Teaching Secondary and Middle School Mathematics

by Brahier, Daniel J.

• ISBN13: 9780205286140
• ISBN10: 0205286143
• Edition: 1st
• Format: Hardcover
• Copyright: 2000-01-01
• Publisher: Allyn & Bacon

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