bluuebunny/crossref_metadata_2025 huggingface dataset:
In My Opinion: Five Reasons Why Classroom Teachers Should Write Articles for TCM
Authors: Watanabe Tad , White Dorothy
Published: December 2020

Over the past three years, 2001–2004, we had the privilege of serving on the Editorial Panel of Teaching Children Mathematics. During this time, many readers have expressed a desire for more articles written by classroom teachers. As members of the TCM Editorial Panel, we have tried to encourage classroom teachers to submit manuscripts, but with little success. We realize that classroom teachers are extremely busy and have to juggle many different responsibilities; however, we would like to present five reasons why classroom teachers should consider writing articles for TCM (or other professional journals).
Math by the Month: Mathematical Heroes
Authors: Marsh Julia , Loesing Jenine , Soucie Marilyn
Published: December 2020

The “Math by the Month” activities are designed to engage students to think like mathematicians. Students may work on the activities individually or in small groups. No solutions are suggested so that students will look to themselves for mathematical justification, thereby developing the confidence to validate their work.
By Way of Introduction: Teaching Children Mathematics: New (School) Year Resolutions
Authors: Lewis Cathie
Published: December 2020

The Editorial Panel of Teaching Children Mathematics (TCM) welcomes you to volume 12 and invites you to take an active role in our community of mathematics educators. Once again, we offer you an August issue to begin the school year. Continuing this new publishing schedule is just one indication of how committed we are to bringing you timely and informative articles and ideas. As always, the volume 12 publishing calendar will include nine issues, one each month from August through May, with a combined December/January issue. We will also offer the annual focus issue in October. This year, the theme is “Posing and Solving Problems.” Throughout the volume year, TCM will support NCTM's yearlong professional development focus, “Assessing to Learn and Learning to Assess.” A special icon on the table of contents will signify related articles and departments.
Problem Solvers: What's the Overlap?
Authors: Tayeh Carla
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: September 2006
Authors: Forrest Kristen , Schnabel Denise , Williams Margaret E.
Published: December 2020

The “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. In order to encourage students to look to themselves for mathematical justification and develop confidence to validate their own work, no solutions are suggested here.
Developing Number Sense through Real-Life Situations in School
Authors: Yang Der-Ching
Published: December 2020

An example of a fourth-grade lesson from Taiwan in which number sense is developed through real classroom interactions.
By Way of Introduction
Authors: Lewis Cathie , Schad Brian
Published: December 2020

“Measurement, the Forgotten Strand” was the title of a presentation given by Glenda Lappan, past president of the National Council of Teachers of Mathematics, at the 79th Annual Meeting in Orlando in April 2001. What an apt title! Measurement is a concept that, if not completely forgotten, is often taken for granted. Yet measurement is an integral part of all mathematics content as well as the content of most other subjects. Measurement is central in geometry lessons as well as in science. Despite their wide application, however, measurement lessons are often found at the end of traditional textbooks—in chapters that most teachers do not have time to teach or are insufficiently addressed. This fact is troubling when we stop to consider how completely measurement is integrated into our lives.
Teaching Mathematics Then and Now: Algebra in the Elementary Schools
Authors: Shipley James H.
Published: December 2020

I have never yet heard of a high school teacher's being satisfied with the first-year pupil's knowledge of common fractions, and the other day a 1. A. [a specific grade level] girl frankly admitted that she could not multiply 12 2/3 by 15 3/4 because she had skipped one grade, had then had algebra and geometry, and the review didn't touch on mixed numbers. Of course, this was not the fault of any teacher, but the fault of a system which is trying to crowd too many things into too small a space. The real efficiency of the schools does not depend upon their being housed in million-dollar buildings, under a well-organized administrative force, excellent equipment, etc.; it depends on two things,—what is taught, and how it is taught; and more especially upon the latter; for every teacher of mathematics knows that a pupil can derive as much permanent good from the study of a few topics or theorems, so presented as to be pleasing to the pupil, or at least interesting, and at the same time make him think, as he can from ten times the amount of material “rammed home” with the sole object of being reproduced at examinations. The policy of standardizing everything by examinations is doing our expensive school system an untold injury; the report of the city superintendent compares the schools according to the number of their pupils who pass the examinations, and the principal warns the teacher that he is rated according to the number of his pupils that pass, and this pressure is passed on to the pupil. Until some method of close class-room observation and supervision is introduced with a view to allowing free rein to a teacher's individuality and originality even at the expense of his pupil's failing the conventional examinations, it is hardly worth while suggesting other changes.
Math by the Month: Supermarket Math
Authors: Yagi Seanyelle , Olson Melfried
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 the confidence to validate their work.
Supporting Teacher Learning: Preservice Teachers Examine Gender Equity in Teaching Mathematics
Authors: Neumann Maureen D.
Published: December 2020

The National Council of Teachers of Mathematics recognizes that mathematical knowledge is essential for employment and full participation in our society. The strategic inclusion of the Equity Principle in NCTM's Principles and Standards for School Mathematics (2000) reflects the need in the mathematics education community to eliminate long-standing disparities in mathematics performance. However, incorporating equitable pedagogical practices into one's instruction does not mean that every student should receive identical instruction; rather, it “demands that reasonable and appropriate accommodations be made as needed to promote access and attainment [of mathematics knowledge] for all students” (NCTM 2000, p. 12).
Measure Up for Understanding: Reflect and Discuss
Authors: Dougherty Barbara J. , Venenciano Linda C. H.
Published: December 2020

How first graders' sense of number can be developed through the perspective of measurement. Includes a Reflect and Discuss component to use with colleagues. Measure Up is a research project for grades 1-5, and there is a summary of impact on math learning in later years.
Posing Problems That Matter: Investigating School Overcrowding
Authors: Turner Erin E. , Strawhun Beatriz T. Font
Published: December 2020

Angel and Naisha, two sixth-graders in Ms. Font's mathematics class, had the following conversation as they reflected on their experience with posing and investigating problems related to overcrowding at their school.
The Power of String: Building a Conceptual Foundation for Measuring Rate
Authors: Lucey Linda Polhemus , Jennings Sybillyn , Olson Peter , Rubenfeld Lester , Holmes Aliya E.
Published: December 2020

How can a qualitative manipulative such as string help students understand measurement? Specifically, can string help students conceptualize rate? Our analysis of the concept of rate led us to design lessons that isolated time and distance as variables and culminated in the string activity presented here. In this article, we describe the progression of these lessons and how they helped students build a conceptual foundation for rate. In fits and starts, we have come to appreciate the power of string as an instructional strategy that helps students connect their intuitive sense of speed with a beginning understanding of rate. Conceptually, this progression leads learners to reorganize the relationship between time and distance. The string lessons captivated us because we work in the world of Lego robotics. We mentor teachers in integrating new learning technologies into their mathematics curriculum. The lessons using string have reminded us that the value of integrating any technology, old or new, lies in its support of learning.
An Arts-Based Approach to Teaching Fractions
Authors: Goral Mary Barr , Wiest Lynda R.
Published: December 2020

“Fractions have always represented a considerable challenge for students, even into the middle grades,” noted Van de Walle (2004, p. 242), and the instructional experiences of most teachers validate this statement. Despite the fact that proportional reasoning is an important curriculum topic and a valuable life skill, students struggle to meaningfully grasp fraction concepts. To aid development of the concept of fractions, the National Council of Teachers of Mathematics (2000) recommends that students represent fractions by using physical materials and number lines. The visual and tactile input these materials afford, coupled with carefully designed reflection on the use of these tools, can bolster learning about fractions.
Math by the Month: Inventors and Their Inventions
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 these as problems of the week. Because no solutions are suggested, students will look to themselves for mathematical justification, thereby developing the confidence to validate their work.
Storytelling + Origami = Storigami Mathematics
Authors: Mastin Marla
Published: December 2020

All educators continually search for ways to assist students in learning mathematical concepts. The challenge for teachers is to provide a “thinking” curriculum and creative instructional methods while helping students recognize that they should be actively involved in their own learning. This article presents a way to engage students in mathematics through the use of an innovative instructional method based on constructivist theory, which emphasizes the “building” that takes place in the brain as a person learns and which is rooted in both the social and the cognitive perspective of learning.
Preparing for Problem Solving
Authors: Holden Becky
Published: December 2020

Jazmyne, a first grader in my classroom, gave me a note that read, “Teach me everything you know.” What a daunting responsibility! As a teacher in an urban magnet school where 80 percent of my students receive free or reduced lunch, I find that the challenge of preparing them to reach required mathematics standards can be overwhelming.
Focal Points—Grades 1 and 2
Authors: Sarama Julie , Clements Douglas H.
Published: December 2020

This is the third in a series of articles exploring the use of the 2006 National Council of Teachers of Mathematics (NCTM) publication, Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence. The series introduction from NCTM President Skip Fennell, explaining what the Curriculum Focal Points are and why NCTM developed them, appeared in the December 2007/January 2008 issue of Teaching Children Mathematics (page 315). In subsequent TCM articles, the authors of the various grade bands discuss focal points for one or two grade levels. Because one principle of Curriculum Focal Points is that of cohesive curriculum, in which ideas develop across the grades, we encourage teachers of all grade levels to read the full series.
Problem-Solving Support for English Language Learners
Authors: Wiest Lynda R.
Published: December 2020

According to the National Clearinghouse for English Language Acquisition and Language Instruction Educational Programs, the growing number of students with limited English proficiency includes slightly more than 10 percent of K–12 students in today's U.S. classrooms (NCELA 2006). English language learners (ELLs) may need special support to meet the educational standards we set for students. In its Equity Principle, the National Council of Teachers of Mathematics states, “Some students may need further assistance to meet high mathematics expectations. Students who are not native speakers of English, for instance, may need special attention to allow them to participate fully in classroom discussions” (NCTM 2000, p. 12). This need has become particularly important because mathematics tasks are increasingly contextualized and thus verbal in nature, in addition to the fact that greater emphasis has been placed on communication in mathematics classrooms.
Investigations: 7,000 Pancakes!
Authors: Julien Laurie St.
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 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.
Math by the Month: Passport to Travel
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. Most children have done some type of traveling. Whether it is a trip around their neighborhood, to another city, or to a different state or country, traveling is an adventure. This month, students will use the context of travel to engage in mathematics problems that promote logical thinking, graphing, measurement, number sense, and problem solving. With summer on the way, it is time for a trip!
Identifying Opportunities to Connect Parents, Students, and Mathematics
Authors: Fagan Nancy M.
Published: December 2020

I ran down my to-do list for my first Parent Math Night: Invitations had been sent, handouts copied, overheads prepared, and take-home materials packaged. Everything was planned and organized, and I was excited about the event—“Math Night for Parents: What Does Computation Look Like These Days?” I thought my title was creative and certainly addressed concerns parents had about these “newfangled” ways to do mathematics. Imagine my disappointment when a grand total of three parents came!
Math by the Month: Don't Burst My Bubble
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 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. The following activities are designed to help you and your students explore bubbles and spheres through mathematical investigations involving number sense and operations, data collection, pattern and algebra, measurement, communication, and representation.
On-the-Spot Assessments
Authors: Diezmann Carmel
Published: December 2020

Informal evaluations informed this teacher's instruction, facilitating her young students' prediction skills throughout a series of number investigations.
Investigations: Connecting Multiplication to Contexts and Language
Authors: Sullivan A. Deanie , McDuffie Amy Roth
Published: December 2020

This department features children's explorations in mathematics and presents teachers with open-ended investigations to enhance mathematics instruction. The tasks invoke problem solving and reasoning, require communication skills, connect various mathematical concepts and principles, and have been classroom tested.
Become “Environmentally” Aware
Authors: Allen Rob , Chval Kathryn B.
Published: December 2020

Facing a classroom of students with a plethora of academic and social needs, this fifth-grade teacher recognizes an obligation to analyze his teaching approach.
Second-Grade “Professors”
Authors: Wu Zhonghe , An Shuhua , King Joyce , Ramirez Melissa , Evans Stacee
Published: December 2020

Using graphic organizers and the mathematician's chair enhances second graders' proficiency in solving word problems.
Models for Initial Decimal Ideas
Authors: Cramer Kathleen A. , Monson Debra S. , Wyberg Terry , Leavitt Seth , Whitney Stephanie B.
Published: December 2020

Put a twist on the familiar 10 × 10 grid model to build your students' understanding of effective decimal models.
In My Opinion: Does Race Matter?
Authors: Martin Danny Bernard
Published: December 2020

To the detriment of young African American learners, racial achievement gap rhetoric impacts social constructs in American classrooms. In my opinion, recent mathematics education reforms, despite equity-oriented rhetoric expressing concern for all children (NCTM 1989, 2000; RAND Mathematics Study Panel 2003), have instead helped foster an environment where African American children continue to be viewed as intellectually inferior and mathematically illiterate, usually in relation to children who are identified as white or Asian.
Cultural Capital in Children's Number Representations: Reflect and Discuss
Authors: McCulloch Allison W. , Marshall Patricia L. , DeCuir-Gunby Jessica T.
Published: December 2020

Youngsters' out-of-school knowledge influences their pictorial representations of number.
Promoting equity through reasoning
Authors: Mueller Mary F. , Maher Carolyn A.
Published: December 2020

Learn how five characteristics of tasks and learning environments led these sixth graders to successful problem solving using direct and indirect reasoning to justify their solutions, make their justifications public, and respond to mathematical arguments.
From the Classroom: Student-constructed problems extend proportional reasoning
Authors: Lamm Millard W. , Pugalee David K.
Published: December 2020

Proportional reasoning is perhaps one of the most important types of mathematical thinking for elementary school students to develop. It includes aspects of rational numbers, spans the entire mathematics curriculum, and is a significant foundation for mathematical proficiency. Understanding students' use of proportional reasoning is a basis on which to develop benchmarks or guideposts that can provide a descriptive picture of the learning progression between elementary school math and mathematics encountered in later grades.
From the Classroom: Two of everything
Authors: McNamara Julie C.
Published: December 2020

I have found the story of the Haktaks and their magic pot to be a very meaningful way to introduce third through fifth graders to the idea of a rule, or function, and how to express one algebraically. Although this can be a difficult topic for elementary students to understand because of the “developmental nature of mathematical skills,” when topics are introduced in meaningful ways, even young students can understand and use them successfully (Carraher et al. 2006).
Building word problems: What does it take?
Authors: Barlow Angela T.
Published: December 2020

Use this framework to open a window between your students' experiences and the world of problem solving.
Connections: Prime decomposition using tools
Authors: Kurz Terri , Garcia Jorge
Published: December 2020

Factoring numbers through multiplication using primes is an important concept for students to understand. Those in grades 3–5 should be able to find equivalent representations of the same number by de composing and composing numbers (NCTM 2000). One aspect of this essential skill is prime decomposition, which relates to such mathematical topics as simplifying, divisibility, square roots, and fractions. Prime numbers are crucial building blocks for understanding numbers and their multiplicative relationships (Zazkis and Liljedahl 2004).
Math by the Month: A trip to the Zoo
Authors: Ricks Leitze Annette , Adams Jacqueline , Alexander Asheley S. , Gray Ian A. , Hampton Holly , Janke Susan E. , Stith Antoinette M.
Published: December 2020

Most of us will never be up close and personal with exotic wildlife or endangered species. However, with an active imagination, a field trip can become a jungle safari. This month, join our imaginary mathematical zoo trip.
What children taught us about rigor
Authors: Bintz William P. , Delano Moore Sara
Published: December 2020

The stars aligned when two demonstration lessons to integrate math and literature revealed the disconnect between the “constellations” of curriculum and learning.
The one-minute challenge
Authors: Clarke Doug M. , Downton Ann , Roche Anne
Published: December 2020

Learn a simple game to support your students' mathematical learning across a range of content areas.
Creative Use of Worksheets: Lessons My Daughter Taught Me
Authors: Anderson Ann
Published: December 2020

Now that equating mathematics with drill and practice has run its course, worksheets are a thing of the past.
A Teacher's Journal: Adding Taste to Mathematics
Authors: Kemp Champee C.
Published: December 2020

To help meet the special needs of my Chapter I mathematics students, those in grades 2-5 who have been identified as performing below grade-level expectations, I implemented a unit on measurement and fractions. This unit included using the computer, going on a field trip, and reinforcing the concepts taught by continued use of a specific computer program.
A Common-Cents Approach to Fractions
Authors: Rocke Judy
Published: December 2020

Do students really understand what a school's speed-limit sign means? Does the 20 niph speed limit apply every school day, all day long, or does it apply only during the time the children are present in the school yard? Signs can be so confusing!
Implementing the Assessment Standards for School Mathematics: Seamless Assessment/Instruction = Good Teaching
Authors: Lambdin Diana V. , Forseth Clare
Published: December 2020

[Assessment serves] to help teachers better understand what students know and make meaningful instructional decisions. (NCTM 1989, 189)

Assessment of students and analysis of instruction are fundamentally interconnected. Mathematics teachers should monitor students' learning on an ongoing basis in order to assess and adjust their teaching. (NCTM 1991, 63)
An Exploration of Fifty Nifty Stages
Authors: Orman Sheryl A. , Schneider Debra J.
Published: December 2020

Studying the United Slates is a traditional part of the upper-elementary social studies curriculum. A common approach is for students to acquire facts about regions, states, capitals, natural resources, industries, agriculture, and tourist attractions and to work individually or in pairs to study one state in depth and to prepare a written or oral report. Despite these efforts, we continually hear that the people of the United States have a weak understanding of geography as well as of their responsibilities as citizens. A more effective approach to studying various aspects of the United States is needed.
Investigations: Building Mathematics
Authors: Small Marian S.
Published: December 2020

The “investigations” section 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 investigations are designed to he rich tasks that tend to evolve as they are conducted.
Investigations
Authors: Brahier Anne F. , Brahier Daniel J.
Published: December 2020

The “investigations” department recognizes the importance of children's exploring hands-on and minds-on mathematics and, therefore, presents teachers with open-ended explorations to enhance mathematical instruction. These meaningful tasks are designed to evolve as they are conducted.
Mathematical Communication Through Student-Construced Questions
Authors: Menon Ramakrishnan
Published: December 2020

Mathematical communication among students should receive increased emphasis in the classroom according to NCTM's Curriculum and Evaluation Standarda for School Mathematics (1989). Two modes of student communication are evident in the mathematics classroom, the expressive mode and the receptive mode, as identified by Del Campo and Clements (1987).
Links to Literature: Counting on Company Row
Authors: Smith Jacquelin J.
Published: December 2020

Children's literature generates many opportunities for contextual problem solving. Some problems arising from the literature clarify mathematical understandings, but reasoning about a mathematical problem embedded in a story passage can also enhance understanding of the literature as well as the mathematics.
Promising Research, Programs, and Projects: The Jefferson Math Lab
Authors: Brun Mary
Published: December 2020

Welcome to the Jefferson Math Lab, where mathematics, technology, and manipulates have come together to form a state-of-the-art approach to turning students on to mathematics. Inspired by “Teaching Math Their Way,” an article by Karen Tankersley in Educational Leadership (May 1993), our staff envisioned a special room in our building dedicated to mathematical pursuits, including critical thinking, cooperative problem solving, and meaningful concept development.
Probing the Foundations of Algebra: Grade-4 Pattern Items in NAEP
Authors: Kenney Patricio Ann , Silver Edward A.
Published: December 2020

Suppose that you asked fourth-grade students to predict whether the number 375 would ever appear in a sequence of numbers generated by multiplying 2s (4, 8, 16, 32, …). Would students recognize the impossibility of 375 appearing in the sequence? Would they give a clear, complete explanation as to why 375 would not appear?
A Foundation for Algebraic Reasoning In the Early Grades
Authors: Yackel Erna
Published: December 2020

For many adults, algebra means solving systems of equations; finding the value of an unknown; using the quadratic formula; or otherwise working within a system of formulas, equations, and literal symbols.
Doing Algebra in Grades K-4
Authors: Usiskin Zolman
Published: December 2020

About thirty-five years ago the movement to incorporate geometry into the elementary grades began. To many elementary school teachers, the mention of the word geometry brought back memories of a high school geometry course that dealt with abstraction and proof. The thought of teaching children this geometry was naturally viewed with incredulity.
Connecting Process Problem Solving to Children's Litcrature
Authors: Leitze Annette Ricks
Published: December 2020

Since the publication of the Curriculum and evaluation Standards for School Mathematics (NCTM 1989), many mathematics teachers and educators have become especially interested in making mathematical connections, such as that found between mathematics and children's literature.
Math by the Month
Authors: LeBeau Sue
Published: December 2020

The Math by the Month activities are designed to appeal directly to students. Students may work on the activities individually, in pairs, or in small groups. No solutions are suggested or provided for the 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.
Research into Practice: Place Value as the Key to Teaching Decimal Operations
Authors: Sowder Judith
Published: December 2020

Some years ago I examined several middle school students' understanding of numbers (Threadgill-Sowder 1984). The answers that students gave me during that study showed me that their understanding, developed largely through experiences in the elementary grades, was fuzzy and led me to undertake a decade of research on children's number sense in the elementary and middle school grades. I will set the stage for this article by sharing two of the questions I gave the students during that study and some of the responses I received.
Links to Literature: Serving Up Number Sense and Problem Solving: Dinner at the Panda Palace
Authors: Wickett Maryann S.
Published: December 2020

I have a book I would like to share with you. It's about a panda ….” Thus began our class discussion of Dinner at the Panda Palace (Calmenson 1991), a predictable book that begins with the arrival of one elephant, followed by two lions, three pigs, and so on (figs. 1 and 2).
Reviewing and Viewing
Authors: Whitin David J.
Published: December 2020

Prices on software, books, and materials are subject to change. Consult the suppliers for the current prices The comments reflect the reviewers' opinions and do not imply endorsement by the National Council of Teachers of Mathematics.
Making the NCTM's Standard Work for Emergent English Speakers
Authors: Garrison Leslie
Published: December 2020

When the National Council of Teachers of Mathematics published the Curriculum and Evaluation Standard for School Mathematics in 1989, new guidelines for mathematics curriculum and instruction were established. At the heart of the new standards were four guiding principles for mathematics instruction.
A Teacher's Journal: From Caterpillar to Butterfly A Mathematics Teacher's Struggle to Grow Professionally
Authors: Lawson Doris P.
Published: December 2020

This quote is part of the letter that Barry B. wrote about the fourth-grade mathematics program at Saint Thomas, Regional School. I doubt that he or anyone else would have written such a letter to me five years ago. My mathematics program, like so many around the country, was textbook driven, linear, abstract.
Math by the Month
Authors: Holly Karen
Published: December 2020

These activities are designed to appeal directly to students, giving them open-ended questions to engage their intellect. Students may work on the activities individually or in small groups. No solutions are suggested so that students may develop the confidence to validate their own work. Teachers are encouraged to adapt these activities from one grade level to another, coordinate them with other mathematical topics, and integrate them in other curriculum areas.
The Function Box and Fourth Graders: Squares, Cubes, and Circles
Authors: Sulzer James S.
Published: December 2020

The function box is a familiar teaching tool in many elementary schools. Its basic idea is simple: a box has an “in” slot and an “out” slot. A certain quantity goes in and comes out changed. Students have to guess the function that changed the quantity. For instance, if three pencils go in and eight come out, the function rule could be “plus 5” and expressed as x + 5, or it could be 2x + 2 or x2 − 1, among other possibilities.
Implementing the Assessment Standards: Make New Lessons, But Keep the Old: One Is Silver, the Other Is Gold
Authors: Nieding Deborah A.
Published: December 2020

Teachers are good examples of the truth that learning is a lifelong process. As a teacher educator, I am faced with the task of assisting teachers as they reflect on their classroom practices and look for methods and resources to improve their practices. Although developmental growth is ongoing, certain events and situations serve as catalysts for growth surges. A current catalyst, educational reform, has been lauded for the last six decades.
What Makes a Corner a Corner?
Authors: Wallace John , Pearson Jennifer
Published: December 2020

The group of grade-3 boys enthusiastically grabbed the box of blocks and headed for their desks. The boys had been waiting three days for their turn to use the blocks. I had let them play with the blocks before school or if they mate privilege.
Problem Solvers: How Many Times Can You Take One-Half?
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.
Problem Solvers
Authors: Olson Judith
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 the students’ work, analyze the classroom dialogue, and submit the resulting insights to this department. Remember that even student misconceptions are interesting.
Students’ Explanations of Place Value in Addition and Subtraction
Authors: Nagel Nancy G. , Swingen Cynthia Carol
Published: December 2020

Research studies and experiences with young children reveal that many of them have difficulty learning and applying place-value concepts in mathematics.
Problem Solvers: What Shapes Can You Make?
Authors: Olson Judith
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.
Research, Reflection, Practice: Geometry Results from the Third International Mathematics and Science Study
Authors: Battista Michael T.
Published: December 2020

How well would your students do on this problem?
Geometric Flips via the Arts
Authors: Sellke Donald H.
Published: December 2020

The activities described here are designed to enhance students' spatial-reasoning ability, a neglected part of the geometry curriculum, while encouraging them to reason, problem solve, communicate, and make connections between school subjects and between geometry and the real world. These activities involve tasks which, whether done in a large-group setting, smaller cooperative groups, or individually, require students to conjecture and then verify their conjectures as they investigate reflections of objects–letters and words–from the discipline of language arts. The tasks give teachers opportunities to question, listen, and assess decision- making skills, which are all part of the NCTM's vision of effective teaching (1991).
Early Childhood Corner: Helping at Home
Authors: Kline Kate
Published: December 2020

Parents often ask for suggestions about activities to do with their young children at home to help further their mathematical understanding. Many of them have helped their children learn the counting sequence or recognize numerals, but they are also interested in activities that extend children's thinking about numbers and that the whole family can do together. Many school districts have adopted new Standards-based curricula that develop children's thinking in a way that may not be familiar to parents; therefore, they need assistance in doing at-home activities that are consistent with the development of number ideas in school.
Problem Solvers: The Orange Game
Authors: Sakshaug Lynae
Published: December 2020

The goal of the “Problem Solvers” department is to foster improved communication among teachers by posing one problem each month for K–6 teachers to try with their students. Every teacher can become an author: pose the problem, reflect on your students' work, analyze the classroom dialogue, and submit the resulting insights to this department. Remember that even student misconceptions are interesting.
Strategies for Basic-Facts Instruction
Authors: Isaacs Andrew C. , Carroll William M.
Published: December 2020

In a class of beginning second graders, children explained with these typical replies how they solved the number fact 8 + 7: “I know 7 + 7 is 14, and 1 more is 15”; “8 + 2 makes 10. But 7 has 5 more, so the answer is 15”; and “I just knew the answer was 15.” Teaching basic number facts like 8 + 7 has been a goal of elementary mathematics instruction for more than 100 years and continues to be important today.
Math by the Month: Are You Measuring Up?
Authors: Reeves Muffet
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.
The Language of Time
Authors: Friederwitzer Fredda , Berman Barbara
Published: December 2020

A logical model to teach about time, making a strong connection to fractions.
Why Are Some Solids Perfect? Conjectures and Experiments by Third Graders
Authors: Lehrer Richard , Curtis Carmen
Published: December 2020

Describes how children searched for Platonic solids and constructed a precise definition to classify these solids.
How Many Spots Does a Cheetah Have?
Authors: Reed Kristine M.
Published: December 2020

First graders' mathematical investigation of the number of spots on a cheetah. Young children invented counting and estimation strategies, and a spirit of mathematical inquiry grew in the classroom.
A Parent's Portfolio Observing the Power of Matt, the Mathematician
Authors: Moldavan Carla C.
Published: December 2020

Relates some mathematical episodes involving a young child and discusses implications for teachers.
The Role of Tasks in Developing Communities of Mathematical Inquiry
Authors: Peressini Dominic , Knuth Eric
Published: December 2020

Examines students' responses to a mathematically rich task and explores approaches for using such tasks to foster inquiry that engages children in mathematical practice.
Research, Reflection, Practice: Children's Inventions for Multidigit Multiplication and Division
Authors: Caliandro Christine Koller
Published: December 2020

Children can invent their own methods for solving multidigit multiplication and division problems without learning the conventional algorithms that we normally teach them. Strong arguments can be made for the importance of encouraging children to invent their own arithmetic. Steffe (1994) says, “Children, when faced with their first arithmetical problems, use their current mathematical schemes to attempt to solve them” (p. 3) and “ ‘knowledge’ that involves carrying out actions or operations cannot be instilled ready-made into students or children but must, quite literally, be actively built up by them” (p. 4). These exciting thoughts make a great deal of sense to me, and they correspond to the way that I like to teach.
A Teacher's Journal: Don't Laugh-That's Math
Authors: Zaino Judith A.
Published: December 2020

Through years of teaching, I have found that parents tend to be more intimidated by mathematics than by any other subject in the curriculum. They often say that they are “not good in math” and that they feel helpless in solving problems that require more than rote recitation of facts. Some feel frustrated by what they perceive as the “new math.” Most parents are very interested in their children's education; they want to help but are not sure that they are doing an adequate job.
Problem Solvers: Nets and Polyhedra
Authors: Sakshaug Lynae , Voorst Conrad Van
Published: December 2020

The goal of the “Problem Solvers” department is to foster improved communication among teachers by posing one problem each month for K–6 teachers to try with their students. Every teacher can become an author: pose the problem, reflect on your students' work, analyze the classroom dialogue, and submit the resulting insights to this department. Remember that even students' misconceptions are interesting.
Links to Literature: From Habitats to Legs: Using Science-Themed Counting Books to Foster Connections
Authors: Fleege Pamela O. , Thompson Denisse R.
Published: December 2020

Principles and Standards for School Mathematics (NCTM 2000) recommends that the elementary school curriculum provide opportunities for students to connect mathematics with other subject areas. The elementary school science curriculum is one area in which such connections are natural. In particular, National Science Education Standards (NRC 1996) recommends that mathematics and science be integrated “to enhance student use and understanding of mathematics in the study of science and to improve student understanding of mathematics” (p. 214). With the increasing availability of children's books that have strong mathematics and science connections, opportunities arise for teachers to connect language arts, mathematics, and science in ways that appeal to children.
In My Opinion: May 2001
Authors: Midobuche Eva
Published: December 2020

The class had just finished a mathematics lesson on multiplication and was preparing for lunch. The students had created edible “spiders” out of crackers, peanut butter, pretzels, and raisins. The teacher had given the class a recipe for one spider. The challenge for students was to calculate how much of each ingredient was needed for each small group so that each group member could make his or her own spider. The smell of peanut butter was making the children very hungry, and some had started to eat their peanut-butter-andcracker spiders. However, most of the Hispanic children were wrapping their spiders in paper napkins and putting them in their desks. They were saving their treats to take home so that they could share them with their families. As the children were doing this, many of my childhood memories began to surface. How many times had I saved things to share at home?
Problem Solvers: Everyone's Playing Basketball
Authors: Sakshaug Lynae , Voorst Conrad Van
Published: December 2020

The goal of the “Problem Solvers” department is to foster improved communication among teachers by presenting one problem each month for teachers in grades K–6 to try with their students. Pose the problem to your students, reflect on their work, analyze the classroom dialogue, and share your analyses with others by submitting the resulting insights to this department. Every teacher can help us all better understand children's capabilities and thinking about mathematics with their contributions to the journal. Remember that even students' misconceptions are interesting.
Links to Literature: May 2001
Authors: Borden Jorie , Geskus Elsa
Published: December 2020

The phenomenal resurgence of children's literature in the marketplace has allowed teachers to help their students construct new knowledge by fostering the love of literature while teaching skills and knowledge. Principles and Standards for School Mathematics (NCTM 2000) recommends connecting mathematics with the real-world experiences of children. The authors chose Cook-a-Doodle-Doo! (Stevens and Crummel 1999) to provide students with opportunities for problem solving, estimating, predictive reading, and enjoyable eating.
Investigations: Bubble-Mania!
Authors: Cline Laura J.
Published: December 2020

The purpose of the “Investigations” department is to provide mathematically rich and inviting contexts in which children and their teachers solve problems, communicate, and reason. Investigations encourage students to make connections among mathematical ideas, as well as connections with contexts outside of mathematics. As students collaborate, experiment, explore, collect data, research various sources, and engage in activities during the investigation, they will have opportunities to represent their mathematical ideas in multiple ways.
Teaching Addition and Substraction Facts: A Chinese Perspective
Authors: Sun Wei , Zhang Joanne Y.
Published: December 2020

In its Principles and Standards for School Mathematics, the NCTM suggests that fluency with basic addition and subtraction number combinations is a goal in teaching whole-number computation (NCTM 2000, p. 84). A mastery of lower-order skills instills confidence in students and facilitates higher-order thinking. The ability to automatically recall facts strengthens mathematical ability, mental mathematics, and higher-order mathematical learning. Without this automation, students have difficulty performing advanced operations.
Early Childhood Corner: October 2001
Authors: Copley Juanita V.
Published: December 2020

At 6:45 in the morning on the first day of the Early Childhood Mathematics Collaborative, I arrive at Jessup Elementary School and am greeted by several early kindergartners: “Hey, Mrs. Copley, is everyone coming?” “Where have you been? Hey, our class can get twelve people standing in the counting circle.” “I've lost a tooth since you were here!” A first-grade teacher walks in with me, explaining that she has wonderful work from her students: “Just wait till we meet and you see their word problems. The students' thinking and reasoning are so obvious!” As we begin to unload, two very nervous undergraduate students wander in and explain that they have arrived more than ninety minutes early “so we wouldn't be late!” They quickly explain that they have been up all night worrying about teaching mathematics to real children and that if possible, they would like to observe today and perhaps teach on another day. I smile and assure them that everything will be fine. Within two hours, more than 800 students, 40 preservice teachers, and 50 faculty members arrive. Another semester of the Early Childhood Mathematics Collaborative (ECMC) has begun.
Horizons A Mother-Daughter Mathematics Club
Authors: Boling Kimberly B. , Larson Carol Novillis
Published: December 2020

The idea for organizing a mother-daughter Saturday mathematics club came from readings that one of the authors did for a graduate course in elementary mathematics curriculum. As a thirdgrade teacher, Boling was startled by Boswell's (1985) claim that by third grade, children perceive mathematics to be in the male domain of the adult world. Phillips and Ebrahimi (1993) explain, “By the time students reach high school, the overwhelming majority are already mathematically scarred … they dislike mathematics” (p. 62). Heid and Jump (1993) state that women make up 51 percent of the population, 45 percent of the nation's work force, yet only 11 percent of scientists, mathematicians, and engineers. They claim that “the early adolescent years of 9–13 are critical for psychological, social, and cognitive development in the fields of math and science” (p. 161).