bluuebunny/crossref_metadata_2025 huggingface dataset:
CoronaPandemie und organisierte Zivilgesellschaft: Krise oder Chance? Ergebnisse eines real-time-Führungskräfte-Panels
Authors: Tahmaz Birthe
Published: December 2020

Die Corona-Pandemie hat durch die Erkrankung und den Tod vieler Menschen Deutschland in eine Krise gestürzt. Die Maßnahmen zur Eindämmung des Virus bedingen weitere Einschränkungen für das zivilgesellschaftliche Engagement. Krisen als Prozesse des Wandels bergen jedoch auch immer Momente der Chance, so auch für die organisierte Zivilgesellschaft. Diese These beleuchtet der Beitrag anhand der Ergebnisse des Engagement-Barometers, einer Panelbefragung von Zivilgesellschaft in Zahlen (ZiviZ) im Stifterverband. Mit finanzieller Unterstützung der Länder Bayern, Berlin, Rheinland-Pfalz und der Ehrenamtsstiftung Mecklenburg-Vorpommern hat ZiviZ im Frühjahr und Sommer 2020 Führungskräfte von Verbänden und Infrastruktureinrichtungen gemeinnütziger Organisationen zur Situation in der Pandemie befragt. Im Mittelpunkt standen vor allem die Mitglieder- und Engagemententwicklung, die finanzielle Situation sowie Digitalisierungsprozesse.
Approaches to the World
Authors: Lindemann Gesa
Published: December 2020

Responding to the critique of methodological ethnocentrism, Lindemann develops a new general social theory that is also highly sensitive to socio-cultural differences. Drawing on Helmuth Plessner’s theory of excentric positionality, social order is understood as a symbolically and technically mediated spatio-temporal order that is integrated by an order of violence. Lindemann hereby brings together three significant aspects of recent debates: the debates on the necessity of a theoretical turn (such as the linguistic turn, the material turn, the body turn, the pictorial turn and the spatial turn); second, the debates on the actor status of non-humans and the borders of the social world, and third, the discussions about the role of violence in structuring social processes.
Xeroderma Pigmentosum in Children: Report of 4 Cases
Authors: Miri-Aliabad Ghasem , Asgarzadeh Leila
Published: December 2020

: Xeroderma pigmentosum (XP) is a rare genetic disorder inherited in an autosomal recessive pattern. Patients with XP are extremely sensitive to ultraviolet (UV) radiation that leads to defective DNA repair. People with XP often suffer from problems in the eyes, face, neck, and other areas of the body, frequently exposed to sunlight. It is characterized by photosensitivity, dry skin, pigmentary changes of the skin, premature skin aging, and a considerable increase in incidence rates of malignant skin tumors. There is no cure for XP. In this article, we have described four patients from two families, three of whom had malignant skin tumors.
Handbook of Item Response Theory: Recenze třídílného sborníku (van der Linden, 2016)
Authors: Cígler Hynek
Published: December 2020

Teorie odpovědi na položku je jednou z dominantních psychometrických teorií měření v psychologii, pedagogickém výzkumu a sociálních vědách vůbec. Zatímco však v případě klasické testové teorie, teorie zobecnitelnosti  a dalších „tradičních“ teorií máme k dispozici řadu přehledových, autoritativních zdrojů, v případě teorie odpovědi na položku dosud podobná kniha chyběla. Nedávno vydaný třídílný Handbook of Item Response Theory (van der Linden, 2016) však více než zaplnil tuto mezeru. Na zhruba 1.500 stranách předkládá vynikající a hlavně komplexní shrnutí aktuálního stavu poznání, a to od jednotlivých modelů přes statistické postupy a estimační nástroje až po aplikaci a konkrétní příklady dobré praxe. Domnívám se, že přinejmenším první a třetí díl sborníku by neměl chybět v příruční knihovně žádného psychometrika či kvantitativně orientovaného sociálního vědce; své si v něm však nečekaně najdou i statistikové, informatici a další.
Math by the Month
Authors: Shipley Lydia Moore
Published: December 2020

These activities are designed to speak directly to students, giving them open-ended questions to engage their intellect through their interests. Students are encouraged to work on the activities individually, in pairs, or in small groups. No answers are given for the questions so that students are encouraged to look to themselves as the mathematical authority, thereby developing the confidence and critical-thinking skills necessary to validate their thinking.
Student-Authored Minimath
Authors: Fox Becky , Guenther Jeon , Lubarski Diane
Published: December 2020

First-grade children at Kingsley Elementary School in Naperville, Illinois, frequently arrive at school with shouts of “Minimath! Minimath! Who's the author today? Can we begin now?” Minimath is a written daily review of mathematics problems that Naperville School District 203 has furnished for its teachers in grades 1-5. Topics include arithmetic, patterning, number sense, geometry, measurement, and fractions. Children use strategies and computational skills to solve the problems.
Our Heritage Leads to Future Challenges
Authors: Gates James D.
Published: December 2020

The seventy-fifth anniversary of the founding of the National Council of Teachers of Mathematics is being celebrated during 1994-95. We are celebrating the teaching of school mathematics and the many contributions of teachers of mathematics.
Tricky Triangles: A Tale of One, Two, Three Researchers
Authors: Woleck Kristine Reed
Published: December 2020

The manner in which research can inform classroom practice, the manner in which classroom practice can contribute to research in the field, and the valuable dialogue that can occur between classroom teacher and university researcher.
A Teacher's Journal: Opportunities to Develop Place Value through Student Dialogue
Authors: Kari Amy R. , Anderson Catherine B.
Published: December 2020

The problem 11 + 9 was written on the board at the front of the room. Eleven first graders and nine second graders sat on the carpet, their facial expressions intent as they thought about solutions. I had asked them to try to think of strategies they could use that did not involve counting on their fingers. They did not use paper and pencil because this was what we call “Mental Math” time at our school.
News from the Net: The MegaPenny Project
Authors: Irving Kimberly J.
Published: December 2020

Every year teachers start their mathematics instruction with lessons on place value, even though they know that the teachers before them taught the same lesson. When I found the MegaPenny Project at www.kokogiak.com/megapenny, I knew the site would put a new spark in my review of place-value skills.
A Teacher's Journal: Large-Scale Family Math Nights: A Primer for Collaboration
Authors: Schussheim Joan Yares
Published: December 2020

NCTM's vision for mathematics in the new millennium includes an invitation to parents to become partners in the mathematics education of their children (NCTM 2000). Encouraging families to become problem-solving risk takers as they turn daily mathematics moments into mathematics events, to establish learning environments at home, and to informally work together on mathematics games and concept development are positive goals for all educators. The purpose of our school's Family Math Night is to provide a friendly, nonthreatening environment for teachers to initiate a dialogue, demystify a subject, and share new challenges; the event is about mathematics learning, mathematics sharing, and having fun with mathematics.
Supporting Teacher Learning: Focusing Conversations to Promote Teacher Thinking
Authors: Huinker DeAnn , Freckmann Janis L.
Published: December 2020

Tamara, a preservice teacher, taught a lesson on fractions to a class of fourth-grade students in her field-experience practicum. The instructor of her mathematics methods course observed the lesson. As they met in the hallway to debrief the teaching experience, the instructor began by asking, “How do you think your lesson went?” Tamara replied, “Great. I got through my entire lesson plan.” Tamara's comment and the subsequent discussion revealed that she was focused on her actions as the teacher but not on the dynamics of instruction (Cohen and Ball 2001).
Investigations: Picnicking with Fractions
Authors: Kosbob Sarah , Moyer Patricia S.
Published: December 2020

This department features children's hands-on and minds-on explorations in mathematics and presents teachers with open-ended investigations to enhance mathematics instruction. These tasks invoke problem solving and reasoning, require communication skills, and connect various mathematical concepts and principles. The ideas presented here have been tested in classroom settings.
Lessons Learned from Students about Assessment and Instruction
Authors: Kitchen Richard S. , Wilson Linda
Published: December 2020

“Joey, can you tell me what you were thinking when you were looking at the diagram?” “It looks like the keel of a boat.”
Zero: A None Number?
Authors: Anthony Glenda J. , Walshaw Margaret A.
Published: December 2020

In his book The Mathematical Brain, Brian Butterworth (1999) claims that one of the most important abilities modern man possesses is the ability to use numbers. Butterworth argues that this ability has “raised us from cave-dwellers using stone tools to creators of great cities and modern science” (p. 1). In the history of the development of our decimal number system, the introduction of zero was the most significant achievement—an achievement that enabled calculation with greater numbers to become commonplace. Although we use the symbol 0 constantly, many misconceptions abound, and the placement of zero in school curricula mirrors the somewhat meandering pathway of its development.
Planning Strategies for Students with Special Needs: A Professional Development Activity
Authors: Brodesky Amy R. , Gross Fred E. , McTigue Anna S. , Tierney Cornelia C.
Published: December 2020

In today's mathematics classrooms, teachers are confronted with an increasing range of learners, including students with special needs. On the national level, 13.2 percent of students have identified disabilities. This translates to 6,195,113 students, a jump of 30 percent from 1990 to 2000 (National Center for Education Statistics 2001). The Individuals with Disabilities in Education Act of 1997 (IDEA) mandates that students with disabilities have access to the general education curriculum. This legislation has led to an increase in the number of students with disabilities who are included in regular education classes. Many classroom teachers feel overwhelmed by the challenges of responding to the learning needs of all their students. We often hear teachers say, “I want all my students to be successful in math, but I'm not sure what to do. I don't have training in special education and I don't have much support.”
Research, Reflection, and Practice: Culturally Responsive Mathematics Teaching and English Language Learners
Authors: Torres-Velasquez Diane , Lobo Gilberto
Published: December 2020

Culturally responsive teaching is a dynamic form of teaching that builds on and supports students' home culture. The strategies that we recommend in this article for English Language Learners (ELL) are based on research or classroom experience. We provide real-life examples of how the second author, Gilberto Lobo, implements these ideas in the context of data analysis.
Overcoming the Walls Surrounding Word Problems
Authors: Ponce Gregorio A. , Garrison Leslie
Published: December 2020

The integration of two powerful instructional theories (Daily Oral Language and Cognitively Guided Instruction) into one classroom activity that is helping break the barriers teachers and students face when working with word problems. Teachers will gain informative techniques to integrate these strategies to include reading, writing, and mathematics in the classroom.
Aiming for Understanding: Lessons Learned about Writing in Mathematics: Reflect and Discuss
Authors: O'Connell Susan R. , Beamon Celia , Beyea Jennifer M. , Denvir Susan S. , Dowdall Leila A. , Friedland Nikki G. , Ward Joelle D.
Published: December 2020

Finding ways to help students effectively communicate their mathematical thinking is a challenge for teachers across the country. Through a Professional Development Schools (PDS) partnership between the University of Maryland and several elementary schools in a neighboring district, school and university partners worked together to explore, discuss, and reflect on the challenges of helping students write about mathematics. Along with gaining insights into effective instructional strategies, partners from both institutions gained a deeper appreciation for the benefits of school-university dialogue.
A Mathematical Exploration of Grandpa's Quilt
Authors: Reynolds Anne , Cassel Darlinda , Lillard Eileen
Published: December 2020

Grandpa's Quilt, by Betsy Franco (1999), tells a story about three children who solved the problem of their grandfather's quilt being too short to keep his feet warm in winter. Over the four years that we have used this book with secondgrade students, we have discovered that we can use it to make connections with a number of areas of mathematics, particularly patterns and relationships, measurement, and geometry and spatial sense, as well as to lead into multiplication activities. We have found the book to be an excellent springboard to engage students in discussion and significant problem solving.
By Way of Introduction: Show Me the Mathematics!
Authors: Taylor P. Mark
Published: December 2020

The Editorial Panel of Teaching Children Mathematics (TCM) welcomes you to volume 13! We are committed to the goals and ideals summarized in TCM's mission statement, which can be found at the bottom of the masthead page of each issue. The mission statement embraces the NCTM ideal of more and better mathematics for all students through the exchange of mathematical ideas, activities, and pedagogical strategies and through sharing and interpreting research. In view of NCTM's professional development focus of the year—“Show Me the Mathematics: Learning through Representation” (www.nctm.org/focus/)—we would like to highlight the specific mathematics represented in this volume of Teaching Children Mathematics.
Differentiating the Curriculum for Elementary Gifted Mathematics Students
Authors: Wilkins Michelle Muller , M. Wilkins Jesse L. , Oliver Tamra
Published: December 2020

Description of the Mathematics Investigation Center (MIC), a tool to help elementary teachers differentiate the curriculum for their gifted mathematics students. Using the same mathematical theme that the rest of the class is studying, the activities provide depth for the gifted students by shifting from a computation level to a problem solving level.
Fostering Communication about Measuring Area in a Transitional Language Class
Authors: Bray Wendy S. , Dixon Juli K. , Martinez Marina
Published: December 2020

A series of lessons focused on development of invented strategies for measuring areas of irregular polygons in a fourth grade transitional language class. Of focus are strategies that teachers can use to engage students with limited English proficiency (LEP) in communicating and justifying mathematical ideas.
Counting Collections
Authors: Schwerdtfeger Julie Kern , Chan Angela
Published: December 2020

How counting collections of objects helps elementary–age children develop number sense and number relations. The authors provide evidence that counting collections offers multiple entry points for children at different places on the counting trajectory. The teacher's role is one of noticing, questioning, and extending what children naturally do, moving them to more sophisticated strategies as children count, organize, and record their collections. Includes multiple examples of student work.
Solving Problematic Addition and Subtraction Word Problems
Authors: Contreras José N. , Martínez-Cruz Armando M.
Published: December 2020

Word problems can play a prominent role in elementary school mathematics because they can provide practice with real-life problems and help students develop their creative, critical, and problem-solving abilities. However, word problems as currently presented in instruction and textbooks fail to accomplish these goals (Gerofsky 1996; Lave 1992). This failure is due, in part, to the unrealistic approach needed to solve them: the straightforward application of one arithmetic operation. Consequently, when faced with word problems in which context is critical to the solution, students fail to connect school mathematics with their real-world knowledge. Problems that cannot be solved by applying a straightforward arithmetic operation are called problematic. Several researchers have examined children's lack of use of their real-world knowledge to solve problematic word problems (Greer 1997; Reusser and Stebler 1997; Verschaffel and De Corte 1997).
Supporting Teacher Learning: Shaping Prospective Teachers' Justifications for Computation: Challenges and Opportunities
Authors: Grant Theresa J. , Lo Jane-Jane , Flowers Judith
Published: December 2020

This article discusses the challenges and opportunities that arose in attempting to support prospective elementary teachers in developing mathematical justifications in the context of wholenumber computation. Justification for whole-number computation is important for three reasons. First, this is the introductory topic in the first of three mathematics courses for prospective elementary teachers. Second, the number and operations strand is a major focus in elementary school. Third, in our experience as teacher educators, prospective elementary teachers have a difficult time considering how and why to teach whole-number computation in a conceptual manner. If prospective teachers' reasoning and justifications can be shaped in this area of mathematics, sense making and mathematical justification in other areas of mathematics can be shaped as well (Simon and Blume 1996).
Journeying into Mathematics through Storybooks: A Kindergarten Story
Authors: Wilburne Jane Murphy , Napoli Mary , Keat Jane B. , Dile Kimberly , Trout Michelle , Decker Suzan
Published: December 2020

“I just can't seem to find time to get math into the [instructional] day with everything else we are expected to cover in kindergarten. Our curriculum is so heavy on literacy.”—Michelle, an urban kindergarten teacher, January 2006
Learning Our Way to One Million
Authors: Whitin David J.
Published: December 2020

David Schwartz's classic book How Much Is a Million? (1985) can be the catalyst for sparking many interesting mathematical investigations. This article describes five episodes in which children in grades 2–5 all heard this familiar story read aloud to them. At each grade level, they were encouraged to think of their own way to explore the concept of one million. During these investigations, which included whole-class, small-group, and individual projects, the children used many different mathematical concepts, such as place value, length, area, money, and ratio. They also used skills, such as estimating, measuring, and comparing, as well as learning an appropriate use of the calculator. All of the examples showcase children as active problem solvers who developed ownership of the problems they posed for themselves. They found relevance in the explorations because they tied them to familiar contexts, such as a classroom carpet, Girl Scout cookies, or a set of toy train tracks. As the children demonstrated their ability to communicate their reasoning, solve challenging problems, and connect mathematical concepts and skills to real-world contexts, their work reflected many of the goals of the Principles and Standards for School Mathematics (NCTM 2000).
Investigations: Predictions and Probability
Authors: McMillen Sue
Published: December 2020

The “Investigations” department features children's hands-on, minds-on mathematics explorations 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.
Insights into Our Understandings of Large Numbers
Authors: Kastberg Signe E. , Walker Vicki
Published: December 2020

How much is a million? This question is familiar to many elementary teachers who have challenged their students to think about and explore large numbers. Much has been written about the importance of having children explore large numbers, think about large amounts of something, estimate large quantities of objects, and be able to gain a sense of how much is “a lot.” Explorations with these goals in mind often invite students to use a familiar context or an everyday object to think about how much a million or some other very large number is. The children's book How Much Is a Million? (Schwartz 1993) is well known in many classroom settings and frequently used as a springboard for lessons posing this kind of challenge. In fact, there may be millions of resources available to teachers who are looking for ways to help their students conceptualize large numbers.
Introducing Complex Systems into the Mathematics Curriculum
Authors: English Lyn D.
Published: December 2020

Our children live in a highly sophisticated world composed of interlocking complex systems. An appreciation and understanding of such systems is critical for making effective decisions about our lives as individuals and as community members. The activities presented in this article provide rich opportunities for children to experience an introduction to complex systems during which they think mathematically about relevant relationships, patterns, and regularities in dealing with authentic problems (English 2006; Lesh and Doerr 2003).
Technology-Rich Mathematics Instruction
Authors: Thach Kim J. , Norman Kimberly A.
Published: December 2020

Over the past decade, technology—particularly computer technology—has become more accessible to students in public school settings. From 2000 to 2005, the ratio of students to computers with Internet access improved from approximately seven students per computer to four students per computer (Wells and Lewis 2006). Although access continues to increase, one of the remaining challenges is the successful integration of technology as a tool for facilitating learning across the curriculum.
Making the Most of Story Problems
Authors: Jacobs Victoria R. , Ambrose Rebecca C.
Published: December 2020

Honoring students' solution approaches helps teachers capitalize on the power of story problems. No more elusive train scenarios!
Strengthening Connections between Elementary Classroom Mathematics and Literacy
Authors: Altieri Jennifer L.
Published: December 2020

Enjoyable literacy strategies help elementary teachers reinforce students' mathematical knowledge.
Investigations: Using Base-Ten Block Diagrams for Divisibility Tests
Authors: Harrell Marvin E. , Slavens Dawn R.
Published: December 2020

“Investigations” 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.
Mathematics Teaching Today
Authors: Martin Tami S. , Speer William R.
Published: December 2020

Features, consistent messages, and new components of Mathematics Teaching Today: Improving Practice, Improving Student Learning (NCTM 2007), an updated edition of Professional Standards for Teaching Mathematics (NCTM 1991). The new book describes aspects of high-quality mathematics teaching; offers a model for observing, supervising, and improving mathematics teaching; and outlines guidelines for the education and continued professional growth of teachers.
Research, Reflection, Practice: Children Generate their Own Representations
Authors: Cengiz Nesrin , Grant Theresa J.
Published: December 2020

“How many teeth have you lost?” Imagine second graders collecting data from their peers about how many teeth each child is missing and then creating their own data representations that mean something to them. Instead of showing her students how to create a bar graph of the data, this teacher asks them to display the information in some way that helps them make sense of their data. Students work in small groups, discuss their ideas with peers, and create their own data representations. Then they share their data with the entire class, discussing differences in their representations and interpretations.
Math by the Month: Watch It Grow
Authors: Gallego Christine , Saldamando Dora , Tapia-Beltrán Grace , Williams Karolyn , Hoopingarner Thomas C.
Published: December 2020

“Math by the Month” activities are designed to engage students to think mathematically. 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. The following activities are designed to help you and your students investigate growth through mathematical investigations involving number sense and operations, statistics, data collection, communication, and representation.
Problem Solvers: August 2009
Authors: Bell Lori
Published: December 2020

This month the “problem solvers” department editors launch the first in a series of thematic problems to explore a variety of environmental topics. Our goal is to not only provide rich, authentic problems but also promote local community “go green” efforts. Tell us about how you and your students tackle each problem, as well as any environmental projects that this series inspires.
Support Preservice Teachers' Reasoning and Justification
Authors: Rathouz Margaret M.
Published: December 2020

Engaged in using related division problems to support community building, teacher candidates examined video and other records, developed explanations and mental models, and analyzed task elements and implementations.
Problem Solvers: Problem: Counting is for the birds
Authors: Jones Carolyn M.
Published: December 2020

Connecting mathematical thinking to the natural world can be as simple as looking up to the sky. Volunteer bird watchers around the world help scientists gather data about bird populations. Counting all the birds in a large flock is impossible, so reasonable estimates are made using techniques such as those described in this problem scenario. Scientists draw on these estimates to describe trends in the populations of certain species and to identify areas for further research.
Raise the bar on problem solving
Authors: Englard Lisa
Published: December 2020

The Singapore model method provides a visual approach to help our future astronauts, engineers, and other workers focus on mathematical relationships, operations, and actions.
Balancing act
Authors: Haman Lynne
Published: December 2020

District and teachers' union personnel collaborated in creating a teaching and learning cooperative to maintain ongoing, high-quality professional staff development.
Integrating literature and math
Authors: Lamberg Teruni , Andrews Carolyn
Published: December 2020

First-grade teacher Carolyn loves literature. She finds that reading stories to her students sparks their imaginations and motivates them to learn. Wanting to leverage their enthusiasm, Carolyn researched how to use literature in math class. She learned that stories establish familiar, interesting, realworld scenarios where students can explore mathematics within context and communicate their thinking in ways that makes sense to them (Moyer 2000). Storybooks present opportunities to examine mathematics in ways that reflect children's own experiences and interests and to talk about math in a “natural context” (Moyer 2000; McDuffie and Young 2003).
Creative Problem Solving
Authors: Loewen A. Craig
Published: December 2020

To talk about “creative” problem solving some how seems redundant. After all, what else is meant by finding the solution to a set of conditions but engaging in some creative process?
Investigations: Food for Thought
Authors: Trezise Kathy
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.
Pause, Prompt, and Praise: Cross-Age Tutoring
Authors: Eggers Janie E.
Published: December 2020

Brian: You are so smart. I can't believe you are only in first grade. You are already doing multiplication problems. Let's see how you do on this next one.
Pictures, Tables, Graphs, and Questions: Statistical Processes
Authors: Isaacs Andrew C. , Kelso Catherine Randall
Published: December 2020

In an address to the American Association for the Advancement of Science, John Dewey (1910) contrasted the facts of science with the method of science and argued that the method, rather than the facts, should he preeminent in the school curriculum.
A Teacher's Journal: Gummy Bears in the White House
Authors: Bonsangue Martin Vern , Pagni David L.
Published: December 2020

Representation is an essential issue in statistical sampling. Policy in educational, scientific, and political arenas is driven by results based on samples that ideally reflect the characteristics of the larger group from which they are drawn.
Problem Solving With Discrete Mathematics
Authors: friedler Louis M.
Published: December 2020

The NCTM's Curriculum and Evaluation Standards for School Mathematics (1981) calls for an emphasis on problem solving at all levels and recommends introducing discrete mathematics topics. In fact, the first standard for grades K-4 states that “the study of mathematics should emphasize problem solving …” (p. 23).
Fourth Graders Invent Ways of Computing Averages
Authors: Kamii Constance , Pritchett Michele , Nelson Kristi
Published: December 2020

Children easily learn the conventional algo-rithm of averaging: to find the average of a set of numbers, such as 80, 90, 94, and 100, just add rhe four numbers and divide the total by four. However, the authors are working on an approach to mathematics based on Piaget's theory, constructivism. For reasons explained later in this article and elsewhere (Kamii 1985, 1989, 1994), our approach is to encourage children to do their own thinking and to refrain from giving rules made by someone else. The purpose of this article is to describe what fourth graders can do when they are encouraged to invent their own ways of getting the average. The article also shows the teacher's active role in constructivist teaching.
Math by the Month: Patterns and Functions
Authors: Holly Karen R.
Published: December 2020

These activities are designed to appeal directly to students, giving them open-ended questions to engage and challenge their intellect. Students may work on the activities individually, in pairs, or in small groups.
Patterns as Tools for Algebraic Reasoning
Authors: Herbert Kristen , Brown Rebecca H.
Published: December 2020

One teacher made up this story to introduce her sixth-grade students to “Crossing the River,” one of the lessons in a unit called Patterns in Numbers and Shapes.
Cooperative Problem Solving: Using K-W-D-L as an Organizational Technique
Authors: Show Jean M. , Chambless Martha S. , Chessin Debby A. , Price Vernetta , Beardain Gayle
Published: December 2020

Cooperative learning continues to prove its effectiveness in many facets of mathematics education. Not only does cooperative learning promote achievement with many levels and types of students (Slavin 1991), but as students work together in groups, communication and interpersonal-relations skills are refined (Greenes, Schulman. and Spungin 1992; AAAS 1989, 1993).
Implementing the Assessment Standards for School Mathematics: Breathe O2 into Your Mathematics Program — Promote Openness and Ownership
Authors: Pitts Gay S.
Published: December 2020

The following is a set of directions that you must follow to arrive at your destination: Go three miles east on 1-40 until you come to Exit 103. Turn left at the end of the exit ramp and proceed…. You will be given all the information needed to arrive at the correct destination. However, only the person who is assessing your performance will know the destination and the reason you need to arrive there.
Links to Literature: Investigating Probability and Patterns with the Thirteen Days of Halloween
Authors: Wickett Maryann
Published: December 2020

It was week 2 of a probability unit in my 3-4 multi-grade class. My students had experienced several activities that involved making predictions based on sampling with replacement, but for most students, their understanding was fragile.
In My Opinion: (Mis?)Constructing Constructivism
Authors: Clements Douglas H.
Published: December 2020

Many educators base recommendations for teaching mathematics on “constructivist” thinking. However, they often misunderstand constructivism, so their recommendations may be incorrect or inappropriate. We need to examine what constructivism is and is not, what myths have grown up around constructivism, and what characteristics define it.
Math by the Month: World-Record Mathematics
Authors: Lewis Tom
Published: December 2020

The “Math by the Month” activities are designed to appeal to students, who may work on the activities individually or in small groups. No solutions are provided so that students will look to themselves as the mathematical authority, thereby developing the confidence necessary to validate their work.
Putting Mathematics into Routine Classroom Tasks: Some Ideas for Teams in Cooperative-Learning Structures
Authors: Lemme Barbara S.
Published: December 2020

Cooperative learning has become a successful structure in the classroom. Many quality resources exist for implementing this structure. The CIRC (Cooperative Integrated Reading and Comprehension) Language Program (Stevens et al. 1993) is one example. Another is Kagan's (1994) work describing specific structures where teams of four work together to solve problems and cooperatively work toward crucial life skills that include teamwork and individual accountability. To direct specific routine tasks and cooperative-group lessons, the four members of a team are usually labeled by number (1, 2, 3, 4) or letter (A, B, C, D).
Implementing the Assessment Standards: The Process of Assessment Applied to Tessellations
Authors: Sharp Janet M. , Hoiberg Karen Bush
Published: December 2020

A comprehensive process design, which facilitates the analysis of all events that have an impact on students’ mathematical experiences, is outlined in the Assessment Standards for School Mathematics (NCTM 1995). This process of assessment is held to six standards: Mathematics, Learning, Equity, Openness, Inference, and Coherence. These Standards represent those ideas that are valued and by which mathematical assessment should be judged.
Instead of Teaching Missing Addends
Authors: Kamii Constance , Lewis Barbara A. , Booker Bobbye M.
Published: December 2020

Recently, a principal wrote, “While visiting a first grade classroom one morning, I observed a lesson on missing addends…. Children were struggling with what they were being asked to do and the teacher was visibly frustrated. Afterward, when I discussed the lesson with the teacher, … she replied without hesitation, ‘Most first graders can't do missing addends, but it's on the test’” (Morgan-Worsham 1990, 64).
Problem Solvers: Counting Squares
Authors: Sakshaug Lynae
Published: December 2020

The goal of the “Problem Solvers” department is to foster improved communication among teachers by posing one problem each month for K-6 teachers to try with their students. Every teacher can become an author: pose the problem, reflect on your students’ work, analyze the classroom dialogue, and submit the resulting insights to this department. Remember that even students’ misconceptions are interesting.
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 reviewer's opinions and do not imply endorsement by the National Council of Teachers of Mathematics.
Using Recipes and Ratio Tables to Build on Students’ Understanding of Fractions
Authors: Brinker Laura
Published: December 2020

I recently worked with a teacher in a combined fourth- and fifth-grade class as she taught a unit on fractions and mixed numbers. All the problems given to students during this unit were situated within various real-world contexts.
Developing Geometric Thinking through Activities That Begin with Play
Authors: van Hiele Pierre M.
Published: December 2020

For children, geometry begins with play. Rich and stimulating instruction in geometry can be provided through playful activities with mosaics, such as pattern blocks or design tiles, with puzzles like tangrams, or with the special seven-piece mosaic shown in figure 1. Teachers might ask, How can children use mosaics, and what geometry do they learn? Before addressing these questions and exploring the potential of the mosaic puzzle for teaching geometry, I note some misconceptions in the teaching of mathematics and present some of my ideas about levels of thinking in geometry.
And the Answer Is … Symbolic Literacy
Authors: Witherspoon Mary Lou
Published: December 2020

M.J. is in the first grade. While he and his mother waited in a classroom for the teacher, M. J. entertained himself by writing number sentences, such as 3 + 5 = 8, on the chalkboard. His mother, who is a mathematics professor, wrote 3 + 4 = 5 + 2 on the chalkboard. M. J. told her that her sentence was not right because only one number could be written after the equals sign. When asked what he thought the equals sign meant, M. J. replied, “And the answer is.”
News from the Net: Aunty Math's Challenges for Kids
Authors: Lazerick Beth
Published: December 2020

Aunty Math, for students and their teachers, is a terrific site that emphasizes problem-solving strategies listed in the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989). The site is designed for children; the layout is easy to use, and the graphics are inviting. Aunty Math's problems, called “challenges,” are set in stories about Aunty Math's nephews and niece. The real Aunty Math behind the Web site is an experienced, awardwinning teacher who is very involved in mathematics education.
Creating Opportunities for Children to Think Mathematically
Authors: Kajander Ann E.
Published: December 2020

The children dived into the pile of hoops, scarves, and other materials. It was the last day of Kindermusik (Music Resources Development 1988), and the seven-year-olds were sharing some of their favorite musical activities with parents.
A Flying Start to Algebra
Authors: MacGregor Mollie , Stacey Kaye
Published: December 2020

Algebra learning has its roots in the early grades, when children notice regularities in the ways that numbers work. From this beginning, they develop a knowledge of the properties of numbers and operations, later generalized as algebra. We have conducted research over several years with middle school and high school students learning algebra (MacGregor and Stacey 1993, 1995, 1997; Stacey and MacGregor 1997a, 1997b).
Problem Solvers: The Talking Club
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.
Problem Solvers: Fair Share
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.
Tech Time: Predicting Pattern Blocks on and off the Computer
Authors: Clements Douglas H. , Sarama Julie
Published: December 2020

If used properly, manipulatives can support the learning of mathematics and motivate students. The intelligent use of manipulatives takes advantage of their features, especially the extra features of computer manipulatives (Clements and McMillen 1996). The use of manipulatives must be integrated into a sound mathematical lesson. In this article, we present one example of an activity that capitalizes on the particular advantages of physical and computer pattern blocks.
Math Is Art
Authors: Granger Tim
Published: December 2020

The beginning of the school year is an exciting time for everyone. Teachers and students are filled with enthusiasm about what the new year holds. Unfortunately, when I begin the first mathematics lesson of the year with my fifth graders, this enthusiasm is often replaced by myriad student anxieties. By the time that students reach fifth grade, they carry with them any number of negative feelings about school in general and mathematics in particular. How can I share with my students the beauty of mathematics if they have the mindset that mathematics is nothing more than numbers?
Lessons from the TIMSS Videotape Study
Authors: Geist Eugene A.
Published: December 2020

The Third International Mathematics and Science Study (TIMSS) reported more than just numerical achievement data. The study also contained information on teachers' lives, students' lives, and curricula, as well as a videotape of eighth-grade mathematics classes (OERI 1996a). These data, especially the videotaped study, go beyond comparisons of achievement scores and allow for cross-cultural comparisons of mathematics instruction in the United States and other countries. In particular, we can learn many lessons from examining instructional methods in the United States and comparing them with those of Japan. This comparison has significant implications for implementing NCTM's Standards in U.S. classrooms and teaching our students as if they were young mathematicians.
Math By the Month: January 2001
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.
In My Opinion: What Is Ethnomathematics, and How Can It Help Children in Schools?
Authors: D'Ambrosio Ubiratan
Published: December 2020

The term ethnomathematics is used to express the relationship between culture and mathematics. The term requires a dynamic interpretation because it describes concepts that are themselves neither rigid nor singular—namely, ethno and mathematics (D'Ambrosio 1987). The term ethno describes “all of the ingredients that make up the cultural identity of a group: language, codes, values, jargon, beliefs, food and dress, habits, and physical traits.” Mathematics expresses a “broad view of mathematics which includes ciphering, arithmetic, classifying, ordering, inferring, and modeling” (pp. 2–3).
Problem Solvers: How Big Was the Cat?
Authors: Sakshaug Lynae , Wohlhuter Kay
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 in, and thinking about, mathematics with their contributions to the journal. Remember that even student misconceptions are interesting.
Geometry through Beadwork Designs
Authors: Barkley Cathy , Cruz Saundra
Published: December 2020

The fifth-grade children eagerly picked out envelopes containing brightly colored, geometric shapes to begin making their Ute Indian beadwork designs. Each child had a strip of construction paper simulating a tanned hide, or buckskin, to decorate with shapes traditionally used in Ute designs. Much excitement was evident as the students discussed how they wanted their patterns to look and what colors they wanted to use. The colorful geometry pieces were traded back and forth as the designs began to emerge on their papers.
Mathematics Instruction Developed from a Garden Theme
Authors: Civil Marta , Khan Leslie H.
Published: December 2020

Can rigorous mathematics be developed from everyday experiences?” This question brought together an intermediategrades teacher and a university researcher to collaborate on a project that incorporated students' and families' knowledge and experiences. The importance of designing culturally relevant instruction is well documented (Lipka, Mohatt, and the Ciulistet Group 1998; Zaslavsky 1996, 1997). (For more general information, see also the newsletter from the International Study Group on Ethnomathematics.) For us, culturally relevant instruction refers to instruction that links home and school by building on experiences shared by most students in the class. It includes creating a learning environment that captures the flavor of the apprenticeship style that often characterizes how children acquire knowledge outside of school, alongside their family members. The teacher, Leslie Khan, had developed a relationship with many of her students' families and knew that gardening was a commonly shared family activity. We developed a garden theme to explore the interplay between everyday knowledge and school mathematics.
Mouse Maze Tournament: Connecting Geometry and Measurement
Authors: Curtis Shirley
Published: December 2020

Actively engaging children in making connections among mathematical strands fosters understanding. Making connections not only helps children observe and experience “the rich interplay among mathematical topics” but also allows students to be responsible for their learning and “for using their knowledge to understand and make sense of new ideas” (NCTM 2000, p. 64).
A Four-Point Instructional Model
Authors: Manouchehri Azita
Published: December 2020

Imagine that a colleague says to you, “The new Principles and Standards [NCTM 2000] tells us that we should expect our students to ‘act as mathematicians.' That is a tall order for my students.” How would you respond? Is the same true for your students? Have you found any successful approaches for engaging students in working as young mathematicians?
A Teacher's Journal: December 2001
Authors: Naylor Michael , Naylor Pamela
Published: December 2020

The abacus has been used for centuries in Asia and is still an essential part of education and commerce in many Asian countries. Abacus is a Latin word that comes from the Greek abax, meaning “table,” and possibly from the Hebrew abaq, which means “dust.” Long ago, calculations were done by writing in sand or dust sprinkled on a table or by manipulating stones on a table. A counting stone was called a calculus, from which the word calculate originates. The abacus as we know it today—a frame with beads that slide on rods—is a Chinese invention that dates to at least the thirteenth century. The Chinese term for the device is suan pan, which means “calculating board,” and the Japanese call it a soroban, also meaning “calculating board.”
Culture in the Curriculum: Enriching Numeration and Number Operations
Authors: Moldavan Carla C.
Published: December 2020

Students hear, “Pretend that you live on an island. You have no contact with others. You do not know words or written symbols for numbers. Your task is to develop a numeration system—a method that would allow you to count coconuts or shells, for example.” This task was the first one given to fourth graders in an attempt to embed multiculturalism in their mathematics curriculum. This article describes the content of the project and the students' reactions.