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"Mathematics Teacher" (MT) is celebrating 100 years of publication. Help commemorate this centennial with this special issue of MT, filled with information on the journal's history, with notable articles and fresh perspectives on mathematics education from the past 100 years.

This book's activities probe rational and irrational numbers and investigate properties of integers and complex numbers. They explore numbers and operations embedded in physical objects and show how simple problems can lead to sophisticated considerations. Students examine the usefulness of irrational numbers in designing musical scales and of prime numbers in devising encryption schemes, for example, and they discover powerful ideas from graph theory in a concrete context of dikes, towers, and enclosed regions.

This book provides a rationale for focal points for each grade level, prekindergarten-8. Focal points are important mathematical topics that represent major areas of content emphasis. Building on "Principles and Standards for School Mathematics," this publication is presented to begin a dialogue on what is important at particular levels of instruction and as an initial step toward a more coherent, focused curriculum. Each focal point topic is a key area of mathematics and is identified in depth. Three focal points for each level, prekindergarten-8, are presented, with connections to supporting content areas. Following a preface and introduction, this book is divided into five chapters: (1) Why Identify Curriculum Focal Points? (2) What Are Curriculum Focal Points? (3) How Should Curriculum Focal Points Be Used? (4) How Do the Curriculum Focal Points Relate to "Principles and Standards for School Mathematics"? and (5) Curriculum Focal Points for Mathematics in Prekindergarten through Grade 8. Appended is: A Comparison of the Curriculum Focal Points and Connections with the Expectations of the Content Standards in "Principles and Standards for School Mathematics." A list of references concludes the book.

Designing high-quality professional development for mathematics educators requires close attention to many facets of teacher learning. "Learning from NAEP" is a valuable manual-plus-CD resource containing activities and workshops that facilitators can use as is or tailor to the unique needs of participants in their school's or district's professional development program. The materials, which draw on the experiences of educators and the expertise of researchers, help educators better understand the intricacies of national assessment data and how such data relate to student learning in mathematics classrooms. The CD-ROM provides the materials and tools necessary to facilitate the workshops, as well as resources to help expand or create a workshop.

Making connections becomes increasingly important as students proceed through middle school and high school. This book shows ways of embedding connective processes in instruction in grades 9-12. Problems invite mathematical modeling, unify diverse content, call for different representations, and encourage students to look back at their work to find connections. Activities feature such tasks as determining a dosage schedule for a prescription drug, making "transit graphs" to maximize travel through a canal, and deciding when to accept a "double dare" in a simple game. Mathematics is a highly interconnected discipline. Teaching isolated concepts can limit students' understanding and diminish their interest. The NCTM Process Standards recommend highlighting mathematical connections by actively involving students in five processes: problem solving, reasoning and proof, communication, connections and representation. Following an introduction, this book is divided into four chapters: (1) Connecting with Models; (2) Connecting with a Unifying Theme; (3) Connecting with Multiple Representations; and (4)Connecting with Problem-Solving Processes. Blackline masters and solutions are appended. A list of references and information on the contents of the accompanying CD-ROM are also included.

The 2006 NCTM Sixty-eighth Yearbook focuses on students' and teachers' learning in statistics centered on a set of activities. Topics include the relation between mathematics and statistics, the development and enrichment of mathematical concepts through the use of statistics, and a discussion of the research related to teaching and learning statistics. The yearbook articles cover a variety of broad areas, including sections on Learning about Data and Chance, Reasoning with Data and Chance, and Reflecting on Issues Related to Data and Chance. Articles focus on such topics as examining children's beliefs about "what is fair" and using simulation techniques in the classroom. The accompanying CD-ROM offers support material for many of the articles, including lessons, software demonstrations, and even video clips of classrooms. NCTM yearbooks focus concerted attention on timely issues by viewing them in depth, from multiple perspectives, through interdisciplinary lenses, and across different grade bands. The year 2006 marks the sixty-eighth yearbook in the NCTM yearbook series. Following a preface, this book is divided into three parts. Part, Learning about Data and Chance, presents: (1) Graphing with Four-Year-Olds: Exploring the Possibilities through Staff Development (Sydney L. Schwartz and David J. Whitin); (2) What Does It Mean That "5 Has a Lot"? From the World to Data and Back (Susan Jo Russell); (3) Learning to Talk Back to a Statistic (David J. Whitin); (4) Engaging Students in Authentic Data Analysis (Randall E. Groth); (5) Students' Probabilistic Thinking Revealed: The Case of Coin Tosses (Laurie H. Rubel); (6) Assessing the Development of Important Concepts in Statistics and Probability (Jane M. Watson); and (7) Research on Students' Understanding of Some Big Concepts in Statistics (J. Michael Shaughnessy). Part 2, Reasoning with Data and Chance, continues with the next chapters: (8) A Statistical Study of Generations (Henry Kranendonk and Roxy Peck ); (9) More than "Meanmedianmode" and a Bar Graph: What's Needed to Have a Statistical Conversation? (Susan N. Friel, William O'Connor, and James D. Mamer); (10) When Data and Chance Collide: Drawing Inferences from Empirical Data; (James E. Tarr, Hollylynne Stohl Lee, and Robin L. Rider); (11) Experimental Design: Learning to Manage Variability (Daniel J. Teague); (12) "We Were Nicer, but We Weren't Fairer! Mathematical Modeling Exploring "Fairness" in Data Management; (Susan London McNab, Joan Moss, Earl Woodruff, and Rod Nason); (13) Using Real Data and Technology to Develop Statistical Thinking (Doreen Connor, Neville Davies, and Peter Holmes); (14) Using Regression to Connect Algebra to the Real World (Jim Bohan); (15) Using Data to Enhance the Understanding of Functions: Data Analysis in the Precalculus Curriculum (Peter Flanagan-Hyde and John Lieb); (16) Changing the Face of Statistical Data Analysis in the Middle Grades: Learning by Doing (Kay McClain, Julie Leckman, Paula Schmitt, and Troy Regis; (17) Understanding Data through New Soft ware Representations (Andee Rubin and James K. Hammerman); (18) Using Graphing Calculator Simulations in Teaching Statistics (Michael H. Koehler); (19) What Is Statistical Thinking, and How Is It Developed? (Sharon J. Lane-Getaz); and (20) Using Graphing Calculators to Redress Beliefs in the "Law of Small Numbers" (Alfinio Flores). Part 3, Reflecting on Issues Related to Data and Chance, continues with: (21) Statistics and Mathematics: On Making a Happy Marriage (Richard L. Scheaffer); (22) Some Important Comparisons between Statistics and Mathematics, and Why Teachers Should Care (Allan Rossman, Beth Chance, and Elsa Medina); (23) The Statistical Education of Grades Pre-K-2 Teachers: A Shared Responsibility (Christine A. Franklin and Denise S. Mewborn); (24) The GAISE Project: Developing Statistics Education Guidelines for Grades Pre-K-12 and College Courses (Christine A. Franklin and Joan B. Garfield); (25) Why Variances Add--and Why It Matters (David Bock and Paul F. Velleman); (26) Bootstrapping Students' Understanding of Statistical Concepts (Tim Hesterberg); (27) Interpreting Probabilities and Teaching the Subjective Viewpoint (Jim Albert); (28) Assessments, Change, and Exploratory Data Analysis (John A. Dossey); (29) Fish "n" Chips: A Pedagogical Path for Using an In-Class Sampling Experiment (Heather A. Thompson, Gail Johnston, and Tamara Pfantz); and (30) Research in the Statistics Classroom: Learning from Teaching Experiments (Dani Ben-Zvi, Joan B. Garfield, and Andrew Zieffler).

Middle school students consolidate their understanding of integers and rational numbers, increasing their facility with fractions, decimals, and percents and encountering proportionality. This book shows how students can explore these important ideas in such diverse activities as exchanging currency and using area models to develop algorithms for multiplying and dividing fractions. Underlying each activity is the belief that students learn best when they build computational fluency on a firm conceptual foundation. Numbers and the operations that we perform with them are the starting points for all mathematics. Accordingly, "Principles and Standards for School Mathematics" makes the "Number and Operations Standard" first among the five Content Standards and gives it a centrality across the mathematics curriculum from prekindergarten through grade 12. Following an Introduction, this book is divided into three chapters: (1) Fractions, Decimals, and Percents; (2) Working with Fractions, Decimals, and Percents; and (3) Proportional Reasoning. Following Chapter 3 is a section titled "Looking Back and Looking Ahead." An appendix titled "Blackline Masters and Solutions" and a list of references conclude the book. An accompanying CD-ROM contains: (1) Table of Standards and Expectations, Number and Operations, Pre-K-12; (2) Applets; (3) Blackline Masters; and (4) Readings from Publications of the National Council of Teachers of Mathematics.

This sampler presents assessment tasks that are appropriate for use with students from age 4 through age 8. The book provides teachers of primary grades mathematics with examples of assessment tasks that reflect the various ways assessments can be used prior to, during, and following mathematics instruction. Teachers can then consider the potential of these tasks to uncover the mathematical understandings of their students for the purpose of planning further instruction. Each task can be altered by changing the context, breaking the task into subparts, limiting the scope or complexity of the task, or extending the task to provide more challenge or enhance the depth of understanding being assessed.

The sample assessment items in this volume are sorted according to the strands of number and operations, algebra, geometry, measurement, and data analysis and probability. Because one goal of assessment is to determine students' abilities to communicate mathematically, the writing team suggests ways to extend or modify multiple-choice and short-answer items to elicit students' thinking. The writers also present various rubrics as examples of how teachers might score extended-response questions. When students know in advance how their answers will be evaluated, they will strive to meet expected criteria. The hope is that teachers will find this material useful as they plumb their students' thinking and consider how students' responses can guide their instructional decisions. Following a preface and introduction, this book is divided into six chapters: (1) Number and Operations; (2) Algebra; (3)Geometry; (4) Measurement; (5) Data Analysis and Probability; and (6) Professional Development. Items Matrices are appended. A bibliography and list of sources for assessment items are also included.

Get students into math using outer space! Mission Mathematics translates the NASA experience into language and experiences appropriate for young learners, and provides teachers with mathematics activities that complement many of the available NASA resources for students and educators. In these motivating investigations, young children engage in deep and sustained interactions with fundamental mathematical ideas; reason and communicate; identify and explore patterns and relationships; apply problem solving strategies; and discover connections with other mathematical concepts. Sample student activities involve covering a model airplane; constructing a "veggie" space shuttle; making fizzy-tablet rockets; exploring gravity and weight; launching protractor rockets; and collecting the sun's rays over time. The Mission Mathematics II series is developed by NASA and National Council of Teachers of Mathematics (NCTM) in an unprecedented effort to link the science of aeronautics with the Standards that NCTM has developed for all aspects of mathematics education. Following the publication of the original Mission Mathematics series in 1997, this revision focuses on aligning the activities with NCTM's "Principles and Standards for School Mathematics" (2000) in the context of aerospace activities. The activities in each book focus on actively engaging students in NCTM's Process Standards, translating the work of engineers and scientists at NASA into language and experiences appropriate for young learners, and providing teachers with mathematics activities that complement many of the available NASA resources for students and educators. The CD-ROM that accompanies this book features resource pages, links, and posters for your classroom. Following a foreword, preface, and "Matrix of Activities and Mathematics Standards," this book is divided into 10 sections: (1) Aerospace Technology; (2) Space Flight; (3) Space Science; (4) Earth Science; (5) Biological and Physical Research (includes appendixes: NASA Resources for Educators; NCTM Information; Charting the Planets; and Resource Pages); (6) Aerospace Technology; (7) Space Flight; (8) Space Science; (9) Earth Science; and (10) Bibliography. The book concludes with information on the contents of the CD-ROM.

This book follows students' natural progression from measuring with informal or nonstandard units to using standard units to measure such attributes as length, weight, angle, and temperature. Activities extend students' learning to the measurement of two- and three-dimensional objects. Students work in a variety of lively real-world contexts, gathering measurement benchmarks in a classroom scavenger hunt and investigating the area of a rectangle while acting as owners of a sticker factory, for example. Following an introduction, this book is divided into the following four chapters: (1) Understanding the Process of Measurement; (2) Understanding Standard Units of Measurement; (3) Measuring Two-Dimensional Shapes; and (4) Measuring Three-Dimensional Objects. A section titled "Looking Back and Looking Ahead," as well as appendices, follows. The supplemental CD-ROM features interactive electronic activities, master copies of activity pages for students, and additional readings for teachers.

Often referred to as "The Nation's Report Card," the mathematics assessments of the National Assessment of Educational Progress (NAEP) have come to be regarded by many policymakers as the primary yardstick by which to judge our schools' success in meeting national expectations. This monograph reports and interprets trends in NAEP mathematics data collected between 1990 and 2000. Following a preface, this book is divided into four sections. Section 1, Background and Perspectives, includes: (1) Interpreting the 2000 NAEP Mathematics Data: Issues and Monograph Overview (Peter Kloosterman); (2) A Brief History of the NCTM NAEP Interpretive Reports Projects (Patricia Ann Kenney); and (3) Using the NAEP Online Tools (Peter Kloosterman, Paul Kehle, and Yusuf Koc). Section 2, Students' Knowledge about Mathematics, contains: (4) Fourth-Grade Students' Knowledge of Mathematics and Perceptions of Learning Mathematics (Peter Kloosterman, Janet Warfield, Diana Wearne, Yusuf Koc, W. Gary Martin, and Marilyn Strutchens); (5) What Do 8th-Grade Students Know about Mathematics? Changes over a Decade (Judith T. Sowder, Diana Wearne, W. Gary Martin, and Marilyn Strutchens); (6) What Do 12th-Grade Students Know about Mathematics? (Paul Kehle, Diana Wearne, W. Gary Martin, Marilyn E. Strutchens, and Janet Warfield); (7) Long-Term NAEP: Mathematics Learning over Three Decades (Enrique Galindo, Kelly McCormick, Doris Mohr, and Richard Caulfield); and (8) State NAEP and Mathematics Achievement (Norman L. Webb and Janet H. Kane). Section 3, Special Topics, continues with: (9) The Preparation and Teaching Practices of United States Mathematics Teachers: Grades 4 and 8 ( Douglas A. Grouws, Margaret Schwan Smith, and Paola Sztajn); (10) NAEP Findings Regarding Race and Ethnicity: Students' Performance, School Experiences, Attitudes and Beliefs, and Family Influences (Marilyn E. Strutchens, Sarah Theule Lubienski, Rebecca McGraw, and Sarah K. Westbrook); (11) NAEP Findings Regarding Gender: Mathematics Achievement, Student Affect, and Learning Practices (Sarah Theule Lubienski, Rebecca McGraw, and Marilyn E. Strutchens); (12) Students' Ability to Construct Responses (1992-2000): Findings from Short and Extended Constructed-Response Items (Fran Arbaugh, Catherine Brown, Kathleen Lynch, and Rebecca McGraw); (13) Beyond Reading Graphs: Student Reasoning with Data (Beatriz S. D'Ambrosio, Signe Kastberg, George McDermott, and Nivan Saada); (14) NAEP, TIMMS, and PISA: What Can We Learn? (Paola Sztajn, Holly G. Anthony, Jeong-lim Chae, Ayhan Kursat Erbas, Dennis Hembree, Jongsuk Keum, Jacob T. Klerlein, and Zelha Tunc-Pekkan); and (15) NAEP and State Accountability Measures (W. Gary Martin and Joy W. Black). Section 4, Appendixes, contains: (1) Released Item Codes; and (2) NAEP-Related Publications: 1990-2000 Mathematics Assessments.

Teaching is a complex, ongoing endeavor that involves a myriad of decisions. The National Council of Teachers of Mathematics' (NCTM's) Sixty-Sixth Yearbook is organized around three aspects of teaching: foundations for teaching, the enactment of teaching, and the support of teaching nurtured in preservice education and strengthened throughout a teacher's career. The 72-page companion professional development guidebook, edited by George W. Bright, contains activities that illustrate and extend some of the ideas in the yearbook in order to further teachers' growth and development in understanding and implementing effective mathematics instruction. Following a preface, this book is divided into three parts and 22 chapters. Part 1, Foundations for Teaching, contains: (1) Equity in Mathematics Education Is about Access (Carol Malloy); (2) Developing a Well-Articulated Algebra Curriculum: Examples from the NCTM Academy for Professional Development (Jennifer M. Bay-Williams, Elizabeth M. Skipper, and Susan K. Eddins); (3) What Makes a Mathematical Task Worthwhile? Designing a Learning Tool for High School Mathematics Teachers (Fran Arbaugh and Catherine A. Brown); (4) Mathematical Foundations for a Functions-Based Approach to Algebra (M. Kathleen Heid, Rose Mary Zbiek, and Glendon W. Blume); and (5) Language Pitfalls and Pathways to Mathematics (Carne Barnett-Clarke and Alma Ramirez). Part 2, The Enactment of Teaching, contains: (6) Mathematics Teaching in Grades K-2: Painting a Picture of Challenging, Supportive, and Effective Classrooms (Barbara Clarke and Doug Clarke); (7) The NCTM Standards in a Japanese Primary School Classroom: Valuing Students' Diverse Ideas and Learning Paths (Aki Murata, Naoyuki Otani, Nobuaki Hattori, and Karen C. Fuson); (8) Beyond Presenting Good Problems: How a Japanese Teacher Implements a Mathematics Task (Margaret Smith); (9) Teaching to Develop Students as Learners (Debra I. Johanning and Teri Keusch); (10) Enlarging the Learning Community through Family Mathematics (Phyllis Whitin); (11) Building a Mathematical Community through Problem Posing (David J. Whitin); and (12) Promoting Equity in Mathematics Education through Effective, Culturally Responsive Teaching (Joan Cohen Jones). Part 3, Support of Teaching, contains: (13) Enhancing the Mathematical Understanding of Prospective Teachers: Using Standards-Based, Grades K-12 Activities (Charlene E. Beckmann, Pamela J. Wells, John Gabrosek, Esther M. H. Billings, Edward F. Aboufadel, Phyllis Curtiss, William Dickinson, David Austin, and Alverna Champion); (14) Promoting Content Connections in Prospective Secondary School Teachers (Irene Bloom); (15) Facilitating Teachers' Growth in Content Knowledge (Kathleen Cramer); (16) Embracing the Complexity of Practice as a Site for Inquiry (Theresa J. Grant and Kate Kline); (17) The Reflective Teaching Model: A Professional Development Model for In-Service Mathematics Teachers (Lynn C. Hart, Deborah Najee-Ullah, and Karen Schultz); (18) Encouraging Professional Growth and Mathematics Reform through Collegial Interaction (P. Mark Taylor); (19) Developing a Support System for Teacher Change in Mathematics Education: The Principal's Role (Patricia A. Jaberg, Cheryl A. Lubinski, and Sigrid Aeschleman); (20) A Tool for the Teaching Principle: Professional Development through Assessment (Sandra Wilcox and Elizabeth M. Jones); (21) Teaching Mathematics with Technology: An Evidence-Based Road Map for the Journey (Karen Hollebrands and Rose Mary Zbiek); and (22) Teachers Teaching Teachers (Janet Warfield and Cheryl A. Lubinski).

In 1999-2000, the National Council of Teachers of Mathematics (NCTM) Board of Directors established the Standards Impact Research Group (SIRG) in response to the continuing need for a clearer understanding of the role of standards in the improvement of mathematics education. SIRG has undertaken a number of activities in support of its objectives, culminating in the September 2003 Research Catalyst Conference. These proceedings document the discussions and outcomes of eight working groups, as well as the presentations made at three plenary sessions during the conference. Also included are the SIRG research briefs, produced as background documents and distributed to all participants in advance of the conference. This book begins with a foreword (Johnny W. Lott), Acknowledgments (Board of Directors of the National Council of Teachers of Mathematics), and Introduction: Studying the Role and Influence of Standards on K-12 Mathematics Education--The Standards Impact Research Group Catalyst Conference (Joan Ferrini-Mundy). It then is divided into eight SIRG Briefs, four Panel Summaries, and eight Working Group Reports, which follows. The SIRG Briefs section contains: (1) Overview of the SIRG Research Briefs and Research Agenda (Standards Impact Research Group); (2) What Is a Standard? (William F. Tate); (3) What Does It Mean to Be Standards-Based? Issues in Conceptualizing, Measuring, and Studying Alignment with Standards (Joan Ferrini-Mundy); (4) Recent Research on the Influence of Standards: Insights and Methodological Approaches (Robert E. Floden and Suzanne M. Wilson); (5) Are the NCTM Standards Working? Perspectives on Student Outcomes as a Point of Impact in Research on Standards (W. Gary Martin); (6) Advocating for Equity and Diversity within the Context of Standards-Based Reform (Danny Bernard Martin, Jose Franco, and Karen Mayfield-Ingram); (7) Examining Teacher Quality (Mary M. Kennedy); and (8) Studying the Influence and Impact of "Principles and Standards for School Mathematics": The Role of Schools and Districts in Teacher Capacity Building (Mary Kay Stein). The Panel Summaries section contains: (1) Plenary Panel: Current Education Research in the United States (Robert E. Floden); (2) Perspectives Panel I: Policy, Practice, and Research (Joan Ferrini-Mundy); (3) Perspectives Panel II: International Perspectives (Judith Sowder); and (4) Summary of Remarks by Finbarr (Barry) Sloane (Judith Sowder). The Working Group Reports section contains: (1) Assessment and Student Achievement (Linda Dager Wilson and Kaye Stacey); (2) The Changing Nature of Schooling and School Demographics (William F. Tate and Pauline Lipman); (3) Instructional Materials and Curriculum (Jo Ellen Roseman); (4) Local Policy and Community Context (Mary Kay Stein and Patrick Shields); (5) State and National Policy (W. Gary Martin and Andrew Porter); (6) Teaching and Learning (Hilda Borko, Carolyn Kieran, and Frank K. Lester); (7) Teacher Preparation (Robert E. Floden and Randolph Philipp); and (8) Teacher Quality and Professional Development (Michael Knapp and Judith Sowder). The book concludes with three appendices listing conference participants, speakers, and agenda.

In their second book copublished by the National Council of Teachers of English and the National Council of Teachers of Mathematics, David and Phyllis Whitin offer K-6 teachers a wealth of ideas for integrating literature and mathematics, including: (1) Specific criteria for evaluating math-related books, with emphasis on inquiry, critical thinking, diversity, and individual challenge; (2) Practical discussions about books and their use in K-6 classrooms; (3) An in-depth look at problem posing and book pairs as effective strategies for engaging all students; (4) Explicit connections made to NCTM's "Principles and Standards for School Mathematics" (2000) and NCTE and IRA's "Standards for the English Language Arts" (1996); (5) Interesting sidebars of extension activities and text sets; (6) Practical strategies for introducing math-related books to children; and (7) An annotated list of the best math-related literature available. This is a book filled with numerous examples of children's work, many of which are drawn from widely diverse, multicultural classrooms. Each chapter discusses a range of books and classroom applications to show how teachers can skillfully integrate such books to meet school objectives in language arts and mathematics. It is this dual perspective that makes the book unique. With its inviting tone and practical suggestions, "New Visions for Linking Literature and Mathematics" is an invaluable resource for the elementary school classroom. Following a foreword by Judith Lindfors, and an introduction, this book is divided into the following five chapters: (1) Criteria for Selecting Math-Related Books; (2) Book for a Wide Range of Ages; (3) Problem Posing with Children's Literature; (4) Using the Strategy of Book Pairs; and (5) Best Books for Exploring. (Contains 6 appendixes.)

Written for all teachers of young children, this book illustrates activities that promote early mathematics development for children ages three to five and "showcases" mathematics for the young child. The thirty-five activities in this book are distributed into five content areas: number and operations, geometry, algebra, measurement, and data analysis. The content areas are connected by a continuing story, "Hanny the Honey Bear Discovers the World of Mathematics in the Big Zoo." Teachers can use this book to help themselves teach mathematics, learn mathematics, and most important, "listen to children think!" This book is divided into the following six sections: (1) Introduction; (2) Number and Operations; (3) Geometry; (4) Algebra; (5) Measurement; and (6) Data Analysis. Appended are: (1) Selected Expectations from "Principles and Standards for School Mathematics" (NCTM 2000); (2) Early Childhood Mathematics: Promoting Good Beginnings: A Joint Position Statement of the NAEYC and the NCTM; (3) Templates for Animal Stick Puppets; and (4) Templates for Creature Cards. A list of references concludes the book.

Measurement can develop in the earliest years from children's experience, and it readily lends itself to real-world application. Focusing on research and practice, NCTM's 2003 Yearbook presents current thinking about the learning and teaching of measurement, including students' understanding, the mathematics of measurement, estimation and approximation, connections, and pedagogy. The 331-page yearbook divides into two parts and twenty-four chapters, as follows. Part 1: "Elementary School," contains: Introduction (Michelle Stephan and JoAnne Mendiola); (1) Linear, Area, and Time Measurement in Prekindergarten to Grade 2 (Michelle Stephan and Douglas H. Clements); (2) Understanding Children's Developing Strategies and Concepts for Length (Jeffrey E. Barrett; Graham Jones; Carol Thornton; Sandra Dickson); (3) Making Connections with Powerful Ideas in the Measurement of Length (Nicola Yelland); (4) Developing the Building Blocks of Measurement with Young Children (Theresa J. Grant and Kate Kline); (5) Benchmarks as Tools for Developing Measurement Sense (Elana Joram); (6) Assessing and Developing Measurement with Young Children (Doug Clarke; Jill Cheeseman; Andrea McDonough; and Barbara Clark); (7) Count Me into Measurement: A Program for the Early Elementary School (Lynne Outhred; Michael Mitchelmore; Diane McPhail; and Peter Gould; (8) Developing an Understanding of Measurement in the Elementary Grades (Richard Lehrer; Linda Jaslow; and Carmen L. Curtis); (9) Understanding Students' Thinking about Area and Volume Measurement (Michael T. Battista); (10) Structuring a Rectangle: Teachers Write to Learn about Their Students' Thinking (Deborah Schifter and Janice Szymaszek); (11) About Students' Understanding and Learning the Concept of Surface Area (Cinzia Bonotto); (12) The Measurement of Time: Transitivity, Unit Iteration, and Conservation of Speed (Constance K. Kamii and Kathy Long); and (13) Bridging Yup'ik Ways of Measuring to Western Mathematics (Jerry Lipka; Tod Shockey; and Barbara Adams). Part 2: "Secondary School," contains: Introduction (Veronica Meeks and Robert F. Wheeler); (14) What Students Know about Measurement: Perspectives from the NAEP (Marilyn E. Strutchens; W. Gary Martin; and Patricia Ann Kenney); (15) Providing Opportunities for Students and Teachers to "Measure Up" (Melissa Boston and Margaret Smith); (16) Measuring Montana: An Episode in Estimation (Ted Hodgson; Linda Simonsen; Jennifer Lubek; and Lyle Anderson); (17) Estimation at Work (Thomasenia Lott Adams; and Gregory Harrell); (18) Exploring Measurement Concepts through Literature: Natural Links across Disciplines (Richard Austin; Denisse Thompson; and Charlene Beckmann); (19) Using the Geoboard to Enhance Measurement Instruction in the Secondary School Mathematics Classroom (Barbara A. Burns and Gail A. Brade); (20) Using Measurement to Develop Mathematical Reasoning at the Middle and High School Levels (Mary C. Enderson); (21) Is Our Teaching Measuring Up? Race-, SES-, and Gender-Related Gaps in Measurement Achievement (Sarah T. Lubienski); (22) Measurement, Representation, and Computer Models of Motion (Christopher Hartmann and Jeffrey Choppin); (23) Measuring the Unmeasurable: Using Technology to Study the Irrational (Maurice Burke); and (24) Measurement in Adult Education: Starting with Students' Understandings (Myriam Steinback; Mary Jane Schmitt; Martha Merson; and Esther Leonelli). The 77-page companion booklet, which not only illustrates some of the issues from the yearbook but also contains activities that go beyond the content, contains teaching notes and ready-to-use handouts. The booklet contains the following eighteen chapters: (1) A Word to Teachers; (2) Woolly Worms (Andrea McDonough; Jill Cheeseman; and Doug Clarke); (3) Teddy Counters (Andrea McDonough; Jill Cheeseman; and Doug Clarke); (4) Broken Rulers (Jeffrey Barnett and Sandra Dickson); (5) Benchmarks for Measurement Units (Elana Joram); (6) Measuring Volume Informally (Sinan Olkun); (7) Angle Measurements (George W. Bright); (8) Estimation (George W. Bright); (9) Greatest Perimeter (George W. Bright); (10) Measuring the Mountain State (Ted Hodgson); (11) Area of Kite: Teaching Notes (George W. Bright); (12) Making Rabbit Pens (Margaret S. Smith and Melissa Boston); (13) The Perimeter and Area of Similar Figures (Barbara A. Burns and Gail Brade); (14) Ratios--Surface Areas and Volumes (George W. Bright); (15) Look-Alike Rectangles (Suzanne Levin Weinberg); (16) Perimeter and Area of Similar Figures (Mary C. Enderson); (17) Determining Densities of Various Kinds of Wood (Joseph I. Stepans); and (18) Investigating Densities of Different Paper Materials (Joseph I. Stepans).

This yearbook contains articles that give insight into students' thinking about factions, ratios, and proportions. Suggestions are offered on how to develop the concepts and skills associated with these topics. The book is divided into elementary, middle school, and professional development sections. Chapters include: (1) "The Development of Students' Knowledge of Fractions and Ratios" (John P. Smith); (2) "Children's Development of Meaningful Fraction Algorithms: A Kid's Cookies and a Puppy's Pills" (Janet M. Sharp, Joe Barofalo, and Barbara Adams); (3) "Organizing Diversity in Early Fraction Thinking" (Susan B. Empson); (4) "Using Manipulative Models to Build Number Sense for Addition and Fractions" (Kathleen Cramer And Apryl Henry); (5) "Young Children's Growing Understanding of Fraction Ideas" (Elena Steencken and Carolyn A. Maher); (6) "Go Ask Alice about Multiplication of Fractions" (Susan B. Taber); (7) "Examining Dimensions of Fraction Operation Sense" (Deann Huinker); (8) "Part-Whole Comparisons with Unitizing" (Sue Lamon); (9) "Butterflies and Caterpillars: Multiplicative and Proportional Reasoning in the Early Grades" (Patricia Ann Kenney, Mary M. Lindquist, and Cristina L. Heffernan; (10) "Percents and Proportion at the Center: Altering the Teaching Sequence for Rational Number" (Joan Moss); (11) "Making Explicit What Students Know about Representing Fractions" (Barbara M. Moskal and Maria E. Magone); (12) "Using Literature as a Vehicle to Explore Proportional Reasoning" (Denisse R. Thompson, Richard A. Austin, and Charlene E. Beckmann); (13)"Proportional Reasoning: One Problem, Many Solutions!" (Suzanne Levin Weinberg); (14) "Using Representational Contexts to Support Multiplicative Reasoning" (Laura B. Kent, Joyce Arnosky, and Judy McMonagle); (15) "Fraction Division Interpretations" (Rose Sinicrope, Harold W. Mick, and John R. Kolb); (16) "Developing Understanding of Ratio and Measure as a Foundation for Slope" (Joanne Lobato and Eva Thanheiser); (17) "Using Technology to Teach Concepts of Speed" (Janet Bowers, Susan Nickerson, and Garrett Kenehan); (18) "Developing Students' Proportional Reasoning: A Chinese Perspective" (Jinfa Cai and Wei Sun); (19) "The Development of Rational Number Sense" (Irene T. Miura and Jennifer M. Yamagishi); (20) "Multiplicative Reasoning: Developing Student's Shared Meanings" (Cristina Gomez); (21) "Fraction Instruction That Fosters Multiplicative Reasoning" (Lee Vanhille); (22) "Profound Understanding of Division of Fractions" (Alfinio Flores); and (23) "Connecting Informal Thinking and Algorithms: The Case of Division of Fractions" (Daniel Siebert). (KHR)

This book describes children's mathematical thinking to guide and support teachers in their reflection upon student thinking and teaching and learning. It is organized into five parts: (1) reasoning, student thinking, and invented strategies independent of the mathematics content domain which addresses the role of discourse in helping students clarify their thinking, communicate their thinking to other students, and communicate their thinking to the teacher, thus permitting access to their thinking; (2) children's thinking in the specific content domains of numbers, number sense, number operations, place value, fractions, geometry, geometric reasoning, spatial sense, algebra and algebraic reasoning, and statistics and statistical reasoning; (3) research on tools for representing mathematical ideas including concrete materials, electronic tools, and mathematical symbols as tools; (4) equity issues and research that can help teachers reduce inequity in their classrooms; and (5) additional resources and ideas for using research in the classroom. (KHR)

This collection of articles relating to elementary and middle school mathematics illustrate the goals outlined in the National Council of Teachers of Mathematics (NCTM) documents' six Principles and 10 Standards. These goals provide effective lenses for carefully examining and thinking deeply about the classroom episodes described in each article. The articles illustrate the variety of ways in which the vision of the "Principles and Standards" can be actualized within the constraints, realities, and challenges of today's classrooms. The articles are organized into three parts: (1) Principles; (2) Content Standards; and (3) Process Standards. Individual goals are listed for each principle and standard, and three or four articles are presented as exemplars of each set of goals. Activities are included at the end of each section to encourage further reflection upon the nature of these goals and their implications for classroom teaching and learning. (KHR)

This book provides resources and practical ideas for classroom teachers, administrators and principals, curriculum supervisors and program developers, and ethnomathematicians and researchers who wish to develop a deeper understanding of the mathematics and pedagogy of the indigenous peoples of North America. Chapters 1-6 focus on the theoretical foundation that undergirds indigenous ethnomathematics. Chapter 7 addresses the issue of portfolio assessment. Chapters 8-17 include classroom lessons and activities that elementary and middle school teachers will find useful while chapters 18-24 focus on middle school and high school topics. (KHR)

This book contains activities related to fractions and proportions. The activities span many grade levels as well as many levels of sophistication. Each activity is accompanied by a set of Teachers Notes that include a discussion of the mathematics topics, grade range, materials needed, mathematics of the activity, and implementation notes. All activities also include one or more handouts for use directly with students. (KHR)

Teachers and teacher educators interested in synthesizing their current practice with new mathematics standards will welcome this highly useful volume. The QUASAR Project at the University of Pittsburgh presents prevalent cases of mathematics instruction drawn from their research of nearly 500 classroom lessons. The Mathematical Tasks Framework--which is explained thoroughly in this book--offers teachers and teacher educators the means to evaluate instructional decisions, the choice of materials, and learning outcomes while the case studies afford readers the opportunity to ground these ideas in actual classroom practice. This book aims to provide insight into how to foster a challenging, cognitively rich, and exciting classroom climate that propels students toward a richer understanding of mathematics. (Contains 36 references.) (ASK)

This collection of problems provides a resource for teachers to use in the classroom to improve the problem-solving experiences of their students. This book provides middle school teachers with some perspectives on problem solving. A framework for organizing the problem- solving experience is presented. Each phase of the problem-solving experience is described, and some questions that help to define the phases are listed as well to guide thinking. An example of a particular problem, the thought processes involved, and a list of suggestions to improve problem solving is provided. (KHR)

This book, written on the recommendation of the Task Force on Mathematically Promising Students, investigates issues involving the development of promising mathematics students. Recommendations are made concerning topics such as the definition of promising students; the identification of such students; appropriate curriculum, instruction, and assessment; cultural influences; teacher preparation and enhancement; and appropriate next steps. Chapters include: (1) "Promises, Promises, Promises" (Peggy A. House); (2) "Definition and Identification of Mathematical Promise" (Richard Wertheimer); (3) "Mathematically Promising Students: National Trends and International Comparisons" (Judith Lynn Gieger and Jeremy Kilpatrick); (4) "Serving the Needs of the Mathematically Promising" (Linda Jensen Sheffield); (5) "The Mathematically Promising and the Mathematically Gifted" (Zalman Usiskin); (6) "Effective Learning Environments for Promising Elementary and Middle School Students" (Grayson H. Wheatley); (7) "A Community of Scholars: Working with Students of High Ability in the High School" (Mark Saul); (8) "Helping Students See the World Mathematically" (Solomon Garfunkel and Gary Froelich); (9) "The Open Approach to Teaching Mathematics--Creating a Culture of Mathematics in the Classroom: Japan" (Yoshihiko Hashimoto and Jerry Becker); (10) "Empowering Teachers to Discover, Challenge, and Support Students with Mathematical Promise" (Carole Greenes and Maggie Mode); (11) "Why Jane Doesn't Think She Can Do Math: How Teachers Can Encourage Talented Girls in Mathematics" (Sally M. Reis and M. Katherine Gavin); (12) "Building Programs for Promising Students Beyond the Classroom" (Harvey Keynes, Andrea Olson, Doug Shaw, and Karen Singer); (13) "The Missing Link: Connecting Parents of Mathematically Promising Students to Schools" (Jennie Bennett); (14) "Organizational Alternatives for the Mathematically Promising" (Betty J. Krist); (15) "Providing Opportunities through Competitions" (George Berzsenyi); (16) "International Perspectives on Cultivating Talent in Mathematics" (Frances R. Curcio); (17) "Making Children Count: Fostering Mathematical Literacy" (Mary Anne Anthony-Smith); (18) "The Gifted Dozen As They Move from Grades 2 through 4" (Gerald Elgarten); (19) "Ronnie Taught Us While We Mentored Him" (Marcia Nicol and James Fitzsimmons); (20) "A Boy Named Billy" (Linda Hall); (21) "You'll Do Better Next Time--You Can!" (Thomasenia Lott Adams); (22) "Everybody Counts--Including the Mathematically Promising" (Christian R. Hirsch and Marcia Weinhold); (23) "Instituting a Mathematics Research Program for Your School's Promising Mathematics Enthusiasts" (Robert Gerver); (24) "Nurturing Mathematical Promise during the School Day" (Paul Eenigenburg and Carol McCarthy); (25) "Project-Based Calculus 1 Students: A Case Study" (Cynthia Ramey); (26) "Identifying and Developing Mathematically Promising Students through Honors Calculus and the University Scholars Program" (John Douglas Faires, John Paul Holcomb, and Nathan Paul Ritchey); (27) "Supporting Students as Emerging Scholars" (James A. Mendoza Epperson); (28) "The Young Scholars Program at Ohio State University" (Arnold E. Ross); (29) "Developing Mathematically Promising Students Outside of Formal Education" (Richard Alvarez); (30) "The Charlotte Mathematics Club: A Greenhouse for Talent" (Ashley Reiter); (31) "Addiction to Mathematics: How Can We Cause It?" (William E. Geeslin); (32) "Nurturing the Growth of Young Mathematicians through Mathematics Contests" (Richard Grassl and Tabitha Mingus); (33) "MATHCOUNTS" (Madeline J. Bauer and Joseph P. Fagan); and (34) "Enriched Students Need Enriching Teachers: The Australian Mathematics Teacher Enrichment Project" (Steve Thornton and Francesca Peel). (ASK)

This book focuses on a number of salient research and practice issues in the teaching and learning of mathematics among the second largest minority group in the United States, Latinos. Chapters include: (1) "Understanding the Needs of Latino Students in Reform-Oriented Mathematics Classrooms" (Judit N. Moschkovich); (2) "Latinos, Income, and Mathematics Achievement: Beating the Odds" (Luis Ortiz-Franco); (3) "Isn't English a Trip?" (Jose Franco); (4) "Spanish-English Language Issues in the Mathematics Classroom" (Pilar Ron); (5) "Adapting Mathematics Instruction for English-Language Learners: The Language-Concept Connection" (Leslie Garrison and Jill Kerper Mora); (6) "The Mathematics-Bilingual Education Connection: Two Lessons" (Norma G. Hernandez); (7) "Mathematizing Children's Stories, Helping Children Solve Word Problems, and Supporting Parental Involvement" (Ana Maria Lo Cicero, Karen C. Fuson, Martha Allexsaht-Snider); (8) "Challenging Conventional Wisdom: A Case Study" (Lena Licon Khisty); (9) "Teachers and Students' Attitudes toward the Use of Manipulatives in Two Predominantly Latino School Districts" (Maria L. Bustamante and Betty Travis); (10) "Portafolio de Matematica: Using Mathematics Portfolios with Latino Students" (Leslie Garrison); (11) "Taking on the Challenge of Mathematics for All" (Richard G. Doty, Susan Mercer, and Marjorie A. Henningsen); (12) "Staff Development to Foster Latino Students' Success in Mathematics: Insights from Constructivism" (Gary Ivory, Dolores R. Chaparro, and Stanley Ball); (13) "TexPREP and Proyecto Access: Making Mathematics Work for Minorities" (Julio Guillen and Manuel P. Berriozabal); (14) "The Minority Mathematics and Science Education Cooperative (MMSEC) Success Story" (Olga M. Ramirez and John E. Bernard); (15) "A Model of Tutoring that Helps Students Gain Access to Mathematical Competence" (Yolanda De La Cruz); and (16) "There's More to Mathematics Than Choosing the Letter C: The Limitations of Test-Driven Intervention" (Milagros M. Seda and Carmen M. Seda). (ASK)