(1)
Motivation
134(1)
Lesson Procedure
135(2)
Closure
137(1)
Extension
137(1)
Assessment
137(1)
Sample Lesson Plans
138(10)
Lesson Imaging versus Lesson Planning
148(2)
Reflecting on a Lesson
150(1)
Conclusion
151(1)
Glossary
152(1)
Discussion Questions and Activities
153(1)
Bibliographic References and Resources
153(3)
Activities---Selected Lesson Plan Ideas from The Mathematics Teacher
154(2)
Teaching Tools and Strategies
156(38)
Teaching Standards and Principles
158(2)
The NCTM Professional Teaching Standards
158(2)
The Teaching and Learning Principles
160(1)
Selecting Activities and Problems
160(4)
Classroom Tools
164(10)
Hands-On Manipulative Materials
164(5)
Use of Technology
169(3)
Diagrams, Graphs, and Other Discussion Starters
172(2)
Classroom Discourse
174(8)
Student and Teacher Roles
174(1)
Questioning Skills
175(3)
Cooperative Learning
178(4)
Learning Environment
182(6)
Reflective Practices
188(1)
Conclusion
189(1)
Glossary
190(1)
Discussion Questions and Activities
191(1)
Bibliographic References and Resources
192(2)
Teaching Specific Mathematics Content
194(47)
The Teaching of Algebra
196(9)
Algebra---Sample Lesson Plan
198(2)
Algebra---Activities Sampler
200(5)
The Teaching of Geometry
205(9)
Geometry---Sample Lesson Plan
207(3)
Geometry---Activities Sampler
210(4)
The Teaching of Data Analysis and Probability
214(12)
Data Analysis and Probability---Sample Lesson Plan
217(2)
Data Analysis and Probability---Activities Sampler
219(7)
The Teaching of Discrete Mathematics
226(10)
Discrete Mathematics---Sample Lesson Plan
228(3)
Discrete Mathematics---Activities Sampler
231(5)
Conclusion
236(1)
Glossary
237(1)
Discussion Questions and Activities
237(1)
Bibliographic References and Resources
238(3)
UNIT IV ASSESSMENT IN MATHEMATICS
241(64)
The Role of Assessment
243(35)
What Is Assessment?
244(1)
Purposes for Assessment
245(3)
Test Construction
248(7)
Preparing Items
248(3)
Ensuring Validity and Reliability
251(1)
Scoring Student Work
252(1)
Including Review Items
253(1)
Limitations to Written Tests
253(2)
Alternate Strategies for Assessing Student Progress
255(17)
Journals
255(3)
Open-Ended Questions and Rubrics
258(3)
Individual and Team Projects
261(4)
Observations and Checklists
265(3)
Interviews
268(2)
Portfolios
270(2)
Conclusion
272(2)
Glossary
274(1)
Discussion Questions and Activities
275(1)
Bibliographic References and Resources
276(2)
Principles of Assessment Practices
278(27)
NCTM Recommendations on Assessment
279(5)
The Assessment Standards
279(5)
The Assessment Principle
284(1)
Equity and Assessment
284(2)
Homework Assignments
286(10)
Homework Amount and Frequency
287(4)
Checking Homework Assignments
291(2)
Using Homework Assignments in Assessment
293(3)
Evaluation: Determining Final Grades
296(5)
Conclusion
301(1)
Glossary
302(1)
Discussion Questions and Activities
302(1)
Bibliographic References and Resources
303(2)
UNIT V MEETING INDIVIDUAL STUDENT AND TEACHER NEEDS
305(54)
Meeting the Needs of All Students
307(26)
Defining and Achieving Equity
309(16)
Students with Special Needs
310(5)
Gender
315(5)
Ethnic and Cultural Issues
320(5)
General Suggestions for Meeting Diverse Student Needs
325(3)
Conclusion
328(1)
Glossary
328(1)
Discussion Questions and Activities
329(1)
Bibliographic References and Resources
330(3)
The Teacher of Mathematics in the School Community
333(26)
Working with Parents
334(7)
The Supervision and Evaluation of Teachers
341(6)
Functioning in a Department
347(1)
Ongoing Professional Development
348(7)
Making the Case for Long-Term Development
348(3)
Opportunities for Professional Development
351(3)
The Professional Development Plan
354(1)
Conclusion
355(1)
Discussion Questions and Activities
355(1)
Bibliographic References and Resources
356(3)
Appendix A Recommended Web Sites
359(3)
Professional Organizations
359(1)
Curriculum Projects
359(1)
Activities and Lesson Plan Ideas
360(1)
General Mathematics Education Sites
361(1)
Appendix B Cases
362(21)
Case 1: The Marble Line (algebra)
363(12)
Case 2: Chances Are (probability)
375(8)
Index 383


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