Teaching Secondary and Middle School Mathematics

by Brahier, Daniel J.

• ISBN13: 9780205412631
• ISBN10: 0205412637
• Edition: 2nd
• Format: Hardcover
• Copyright: 2004-07-07
• Publisher: Pearson

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