bluuebunny/crossref_metadata_2025 huggingface dataset:
Tracking Time: Representing Elapsed Time on an Open Timeline
Authors: Dixon Juli K.
Published: December 2020

Elapsed-time problems are notoriously difficult for children (Monroe, Orme, and Erickson 2002). Instruction on techniques for teaching and learning elapsed time is not emphasized in current mathematics education literature. Nor is it addressed in Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence (NCTM 2006). This absence of instruction may be due to a position held by some mathematics educators that telling time and determining elapsed time are life skills rather than skills delegated to mathematics instruction. (See Editor's note.) However, time is addressed in the Principles and Standards for School Mathematics (NCTM 2000) Measurement Standards for both the pre-K–2 and 3–5 grade bands. And regardless of one's perspective on the delegation of time as a discrete content area, determining elapsed time is encountered during mathematics instruction by most children at some point and is often met with frustration. This is especially true when the start or end time falls between the hour and half hour. Children find it challenging to keep track of unit changes between hours and minutes. On a national assessment, only 58 percent of eighth-grade students were able to correctly identify that 150 minutes equals 2 1/2 hours (Jones and Arbaugh 2004). Elapsed-time instruction often focuses on converting units and keeping track of those conversions rather than on counting up or back from one time to another. This article examines how students are able to make sense of elapsed-time problems when instruction is connected to open number-line strategies. Adapting this technique–typically used for recording addition and subtraction counting strategies–provides a method for supporting students' thinking about elapsed-time problems.
Investigations: Reflections and Kaleidoscopes: Not Always What You Expect
Authors: Magner Jodelle
Published: December 2020

The “Investigations” department features children's hands-on and minds-on explorations in mathematics and presents 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.
Assessing Student Thinking about Arithmetic: Videotaped Interviews
Authors: Ellemor-Collins David L. , Wright Robert J.
Published: December 2020

An approach to detailed assessment involving videotaping clinical interviews. The authors highlight strengths of this approach to help teachers understand children's thinking, inform instruction, and further professional learning.
Shifting Roles and Responsibilities to Support Mathematical Understanding
Authors: Hansen Pia , Mathern Donna
Published: December 2020

“Matt, I hear what you are saying, but I respectfully disagree with you. I have another way to think about that.”
Case-Based Tasks in Mathematics Teacher Preparation: What Is Appropriate?
Authors: Manouchehri Azita , Almohalwas Akram
Published: December 2020

In recent years, the use of case-based tasks in the pedagogical preparation of teachers has gained considerable popularity in teacher education (Broudy 1990; Merseth 2003).
Emphasizing Standards with Classroom Activity Extensions
Authors: Coffland David A.
Published: December 2020

Even a simple exercise has potential to provide extensions for multiple standards, thereby increasing students' mathematical skills and confidence.
Early childhood corner: The Power of Representation: Graphs and Glyphs in Data Analysis Lessons for Young Learners
Authors: Lacefield William O.
Published: December 2020

Skillful teachers capitalize on youngsters' proclivity for exploration by implementing lessons that allow for collecting, organizing, analyzing, and discussing data—including constructing graphs and glyphs (picture graphs) with concrete materials. Such opportunities can strengthen children's abilities to develop inferences, make predictions, and recognize patterns. In the past, data analysis was often neglected in early childhood mathematics curriculum. However, educators now recognize that children's natural inquisitiveness about their experiences and about the world in which they live can stimulate them to raise a variety of questions that lead to data analysis: What kind? How much? Which of these? How many?
Using the Mathematics We Do Every Day
Authors: Kalchman Mindy S.
Published: December 2020

Preservice teachers gain a new perspective by recognizing the mathematics in everyday situations.
Math by the Month: Tantalizing Thirteen
Authors: Columba Lynn
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 these as problems of the week. Because no solutions are suggested, students will look to themselves for mathematical justification, thereby developing confidence to validate their work.
Learning to Share Equally
Authors: Polly Drew , Ruble Laura
Published: December 2020

After five weeks of assessing and improving their third graders' understanding of partition and measurement models of division, these authors challenge students to attempt their own division story problems.
Early Childhood Corner: Engage Families in Meaningful Mathematics
Authors: Burton Megan , Baum Angela C.
Published: December 2020

Young children enter school with natural curiosity and understanding of many mathematical concepts (Clements 2001). Principles and Standards for School Mathematics (NCTM 2000) highlights the necessity for caregivers to support and encourage this natural mathematical curiosity. Together, teachers and families can build on children's conceptual foundations and nurture positive emotional growth in mathematics (Kavkler et al. 2000).
In My Opinion: Too Little, Too Early
Authors: Jacobson Erik D.
Published: December 2020

Mathematicians and university math educators insist that multiplication is not repeated addition; however, the interpretation works when solving most elementary school mathematical problems. Sure, mathematicians might make a distinction, but does such hair splitting matter to third graders? Should it matter to their teachers?
Links to Literature: Legs and More Legs
Authors: Whitin David J. , Whitin Phyllis
Published: December 2020

One way to learn to understand word problems is to write your own. In one multiage classroom, we involved second and third graders and their teacher in composing problems for their peers to solve (Whitin and Whitin 2008). They posed problem variations by changing the known and unknown problem elements. This article describes how we used a children's book to initiate the experience. We then give examples of the student-created problems and analyze their various solution strategies.
By Way of Introduction: Equity: Teaching, Learning, and Assessing Mathematics for Diverse Populations
Authors: Berry Robert Q. , Wickett Maryann S.
Published: December 2020

Principles and Standards for School Mathematics (National Council of Teachers of Mathematics 2000) highlights the Equity Principle by stating, “Excellence in mathematics education requires equity—high expectations and strong support for all students” (p. 12). Working toward equity requires mathematics educators to think about curriculum and instruction issues as well as mathematics teaching and learning within a larger context of society.
Shopping carts and apple tarts
Authors: Walker Lewis H. , Waldron Lynn S.
Published: December 2020

Typical of many teacher preparation programs, the preservice teachers at Lander University in Greenwood, South Carolina, engage in a number of field experiences prior to their extended student teaching. During the field experience that immediately precedes student teaching, each preservice teacher spends fifty hours working with students in a single classroom. In preparation for this experience, the preservice teachers develop and design ten-day units centering on social studies that integrate mathematics, language arts, natural science, health, and the creative and kinesthetic arts. One requirement of designing the unit is to include at least two integrated lessons involving mathematics in which the classroom students operate outside the school classroom.
Back Talk: Tuheen's Thinking about Place Value
Authors: Wickett Maryann
Published: December 2020

It was early September, and my class of third graders was working to understand and strengthen their skills in adding large numbers. I wrote “59 + 67 = ” horizontally on the board and asked students to solve the problem using a strategy that made sense to them.
Math by the Month: A Treasure Trove of Triangles
Authors: Columba Lynn , Waddell Lanette
Published: December 2020

Children and adults alike enjoy the classic How many triangles? puzzle shown at the left. This month, the “math by the month” problems explore much more than counting the number of triangles in a figure. Join the fun as we discover a wealth of knowledge and connections with these fascinating three-sided polygons.
Identifying logical necessity
Authors: Yopp David
Published: December 2020

As the ability to reason receives increasing attention across all grade levels, this author learns that furnishing preservice teachers with opportunities to evaluate mathematical arguments will help them recognize valid proofs in their own classrooms.
Problem Solvers: Solutions: Where is the center?
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.
From the classroom: The trouble with long division
Authors: Sellers Patricia A.
Published: December 2020

The fourth graders were ready to learn long division; however, their teachers were hesitant to begin the unit—just as they are every year. In a grade-level meeting with the school's math consultant, the teachers voiced their typical concerns. The math consultant was a university mathematics education professor spending a semester of sabbatical working with teachers to find ways to help elementary-aged students get excited about doing math and about learning to make sense of math through problem-solving activities.
Connections: I have the answer; who has the question?
Authors: Kuntz Jeffrey J.
Published: December 2020

“Six bites, a core, a stem, and three apple seeds.”
Problem Solvers: Problem: Pencils and crayons
Authors: Simmt Elaine
Published: December 2020

Each school year, children begin with their new supplies in hand, eagerly waiting to sharpen their pencils and get started. However, it is not long before the teacher overhears one student asking to borrow a pencil from another. Whereas some students delight in having a collection of pencils and crayons to use for their lessons, others manage just fine with only one or two writing utensils; and at least one student always seems to need to borrow a pencil.
From the inside out
Authors: Fillingim Jennifer G. , Barlow Angela T.
Published: December 2020

Consider both internal and external motivational factors to promote and extend students' success as doers of mathematics beyond the classroom, preparing them for success in a flat world.
Computational estimation
Authors: Fung Maria G. , Latulippe Christine L.
Published: December 2020

Preservice teachers learn how to ground their own number sense so their future students' skills will soar.
First graders outwit a famous mathematician
Authors: Bishop Jessica Pierson , Lamb Lisa L. C. , Philipp Randolph A. , Schappelle Bonnie P. , Whitacre Ian
Published: December 2020

Find zero minus four? Pascal argued it was impossible! Twenty-first-century students, given the right tools, can solve counterintuitive problems.
In My Opinion: Mathematics in the Slow Lane: Taking the Scenic Route
Authors: Berkman Robert M.
Published: December 2020

An old Woody Allen joke involves the comedian's boasting to an acquaintance about reading War and Peace in a single night after taking a speed-reading course.
Links to Literature: Popping Up Number Sense
Authors: Hopkins Lindy
Published: December 2020

Popcorn. This simple, inexpensive manipulative led to myriad unforeseen benefits—student excitement, whole-school participation, and even community involvement—as our project to count a million popped pieces unfolded.
Links to Literature: Plotting Margo's Party
Authors: Grummer Debra
Published: December 2020

Literature can be a rich source for data exploration in elementary classrooms. This article describes one lesson I have designed by incorporating data from the story Ten for Dinner by Jo Ellen Bogart (1989) into my teaching of a week-long series of lessons on data exploration and graphing.
Investigations: Nuts about Mathematics
Authors: Brahier Daniel J. , Speer William R.
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.
Polishing a Data Task: Seeking Better Assessment
Authors: Zawojewski Judith S.
Published: December 2020

Data handling has been recommended as a major strand of instruction by the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) and illustrated in one of the NCTM's K-6 Addenda Series. Making Sense of Data (Lindquist et al., 1992).
Dolphins or Wildcats: Exploring Election Statistics
Authors: Clous Alisen S.
Published: December 2020

Election years inspire holding mock elections in many schools. To parallel the real world, our elementary school's grades K-4 held an exciting mock election during a recent national campaign. To make the process more clear to our young students and involve a topic that would have real meaning for them, the principal and faculty designed an election to choose a school mascot.
Implementing the Assessment Standards for School Mathematics: Look! How I Am Growing!
Authors: Midgett Carol
Published: December 2020

Look! Look! Come see my pattern! I grew it by adding blocks all around the center!” exclaimed Ray.
Cooking Up Mathematics in the Kindergarten
Authors: Partridge Elizabeth , Austin Sue , Wadlington Elizabeth , Bitner Joe
Published: December 2020

Although cooking activities have been an integral part of kindergarten classes for years, teachers and administrators often do not perceive these experiences as being a springboard for integrating mathematics with other areas of the curriculum.
Investigations
Authors: Brahier Daniel J.
Published: December 2020

The “Investigation” department recognizes the importance of children's exploring handson and minds-on mathematics and, therefore, presents teachers with open-ended explorations to enhance mathematical instruction.
Computers Support Algebraic Thinking
Authors: Clements Douglas H. , Soromo Julie
Published: December 2020

Try this problem: Write an equation using the variables S and P to represent this statement: “There are six times as many students as pro-lessors at this university.” Use S for the number of students and P for the number of professors.
Investigations
Authors: 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.
Math by the Month
Authors: O'Connell Sue
Published: December 2020

The Math by the Month activities are designed to appeal directly to students. They 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.
Early Childhood Corner: Too Easy for Kindergarten and Just Right for First Grade
Authors: Richardson Kathy
Published: December 2020

Those of us who find teaching a rewarding and challenging profession know that we will never have it all figured out. We always have something to ponder as we work to create the best educational experiences we can for our students. Some recent experiences raised new questions about how children develop number concepts and led me to new understandings.
A Teacher's Journal: Math Pals Write to Solve
Authors: Bochese Joan
Published: December 2020

Fostering communication in mathematics took a unique twist with the implementation of the “Math Pals” program between the Jackson Avenue School in Hackensack and the Maugham School in Tenafly, New Jersey. This program, which emphasized mathematics communication, allowed students to become active problem solvers with a pal in a different school. In addition, it gave students a multicultural experience.
Exploring Area with Geoboards
Authors: Trafton Patricia A. , Hartman Christina
Published: December 2020

I had a wonderful opportunity to experience the kind of lesson that all teachers dream about, a true magical mathematics moment. In such a lesson, children explore rich mathematical ideas, share their thinking and their work with one another, and make connections to other mathematical ideas. The plan for the day's lesson extended some initial geoboard work from the previous day, when children had created various designs and shapes and explored the concept of symmetry.
Implementing the Assessnment Standards: Assessment through Incredible Equations
Authors: D'Aboy Diana A.
Published: December 2020

Take out your base ten-materials; our number today is eighty-eight. Build that amount, then tell me some of your mathematical thoughts in a sentence to describe what you have in front of you.” Or the teacher might have said on another day, “Using your play money, show me one way to make today's number, one hundred thirty-five, and tell me a mathematical sentence to show how you grouped and sorted your play money for that amount.”
Early Childhood Corner: Recognizing the Mathematics
Authors: Corneille Birgitta
Published: December 2020

The mathematics that young children explore or to which they are exposed depends on what is important in their everyday lives. One year when teaching nursery school. I found that groups of children on the playground were counting back from ten to zero to “Blast off!” They were usually perched on different climbing apparatus.
In My Opinion: Mathematics for the Twenty-First Century
Authors: Orey Daniel C.
Published: December 2020

Education is a process, not just an event. This axiom underlies an important reform movement described by the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989), which presents standards designed to improve mathematics instruction in schools and accelerate our young people toward a demanding future. By adopting such reforms, state and school-district trustees have a watershed opportunity to join other progressive leaders determined to reverse negative trends in student achievement.
Parents as Math Partners: A Successful Urban Story
Authors: Carey Linda M.
Published: December 2020

The student population of my second-grade, self-contained, urban classroom is unusual. My class contains thirteen boys and nine girls. All but one child are below the minimum income level set up by the state of Ohio and qualify for a federally funded meal at school. Of the twenty-two students, thirteen are classified as English-as-a-Second-Language (ESL) learners and come from countries other than the United States, especially from Near and Far Eastern countries.
Doing Mathematics with Your Child
Authors: Hartog Martin D. , Diamantis Maria , Brosnan Patricia
Published: December 2020

Parents have the wonderful opportunity and responsibility to nurture children. This nurturing process takes place in several areas of development: physical, emotional, and intellectual. Although parents have little trouble taking time to read a story to their children, which helps instill a love for literature. they are often at a loss when confronted with the task of introducing their children to the world of mathematics.
Math by the Month: Family Math by the Month
Authors: Coates Grace Dávila , Thompson Virginia
Published: December 2020

These activities are designed to appeal directly to students and their families, giving them open-ended questions to engage their intellect. Students may work on the activities with family members or in small groups in the classroom. No solutions are suggested so that students can develop the confidence to validate their own work.
Math by the Month: Mission Mathematics by the Month
Authors: Belsky Nancy Ann
Published: December 2020

These activities are designed to appeal directly to students. No solutions are suggested for the activities so that students will look to themselves as the mathematical authority, thereby developing the confidence to validate their work.
Tech Time's News from the Net: Global SchoolNet Foundation; Education World
Authors: Lazerick Beth
Published: December 2020

Most early childhood and elementary school teachers are generalists. The following sites reflect that reality. They are general sites that also include mathematical content.
There Are No Algorithms for Teaching Algorithms
Authors: Curcio Frances R. , Schwartz Sydney L.
Published: December 2020

What comes to mind when we hear the word algorithm? We may think of it as a procedure, an efficient method, or a rule for computation. From our own formal school experiences, we may recall pages of skill drill and practice, or lengthy efforts to accomplish rote memorization. Those of us fortunate enough to have experienced and understood the power of an algorithm may recognize its usefulness as a problem-solving tool. For those of us who have learned algorithms without meaning and understanding, practicing algorithms reinforces the view that the imposition of methods, rules, and procedures will ensure the accuracy and efficiency of computation and symbol manipulation.
Title I and Mathematics Instruction: Making the Marriage Work
Authors: LeTendre Mary Jeane , Wurtzel Judy , Bouckris Robin
Published: December 2020

Mathematics teachers face daily challenges in using scarce resources to address the needs of students, particularly those who are disadvantaged. Federal education resources can be used to support your efforts to improve learning. This article explains how Title I of the Elementary and Secondary Education Act (ESEA), which at over $7 billion is the largest federal investment in K–12 education, can support your work. We hope that you will read this article and begin a discussion with principals and administrators about how Title I resources can be used to improve mathematics teaching and learning in your school and district.
Promising Research: Reversing the Trend: Latino Families in Real Partnerships with Schools
Authors: Cruz Yolanda De La
Published: December 2020

Señor Lopez walked up to the project director after the last mathematics class and said, “De todos los años que he tenido hijos en estas escuelas, esta es la primera vez que me han tratado con tanta dignidad” (In all the years I have had children attend these schools, this is the first time that I have been treated with so much dignity).
A Journey through Geometry: Designing a City Park
Authors: Tepper Anita Benna
Published: December 2020

With a little imagination and a strong instructional program, teachers can initiate numerous projects that develop their students' mathematics and science skills. Developing Logical Thinking (DLT) in Science and Math is an integrated science and mathematics program that uses a problem-based learning environment in conjunction with a constructivist teaching style. Mitchell and Miller (1995) have shown that such a learning environment enhances the transfer of acquired skills to real-life situations, resulting in intrinsically motivated students.
Gingerbread-House Geometry
Authors: Emenaker Charles
Published: December 2020

As the holiday season nears, it is difficult for children to keep their minds focused on academics. The last week or two before vacation can sometimes be difficult, but this is an ideal time for a unit on “gingerbread-house geometry.” The activities presented here can be used by themselves or as a part of a larger interdisciplinary unit.
Math Curse or Math Anxiety?
Authors: Stuart Vanessa
Published: December 2020

Explores the phenomenon of math anxiety in a group of elementary school students. Discusses strategies to reduce math anxiety.
Nurturing the Voices of Young Mathematicians with Dyads and Group Discussions
Authors: Wickett Maryann S.
Published: December 2020

How dyads and group discussions can build student confidence and bring out the mathematical abilities of students.
Investigations: Midpoint Shapes
Authors: Welchman Rosamond , Urso Josephine
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 explorations invoke problem solving and reasoning, require communication skills, and connect various mathematical concepts and principles. The ideas presented here have been tested in various classroom settings.
Problem Solvers: Stair Skipping
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.
Links to Literature: A Remainder of One: Exploring Partitive Division
Authors: Moyer Patricia Seray
Published: December 2020

Children's literature can be a springboard for conversations about mathematical concepts. Austin (1998) suggests that good children's literature with a mathematical theme provides a context for both exploring and extending mathematics problems embedded in stories. In the context of discussing a story, children connect their everyday experiences with mathematics and have opportunities to make conjectures about quantities, equalities, or other mathematical ideas; negotiate their understanding of mathematical concepts; and verbalize their thinking. Children's books that prompt mathematical conversations also lead to rich, dynamic communication in the mathematics classroom and develop the use of mathematical symbols in the context of communicating. The National Council of Teachers of Mathematics (1989) emphasizes the importance of communication in helping children both construct mathematical knowledge and link their informal notions with the abstract symbols used to express mathematical ideas.
Math by the Month: Olé for Math
Authors: Benning Jennifer D. , Bonenberger Laura , Hickey Kevin A. , Steward Carey
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 collection uses Spain and Spanish culture as a setting for activities that involve graphing, estimation, logical reasoning, geo-metry, measurement, and computation.
Math by the Month: Celebrate Metric Day
Authors: Mistretta Regina , Porzio Joseph A.
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 measurement. We begin by using language to compare and contrast measurements, next work with nonstandard units of measure, and then conclude with standard units of measure. To learn more about National Metric Day and Metric Week, go to lamar.colostate.edu/~hillger. Remember to celebrate Metric Day on 10 October 2000!
Making Informed Choices: Selecting Children's Trade Books for Mathematics Instruction
Authors: Hellwig Stacey J. , Monroe Eula Ewing , Jacobs James S.
Published: December 2020

Traditionally, mathematics has been taught as a series of isolated subskills, with the emphasis on the product rather than on the problem-solving process. Many students have emerged from such instruction with memorized formulas in their minds but not at their fingertips. Real mathematics, however, is not so cut-and-dried. The practice of mathematics is not merely plugging numbers into an algorithm or a calculator to find a solution, nor is it just a subject in school or a set of rules to memorize. Mathematics is thinking and reasoning, solving problems, making connections, and being able to communicate ideas mathematically.
Principles and Standards: Developing Computational Fluency with Whole Numbers
Authors: Russell Susan Jo
Published: December 2020

Principles and Standards for School Mathematics (NCTM 2000) emphasizes the goal of computational fluency for all students. It articulates expectations regarding fluency with basic number combinations and the importance of computational facility grounded in understanding (see a summary of key messages regarding computation in Principles and Standards in the sidebar on page 156). Building on the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) and benefiting from a decade of research and practice, Principles and Standards articulates the need for students to develop procedural competence within a school mathematics program that emphasizes mathematical reasoning and problem solving. In fact, learning about whole-number computation is a key context for learning to reason about the baseten number system and the operations of addition, subtraction, multiplication, and division.
Tech Time: Developing Numbers and Operations with Affordable Handheld Technology
Authors: John Denny St. , Lapp Douglas A.
Published: December 2020

The four-function calculator is widely used by students and teachers in elementary schools. Although other types of calculators are available, the number of choices has been limited up to now. Recently, however, calculator manufacturers, including Casio (fx-991Wplus, fx-115Wplus, and fx-300Wplus), Sharp (EL-520RB and EL-506RB), and Texas Instruments (TI-30X IIS, TI-34 IIX, and TI-15), have introduced two-line calculators, and more are being developed. These calculators can display an expression on one line and the computed result on the second line. These calculators offer a variety of features in addition to the two-line display, but this article focuses on the development of numbers and operations using the TI-15, which is specifically designed for use in elementary school and middle school classrooms.
Oil and Water Don't Mix, but They Do Teach Fractions
Authors: Anderson Cindy L. , Anderson Kevin M. , Wenzel Edward J.
Published: December 2020

nderstanding and using fractions have traditionally been difficult tasks for students. National assessment results (NCTM 1988) show that even older students experience difficulty in working with and understanding fractions. The National Center for Educational Statistics (1990) reported that only 46 percent of twelfth graders who took the National Assessment of Educational Progress could consistently solve problems involving fractions. Baroody and Hume (1991) suggest that student errors in fractions may be caused by poor understanding of underlying concepts, as well as by an inability to recognize accurate visual representations.
Fractions: What Happens between Kindergarten and the Army?
Authors: Riddle Margaret , Rodzwell Bette
Published: December 2020

Why is it that many adults, even after years of schooling, still do not understand some mathematics topics, such as fractions? Those who enter continuing education programs, for instance in the armed services, often specify fractions as an area of mathematics that has always confused them. Kindergarten teachers, however, observe young children in everyday situations demonstrating a beginning understanding of fraction concepts. What happens between kindergarten and the army?
A Game Involving Fraction Squares
Authors: Ortiz Enrique
Published: December 2020

Fractions are a major area of concept and skill study in elementary school mathematics. The game in this article helps students practice many of these concepts and skills in a motivational and informal setting. The major concepts covered by this game include identifying fractions, equivalent fractions, and improper fractions; performing operations with fractions; and reading and writing numerals for fractions. This game also helps develop number sense and uses models to explore operation sense with fractions. The emphasis is on developing and understanding fraction concepts and operations.
Math by the Month: It's about Time
Authors: Mistretta Regina , Porzio Joseph A.
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 investigating and exploring questions related to time, calendars, and the New Year.
Problem Solvers: Tiles and Sides
Authors: Olson Judith , 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. Pose the problem, reflect on your students'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.
Research into Practice: February 2001
Authors: Bishop Alan J.
Published: December 2020

On the first day back after the winter holiday, you are visiting with your fourthgrade class before getting down to work. You ask whether anyone received any “mathematical” presents. One boy says that he was given a mathematics game from his uncle's country. He says that the game is very interesting and has lots of variations and asks whether he may show how it is played.
Seeding Ethnomathematics with Oware: Sankofa
Authors: Powell Arthur , Temple Oshon
Published: December 2020

The word sankofa, as used by the Akan-speaking people of Ghana, is a grammatical imperative, meaning that to advance, one must reflect on and reclaim traditional cultural ideas. Reflecting on mathematical ideas expressed in cultural products and practices is an important part of ethnomathematics (D'Ambrosio 1990; Gerdes 1999). As Powell and Frankenstein (1997) suggest, ethnomathematics emerges from discourse about the “interplay among mathematics, education, culture, and politics” (p. 5). In classrooms, ethnomathematics can be implemented by investigating the mathematics of cultural products and practices, such as games, with people from that culture or by exploring the mathematics of a different culture to help students enrich their construction of mathematical ideas (Powell and Frankenstein 1997, p. 249).
Promising Research, Programs and Projects: March 2001
Authors: Uslick JoAnn , Barr Susan
Published: December 2020

Probability is intimidating to many adults, but through experiencing probability in the context of game situations, even young children can gain intuitive notions about the concept. Camp Invention is a summer program based on the premise that children learn best by doing activities that they enjoy. At Camp Invention, children “play math” instead of traditional games, such as soccer or Monopoly. Camp Invention features two mathematics-based modules—Probability Carnival and Moving Math Murals—that students find enjoyable and mathematically worthwhile. Probability Carnival includes some games typically found in the midway of a carnival; Moving Math Murals includes subjects related to art, such as tessellations, fractals, chaos, and so forth.
Principles and Standards (2001): March 2001
Authors: Lindquist Mary , Clements Douglas
Published: December 2020

At the beginning of the twentieth century, David Eugene Smith wrote a book about teaching geometry. Although it was written for secondary school geometry teachers, his preface describing why he wrote the book is applicable for all grades. He said that his book “… stands for vitalizing geometry in every legitimate way; for improving the subject matter in such a manner as not to destroy the pupil's interest; for so teaching geometry as to make it appeal to pupils …” (Smith 1911, p. iv). At the beginning of the twenty-first century, the Principles and Standards for School Mathematics (NCTM 2000) gives us guidance in revitalizing geometry for elementary school students. In this article, we share some of its messages for teachers of prekindergarten through grade 5.
Math By the Month: March 2001
Authors: Mistretta Regina
Published: December 2020

The “Math by the Month” activities are designed to appeal directly to students. Students may work on the activities individually, with a partner, 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 “March Ahead to Basics” activities focus on students' identifying and using strategies derived from the generalizations and patterns that they discover in explorations using hundreds charts, manipulatives, and other models.
Strategies for Advancing Children's Mathematical Thinking
Authors: Fraivillig Judith
Published: December 2020

Ms. Smith, a first-grade teacher, asked her students how they could add thirty cents and twenty-seven cents. The students suggested several different solution methods. One student said that they could use the number grid to count. Ms. Smith asked where they should start, and the student said, “At thirty.” Together with the student, Ms. Smith counted twenty-seven more squares on the grid. After finishing, Ms. Smith asked whether the students knew a shortcut. Another student said to start on 27 and count by tens to end at 57.
Principles and Standards: Learning through Problems: A Powerful Approach to Teaching Mathematics
Authors: Trafton Paul R. , Midgett Carol
Published: December 2020

Problem solving has been a major focus of mathematics education over the past two decades. Much has been learned about the problem-solving capabilities of elementary school children and their use of strategies in solving problems. However, problem solving has typically existed apart from core curriculum objectives. In many situations, it is a focus only after specific concepts and skills are taught and only then to provide practice for those concepts and skills.
In My Opinion: October 2001
Authors: Watanabe Tad
Published: December 2020

As the statement above shows, Principles and Standards for School Mathematics (NCTM 2000) calls for focused and cohesive school mathematics curricula. To create such curricula, we must make hard decisions about what topics to include and what to remove from the curricula. What, then, are the “big ideas” in mathematics for primary grades? The current crowded state of primary curricula is the result of our inability to make hard decisions. It is about time that we tackle this difficult issue.
News from the Net: November 2001
Authors: Wilkinson Mary E.
Published: December 2020

Visit NASA online to find out about its videotape series, called NASA Connect, that began last year. Each program year offers seven 30- minute, fast-paced, entertaining videotapes that were filmed at various space centers and show how mathematics is used every day by NASA scientists and engineers. The shows are hosted by two young people and include spots by celebrity guests whom students will recognize.
Responses to the Patterns in Squares Problem
Authors: Boerst Tim
Published: December 2020

The problem that appeared in the November 2000.
How Many Marbles in the Jar? Estimation in the Early Grades
Authors: Taylor-Cox Jennifer
Published: December 2020

The all-too-familiar picture of estimation in the primary-grade classroom involves a jar of marbles. Students are required to make “guesses” and “estimates” related to the quantity of marbles that the jar contains. This article examines the known methods of estimation, considers several types of estimation, and attempts to characterize fruitful in-class estimation tasks for young learners by exploring the validity and possible extensions of “marble jar” estimation.
Second Graders Circumvent Addition and Subtraction Difficulties
Authors: Whitenack Joy W. , Knipping Nancy , Novinger Sue , Underwood Gail
Published: December 2020

At the beginning of the school year, Mrs. Underwood's second graders could work with groups of tens or groups of ones, but they did not consider the relationship between the numerals in the tens and ones places. For example, to add 25 + 19, children added the numerals in the tens place, then counted on by ones. First, they would add 20 and 10 to get 30. Next, they would count on by ones to add 14, instead of adding 5 and 9 to make 14, then partitioning 14 into 10 and 4, and adding all the tens and all the ones. To subtract 35 – 17, not surprisingly, students explained that 3 – 1 was 2 and that 5 – 7 was 2 to derive an answer of 22.
News from the Net: December 2001
Authors: Berggren Michelle , Moch Peggy
Published: December 2020

Colorful Mathematics, located at www.math.ucalgary.ca/~laf/colorful/ 4colors.html, presents mathematical concepts and problemsolving skills to students in grades K–12 through a series of games that involve graph theory and computer science. The site requires downloading.
How Do Children Know That What They Learn in Mathematics Is True?
Authors: Flores Alfinio
Published: December 2020

One of the distinctive marks of mathematical thinking is that we do not need to rely on memory or authority to know whether or not an assertion is true. In mathematics, we can prove our theorems. For students, however, the road to formal proofs is a long one. The ways in which children ascertain that a statement or fact in mathematics is true, accurate, and free from error evolve over time. The kind and amount of convincing evidence, or proof, that is appropriate for a child change as the child's mathematical thinking develops. Children must also learn at a young age that they do not need to rely on authority or memory to know that what they learn in mathematics is true.
Math By the Month: Light the Math Within
Authors: Cloke Gayle , Ewing Nola , Stevens Dory
Published: December 2020

These “Math by the Month” activities are designed to appeal directly to students. Students may work on the activities individually or in small groups, or the teacher may use them as problems of the week. No solutions are suggested so that students will look to themselves as the mathematical authority, thereby developing confidence to validate their work.
Developing Spatial Understanding through Building Polyhedrons
Authors: Ambrose Rebecca C. , Falkner Karen
Published: December 2020

What kind of spatial understanding do first and second graders have? What do they see when they look at three-dimensional objects? What words do they use to describe what they see? How might their visualization skills be sharpened by building and describing threedimensional structures? These questions emerged as we, a teacher educator and a classroom teacher, considered infusing spatial tasks into the primary school mathematics curriculum.
Multicultural Literature as a Context for Problem Solving: Children and Parents Learning Together
Authors: Strutchens Marilyn E.
Published: December 2020

In recent years, the mathematics community has given more attention to the role that mathematics plays in our cultural society and the contributions of different cultures to mathematics (Bishop 1988; D'Ambrosio 1985; NCTM 1989; Frankenstein 1990; Joseph 1993). Teachers are encouraged to include culture in a variety of ways in the mathematics classroom. Students can be encouraged to use mathematics as a tool to examine their cultural and social environments, traditions, and artifacts. In addition, mathematics learned by students outside the classroom can be used as a bridge to learning school mathematics.
Research, Reflection, Practice: Mathematics Learning and the Latino Student
Authors: Khisty Lena Licón
Published: December 2020

The mathematics learning—and overall academic achievement—of Latino children is still a major concern of educators across the country. As we think about the educational issues surrounding Latinos, we need to take into account factors related both to learning in two languages and to learning English as a second language (ESL). A major characteristic of the majority of Latino children is their affiliation with Spanish regardless of their proficiency in that language. Even a child who may not seem to be proficient in speaking Spanish may come from a home or community in which Spanish is spoken extensively. Thus, the child's environment is bilingual, which has a profound influence on his or her experiences, perceptions, and knowledge base. The challenge for mathematics educators is to understand and positively use the linguistic strengths and experiences that children bring to school.
Multicultural Mathematics Instruction: Approaches and Resources
Authors: Wiest Lynda R.
Published: December 2020

Mathematics, like all other subject areas, is embedded in cultural contexts. Cultural background frames the way we look at the world. It pervades the whole of who we are and strongly influences our perspectives, manner of thinking and communicating, and other ways of processing and interacting with our surroundings. Clearly, culture is much more at the heart of people than are surface-level customs, such as style of dress or common cuisine. Adding cultural content to instruction is inappropriate, therefore, if the content is merely grafted onto a topic, included as an optional or “extra” feature, or treated superficially.
Investigations: Sizing Up the River
Authors: Merz Alice H. , Thomason Carrie
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.
Celebrating 100 with Number Sense
Authors: Sztajn Paola
Published: December 2020

Joe woke me up. “Mom,” he said, “it's today!” “Today, what?” I managed to mumble. “The hundredth day of school, Mom; it is so special. I want to dress up to go to school and be real nice for our party,” he added. And so he did.
Picasso Masterpiece
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.