bluuebunny/crossref_metadata_2025 huggingface dataset:
Early Childhood Corner: Seasonal Crafts: Discovering Mathematical Relationships and Solving Mathematical Problems
Authors: Schwartz Sydney L.
Published: December 2020

The goal of the math program is to enable children to use math through exploration, discovery and solving meaningful problems. (Bredekamp 1987, 71)
Investigations: Geoboard Patterns and Figures
Authors: Lamphere Patricia
Published: December 2020

The “Investigations” department is designed for teachers who wish to give students new insights into familiar topics in grades 3–6. It includes both directed and open-ended activities. A basic assumption is that the teacher will facilitate the Investigation to let students be actively involved in shaping their learning.
Promoting Calculator Use in Elementary Classrooms
Authors: Drosdeck Carola C.
Published: December 2020

“Paul is using a calculator,” cries one of my fourth-grade-mathematics students. “That's cheating.” This and other similar comments are often heard in my classroom at the beginning of the school year. Before students have had a chance to experience various activities that can spotlight a calculator's power, they often view its use as cheating, as taking an illegal shortcut, or as using an easy way out. Unfortunately, some of their parents share these views as well.
In My Opinion: Japanese Mathematics Education: What Makes It Work?
Authors: Reys Barbara J. , Reys Robert E.
Published: December 2020

Japan's stature as an economic and political power worldwide has caused growing interest in the country's culture and. more specifically, its system of educating its youth. International comparisons of mathematics achievement highlight Japanese students' unquestioned superiority in mathematical performance. Factors that contribute to the relatively high performance include the nature of Japanese schools, the professional stature of teachers, the homogeneity of the school population, the high parental expectations for the educational success of their children, the abundance of jukus (special cram schools), and heavy reliance on entrance and qualifying examinations.
Implementing the Professional Standards for Teaching Mathematics: Beyond the Classroom
Authors: Vacc Nancy Nesbitt , Ervin Criss , Travis Sue
Published: December 2020

To present a mathematical learning environment in which students are challenged by worthwhile activities that stimulate them to make mathematical connections, that promote communication about mathematics, and that offer opportunities for ongoing analysis of teaching and learning, try combining one first grade, one fifth grade, measurement activities, and gorillas.
Promoting Young Children's Mathematical Learning through a New Twist on Homework
Authors: Seo Kyoung-Hye , Bruk Sandra J.
Published: December 2020

How one public school has involved parents in helping three– to five–year–olds do homework that is based on the NCTM Standards.
Problem Solvers: Pattern-Block Quilts
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.
Links to Literature: Building Mathematical Connections with Village of Round and Square Houses
Authors: Kuhns Catherine L.
Published: December 2020

Can primary-grade children imagine life without video games, DVDs, soccer practice, juice boxes, or computers? The book Village of Round and Square Houses (Grifalconi 1986), told from a child's point of view, serves as a springboard for discussion about the joys of a simple life. The descriptive writing is informative and includes great examples of the use of imagery, similes, and descriptive words.
Math By the Month: Become an “Estimatician”
Authors: Larkin Kevin , Perez Kaethe , Webb Darcy
Published: December 2020

The “Math by the Month” activities are designed to engage students to think like mathematicians. The activities allow for students to work individually or in small groups, or they may be used as problems of the week. No solutions are suggested so that students will look to themselves for mathematical justification and authority, thereby developing confidence to validate their work.
The Missouri Elementary Mathematics Contest: Student Performance on Questions That Reflect NCTM Standards
Authors: Plymate Lynda M. , Ashley David I.
Published: December 2020

The Missouri Council of Teachers of Mathematics (MCTM) has conducted an annual elementary mathematics contest for students in grades 4, 5, and 6 since 1985. Twenty-five sites throughout Missouri host regional contests in which school-selected participants (three to five per grade level, depending on the number of students) compete in grade-specific tests that measure mathematical estimation and computation, conceptual understanding, and problem-solving ability. The top three winners from each test event and at each grade level are then invited to compete against the winners from other regional contests at a state finals competition.
Investigations: Junior Architects: Designing Your Dream Clubhouse Using Measurement and Geometry
Authors: Suh Jennifer M. , Moyer Patricia S. , Sterling Donna R.
Published: December 2020

This department features children's hands-on and minds-on explorations in mathematics and presents teachers with open-ended investigations to enhance mathematics instruction. These tasks invoke problem solving and reasoning, require communication skills, and connect various mathematical concepts and principles. The ideas presented here have been tested in classroom settings.
Muffin Mania
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.
Math by the Month: Broken Hearts
Authors: Larkin Kevin , Perez Kaethe , Webb Darcy
Published: December 2020

The “Math by the Month” activities are designed to engage students to think like mathematicians. The activities allow for students to work individually or in small groups, or they may be used as problems of the week. No solutions are suggested so that students will look to themselves for mathematical justification and authority, thereby developing confidence to validate their work. These activities use a “heartfelt” theme to support NCTM's Number and Operations and Geometry Standards. Students represent, compare, and use fractions in “kid friendly” situations. Students also use heart shapes to explore symmetry.
Early Childhood Corner: Mathematics Everywhere, Every Time
Authors: Clements Douglas H. , Sarama Julie
Published: December 2020

“I'm first today!” “Then I want to be second. You gotta be third, Joon.”
Triangular Bicycle Flags
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 interesting.
In My Opinion: Top Ten Ways to Strengthen Your School Mathematics Program
Authors: Reys Barbara , Lewis Cathie , Schad Brian , Contreras José , Kirschner Vicky , Watanabe Tad , White Dorothy
Published: December 2020

Welcome back to school! Take advantage of the renewed energy and commitment that accompany the beginning of the school year by developing a set of specific activities to help improve your school mathematics program. Design activities that focus on supporting the development of teachers' knowledge of teaching and learning mathematics. Plan activities that help parents contribute to the mathematics education of their children. Organize schoolwide activities to promote students' interest in studying mathematics. Here are a few suggestions that the TCM Editorial Panel has assembled to spark your thinking and planning.
The Thirteen Days of Halloween: Using Children's Literature to Differentiate Instruction in the Mathematics Classroom
Authors: Forbringer Linda L.
Published: December 2020

How children's literature can be used to provide meaningful mathematics instruction for children functioning at a variety of instructional levels in a single classroom. Teachers can use this information to select appropriate children's literature to use in their classroom to meet the needs of a diverse group of learners.
Supporting Teacher Learning: Making the Complexities of Teaching Visible for Prospective Teachers
Authors: Chval Kathryn B.
Published: December 2020

Most of the prospective teachers who enter my methods courses assume that teaching mathematics to elementary students will be easy. For example, Jenny wrote, “I thought, ‘I can teach math. How can it be so hard? It's elementary math!’ But I have been proven wrong.” Based on comments such as Jenny's, I realized the importance of giving prospective teachers opportunities to understand that effectively teaching mathematics to elementary students is complex and challenging. I recognized that field experience in my mathematics methods courses had to make the complexities of teaching more visible for prospective teachers. In other words, prospective teachers must study teaching practices. Such study would not only require viewing, analyzing, and discussing practices but also include the opportunity for prospective teachers to practice and analyze their own teaching.
Research, Reflection, and Practice: The Mathematics Pathway for All Children
Authors: Hill Denise
Published: December 2020

The results of the Third International Mathematics and Science Study (TIMSS) indicated that the mathematics performance of eighth-grade students in the United States declined notably when compared with the performance of fourth-grade students (United States Department of Education 1998). Student performance fell five positions from the seventh-ranked U.S. fourth graders to the twelfth-ranked U.S. eighth graders among the twenty-six countries that participated in the study. In response to the TIMSS results, many efforts have been made to reform school mathematics over the past decade, especially in grades 4 through 8.
Galleons, Magic Potions, and Quidditch: The Mathematics of Harry Potter
Authors: Barta Jim , L'Ai Linda
Published: December 2020

“All aboard the Hogwarts Express!” shout the students busily immersed in their studies. No, this is not a casting call for young actors and actresses living out their fantasies of starring in a new Harry Potter movie. Rather, the children are studying mathematics at the Edith Bowen Laboratory School in Logan, Utah. These fourth-grade students are developing mathematical activities around the topic of the child magician Harry Potter.
Investigations: Mr. Greenthumb's Garden
Authors: Sweda Jennifer R. , Knotts Lori A. , Moyer-Packenham Patricia S.
Published: December 2020

This department features children's hands-on and minds-on explorations in mathematics and presents teachers with open-ended investigations to enhance mathematics instruction. These tasks invoke problem solving and reasoning, require communication skills, and connect various mathematical concepts and principles. The ideas presented here have been tested in classroom settings.
What's Your (Mathematics) Story?
Authors: LoPresto Kevin , Drake Corey
Published: December 2020

Using mathematics life stories as tools to aid in the instruction of mathematics methods classes. Instructors will learn how to use the students' past and present experiences in mathematics to help plan instruction and get to know their students.
Connecting the Dots: Network Problems That Foster Mathematical Reasoning
Authors: McGivney-Burelle Jean M.
Published: December 2020

How a group of third-grade students engaged in mathematical reasoning while solving mathematics problems involving networks. Examples of the project and classroom ideas for teachers are included in this article.
Research, Reflection, and Practice: Posing Problems to Develop Conceptual Understanding: Two Teachers Make Sense of Division of Fractions
Authors: Flores Alfinio , Turner Erin E. , Bachman Renee C.
Published: December 2020

Several scholars (e.g., Brown and Walter 1990; English 1997; Silver 1994) have highlighted the benefits of students posing mathematical problems (for example, students become better problem solvers). Posing mathematical problems can also help teachers develop their own mathematical knowledge and understanding. Teachers who learned mathematics mostly as “rules without reasons” now must learn how to teach for conceptual understanding. This article describes how two teachers, Elizabeth and Carolyn, posed problems to develop their own conceptual understanding of division of fractions in terms that would also be meaningful for their students. Each teacher taught a combined fourth-fifth grade in an urban school. The problems that the teachers posed and solved were collected during an initial session and from the draft of an article they wrote. Additional insights and information were obtained from interviews.
Mythmatics
Authors: Buschman Larry E.
Published: December 2020

Principles and Standards for School Mathematics (NCTM 2000) recommends that classroom mathematics instruction be more problem- centered—children need to be given the opportunity to engage in genuine problem solving by answering questions to which the answer is not apparent or the solution method is not known in advance (Charles and Lester 1982; NCTM 2000). Traditionally, problem solving has been associated with routine word, or story, problems. However, almost any mathematical question can be a problem; even computational exercises can be problematic if the answer is not apparent and children have not been taught a solution method, such as a computational algorithm.
Investigations: A Mathematical Cornucopia of Pumpkins
Authors: Gebhard Glenn
Published: December 2020

The “Investigations” department features children's hands-on and minds-on explorations in mathematics and presents teachers with open-ended investigations to enhance mathematics instruc tion. These tasks invoke problem solving and rea soning, require communication skills, and con nect various mathematical concepts and principles. The ideas presented here have been tested in classroom settings.
From the Classroom: Converting Customary Units: Multiply or Divide?
Authors: Klamik Anna
Published: December 2020

“I read the problem, and it asked me how many quarts were in 12 gallons. I know there are 4 quarts in one gallon, but no matter how many times I reread the problem, I couldn't remember if I should multiply the two numbers or divide the numbers. Sometimes I draw a picture, and that helps me, but I wish there were a way for me to remember how to do this problem without drawing it.”
Making Connections through Math-Related Book Pairs
Authors: Whitin Phyllis , Whitin David J.
Published: December 2020

Mirella Rizzo regularly used children's books to give her second graders meaningful contexts for mathematical ideas. The composition of her class reflected its urban setting: culturally and ethnically diverse, including several students who had recently immigrated to the United States. As a naturalized citizen herself, Mirella was especially sensitive to the needs of her English Language Learner (ELL) students. She believed that reading, discussing, and extending math–related books gave her students opportunities to build both English and mathematical proficiency.
Early Childhood Corner: Mathematical Concepts Come Alive in Pre-K and Kindergarten Classrooms
Authors: Huber Lynn L. , Lenhoff Rosalyn S.
Published: December 2020

What do you think of when you are asked to explain how children learn mathematics? Do you visualize algorithms, workbooks, accurate calculations, solitary effort, and one correct answer? Or do you visualize problem solving, multiple ways of knowing, meaning making, working with peers, many possible responses, and numerous ways to represent? Current practice often seems to reflect the first view. Many teachers see themselves as information givers whose goal is to have everyone arrive at the same answer in the same way. However, research on children's learning clearly supports the second view, in which teachers see themselves as facilitators who guide students to think and solve problems on their own, discuss their ideas with peers, and represent solutions in various ways (Bredekamp and Copple 1997; Kamii 2000; Marcon 1994, 2002). As facilitators, teachers focus on meaningful mathematical tasks, develop rich environments, create opportunities for learners to collaborate, and encourage learners to talk and write about the mathematics learned (Van de Walle 2004).
In My Opinion: A Call for Early Intervention for Mathematically Gifted Elementary Students: A Russian Model
Authors: Colen Yong S.
Published: December 2020

In the July–August 2005 issue of the NCTM News Bulletin, Cathy Seeley, president of the National Council of Teachers of Mathematics at that time, affirmed that “students deserve, and society demands, that we also support and advance our most able students” (p. 3). This article supports her call by examining U.S. gifted programs for elementary students, the needs of mathematically talented students, and an advanced Russian mathematics lesson that demonstrates what is possible when precocious elementary students are provided an opportunity to think critically. For mathematically gifted elementary students to achieve a higher plane of mathematical learning, the education community needs to foster their ability much earlier than at the secondary school level, as is traditional; rather, elementary schools should be created specifically for these students.
What's on Your Nation's Report Card?
Authors: Norton Anderson H.
Published: December 2020

A report on a sample of fourth graders' responses to the 2003 NAEP exam. Readers are invited to analyze the responses to assess students' concepts of fractions. The article has four examples of student work.
Tips for Including Elementary Students with Disabilities in Mathematics Class
Authors: Truelove James E. , Holaway-Johnson Calli A. , Leslie Katherine Mangione , Smith Tom E. C.
Published: December 2020

Tips for classroom teachers for including students with disabilities in elementary mathematics classes, focusing on the role of the teachers and specific interventions.
No Tears Here! Third-Grade Problem Solvers
Authors: Hartweg Kim , Heisler Marlys
Published: December 2020

Description of a year–long professional development project involving the integration of problem solving into the third–grade mathematics curriculum and implications for learning and teaching elementary mathematics.
A Virtual Spin on the Teaching of Probability
Authors: Beck Shari A. , Huse Vanessa E.
Published: December 2020

The study of probability is part of one of the five major mathematics content strands as defined by Principles and Standards for School Mathematics (National Council of Teachers of Mathematics 2000). Traditionally, teaching the concepts of probability has required students to use concrete manipulatives, such as coins and number cubes, in order to perform various probability experiments. With the continued emphasis on integrating technology into the mathematics classroom, the teaching of probability has acquired a “virtual spin”—students now use various virtual manipulatives to perform probability experiments.
Grade-Level Learning Expectations: A New Challenge for Elementary Mathematics Teachers
Authors: Reys Barbara J. , Chval Kathryn , Dingman Shannon , McNaught Melissa , Regis Troy P. , Togashi Junko
Published: December 2020

The similarities and differences in grade-level learning expectations for fourth graders in ten different states that publish mathematics standards.
Ninety Percent of the Game Is Half Mental
Authors: Garrison Leslie , Ponce Gregorio A. , Amaral Olga M.
Published: December 2020

An illustration of effective instructional strategies for English Language learners. Problem solving and conceptual development are discussed, along with sample problems and examples of student work.
Using Research to Develop Computational Fluency in Young Mathematicians
Authors: O'Loughlin Tricia Ann
Published: December 2020

A teacher's journey to improve her teaching of mathematics by conducting classroom-based inquiry to meet the specific mathematical needs in her second grade classroom. Her process to develop and improve computational fluency through research-based methods is detailed.
Tying It All Together: Classroom Practices That Promote Mathematical Proficiency for All Students
Authors: Suh Jennifer M.
Published: December 2020

The five important strands in building mathematical proficiency for all students are: (1) Conceptual Understanding, (2) Procedural Understanding (3) Strategic Competence, (4) Adaptive Reasoning, and (5) Productive Disposition. (National Research Council, 2001). The article also includes suggested classroom activities and student work to enhance teaching and learning with the five strands.
Thinking about Learning Trajectories in Preschool
Authors: Brown Carmen S. , Sarama Julie , Clements Douglas H.
Published: December 2020

Learning trajectories (routes, curves) in preschool and how they helped a teacher develop goals and objectives for her students' mathematical knowledge. Learning trajectories have three parts: a mathematical goal, a developmental path, and a set of activities matched to each of those levels. Activities and a teacher's explanation are included.
Early Childhood Corner: Experiences to Help Children Learn to Count On
Authors: Weiland Linnea
Published: December 2020

Two children are playing a board game with their father. The game involves rolling two dice, finding the sum of the two numbers, and then moving that number of places on the board.
Using Item Analyses and Instructional Conversations to Improve Mathematics Achievement
Authors: Fisher Douglas , Kopenski Donna
Published: December 2020

The significant gains in student achievement in an urban elementary school when teachers worked together to develop, administer, and review assessment items. In grade-level teams, teachers completed item analyses and engaged in instructional conversations about students' needed instruction. Readers of this article will learn how to plan for, write, and assess student assessments to guide teaching and student learning.
Why Math Blogs?
Authors: Pyon Shirley M.
Published: December 2020

While in the elementary mathematics master's program at the University of North Carolina at Chapel Hill, I became interested in the use of Web logs (blogs) as a tool to encourage online discussions. During a summer course titled Reinventing Teaching, my professor used blogs to start or continue discussions concerning various course topics. Intrigued by the depth of my classmates' responses and the freedom of thought that the process gave me as a participant, I wondered how this technological tool could be used in a third-grade classroom. I decided to implement blogs across the curriculum in almost every subject.
Math by the Month: Weather or Not
Authors: Chick Linda , Holmes Andrea S. , McClymonds Nicole , Musick Steve , Reynolds Patti , Shultz Gilda
Published: December 2020

“Math by the Month” activities are designed to engage students to think as mathematicians do. Students may work on the activities individually or in small groups, or the whole class may use them as problems of the week. No solutions are suggested, so students look to themselves for mathematical justification and develop confidence to validate their work. A variety of weather conditions are experienced every day by students all over the country. The activities this month give students opportunities to investigate weather conditions that involve reading and recording temperatures, graphing, making charts, solving word problems, and working with numbers.
We All Have Something That Has to Do with Tens: Counting School Days, Decomposing Number, and Determining Place Value
Authors: Goodrow Anne M. , Kidd Kasia
Published: December 2020

It is the seventieth day of school. As in many other second grades, the children in this class keep track of how many days they have been in school. In the following vignette, the children share number sentences that equal seventy. The second graders and Mrs. K., their teacher, are gathered on the rug in front of the whiteboard. Each child holds a small blue mathematics journal, in which they record their work. Keaton begins sharing expressions that equal seventy. As he dictates, Mrs. K. writes “139 – 39 – 30” on the chalkboard.
Early Childhood Corner: Taking Advantage of Everyday Activities to Practice Math Every Day
Authors: Fernàndez Eileen
Published: December 2020

When my son started kindergarten, I discovered that many everyday activities at home allow us to practice the mathematics he was learning (and would learn) in school and encourage mathematics use in his life. Because “children learn through exploring their world … everyday activities are natural vehicles for developing mathematical thinking” (NCTM 2000, p. 74).
MIM: Math in Motion for K–2
Authors: Chevalier Cheryl , Pippen Mary H. , Stevens Dorothy
Published: December 2020

In spring 2002, the authors attended an algebra workshop sponsored by the NCTM Academy for Professional Development. The workshop presented algebraic standards and activities exploring each aspect of the Learning Principle from Principles and Standards for School Mathematics (NCTM 2000). The hands-on activities were developmentally appropriate for students at grade levels K–2 and could easily be transferred into our classrooms to enhance the curriculum.
Mathematics Thinkers and Doers: Everyone Needs a Positive Story
Authors: Zambo Debby
Published: December 2020

All children—regardless of personal characteristics, background, or physical challenges—deserve an opportunity to learn mathematics to the best of their ability. This declaration is loud and clear, and NCTM's mission of providing sound mathematics instruction and holding high expectations for all children (NCTM 2000) is important in our mathematical world. Mathematics permeates our daily lives from the moment we awaken to the moment we fall asleep. In many ways, our mathematical successes and failures get woven into the life stories that make us who we are.
Math by the month:The Fine Art of Mathematics
Authors: Gallego Christine , Saldamando Dora , Tapia-Beltràn Grace , Williams Karolyn , Hoopingarner Thomas C.
Published: December 2020

“Math by the Month” activities are designed to engage students to think as mathematicians do. Students may work on the activities individually, in small groups, or as problems of the week for the entire class. Because no solutions are suggested, students look to themselves for mathematical justification, thereby developing the confidence to validate their work. The theme for this collection of problems was inspired by the late Ted S. Mankowski, father of “Math by the Month” department editor Dana Islas. Ted's passion was art, particularly creating sculptures using geometric shapes. We hope to encourage students to make a connection between art and mathematics and to inspire their passion for learning through the following activities involving number sense and operations, data collection, pattern and algebra, geometry, measurement, communication, and representation.
You Had to Be There!
Authors: Kotsopoulos Donna , Heide Duane
Published: December 2020

Engaging in dialogue about the implications of mathematics demonstration classrooms becomes a form of professional development for teachers in communities of practice.
Can Teacher Questions Be Too Open?
Authors: Parks Amy Noelle
Published: December 2020

Many educators recommend using open-ended questions to encourage students to share their thinking. However, inexplicit open-ended questions can make it difficult for students to determine the teacher's intentions and to participate confidently in mathematical conversations. This article describes strategies teachers can use to make the language of open-ended ques-tions more explicit in order to provide more support for students in mathematics classrooms.
Early Childhood Corner: Teaching with Blocks
Authors: Taylor-Cox Jennifer
Published: December 2020

Blocks are powerful mathematical tools when used to teach young children early concepts in measurement, number sense, computation, geometry, data analysis, and algebra. For nearly one hundred years, blocks have played a role in early childhood classrooms (Smith 2001). Yet not everyone understands the mathematics conceptbuilding power associated with blocks. From sorting to patterning, young children can build a strong mathematical foundation one block at a time. This article examines how blocks can be especially useful in engaging children in activities that address algebraic, geometric, and spatial thinking.
Teaching Fractions
Authors: McLeman Laura Kondek , Cavell Heather A.
Published: December 2020

The creation and implementation of a module in a mathematics-for-teaching course that was centered on children's written work and verbal explanations. The goal of the module was to support the development of preservice elementary teachers' mathematical knowledge for teaching fractions (MKTF).
Math Fair: Focus on Fractions
Authors: Mokashi Neelima A.
Published: December 2020

A math fair in India with hands-on experiences that simplify conceptual mathematics proves to be the perfect milieu to trigger children's interest in learning mathematics.
Fraction Photo Frenzy: A New Exploration
Authors: Canada Daniel L.
Published: December 2020

Using technology to expand opportunities to share their thinking in a problem-solving environment, these preservice teachers discover exciting possibilities for sharing mathematical reasoning in elementary school classrooms.
The Power of Choice
Authors: Bray Wendy S.
Published: December 2020

Infusing mathematics lessons with opportunities for students to make instructional choices is a teacher strategy to differentiate instruction toward achieving classroom equity.
Problem Solvers: November 2009
Authors: Hall Shaun
Published: December 2020

A simple circuit is created by the continuous flow of electricity through conductors (copper wires) from a source of electrical energy (batteries). Completing a circuit means that electricity flows from the energy source through the circuit and, in the case described in this month's problem, causes the light bulb to light up. The presence of either dead batteries or burned-out light bulbs prevents a complete circuit. Experience with testing the effects of various modifications may help students understand the context of the problem.
Problem Solvers: December 2009
Authors: Cadzow-Wardell Lee-Anne
Published: December 2020

Nicknamed Wake Robin because it blooms around the same time as robins return from winter migration grounds, white trillium has been Ontario's provincial floral emblem since 1937. This perennial herb's white blossom is associated with peace and hope. The distinctive arrangement of the foliage makes white trillium the perfect object of study when exploring growing patterns.
Early Childhood Corner: Storyboards for meaningful patterns
Authors: Dubon Lucille P. , Shafer Kathryn G.
Published: December 2020

Patterns are an important element of developing children's mathematical reasoning. In elaborating ways in which “instructional programs from prekindergarten through grade 12 should enable all students to understand patterns, relations, and functions” (NCTM 2000, p. 90), the National Council of Teachers of Mathematics specifies that representing and interpreting patterns are skills that kindergartners through second graders should build toward developing a robust understanding of algebra.
Problem Solvers: Solution: The library problem
Authors: Small Marian
Published: December 2020

Quilt investigations, such as the Barn quilt problem in the December 2008/January 2009 issue of Teaching Children Mathematics and its solutions in last month's issue, can spark interdisciplinary pursuits for teachers and exciting connections for the full range of elementary school students. This month, North Dakota's centennial quilt problem blends the mathematical strands of measurement, data and probability, geometry, and number.
Trailblazers
Authors: English Lyn D. , Humble Steve , Barnes Victoria E.
Published: December 2020

You, too, can design and implement math trails to promote active, meaningful, real-world mathematical learning beyond your classroom walls.
Investigations: My bar graph tells a story
Authors: McMillen Sue , McMillen Beth
Published: December 2020

Connecting stories to qualitative coordinate graphs has been suggested as an effective instructional strategy (Blubaugh and Emmons 1999; Maus 2005; NCTM 2000). Even students who are able to create bar graphs may struggle to correctly interpret them. Giving children opportunities to work with qualitative graphs can help them develop the skills to interpret, describe, and compare information from a graph even without the availability of numeric labels. This investigation addresses the Data Analysis and Probability Standard (NCTM 2000) and explores the value of connecting stories with qualitative bar graph instruction, which too often focuses on only counting, tallying, and creating bar graphs.
Problem Solvers: Problem: Pizza party
Authors: Lore Patricia
Published: December 2020

Nothing quite captures young people's attention as easily as food does. Ordering pizza for a group can be a meaningful context for elementary school students. Sharing a meal with your class is a rewarding time for everyone and helps build positive relationships.
Math by the Month: Speedy Gonzales
Authors: O'Donnell Patricia , Frick Amanda
Published: December 2020

Do you remember clever, energetic Speedy Gonzales, “the fastest mouse in all Mexico,” one of the animated characters in the Warner Brothers Looney Tunes cartoon series? This month our “math by the month” activities, reminiscent of the spirited Speedy, will have your students calling ¡Ándale! ¡Ándale! ¡Arriba! ¡Arriba! (colloquial Spanish for “Come on! Hurry up!”) as they ask for more problem-solving scenarios based on this month's racing theme.
Problem Solvers: Problem And Problem Solvers: Solutions
Authors: Hauk Marie , Kula Beverley
Published: December 2020

The classic question of mixing water and wine (Ball 1896, p. 27) is the basis of the May problem, which can be solved without using computation.
News&Views: Scholarly teaching
Authors: McGarvey Lynn
Published: December 2020

As teachers and educators, we have a unique opportunity to continue to see the world through the eyes of a child. Together with our students, we engage in an ongoing quest to make sense of the world around us. We have opportunities to experience wonder and fascination with mathematical ideas new to us, concepts never truly understood, and alternative strategies for problem solving. The start of the new school year is a time to renew that sense of curiosity, enthusiasm, and optimism for teaching mathematics to children.
Promote problem-solving discourse
Authors: Bostic Jonathan , Jacobbe Tim
Published: December 2020

A four-day intervention proved highly successful. Here are practical, specific guidelines for you to quickly develop a similar classroom culture.
Math by the Month: Animal kingdom comparisons
Authors: Minetola Janice R.
Published: December 2020

Activities this month are connected to facts and ideas from If You Hopped Like a Frog by David M. Schwartz. For younger children, the author presents information in a comical way through the amazing abilities of nonhuman creatures. The book's appendix, which contains astonishing scientific information related to the animals' abilities, offers upper elementary and middle school students opportunities to calculate and compare.
Strengthen your mathematical muscles
Authors: Wohlhuter Kay A. , Breyfogle M. Lynn , McDuffie Amy Roth
Published: December 2020

What mathematics must teachers understand in order to teach elementary school mathematics? Historically, the answer to that question was that they needed to know only the mathematics concepts and procedures they taught. Research on the teaching and learning of mathematics challenges that myth and indicates that the role and substance of mathematics knowledge needed for teaching has expanded. In addition to a profound understanding of fundamental mathematics content (Ma 1999), teachers need deep knowledge about how students learn particular math concepts and processes and, correspondingly, which teaching approaches and strategies are most effective in meeting students' learning needs. Ball, Hill, and Bass (2005) refer to this kind of knowledge as mathematics knowledge for teaching. For example, to determine whether a child's unique approach for adding fractions can be generalized or how an area model might be used to develop the partial-product algorithm for multiplying two-digit numbers, teachers need a form of mathematical knowledge different from other professionals (e.g., engineers). Aligned with this research, the Teaching Principle identifies the necessity for teachers to develop deep knowledge and understanding of mathematics to meet the needs of their students today and in the future (NCTM 2000).
Connections: Catch the monkey
Authors: Nelson Cheryl , Williams Nicole , Anderson Rhonda
Published: December 2020

Mazes are probably familiar to your students. Perhaps they have run through one at school or have visited a corn maze in the fall. In this rich investigation to connect experimental and theoretical probability, students use principles of probability to analyze a maze from a mathematical standpoint. They connect geometry to probability through the use of an area model and work together to communicate their ideas and use their intuitions whenever it seems reasonable.
News&Views: National Lab Day promotes STEM
Authors: Christie Andrea
Published: December 2020

A year ago this month, President Obama announced the “Educate to Innovate” program to promote science, technology, engineering, and mathematics (STEM) teaching and education. National Lab Day is part of the president's program. Although May 12, 2010, marked the first National Lab “Day,” it is not actually a one-day event, but a yearlong initiative aimed at improving inquiry-based experiences for students in STEM disciplines.
From the Classroom: Symmetry gave me four legs!
Authors: Cole Shelbi
Published: December 2020

A thick, black belt around my midsection is visible to all my students. “This is my symmetry belt,” I tell a roomful of third graders. I ask whether they think my belt is a line of symmetry for my body. Inevitably, a child raises her hand and explains that the belt is not a line of symmetry because the top half of my body is not the same as the bottom half. I then ask whether I have a line of symmetry anywhere. Several students “draw” a line down the center of their faces with their fingers. I act disappointed that I can no longer call it a symmetry belt but ask students to actually draw a picture of what I might look like if the belt were a line of symmetry. Several humorous pictures result, showing me with either four legs or two heads (see fig. 1 and fig. 2).
News&Views: Send your students to outer space
Authors: Christie Andrea
Published: December 2020

Do you want to travel to the moon for research and exploration? Would you like to find out what walking really feels like there? You and your students can do just that in NASA's newest three-dimensional game, Moonbase Alpha, launched in July 2010. Moonbase Alpha is a multiplayer game scenario set on a hypothetical lunar settlement. Players can work together as an exploration team or alone in this twenty-minute game that requires students to apply their knowledge of mathematics in order to succeed.
From the Classroom: A house for Sarah
Authors: Embrey Kerri , Murray Mary
Published: December 2020

Our class of four-year-olds spent seven weeks constructing a two-story dollhouse complete with a balcony and an attic. As students and teachers pass by our class, they are amazed to learn that the youngest children in the school made this elaborate structure.
Preschoolers' thinking during block play
Authors: Piccolo Diana L. , Test Joan
Published: December 2020

Investigating and describing spontaneous, exploratory play opens a window into the types of mathematics that very young students can and do accomplish.
Backtalk: How Nicole uses counting up to subtract
Authors: Surber Maryann V.
Published: December 2020

It is the end of Nicole's firstgrade year, and we have been working on using the numbers one through twenty in addition and subtraction word problems. As a teacher, I feel comfortable that she can explain her thought process of numbers by using pictures and manipulatives.
Neighborhood survey
Authors: Johnson Denise T.
Published: December 2020

And the survey says … Whether listening to the news, reading a newspaper article, or watching reruns of such television game shows as Family Feud, we are frequently bombarded with surveys and survey results. But what do these numbers really tell us? This month your students explore that very question as they analyze survey data.
Developing Spatial Abilities the Early Grades
Authors: Liedtke Werner W.
Published: December 2020

Most, if not all, geometry learned in the early years should be conceptual in nature, state Hiebert and Lindquist in Mathematics for the Young Child (1990). The authors point out that students need the opportunity to develop spatial sense, and they share the observation that “[t]oday, children are often able only to name selected examples of geometric figures.
Research into Practice: Assessing Mathematical Learning
Authors: Robinson G. Edith , Bartlett Karen T.
Published: December 2020

Assessment information is collected for a variety of purposes—assignment of grades, decisions about promotion, diagnosis and remediation, evaluation of the instructional program or curriculum—or because it is mandated at some administrative level. Increasingly, however, attention is being directed to the importance of assessment for guiding instruction.
Links to Literature: Mathematics Is Something Good!
Authors: Oppedal Diane Cradick
Published: December 2020

It was the second week of a new school year, and my second-grade students were working together in pairs. They talked quietly as they arranged and counted interlocking cubes, buttons, plastic disks, counting bears, color tiles, and base-ten units, to name a few.
Early Childhood Corner: Planting Mathematics in the Classroom
Authors: Schwartz Sydney L.
Published: December 2020

Each year, when the classroom is being readied for a new group of four- or five-year-olds, that same rush of excitement occurs. The questions march relentlessly through the mind as to offering this year's group some new experiences that were not thought of, or gotten to, last year.
Reviewing and Viewing
Authors: Clements Douglas H.
Published: December 2020

Prices on software, books, and materials are subject to change. Consult the suppliers for the current prices. The comments reflect the reviewer's opinions and do not imply endorsement by the Notional Council of Teachers of Mathematics.
National Council of Teachers of Mathematics: Selling and Buying Reform: If We Build It, Will They Come?
Authors: Price Jack
Published: December 2020

The remarks published here have been adapted from the Presidential Address at the 73d Annual Meeting of the National Council of Teachers of Mathematics in Boston, Massachusetts, 8 April 1995.
Math by the Month: Math Mysteries
Authors: Lewis Cathie , Lewis Tom
Published: December 2020

These activities are designed to appeal directly to students, giving them open-ended questions intended to engage their intellect through their interests. Students may work on the activities individually, in pairs, or in small groups. No solutions are suggested or 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.
Early Childhood Corner: The Role of Self-Directed Discovery Time in the Development of Mathematics Concepts
Authors: Andrews Angela Giglio
Published: December 2020

I must admit that I was a bit anxious in the late 1980s as I waited for the release of a set of “Math Standards” from NCTM, a document that I believed would have far-reaching implications for the way I taught mathematics to young learners.
In My Opinion: Who Will Be First?
Authors: Wand Jennifer L.
Published: December 2020

Ugh was running as fast as he could. His fur-matted feet barely kissed the pebbles beneath. The animal was gaining on him. He slammed his back against a wall of rock. His lungs ached. Sweat erupted from his body like the ancient geysers surrounding him. He quickly surveyed his roundings.
Math by the Month: Oceans Full of Numbers
Authors: Smith Steven H. , Curtis Vernon
Published: December 2020

Math by the Month activities are designed to speak directly to students, giving them open-ended questions to engage their intellect through their interests. Students are encouraged to work on the activities individually, in pairs, or in small groups. No solutions are given for activities so that students will look to themselves as the mathematical authority, thereby developing the confidence and critical-thinking skills necessary to validate their thinking.
What's In A Glyph?
Authors: Cartland Patricia E.
Published: December 2020

The ancient pictorial symbols of hieroglyphics are the basis for the recent invention of what have become known as glyphs. Doctors, astronomers. meteorologists, geologists, and other scientists discovered that through pictures, they can communicate a wealth of data in a very easy-to-read. simple format. A glyph is a pictorial type of shorthand, in which detailed information can be displayed through features of a glyph symbol.
Hamster Math: Authentic Experiences in Data Collection
Authors: Jorgensen Beth
Published: December 2020

These words adorn one of many posters decorating the halls of our school from time to time, alerting visitors to the class project dubbed “hamster math” by the children who helped create it. This article describes some of the data collection and interpretation engaged in throughout this project by the six- to eight-year-olds involved.
Using Data to Make Decisions About Chance
Authors: Jones Graham A. , Langrall Cynthia W. , Thornton Carol A.
Published: December 2020

Karen and Leon had been constructing their booth for the school fair. They had made a “pull the strings” game in which half the strings had one end painted red and the other half of the strings had one end painted blue. The strings are randomly placed over a board with the colored end hidden. After the first string is pulled, it is replaced to a random location so that ten strings are available for the second pull. A prize would be given whenever two strings of the same color were pulled. Leon was concerned that the game was not fair.
An Alternative to Basic-Skills Remediation
Authors: Hankes Judith E.
Published: December 2020

Three students stand out vividly when recalling twenty years of teaching. The first one is Josh, a second grader who hail been labeled as educable mentally retarded by his kindergarten and first-grade teachers. Josh had serious problems with symbols. He could not memorize his addition and subtraction facts, and at times he seemed not to understand that the numeral 7 stood for the quantity seven.