Teaching Mathematics for the 21st Century : Methods and Activities for Grades 6-12

by Huetinck, Linda; Munshin, Sara N.

• ISBN13: 9780138760793
• ISBN10: 0138760799
• Edition: 1st
• Format: Paperback
• Copyright: 1999-09-01
• Publisher: Pearson (Manual)

Summary

For courses in Mathematics Methods for the Secondary School. This is the first middle and secondary math methods text to focus on reform and the national standards. It prepares teachers for the challenge of assisting all students in reaching the highest level of mathematics according to their interest and realistic ambitions. It also provides contemporary methods of teaching mathematics-which facilitates successful instruction-with a strong understanding of the philosophy and psychology behind sound practices. Coverage includes methodology, curriculum materials, and use of technology, accompanied by many practical suggestions for implementation.

Table of Contents

PART I Prior to Entering The Classroom	1	(204)
History and Introduction to Reform	3	(42)
School Mathematics from the 1950s to 1990	4	(4)
``New Math''	4	(1)
Societal Pressures Toward Increased Equity	5	(1)
Student-Centered Classrooms	6	(1)
Back to Basics and Beyond	7	(1)
The Last Decade of the Millennium	8	(2)
Background of the 1990s Standards Movement/Reform Literature	8	(2)
Changing Teacher Beliefs and Attitudes	10	(1)
Today's Standards-Based Classrooms	10	(5)
Research on Typical Secondary Mathematics Classes	10	(1)
Reconceptualizing the Nature of Mathematics	11	(1)
Applying Research from Cognitive Psychology	12	(1)
Incorporating Technology	12	(1)
Preparing Students for the Workplace	13	(1)
Evaluating Effectiveness	14	(1)
Cooperative Learning in Secondary Mathematics	15	(15)
Classroom Benefits	15	(1)
Considerations for Setting Up Cooperative Groups	15	(5)
Teacher Actions during Cooperative Group Activities	20	(2)
Some Models of Cooperative Group Lessons	22	(7)
Groupwork Follow-Through and Assessment	29	(1)
Logic---A Content Area or A Tool?	30	(6)
Inductive versus Deductive Reasoning	30	(2)
Lewis Carroll's Symbolic Logic	32	(4)
Assignments	36	(1)
Instructional Resources	36	(1)
Additional Activities	36	(9)
Learning, Motivation, and Basic Management Skills	45	(42)
Learning Theories	45	(13)
Behaviorism	46	(1)
Social Cognitive Theory	47	(2)
Information Processing Theory	49	(1)
Constructivism	50	(2)
The Game Show	52	(6)
Alternative Ways to View Learning	58	(2)
Multiple Intelligences	58	(1)
Learning Styles	59	(1)
Motivation	60	(3)
Basic Management Skills	63	(7)
Room Arrangement	65	(3)
Teacher Expectations of Students	68	(1)
Daily Organization	69	(1)
Assignments	70	(1)
Instructional Resources	71	(1)
Additional Activities	71	(16)
Concrete to Abstract with Tools, Manipulatives, Computer Programs, and Calculators	87	(42)
Manipulatives	88	(13)
From Concrete to Abstract with Manipulatives	88	(1)
Using Manipulatives	88	(2)
Fraction Stacks, Pattern Blocks, Fraction Bars, Fraction Circles, and Cuisenaire Rods	90	(4)
Colored Chips, Base-Ten Blocks, Balances, and Algebra Tiles	94	(4)
Mirrors, MIRAs, Patty Paper, and Geoboards	98	(3)
Computer Software	101	(8)
From Concrete to Abstract with Computer Microworlds	103	(1)
Software Emulating Manipulatives	103	(4)
Dynamical Geometry	107	(2)
Calculators	109	(6)
Classroom Changes with Technology	113	(2)
Assignments	115	(1)
Instructional Resources	115	(1)
Additional Activities	116	(13)
Standards-Based Curricula with Sample Lessons	129	(48)
Standards-Based Curricula in Secondary Mathematics	130	(2)
Curriculum Development Background	130	(1)
Data Analysis in Exemplary Programs	131	(1)
Model Middle-School Programs	132	(7)
A General Description of the Programs	132	(1)
An Unresolved Dilemma	133	(1)
Sample Middle-School Instructional Sequences	134	(5)
Model Three-Year College Preparatory Programs	139	(11)
A General Description of the Programs	139	(5)
Sample High-School Instructional Sequences	144	(6)
Elements for Success in Teaching Standards-Based Curricula	150	(5)
Professional Development	150	(1)
Site-Based Joint Planning Time	150	(1)
Taking On a Facilitating Teaching Role	150	(5)
Flexibility	155	(1)
Willingness to Reflect on Teaching Practices and Student Work	155	(1)
Using Probeware	155	(6)
Assignment	161	(1)
Additional Annotated Model Curricula	161	(1)
Instructional Resources	162	(1)
Additional Activities	162	(7)
A Compendium of Data Collecting Activities and Sources	169	(8)
Geometry and Algebra Redefined?	177	(28)
The Nature of Contemporary Geometry	178	(12)
Three-Dimensional Geometry	178	(1)
Geometry---More than Euclid	179	(6)
Inductive and Deductive Reasoning	185	(5)
Noncomputer Tools for Geometric Measurement	190	(1)
The Nature of Contemporary Algebra	190	(6)
Historic Development of Algebra	190	(3)
What is Algebra for All?	193	(3)
Assignment	196	(1)
Instructional Resources	196	(2)
Additional Activities	198	(7)
PART II Teaching and Learning in the Classroom	205	(238)
Planning Instruction	207	(50)
The Broad Contextual Overview	208	(3)
Expectations	208	(1)
Community and Student Characteristics	209	(1)
Resources	210	(1)
Long-Range Planning	211	(8)
Semester Plan	212	(4)
Unit Planning	216	(1)
Balance:Pace, Sequence, Depth, Breadth, Skills, and Processes	216	(2)
Alternative Schedules: Block Schedules, Teaming, Thematic, and Coring	218	(1)
Daily Lesson Planning	219	(6)
Example Lesson Plan for University of Chicago Mathematics Project	220	(3)
Example Lesson Plan for Interactive Mathematics Project	223	(2)
Strategies for Effective Instruction	225	(14)
How to Study for Mathematics	225	(4)
Explicit Instruction	229	(3)
Problem Solving	232	(1)
Inquiry-Discovery	232	(7)
Assignments	239	(1)
Instructional Resources	239	(1)
Additional Activities	240	(17)
Promoting Communication in the Classroom	257	(64)
Worthwhile Tasks	258	(1)
Promoting Discourse	258	(24)
Establishing a Supportive Learning Environment for Discourse	259	(2)
Questioning Techniques for Whole-Group Instruction	261	(7)
Questioning Techniques for Small or Cooperative Groups	268	(1)
Questioning Techniques for Individual Assistance	269	(6)
Listening	275	(7)
Communication Through Writing	282	(11)
Journals	283	(6)
Learning Logs	289	(1)
Student-Written Problems	289	(1)
Other Interesting Ways to Use the Written Word	290	(3)
Discipline---From Control to Community	293	(6)
Kounin's Research	293	(2)
Community in the Classroom	295	(1)
Networking within the School	296	(1)
A Personal Discipline System	297	(2)
The Art of Teaching	299	(6)
Assignments	305	(1)
Instructional resources	305	(1)
Additional Activities	306	(15)
Assessing Individual Student Performance	321	(40)
Formative Assessment: Monitoring Student Progress	322	(8)
The Role of Homework	322	(2)
Gathering and Interpreting Evidence	324	(6)
Summative Assessment:Evaluating Student Achievement/Grades	330	(18)
Promoting Balance Through Tests	330	(1)
Test Design and Construction	330	(11)
Grade Determination	341	(7)
Assignment	348	(1)
Instructional Resources	348	(1)
Additional Investigations	348	(13)
Equity	361	(36)
Tracking
The Study of Schooling	362	(2)
Strategies for Detracking	364	(4)
Mathematics Reform and Multicultural/Multiethnic Students	368	(8)
The QUASAR Project	368	(1)
Making Mathematics Meaningful	369	(1)
Practicalities	370	(3)
More Practicalities	373	(3)
Gender Differences	376	(2)
Special Education	378	(8)
Students with Mild Learning Disabilities	378	(5)
High Achievers and Mentally Gifted and Talented Students	383	(3)
Assignments	386	(1)
Instructional Resources	386	(2)
Additional Activities	388	(9)
More on Assessment	397	(46)
Performance Tasks and Rubric Assessment	400	(27)
Performance Tasks	401	(8)
Ongoing Projects	409	(9)
Investigations	418	(1)
Portfolios	419	(8)
The Role of External Assessments	427	(4)
Standardized Tests	427	(1)
Performance Assessment	428	(1)
Advanced Placement Tests	429	(2)
Assignments	431	(1)
Instructional Resources	431	(1)
Additional Activities	432	(11)
PART III Ongoing Development	443	(66)
Communicating with Parents and Community	445	(32)
Scheduled School-Based Events	446	(13)
Back-to-School Night	446	(7)
Open Houses	453	(2)
Parent-Teacher Conferences	455	(4)
Mathematics Contests and Clubs	459	(2)
Mathematics Contests	459	(1)
Mathematics Clubs	460	(1)
Community-Based Mathematics Activities	461	(7)
The Internet:Extending Mathematics to the Cyberworld	468	(1)
Assignments	468	(1)
Annotated Internet sites for Mathematics Educators or Parents	469	(1)
Additional Activities	470	(7)
Professional Growth	477	(32)
NCTM Professional Standards for Teaching Mathematics	478	(1)
Evaluation	478	(5)
Evaluation by a Supervisor	479	(2)
Reflective Teaching	481	(2)
Continuing Professional Development	483	(7)
Professional Organizations	483	(1)
Participation in Projects, Conferences, and Workshops	484	(1)
Two Projects Supporting Reflective Practice	485	(5)
The National Board for Professional Teaching Standards	490	(1)
High School---Mathematics:Adolescence and Young Adulthood (Students ages 14-18+)	490	(1)
Middle School---Mathematics:Early Adolescence (Students Ages II-15+)	491	(1)
A Lifelong Learner	491	(1)
Master's Degree	491	(1)
Principles and Standards for School Mathematics	491	(1)
Instructional Resources	492	(1)
Additional Activities	492	(17)
Notes to the Teacher	509	(64)
References	573	(14)
Index	587