bluuebunny/crossref_metadata_2025 huggingface dataset:
Ben's Understanding of One-Half
Authors: Watanabe Tad
Published: December 2020

Young children are introduced to simple fractions, such as one-half, as early as kindergarten, even though a formal introduction of fractions in most curricula does not begin until third or fourth grade.
Links to Literature: Huge Trees, Small Drawings: Ideas of Relative Sizes
Authors: Burton Gail
Published: December 2020

Two men walked into the rain forest. Moments before, the forest had been alive with the sounds of squawking birds and howling monkeys. Now all was quiet as the creatures watched the two men and wondered why they had come….
Math by the Month
Authors: Penry Lynda
Published: December 2020

These activities are designed to speak directly to students, giving them open-ended questions to engage their intellect through interests. Students may work on the activities individually, in pairs, or in small groups. No solutions are given for the activities so that students will look to themselves as the mathematical authority, thereby developing the confidence and critical-thinking skills necessary to validate their work.
Using Preservice Teachers’ Mathematics Autobiographies to Promote Learning
Authors: Shaw Jean M. , Chessin Debby A.
Published: December 2020

In preparing preservice teachers for classroom work, some of our goals include getting to know our students hotter and helping them to build confidence in their ability to learn mathematics and communicate it effectively to others.
Math by the Month: Getting Acquainted
Authors: Lewis Cathie , Lewis Tom
Published: December 2020

These activities are designed to appeal directly students, giving them open-ended questions to engage their intellect through interests. Students may work on the activities individually, in pairs, or in small groups.
Investigations: A Tale of Two Stories
Authors: Giancola Heather L. , Maxson Sylvia P. , Usnick Virginia
Published: December 2020

The “Investigations” department recognizes the importance of children's exploring hands-on and minds-on mathematics and, therefore, presents teachers with open-ended explorations to enhance mathematical instruction.
Early Childhood Corner: Encouraging Young Children to Solve Problems Independently
Authors: Myren Christina L.
Published: December 2020

Recently when two kindergarten children shared the same birthday, the teacher posed this mathematical problem: “If I made a cake for Matthew and another for Madeline, how many candles would I need?” After a few moments of struggling with this problem, Tina's face bright-ened as he told her teacher, “I'll just ask my mom. She'll know the answer.”
Where All are Winners: A Mathematics Olympics for Parents, Students, and Teachers
Authors: Koes Mary T. , Saab Joy Faini
Published: December 2020

Welcoming parents to the school environment to participate in a fun-filled mathe-matics-olympics learning activity promotes positive attitudes toward the school. Such participation instills a sense of pride in the educational achievements of the school, which translates into caring that each child is successful. Programs that involve parents from the planning through the implementation stage also foster a strong sense of mutual trust between homes and schools.
Multicultural Mathematics and Alternative Algorithms
Authors: Philipp Randolph A.
Published: December 2020

Up until recently I wasn't even aware that other people in the world did things [arithmetic algorithms] differently. I thought God sent these. That's the way of the world. The first day you [to another teacher] were talking about some way you did things differently in Ireland. It never occurred to me. I thought there was a world standard.
Investigating Flags: A Multicultural Approach
Authors: Dolinko Linda
Published: December 2020

Hispanic heritage month was appraoching. I wanted to come up with a new and exciting activity for my fifth-grade class. An article in the newspaper disscussing the impending statehood vote in Puerto Rico grabbed my attention.
Tech Time: Gender, Ninja Turtles, and Pizza: Using a Classroom Database for Problem Solving
Authors: Seidel Judith Day
Published: December 2020

Aglance at newspaper and magazine headlines reveals how data and statistics shape our views of political, economic, and health-related issues. Massive amounts of manipulate data are also available on the Internet or on CD-ROMs. As the amount of accessible information grows, the ability to organize, synthesize, and analyze data can become as important as the information itself.
May I Take Your Order?
Authors: Kulas Linda Lingenfelter
Published: December 2020

Mom third graders have enjoyed an occasional foray to a fast-food establishment or, if they were lucky, to a more formal restaurant. I decided to build on this experience and to extend the mathematics learning in my classroom with a unit called “restaurant mathematics.”
In My Opinion: Preparing Students to Enter the Gate
Authors: Chappell Michaele F.
Published: December 2020

Algebraic thinking in elementary school?” Individuals pondering this idea might immediately picture a mathematics class of young boys and girls whose eyes are filled with tears of frustration from trying to understand expressions like p(q − 5) or x + 5 = 14. Only having recently learned their ABCs and 1-2-3s, the youngsters must struggle to perform some operations and manipulations on the alphabets and numerals. Sounds outlandish?
Investigations: Becoming Very-Able with Variables
Authors: Speer William R. , Hayes David T. , Brahier Daniel J.
Published: December 2020

The “Investigations” department recognizes the importance of children's exploring hands-on and minds-on mathematics and, therefore, presents teachers with open-ended explorations to enhance mathematical instruction. These meaningful tasks are designed to evolve as they are conducted.
Invented Strategies Can Develop Meaningful Mathematical Procedures
Authors: Carroll William M. , Porter Denise
Published: December 2020

Over the past decade, a growitig consensus among educators favors a shift in mathematics instruction from a curriculum in which children learn and practice the standard school algorithms to one in which reasoning, problem solving, and conceptual understanding play a major role.
Investigations
Authors: Hopkins Martha H. , Brahier Daniel J. , Speer William
Published: December 2020

The “Investigations” department recognizes the importance of children's exploring hands-on and minds-on mathematics and, therefore, presents teachers with open-ended explorations to enhance mathematical instruction. These meaningful tasks are designed to evolve as they are conducted. They invoke problem solving and reasoning, require communication skills, and encourage identification of connections among various mathematical concepts and principles. To ensure usability, the ideas presented in this column have been tested in various classroom settings.
A Teacher's Journal: Ryan's Primes
Authors: Juraschek Bill , Evans Amy S.
Published: December 2020

Why is 1 not a prime number?” This is not a question that is on the minds of most third graders, but Ryan was not your average third grader. Throughout the school year, he had impressed his teacher, Mrs. Evans, with his understanding of the mathematics they studied.
TCM Is Your Journal: Help Make It Better
Authors: Huinker DeAnn
Published: December 2020

In its fourth year of publication, Teaching Children Mathematics (TCM) serves as a forum for discourse on mathematics teaching and learning in prekindergarten through sixth grade.
All About Us: Connecting Statistics with Real Life
Authors: Botula Mary Jean , Ford Margaret I.
Published: December 2020

What are the kids like in Britain? Are they like us?” These questions emerged from our students' enthusiasm for a pen-pal con-Hnection they had established with children in Britain. Elementary students are naturally curious about children that live in other countries, yet many of them have had little or no contact with anyone outside their own neighborhood.
Math by the Month: Calculating the Culture of the Baltic States
Authors: Simonsen Linda M.
Published: December 2020

The Math by the Month activities are designed to appeal directly to students. Students may work on the activities individually, in pairs, or in small groups. No solutions are suggested or provided for activities so that students will look for the mathematical authority within themselves, thereby developing the confidence and critical-thinking skills necessary to validate their work.
Reviewing and Viewing
Authors: Whitin David J.
Published: December 2020

Prices on software, books, and materials are subject to change. Consult the suppliers for the current prices. The comments reflect the reviewers' opinions and do not imply endorsement by the National Council of Teachers of Mathematics.
Young Children Deal with Data
Authors: Taylor Judith V.
Published: December 2020

Walk into a second-grade classroom in my school, and you will likely be greeted with a question: “Would you rather read fiction or nonfiction?” “Which football team do you think will score the most points this weekend?” “How far away from the school do you live?”
“What Do You Mean, ‘It's Impossible’?”
Authors: Ploger Don , Fritzer Penelope , Klingler Lee
Published: December 2020

Young children are fascinated by the concept of impossible, and that interest can lead to an extended exploration in mathematical reasoning. This article describes a set of class-room-tested activities that help children develop convincing arguments by building on their intuitive ideas about what is impossible.
What Did You Say You Do for a Living?
Authors: Manouchehri Azita
Published: December 2020

The Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) recommends that greater attention be devoted to increasing students’ awareness of real-life applications of mathematics at all levels of education.
Problem Solvers: Decoration Delight
Authors: Sakshaug Lynae
Published: December 2020

The goal of the “Problem Solvers” department is to foster improved communication among teachers by posing one problem each month for K-6 teachers to try with their students. Every teacher can become an author: pose the problem, reflect on students’ work, analyze the classroom dialogue, and submit your resulting insights to this department. Remember that even student misconceptions are interesting.
Look Who's Talking: Discourse in a Fourth-Grade Class
Authors: Steele Diana F.
Published: December 2020

In recent years John Travolta and Kirstie Alley have starred in several movies titled Look Who's Talking. In these movies, the person who needs to be talking is often not talking; therefore, important ideas and information are not being heard. “Looking at who's talking” is particularly important when teaching.
What All the Fuss about Mathematics Education?
Authors: Peressini Dominic D.
Published: December 2020

Recent reform recommendations for education have become more inclusive as they call for parents, families, and the community at large to become involved in efforts to improve schools (e.g., National Parent-Teacher Association [1994]; U. S. Department of Education [U. S. DOE] [1994]).
Adventures in Statistics
Authors: Scavo Thomas R. , Petraroja Byron
Published: December 2020

We had just returned from the science fair, and the scientific method was fresh in the students’ minds. In this context we introduced the following unit on data analysis, which we hoped would not only satisfy the district's elementary-statistics requirement but also involve the students in a long-term mathematics project in a meaningful and relevant way.
Tech Time's News from the Net: Annenberg/CPB Projects: Learner Online
Authors: Lazerick Beth
Published: December 2020

The Annenberg/CPB Project and the Annenberg/CPB Math and Science Project have joined forces with a Web site to disseminate their work and to provide resources about many different issues in education.
Reviewing and Viewing
Authors: Whitin David J.
Published: December 2020

Prices on software, books, and materials are subject to change. Consult the suppliers for the current prices. The comments reflect the reviewers’ opinions and do not imply endorsement by the National Council of Teachers of Mathematics.
Links to Literature: Using Literature to Investigate Transformations
Authors: Harris Jacqueline
Published: December 2020

I am always looking for children's literature to make and enrich connections to the elementary school curriculum. In particular, books and stories that use mathematical problem solving not only engage children in the narrative but also give them opportunities to see how mathematics is used in everyday life. A Cloak for the Dreamer by Aileen Friedman (1994) investigates relationships among shapes and, at the same time, tells a wonderful story.
Math by the Month: Mathematics in Our Environment
Authors: Olson Melfried , Olson Judith
Published: December 2020

These activities are designed to appeal directly to students. Students may work individually, in pairs, or in small groups. No solutions are suggested or provided for activities so that students will look to themselves as the mathematical authorities, thereby developing the confidence to validate their work.
Feisty Females: Using Children's Literature with Strong Female Characters
Authors: Karp Karen , Allen Candy , Allen Linda G. , Brown Elizabeth Todd
Published: December 2020

Girls enter school more mathematics ready than boys. By the time they graduate from high school, however, females have been outdistanced by males in the number of higher-level mathematics courses taken and in the results of crucial tests, such as the mathematics portion of the Scholastic Achievement Test (American Association of University Women 1991). They are also much less likely to pursue majors and careers that relate to mathematics.
A Mathematics Lesson the Mayan Civilization
Authors: Lara-Alecio Rafael , Irby Beverly J. , Morales-Aldana Leonel
Published: December 2020

Mayan mathematics, a significant part of the great civilization of the ancient people, is of true interest to all who admire the monuments, architecture, and art of the great Mayan cities.
Math by the Month
Authors: Trowbridge Russ , Guengerich Susan
Published: December 2020

The “Math by the Month” activities are designed to appeal directly to students, who may work on the activities individually, in pairs, or in small groups. No solutions are given so that students will look for the mathematical authority within themselves, thereby developing the confidence to validate their work.
Problem Solvers
Authors: Sakshaug Lynae
Published: December 2020

The goal of the “Problem Solvers” department is to foster improved communication among teachers by posing one problem each month for K-6 teachers to try with their students. Every teacher can become an author: pose the problem, reflect on your students’ work, analyze the classroom dialogue, and submit the resulting insights to this department. Remember that even students’ misconceptions are interesting.
National Council of Teachers of Mathematics: Changes in Your Classroom: From the Past to the Present to the Future
Authors: Burrill Gail
Published: December 2020

Look carefully at the illustration in figure 1 (Kindt and Abels 1998). How much do all three chickens weigh? How much does each chicken weigh?
Links to Literature: Saturday Sancocho: A Tasty Introduction to Barter and Division
Authors: Wickett Maryann S.
Published: December 2020

El sancocho del sobado es el título de mi libro. ¿Qué es sancocho?” I asked my third graders. Even though many of my students come from Mexico, my question met with blank stares.
Solving Geometric Problems by Using Unit Blocks
Authors: Andrews Angela Giglio
Published: December 2020

Sarah, a normally cheerful child, began to cry as she attempted to put together a new puzzle. “This puzzle doesn't work!” she wailed. “There are too many pieces. They won't all fit back in!” Four-year-old Sarah, who did not conserve number, did not realize that the quantity of pieces stays the same regardless of changes in their position or arrangement. To her, the puzzle had somehow “grown” more pieces!
A Teacher's Journal: The Restless Rectangle and the Transforming Trapezoid
Authors: LaSaracina Barbara A. , White Sharon K.
Published: December 2020

When we challenge students to call on previously learned skills to attain concepts independently, the results can be quite surprising. When asked to develop a method to find the area of a trapezoid on the basis of their prior work with finding the area of rectangles, a group of students came up with the following results.
Young Children's Developing Understanding of Geometric Shapes
Authors: Hannibal Mary Anne
Published: December 2020

How can we improve geometry instruction at the preschool and primary levels? To answer that question, I conducted research to analyze young children's understanding of the geometric concepts of triangle and rectangle and to determine patterns in the development of this understanding from ages 3 through 6. The research suggests that early childhood educators need to rethink the way that basic shapes are introduced to young children. Since a basic understanding of shapes is essential to a future study of geometry, teachers need to focus on how best to help children develop that initial understanding of shape categories. After a brief explanation of the research, specific ways to present developmentally appropriate activities designed to enhance children's understanding of basic shapes are discussed.
Problem Solvers: Counting Cubes
Authors: Olson Melfried
Published: December 2020

The goal of the “Problem Solvers” department is to foster improved communication among teachers by posing one problem each month for K–6 teachers to try with their students. Every teacher can become an author: pose the problem, reflect on your students' work, analyze the classroom dialogue, and submit the resulting insights to this department. Remember that even student misconceptions are interesting.
Check Out These Checkbooks: Real-Life Banking for the Classroom
Authors: Tuch Abby
Published: December 2020

The program that I use to reinforce arithmetic, language arts, and social studies skills is also the primary behavior-management program in my third-grade class. It could easily be adapted for use in secondthrough sixth-grade classes.
Math By the Month: May 1999
Authors: Martin Hope
Published: December 2020

These activities are designed to appeal directly to students. Students may work on the activities individually or in small groups. No solutions are suggested so that students will look to themselves as the mathematical authority, thereby developing the confidence to validate their work.
Math-o'-Lanterns
Authors: Angerame Shirlee S.
Published: December 2020

Every year during October, Halloween becomes a main topic of students' conversations. Using this theme, I incorporate mathematics as an important part of their holiday. I ask my fifth-grade students to use their imaginations and pretend that they are in Mathemagic Land. Here, pumpkins are carved into “math-o'-lanterns.” A math-o'-lantern is a jack-o'-lantern in which each carved part is in the shape of a polygon. Math-o'-lanterns are
Using Mathematics to Build an Understanding of the United States
Authors: Clay Ellen L.
Published: December 2020

Mathematics is frequently separated from the rest of the educational experience to such an extent that even in the literature of whole language, with its comprehensive belief systems about integrative study, mathematics is often left out (Armbruster 1992). As a mathematician, I naturally see mathematics abound in the world around us. Therefore, after hearing comments from elementary school teachers that children read and write in every class but do mathematics only in mathematics class, I decided to design a social studies unit that would incorporate the use of mathematics. The resulting unit emphasizes the study of the United States as a whole rather than as fifty individual states.
Math by the Month: Pattern-Block Explorations
Authors: Rigdon Deanna , Raleigh Jolyn , Goodman Shari
Published: December 2020

The “Math by the Month” activities are designed to appeal directly to students. Students may work on the activities individually or in small groups. No solutions are suggested so that students will look to themselves as the mathematical authority, thereby developing the confidence to validate their work. This month's activities focus on using pattern blocks to solve problems related to measurement, geometry, fractions, logical reasoning, and algebraic thinking.
News from the Net: PlaneMath
Authors: Irvine Sarah
Published: December 2020

Fly off and surf at www.planemath.com. Students have the opportunity to make connections between mathematics and aeronautics. InfoUse, a firm that specializes in the development of health, disability, and rehabilitation information using computer technology, produced and maintains this site in cooperation with NASA. The site presents an Internet-based curriculum on mathematics and aeronautics for children with physical disabilities.
A Teacher's Journal: Pantry Math
Authors: Schnur-Laughlin Julia
Published: December 2020

Almost anyone who has been teaching for a few years has experienced a spontaneous “teachable moment” prompted by something that was said by a student. I was fortunate to have had such an experience last December when our kindergartners were involved in a “Twelve Days of Christmas” unit. As the holidays approach this year, I look forward to repeating this unit, which increased my students' awareness of basic number sense and patterning. Because the unit had a writing and drawing component, it also incorporated communication of the mathematical processes involved.
Mathematics Workshop: Mathematics Class Becomes Learner Centered
Authors: Heuser Daniel
Published: December 2020

The preservice teacher watching my firstand second-grade students during a writing workshop was astounded. “Is this a gifted class? I've never seen kids so involved. You must not have any discipline problems.” Actually, this group of children had the same learning and social skills of most classes. The children were deeply involved in their work because the class was not a traditional writing class but a writing workshop.
The Wonderful World of Digital Sums
Authors: Bonsangue Martin , Gannon Gerald , Watson Karen
Published: December 2020

A lesson using digital sums that allows teachers to assess students' understanding of reasoning, arithmetic, and geometry.
Math by the Month: Read Any Good Math Lately?
Authors: Goodman Shari , Rigdon Deanna , Raleigh Jolyn
Published: December 2020

The “Math by the Month” activities are designed to appeal to students, who may work individually or in groups. No solutions are suggested so that students will look to themselves as the mathematical authority to develop confidence in their work.
Designing Questions to Encourage Children's Mathematical Thinking
Authors: Schielack Jane F. , Chancellor Dinah , Childs Kimberly M.
Published: December 2020

Suggestions for an elementary school activity and questions to promote five types of mathematical thinking: modeling, logical analysis, inference, optimization, and abstraction.
Milk-Jug Mosaic: Creating a Mathematical Dove of Peace
Authors: Potts Kathleen
Published: December 2020

Children use skills such as estimation, measurement, and computation of circumference and area in developing and building a mosaic made of milk jugs.
Quality Literature as a Springboard to Problem Solving
Authors: Ducolon Colin K.
Published: December 2020

High-quality children's literature that is captivating for both students and teachers can be used to develop process skills and essential knowledge in children. The provocative power of a “good read” is limitless. Listening to or reading a good book allows all of us, young and old, to think, reason, solve problems, compare and contrast, critique, and communicate in both old and new ways. The educational potential of a well-executed children's story can change how teachers plan their curricula.
Problem Solvers: Which Graph Is Which?
Authors: Sakshaug Lynae
Published: December 2020

The goal of the “Problem Solvers” department is to foster improved communication among teachers by posing one problem each month for K–6 teachers to try with their students. Every teacher can become an author: pose the problem, reflect on your students' work, analyze the classroom dialogue, and submit the resulting insights to this department. Remember that even student misconceptions are interesting.
Early Childhood Teachers Discuss the Standards
Authors: Kline Kate
Published: December 2020

Childhood isn't a race; it's a journey. We need to think about that and give children adequate time to develop as thinkers, as knowers, as mathematicians.
Selecting Books in Spanish to Teach Mathematics
Authors: Jacobs Victoria R. , Bennett Tom R. , Bullock Cathy
Published: December 2020

Explains the use of books in Spanish to teach mathematics, presents examples and book-selection guidelines, and describes a searchable database of appropriate literature.
An Educator's Guide to Answering Parents' Questions on Mathematics
Authors: Pagni David L.
Published: December 2020

Mathematics education in the United States has never been more exciting. New content and pedagogy, enhanced and spurred by technological advances, have grabbed the public's attention. NCTM has led the way to inform and rally professionals to address this renaissance in how we approach the learning of mathematics. Educators are tackling the jobs of dealing with new curricula and keeping up with professional development to align their school district's goals with the NCTM's Standards. Educators are also seeking ways to keep parents more informed and involved. One such effort was to develop a guide to be used by teachers and principals to provide unified responses to the questions most commonly asked by parents.
A Teacher's Journal: Patterns for Giving Change and Using Mental Mathematics
Authors: Perry Betty K.
Published: December 2020

For some of my third-grade students, giving change was difficult because the standard procedure of counting forward is labor intensive. By the time these students counted forward to the dollar amount, they forgot the change that was due. They repeated the process but in doing so, forgot the original amount; the cycle continued, leaving these students feeling exasperated and frustrated.
A Teacher's Journal: Picture This: Second Graders See Symmetry and Reflection
Authors: Johnson Iris , Bomholt Sarah Katherine
Published: December 2020

At Hollingsworth East Elementary School in Eaton, Ohio, students in grades K–2 get excited about walking through a certain hallway on their way to the playground for recess. As I approached this place of attraction, I smiled because I, too, had to stop and stare! On the wall was a graphic display showing two pictures of each child from the classroom across the hall. An observer might well ask, “Could there possibly be so many twins in one classroom?” For the second graders, however, the question is, “Which is the symmetrical you?” I was so intrigued that I asked the teacher, Sarah Bomholt, to tell me more about these pictures.
Multiply with MI Using Multiple Intelligences to Master Multiplication
Authors: Willis Jody Kenny , Johnson Aostre N.
Published: December 2020

Katie sings the multiplication facts quietly to herself. Sam tries to solve problems by tapping his pencil in rhythmic patterns. José draws pictures from his teacher's tile-array models. Alima sorts her crayons into groups to help herself find the answer. Lin checks his solutions with his neighbor. Maria uses logic to extend her knowledge of simple facts to harder ones. These children naturally express their intelligence strengths as they attempt to master their multiplication facts. Their teacher knows that children learn in different ways and seeks to consciously translate these differences into learning methods that will be meaningful.
The Intersection of Two Unlikely Worlds: Ratios and Drums
Authors: Stevens Anthony C. , Sharp Janet M. , Nelson Becky
Published: December 2020

When mathematics lessons are linked with personal experiences, typically, the result is that the student gains a stronger understanding of the content than if the lessons are isolated and unconnected. This premise was recently supported in a local fifth-grade classroom. The students learned to play three mathematically disparate rhythms on conga drums as an introduction to an exploration of ratio. Ratios connect naturally with African and Afro-Cuban drumming because the drummer's combination of many rhythms, each with a pattern repetition of different length results in a polyrhythmic song. The pattern repetitions are comprised of a given quantity of one type of beat mixed with a specified quantity of another type of beat, or a ratio of one beat to the other one. Although we completed this lesson with a group of children of whom half were African American, we believe this lesson can be powerful and meaningful for children of all ethnic backgrounds.
Problem Solvers: Puzzling Prices
Authors: Olson Melfried , Olson Judith
Published: December 2020

The goal of the “Problem Solvers” department is to foster improved communication among teachers by presenting one problem each month for teachers of grades K–6 to try with their students. Pose the problem to your students, reflect on their work, analyze the classroom dialogue, and share your analyses with others by submitting the resulting insights to this department. Every teacher can help us all better understand children's capabilities and thinking about mathematics with their contributions to the journal. Remember that even student misconceptions are interesting and provide insights into the teaching, learning, and assessment processes.
Problem Solvers: Responses to the No Pegs Allowed Problem
Authors: Olsen Melfried
Published: December 2020

The problem in the October 2000 “Problem Solvers”
Principles and Standards (2001): October 2001
Authors: Reys Barbara J. , Arbaugh Fran
Published: December 2020

Since the publication of NCTM's Principles and Standards for School Mathematics in April 2000, considerable discussion has taken place about “key messages” of the document. The breadth of the content of Principles and Standards may hamper attempts to identify messages about particular topics. In addition, many of the fundamental messages are not easily distilled into short phrases. In fact, when such messages are too succinctly articulated, the danger of oversimplification and misunderstanding arises. This misapprehension can be seen in a question that often emerges in discussions about elementary school mathematics and Principles and Standards. That is, what does Principles and Standards say about calculator use in elementary school?
Geo-Dolls: Traveling in a Mathematical World
Authors: Karp Karen S. , Brown E. Todd
Published: December 2020

What do putting a jigsaw puzzle together and structuring a curriculum have in common? James Beane (1995) drew a connection between the two endeavors when he observed that as we begin to put a puzzle together, we often take a single piece and try to identify the portion of the puzzle to which it belongs. We place it in a spot to wait for adjacent pieces to be found. Then we connect sections and clusters of pieces, giving them directionality and location as we refer to the picture on the puzzle's box for guidance. “None of the pieces means anything taken alone; only when the pieces are put together do they mean something” (Beane 1995, p. 1). Putting a puzzle together without a picture is seen as a particularly challenging task and, at times, a frustrating experience.
Principles and Standards: What is Algebra in Elementary School
Authors: Bay-Williams Jennifer M.
Published: December 2020

Patterns have long been part of early mathematics experiences. The K–4 Patterns and Relationships Standard in Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) was replaced in Principles and Standards for School Mathematics (NCTM 2000) with a K–12 Algebra Standard. This Standard encompasses patterns, functions, and some topics that are beyond what traditionally was considered to be algebra. However, the word algebra, often associated with content covered in a traditional middle school or high school course, can evoke feelings of anxiety and raise questions of appropriateness when discussed in relation to elementary school children. What is algebra in elementary school if it is more than identifying and extending patterns in the early grades yet is not the abstract content of an algebra course?
A Teacher's Journal: Problem Solving and At-Risk Students: Making “Mathematics for All” a Classroom Reality
Authors: Robert Margot Fulton
Published: December 2020

For two years, I taught in an affluent suburban school in one state where the children had the advantage of family and school experiences that encouraged their questions, ideas, and experimentation. Their experiences with books, travel, museums, dinner conversations, and school projects gave them confidence in themselves as thinkers. The school itself was committed to authentic project-based learning. We encouraged students to ask questions and think critically and to trust themselves and their classmates as inventors and problem solvers. After teaching a third- and fourth-grade class in this environment, I moved to a rural community in another state where 78 percent of the students live below the federal poverty level and where families struggle to meet the basic needs of their children. I came to this new job confident in my ability to structure learning environments, develop child-centered curricula, and meet the needs of diverse learners. I was in for a rude awakening. This group of students, now fifth graders, came to school with more anger and hunger than they did skills or enthusiasm. On more than one disheartening day, I found myself calling my brother in desperation: “I don't understand. I know I'm a good teacher, but nothing I try is working with these kids.”
Powerful Software to Enhance the Elementary School Mathematics Program
Authors: Kerrigan John
Published: December 2020

Over the last fifteen years, using software evaluations from the Arithmetic Teacher and Teaching Children Mathematics as one of our guides, my students and I have reviewed many mathematics software programs. Our quest was to find engaging and easy-to-use software for integration into the elementary school mathematics curriculum. We discovered good, fair, and poor mathematics software on today's market. In in-service workshops and preservice methods classes, we demonstrated what we found to be good software to current and future teachers and were usually surprised to find that most of them had never seen or heard of the software, even though many of the good programs have been around for a few years. The fact that most practicing teachers have never been exposed to this powerful mathematics software motivated me to write this article.
Principles and Standards (2002): February 2002
Authors: Rich Wendy , Joyner Jeane
Published: December 2020

Few would argue that computers and Internet technology can positively influence teaching and learning. Unfortunately, teachers face many hurdles when integrating technology with a high-quality mathematics instructional program. Several resources are available through NCTM that support Principles and Standards for School Mathematics (NCTM 2000) and assist teachers with this dilemma.
News from the Net: Cool Mathematics for Kids
Authors: Agosto Melinda
Published: December 2020

The site called Coolmath 4 Kids at www.coolmath.com/ is “an amusement park of math” for parents, teachers, and children. The site has multiple sections for all ages, including games, brain benders, lessons, jigsaw puzzles, geometry activities, online calculators, fractals, a special section for ages 3–5, and links to a variety of sites for children.
Problem Solvers: Marble Mayhem
Authors: Mann Robert
Published: December 2020

The goal of the “Problem Solvers” department is to foster improved communication among teachers by posing one problem each month for K–6 teachers to try with their students. Every teacher can become an author: pose the problem, reflect on your students' work, analyze the classroom dialogue, and submit the resulting insights to this department. Every teacher can help us all better understand children's capabilities and thinking about mathematics with their contributions to the journal.
Links to Literature: First Graders, Flies, and a Frenchman's Fascination: Introducing the Cartesian Coordinate System
Authors: Dobler Carolyn Pillers , Klein John M.
Published: December 2020

The Fly on the Ceiling: A Math Myth (Glass 1998) imaginatively recreates the story of René Descartes and the Cartesian coordinate system. Descartes, a French philosopher and mathematician, was unfortunately also a messy and disorganized person. One day, unable to find any food in his room, he ventures to the bakery to buy a loaf of bread. On his way home, deep in philosophical thought, he falls into the Seine River, catching a cold. At home in bed, he gazes at the only clean spot in his room—the ceiling. There, he observes a fly moving from one place to another. How can he track the fly's movement? Does the fly ever land on the same place twice? Using charcoal from the fireplace, René makes a grid on the ceiling, labeling each line with numbers. He can now track the fly's movement using ordered coordinates for each point. His grid (the Cartesian coordinate system) is the solution to his disorganization.
Students Realize Mathematics Is Everywhere!
Authors: Berry Stephanie M.
Published: December 2020

When I announced to my fifth-grade students that the books they created would be on display at the local Barnes & Noble bookstore, their faces glowed and their mouths opened wide. I could see that the students felt a sense of accomplishment and pride in their work; I even heard a few cheers! Only a few months earlier, many children would not have believed me when I said that mathematics is everywhere. Children do not usually recognize the significance of mathematics in their daily lives. Instead of letting children continue to see mathematics as an unnecessary chore and to be afraid of it, I decided to create a project that would encourage them to explore mathematical concepts and skills and, at the same time, realize how useful they really are.
Starting off the School Year with Opportunities for All: Supporting First Graders' Development of Number Sense
Authors: Whitenack Joy W. , Knipping Nancy , Loesing Jenine , Kim Ok-Kyeong , Beetsma Abby
Published: December 2020

One of the most pressing issues for classroom teachers is how to facilitate learning opportunities for all their students, especially at the beginning of each school year. Teachers are faced with new children, who have unique backgrounds and who bring different understandings to the classroom. Ms. Lee, a first-grade teacher, faced this challenge head on as she began implementing material on number sense in the first month of the school year with her twenty-one students.
Meaningful Mathematical Representations and Early Algebraic Reasoning
Authors: Lubinski Cheryl A. , Otto Albert D.
Published: December 2020

Both oral and written communication play an important role in teaching and learning mathematics (NCTM 2000). Students and teachers exchange ideas about their understanding of, and thinking about, mathematics by communicating with one another. An important part of this communication process is the choice of symbols used to represent that thinking (Hiebert 1989). The process of representing mathematical ideas using symbols and expressions should begin at the earliest stages of mathematics instruction and appear in the context of ideas to which young students can relate (Carey 1992).
Research, Reflection, Practice: Why Can't I See the Tree? A Study of Perspective
Authors: Kelly Gwendolyn A.
Published: December 2020

Developing an understanding of threedimensional perspective is an important life skill; we all make judgments continuously about the relationships among three-dimensional objects. We use these relationships to navigate, understand, and follow directions, construct things, and make interpretations and decisions about arranging objects in our homes or offices.
Helping Students Become Mathematically Powerful
Authors: Ittigson Robin
Published: December 2020

Principles and Standards for School Mathematics asks us to imagine a classroom scenario in which all students become engaged in high-quality mathematics instruction (NCTM 2000, p. 13). Students approach problems from different perspectives and represent their thinking and solutions in many different ways. The students involved in this activity are flexible and resourceful problem solvers who communicate ideas and results effectively, both orally and in writing. These students are mathematically powerful because they possess a range of viable approaches, the arguments to support their thinking, and the ability to tell others about their work.
News from the Net: Ole Miss Problems of the Week
Authors: Hodge Tim
Published: December 2020

The University of Mississippi Mathematics Education Program sponsors weekly mathematics contests online at www.olemiss.edu/mathed/contest/contests.htm. David Rock and Doug Brumbaugh started the “Problems of the Week” contests in 1996 at the University of Central Florida. Over the years, the variety of problem classifications has increased. Since the fall of 2000, all five weekly problems have originated at the University of Mississippi, where Rock is a member of the faculty. These contests are viewed each week by thousands of students around the world. Visitors to the site come from more than 1500 cities in 75 different countries, as well as all 50 states in the United States. Each problem receives approximately 800 to 1000 e-mailed solutions per week.
The Shopping Spree
Authors: Hartweg Kim
Published: December 2020

The goal of the “Problem Solvers” department is to foster improved communication among teachers by posing one problem each month for K–6 teachers to try with their students. Every teacher can become an author: pose the problem, reflect on your students' work, analyze the classroom dialogue, and submit the resulting insights to this department. Every teacher can help us all better understand children's capabilities and thinking about mathematics with their contributions to the journal. Remember that even student misconceptions are valuable.
From NCTM's Archives: Meaning and Skill: Maintaining the Balance
Authors: Brownell William A.
Published: December 2020

Computational understanding and proficiency are in many ways the quintessential goals of elementary school mathematics. Although the terminology is somewhat new, the idea of computational fluency has deep historical roots. We searched the archives of Teaching Children Mathematics and its predecessor, The Arithmetic Teacher, for an article that would give readers a sense of the timelessness of some of the issues surrounding the work of teaching for computational fluency. The following piece by William Brownell, published very early in the history of the AT, provides a wonderful balance between historical perspective and contemporary relevance.
Investigations: Weighing the Options
Authors: Merz Alice
Published: December 2020

This department recognizes the importance of children's exploring hands-on and minds-on mathematics and presents teachers with open-ended explorations to enhance mathematics instruction. These tasks invoke problem solving and reasoning, require communication skills, and connect various mathematical concepts and principles.
March Mathness
Authors: Mann Robert
Published: December 2020

The goal of the “Problem Solvers” department is to foster improved communication among teachers by posing one problem each month for K–6 teachers to try with their students. Every teacher can become an author: pose the problem, reflect on your students' work, analyze the classroom dialogue, and submit the resulting insights to this department. Every teacher can help us all better understand children's capabilities and thinking about mathematics with their contributions to the journal. Remember that even student misconceptions provide valuable information.
News from the Net: Mrs. Glosser's Math Goodies
Authors: Clanton Barbara L.
Published: December 2020

The National Council of Teachers of Mathematics (NCTM) lists the Learning Principle as one of its six principles for school mathematics. The Learning Principle suggests that students learn by actively building new knowledge from prior knowledge. In doing so, they will become autonomous learners. NCTM promotes a mathematics classroom environment in which students feel comfortable making mistakes that can lead to learning opportunities. Mrs. Glosser's Math Goodies, located at www.mathgoodies.com, can support teachers' implementation of these two recommendations and is a good resource for students in grades 4–9 as well as parents.
Making the NCTM Standards User Friendly for Child Care Teachers
Authors: Skipper Edith L. , Collins Edna Neal
Published: December 2020

Principles and Standards for School Mathematics (NCTM 2000) asserts that mathematics is an essential part of the early childhood curriculum. The Standards encourage early childhood educators to nurture children's intuitive understandings of mathematical concepts by taking advantage of learning opportunities that naturally occur during everyday activities. In the context of these meaningful activities, learning can be increased by giving children the formal language with which to describe their informal learning (Clements and Sarama 2000), and young children's natural enthusiasm for mathematics can be nourished (Copley 2000). In particular, understanding of the concepts of number, geometry, and pattern is identified as essential in children's early years. Teachers also are encouraged to emphasize the processes involved in learning and doing mathematics, including problem solving, reasoning, communicating, connecting, and representing.
Research, Reflection, Practice: Gender and Mathematics: An Issue for the Twenty-First Century
Authors: Becker Joanne Rossi
Published: December 2020

Is gender still a salient equity issue for today's mathematics classrooms? Although considerable progress in women's participation in mathematics has been achieved in the last twentyfive years, inequities still exist. For example, women represent less than fifteen percent of the employed scientists and engineers in computer science, mathematics, agricultural science, environmental science, chemistry, geology, physics and astronomy, economics, and engineering (NSF 1996). Females score an average of thirty points lower than males on the mathematics section of the SAT. Despite more than two decades of intervention, parity remains a vision for the future. This article discusses our role as teachers in giving girls an equitable foundation in mathematics in the elementary grades.
Research, Reflection, Practice: Collaborative Problem Solving in Mixed-Language Groups
Authors: Edwards Laurie D.
Published: December 2020

An important goal of mathematics teaching is to help all students, including students whose first language is not English, become effective problem solvers. Yet Englishlanguage learners face obstacles that may not apply to native English speakers because they must make sense of mathematical situations while interpreting a new language. The purpose of the research described in this article was to investigate mathematical problem solving involving both native English speakers and native Spanish speakers working in small, collaborative groups. The work of psychologist Lev Vygotsky provides a theoretical justification for having students solve problems in groups. A central tenet of Vygotsky's theory is that people first develop cognitive activity socially, through interaction with others, and later internalize it (Vygotsky 1978). Therefore, we wanted to investigate whether students who worked together to solve mathematical problems would later be more adept at solving similar problems on their own.
Designing Fraction-Counting Books
Authors: Stump Sheryl L.
Published: December 2020

Students design fraction-counting books to develop their understanding of fractional parts and to practice using the language of fractions.