bluuebunny/crossref_metadata_2025 huggingface dataset:
Estimation of selected parameters in stabilographic image depending on physical activity level in children and adolescents
Authors: Filipowicz-Ciepły Justyna , Golec Joanna , Szczygieł Eżbieta , Czechowska Dorota , Cichoń Marta , Balicka-Bom Joanna
Published: December 2020

Introduction: Balance is an extremely important component of everyday human functioning. Assessment of body balance in children can be not only a diagnostic tool, but also information about the maturation of the balance system, diversity in terms of age and sex, as well as factors affecting balance and its development. In practice, maintaining body balance is a dynamic process, consisting in "continuous loss and regaining balance". According to scientific reports, in addition to age, psychosomatic status, the development of specific sensory-motor capabilities and strategies is also influenced by the type of sport.

Objective: The aim of the study was to assess balance in a group of children and adolescents with different levels of sports activity.

Material and methods: The study comprised 64 children and adolescents aged 10 to 13. The group was divided into: Group 1 (15 girls and 17 boys) regularly physically active, and Group 2 (17 girls and 15 boys) not undertaking any physical activity. All participants were assessed regarding postural stability using a CQStab2P stabilometric platform. Four tests were carried out for each participant: standing on both feet, on the left and right limb, and free standing with an additional task. The following parameters were analysed: SP (Sway Path) MA (Mean Amplitude) and MF (Mean Frequency).

Results: In the majority of cases, the variables indicated statistically significant differences from normal distribution – except for MA-R (on the right lower limb) and MF-T (standing on both feet with additional task). In the case of the SP-L indicators (on the left lower limb), SP-B (standing on both feet), SP-T, MA-B and MA-T, the advantage of low results was observed in the examined sample (distribution accuracy) and clear concentration near the average (leptocurticity of distribution). In the case of the trial to stand on the right lower limb, training subjects obtained statistically significantly higher SP results than those non-training. During the standing test, the length of MA was recorded as statistically significantly lower than in other conditions. In addition, the SA index, when trying to stand on the right lower limb, was statistically significantly higher in relation to the length of the radius when standing on the left limb. Training participants had a higher average radius compared to those not training.

Conclusions: Physical training positively affects the results of posturographic examination. Non-training girls have a statistically significantly lower level of SP compared to boys not training and training girls.
UDZIAŁ LASÓW W OCHRONIE PRZYRODY POPRZEZ OGRANICZENIA UŻYTKOWANIA TERENÓW I ZASOBÓW DREWNA
Authors: Grzywacz Andrzej
Published: December 2020

Limitations of the use of timber resources are about 3 million m3 annually compared to the theoretical production capacity. The area in the Treasury owned forests where restrictions in fulfilling economic functions are obligatory was calculated; this represents about 17.5% of their area. According to the proposed estimates for 2021-2030, it is likely to increase the limitation of timber harvesting for natural and social reasons by about 7% and by 4% in forest areas not serving economic functions. These limitations should be treated as public good in favour of nature conservation.
National Revival or National Burden: A Critical Examination of Discourses on Indigenous Birth, Population Growth and Demography
Authors: Togman Richard
Published: December 2020

The dominant Canadian narrative of Indigenous fertility has been told largely from the perspective of non-Indigenous Canadians. Politicians, healthcare professionals, demographers, and economists consistently characterize Indigenous fertility as too high and required to conform to Eurocentric norms. This has resulted in a wide variety of colonial interventions into the reproductive lives of Indigenous peoples. This article will provide a brief overview of the ways in which mainstream Canadian society has characterized Indigenous fertility and explore the subjugated discourse practiced by Indigenous nations in Canada regarding their own fertility, highlighted by original research conducted with Anishinaabe people in Thunder Bay.
Bounty from the Sea
Authors: Bentz Linda , Braje Todd J.
Published: December 2020

Chinese immigrants, like many other fortune seekers from around the world, arrived in California in search of economic opportunities. Enterprising Chinese fishers and merchants soon built the first commercial, trans-Pacific fisheries in the American West by expertly honing time-honored skills and technology, leveraging diverse partnerships, and tapping into international trade networks. Rather than isolated communities living on the economic and cultural fringes of American society, nineteenth-century Chinese immigrants were successful entrepreneurs who helped build the foundations of the West Coast commercial fishing economy. Catch tallies, tax documents, census records, immigration files, and other documents, along with archaeological investigations, contextualize the massive scale of harvest and demonstrate the ingenious ways Chinese fishers built their global fishery.
A New Classification Approach with Deep Mask R-CNN for Synthetic Aperture Radar Image Segmentation
Authors: Yayla Ridvan , Sen Baha
Published: December 2020

In this paper, a hybrid classification approach which is combined with a more deep mask region-convolutional neural network and sparsity driven despeckling algorithm is proposed for synthetic aperture radar (SAR) image segmentation instead of the classical segmentation methods. In satellite technology, synthetic aperture radar images are strongly used for a lot of areas, such as evaluating air conditions, determining agricultural fields, climatic changes, and as a target in the military. Synthetic aperture radar images must be segmented to each meaningful point in the image for a quality segmentation process. In contrast, synthetic aperture radar images have a lot of noisy speckles and these speckles should be also reduced for a quality segmentation. Current studies show that deep learning techniques are widely used for segmentation methods. High accuracy and fast results can be obtained with deep learning techniques for image segmentation. Mask region-convolutional neural network can not only separate each meaningful field in the image, but it can also generate a high accuracy prediction for each meaningful field of synthetic aperture radar images. The study shows that smoothed SAR images can be classified as multiple regions with deep neural networks.
Compost of Biodegradable Municipal Solid Waste as a Fuel in Lignite Co-combustion
Authors: Vasileiadou Agapi , Zoras Stamatis , Dimoudi Argyro , Iordanidis Andreas , Evagelopoulos Vasilios
Published: December 2020

In Greece, 5.8 million tons of municipal solid wastes (MSW) are produced annually, of which 2.47 million tons are bio-wastes. Composting is an alternative treatment of bio-wastes instead of landfill.  Τwo composting plants operate in Greece, one in Ano Liossia (capacity 1,200 tons/day, producing 120 tpd compost) and another in Chania (capacity 70,000 tons/year, producing 20,000 tpa compost). In addition, since 2018, the first integrated waste management plant was set off in the region of Kozani (capacity 120,000 tons/year). An alternative utilization of the compost, produced in the latter plant, was investigated in this study. In particular, instead of using compost as fertilizer, the energy recovery from this bio-waste was attested. Utilization of compost of MSW for energy production purposes has rarely been studied in the literature. Several blends of compost with lignite were prepared and their energetic potential was determined. Proximate analyses and gross calorific value (GCV) determination were conducted. Wastes and biomass-based fuels differ in many ways from fossil fuels. The CLOF sample revealed the highest GCV and the lowest ash content than all analyzed samples. Based on all analytical determinations, compost and its mixtures with lignite could be regarded suitable for energy recovery by thermal processes, such us combustion. Further studies should be done including emission analysis, ash deposition during combustion (corrosion, slagging and fouling).
Reflective Array Solar Water Heater for Milk Pasteurization
Authors: Setiawan Budhy , Nur Wakidah Riska , Yulianto Yulianto
Published: December 2020

The solar water heater is a method of utilizing solar thermal energy by storing heat energy in water which can be used directly. Solar thermal energy has a high utility potential. It has a power of 1 kW/m2 on average on the surface of the earth with energy up to 7 kWh/m2/day on average per year. One of the uses of the solar water heater is that it can be implemented in the milk pasteurization system. The research equipment consists of an accumulator vessel with an area of 2x2 m2 and a water pipe collector. The water that had been heated in an accumulator (thermos) was used directly as the heating source in the milk pasteurization process. Meanwhile, the most common heating method used in the pasteurization process is electricity and gas energy. The result showed that using 82oC of accumulator water, it took 12 minutes (14.48–15.00) to reach the milk temperature needed in the pasteurization process which is 70oC for 6.75 litres of milk. The efficiency of solar heat energy absorption by an accumulator is 47%. This value can be increased by increasing the volume of water.
Der Nutzen zivilgesellschaftlichen Engagements aus der Perspektive der Engagierten vor und während der CoronaPandemie
Authors: Rießen Anne van , Henke Stefanie
Published: December 2020

Der Artikel fasst die Ergebnisse einer Studie im Mixed-Methods-Design zusammen und beleuchtet dabei zivilgesellschaftliches Engagement1 im Rahmen institutioneller Nachbarschaftshilfen vor und während der ersten Wochen der Corona-Pandemie. Dazu wird zunächst analysiert, welche Personen sich während der Pandemie zum Engagement bereit erklären, um dann aus der Sicht der Befragten zu rekonstruieren, welchen Nutzen sie ihrem Engagement zuschreiben. Schließlich wird reflektiert, was Menschen veranlasst, sich in der besonderen Situation der Pandemie bei etablierten Trägern der Wohlfahrtspflege zu engagieren. Im Weiteren werden die Ergebnisse aus der Perspektive gesellschaftlicher Teilhabe interpretiert.
Zwei Strafrechtswelten
Authors: Lagodny Otto
Published: December 2020

German legal thinking in terms of being “consequent” and the Austrian approach of being tolerant are clear-cut contradictions in the field of criminal law and criminal procedure. Lagodny shows these features. He lives, teaches and works as a legal researcher in Salzburg since 20 years. Acquittal for a thief who returns the stolen good before being disvovered? In Germany: impoossible! Kant and others would argue this. In Austria: Why not? Paternalism in the sense of Habsburg’s monarchy and other features serve as explanations. Many of such examples complete a picture which can be understood only from an historic point of view with the eyes of a “foreigner” in the sense of G. Simmel. These findings also show the insurmountable impediments which harmonisation of law in the Euopaen Union has to face. The “Austrian labyrinth which everyone is acquainted with” (Qualtinger), however, is very much stimulating. If one is ready to do so.
Dotazník zmatení rolí pro adolescenty: Předběžné sdělení o vývoji sebeposuzovací metody
Authors: Pivodová Lenka , Daňsová Petra , Lacinová Lenka
Published: December 2020

Cílem studie bylo vyvinout dotazník, který by zachytil míru zmatení rolí tak, jak ji aktuálně prožívají adolescenti. Postup tvorby dotazníku je popsán prostřednictvím dvou studií, které na sebe navazují. Ve studii I bylo pilotováno 9 sebehodnotících položek dotazníku na vzorku adolescentů (n=56; 13-17 let; M=15,02; SD=1,8; z toho 65,5% dívky). Byla ověřena vnitřní konzistence a faktorové příslušnosti položek do dvou faktorů – instrumentální zmatení rolí a emocionální zmatení rolí. Ve studii II bylo pilotováno 16 položek dotazníku (stávající ze studie I, pozměněné a doplněné) na vzorku adolescentů (n=154; 12-19 let; M=15,23; SD = 2,02; 61,7 % dívky). Bylo zde odlišeno zmatení rolí směrem k otci a matce zvlášť, položky jsou rozděleny do tří faktorů: instrumentálního zmatení rolí, emocionálního zmatení rolí v dyádě matka/dítě a emocionální zmatení rolí otec/dítě. Vzhledem k tomu, že obsahově podobné položky pro matku a otce byly administrovány po sobě a sdílely rozptyl, který nebyl možný vysvětlit jejich příslušností do škál, bude dotazník s odlišným pořadím položek podroben následnému zkoumání. The aim of the study was to develop a questionnaire to capture the degree of role confusion as it is currently experienced by adolescents. The process of creating a questionnaire is described through two follow-up studies. In Study I, 9 self-assessment items were piloted on a sample of adolescents (n=56; 13-17 years; M=15,02; SD=1,8; 65,5% girls). The internal consistency and factor relevance of the items into two factors was verified - instrumental role confusion and emotional role confusion. In Study II, 16 questionnaire items (existing from Study I, amended and supplemented) were piloted on a sample of adolescents (n=154; 12-19 years; M=15,23; SD = 2,02; 61,7 % girls). The distinction of role confusion towards father and mother was differentiated, the items being divided into three factors: instrumental role confusion, emotional role confusion in the mother / child dyad, and emotional role confusion in father / child dyad. Since the content-related items for the mother and father were administered one after another and shared the variance, which was not possible to explain their belonging to the scales, the questionnaire with different order of items will be subjected to subsequent examination.
Ethics as Therapy
Authors: Martin Mike W. ,   National Philosophical Counseling Association
Published: December 2020

From the inception of philosophical counseling an attempt was made to distinguish it from (psychological) therapy by insisting that therapy could not be more misleading. It is true that philosophical counselors should not pretend to be able to heal major mental illness; nevertheless they do contribute to positive health—health understood as something more than the absence of mental disease. This thesis is developed by critiquing Lou Marinoff’s book, Plato not Prozac!, but also by ranging more widely in the literature on philosophical counseling. I also interpret philosophical counseling as a form of philosophical ethics.
Humor as a Virtue
Authors: Amir Lydia ,   National Philosophical Counseling Association
Published: December 2020

Dignity is man’s creation, not respected by nature or life. It is part of what has been sometimes considered as dangerous hubris or human pride. The inevitable fall from hubris leads either to humility or to humiliation – a middle stage between hubris and humility. When pride is hurt and dignity impaired by the very nature of indomitable, indif­ferent and secretive life, awareness of humiliation as a preferred stage is crucial. It is crucial because it permits to avoid humility, for all those who feel that humility is beyond their power or below their will, while keeping the fighting and ambitious spirit of hubris. Moreover, awareness of our humiliation enables us to apprehend an important, though painful, truth about the human condition.
But Can It Travel?
Authors: Newton Lisa H. ,   National Philosophical Counseling Association
Published: December 2020

Since the traumas of the last quarter of the 20th century forced all professions into the light of public scrutiny, we have seen the destruction of the parochial boundaries of the ethical understandings of the past, and the development of a cosmopolitan professional ethics. It is now understood that we have to have an ethics that travels well, whose principles operate with equal force and plausibility in all disciplines. Without good passports, principles become locked into their own disciplines, Ethics as a subject loses its integrity, and every profession has an excellent reason to insist that “their” ethics have nothing to do with the rest of the world. Consideration of professional ethics as a whole shows that the general principles that we use travel very well indeed, and rapidly smokes out those that do not. “The Doctrine of Double Effect” is one of the non-travelers; from that fact we explore the possibility that the Doctrine is radically misconceived even in its home discipline of­medicine.
Rectificatory Justice and the Kānaka Maoli of Hawai‘i
Authors: Roberts Rodney C. ,   Philosophy Documentation Center
Published: December 2020

The term “Native Hawaiian” is often used to refer to the indigenous people of the Hawaiian islands; however, the term is itself non-Hawaiian, as is its pronunciation. The Kānaka Maoli, the “true or real persons,” are the indigenous people of Ka Pae ‘Āina O Hawai‘i (the Hawaiian archipelago). After living for centuries in these islands as a sovereign people, with a relationship to the land that is both familial and reciprocal, the last Hawaiian government was overthrown in 1893 with the help of military personnel from the United States of America. Five years after the overthrow the USA annexed the islands, in spite of clear and overwhelming opposition by the Kānaka Maoli. In 1959 the majority of non-Hawaiian residents of Hawai‘i voted in the affirmative for statehood. The aim of this article is to show that the overthrow of the sovereign Hawaiian nation, the annexation of Hawai‘i by the USA, and the incorporation of these islands into the USA as its fiftieth state, are both illegal and unjust. Moreover, justice requires the restoration of a sovereign Hawaiian nation.
Making Connections: From Paper to Pop-Up Books
Authors: Huse Vanessa Evans , Bluemel Nancy Larson , Taylor Rhonda Harris
Published: December 2020

The goal of the elementary mathematics program is to create an environment that supports the active exploration of mathematical ideas while demonstrating the connections between mathematics and everyday life. Many elementary students have limited instruction in geometry, even though this subject is an essential element in the mathematics curriculum. Students with a background in geometry may be able to rec ite geometric facts but often cannot employ the information to visualize practical solutions to problems. The ideas that foiJow describe geometry-related activities that use an inexpensive manipulative, paper, to create a pop-up card.
Investigations
Authors: Lamphere Patricia
Published: December 2020

The “Investigations” department is designed for teachers who wish to give students new insights into familiar topics in grades pre-K-6. It includes both directed and open-ended activities.
Reviewing and Viewing
Authors: O'Shea Thomas , 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 Notional Council of Teachers of Mathematics.
Helping Students Understand Subtraction
Authors: Page Anita
Published: December 2020

A friend, who e adult mathematical skills enable him to balance his checkbook and decide which brand of coffee is a better buy, still remembers the trauma of first grade. “There I was, happily adding away,” he says. “Then one day they hit me with subtraction.”
Links to Literature: Exploring Subject Areas with a Counting Book
Authors: Whitin David J. , Mills Heidi , O'Keefe Timothy
Published: December 2020

When studying a unit on animals, our first-grade class read How Many Snails? A Couming Book by Paul Giganti. The book consists of drawings with a set of classification questions for each page.
The Role of JRME in Advancing Learning and Teaching Elementary School Mathematics
Authors: Battista Michael T. , Larson Carol Novillis
Published: December 2020

Students often apply commonsence knowledge
Assessing Young Children's Mathematical Understandings
Authors: Sgroi Laura A. , Gropper Nancy , Kilker Mary Tom , Rambusch Nancy M. , Semonite Barbara
Published: December 2020

The mathematics education experienced by a young child in school is influenced by the nature of the child and by at least three other variables: the curriculum, the learning environment, and the means of assessment.
Early Childhood Corner: Developing Power in Linear Measurement
Authors: Schwartz Sydney L.
Published: December 2020

Watching young children build their understandings about such attributes of objects as weight and length is fascinating. As teachers, wc have daily opportunities to see students developing power in linear measurement. Along with most teachers of young children, the author can vividly recall observing young children in the early stages of tuning into the length of objects as they used the classroom materials. One three-year-old was struggling to carry a double-unit kindergarten block, all the while saying to herself. “Heavy. Hea-ea-vey Hea-ea-ea-vey.”
Investigations: A New Perspective
Authors: Lamphere Patricia
Published: December 2020

The “Investigations” department is designed for teachers who wish to give students new insights into familiar topics in grades 3-6. It includes both directed and open-ended activities. A basic assumption is that the teacher will facilitate the investigation to let students become actively involved in shaping their own learning.
Place Value: A Vertical Perspective
Authors: Bove Sandra P.
Published: December 2020

Educators know that place value is the foundation of our number system. According to the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989), understanding place value is a crucial step in developing children's comprehension of number concepts. Teachers teach place value. Students pass the teacher's place-value test then telltale questions and comments later reveal their lack of understanding.
Links to Literature: Scrumptious Activities in the Stew
Authors: Schneider Sally
Published: December 2020

The week-long venture began with reading The Wolf's Chicken Stew (Kasza 1987).
In My Opinion: Fractions in the Early-Years Curriculum: More Needed, Not Less
Authors: Powell Carol A. , Hunting Robert P.
Published: December 2020

Watanabe (2001) has argued that the teaching of fractions should be eliminated from the primary mathematics curriculum, based on issues related to curriculum, development, and instructional materials. We disagree, for the following main reasons: First, this approach overlooks young children's developing multiplicative structures, which have their roots in part-whole relationships. Second, although we agree that the teaching of formal symbolism and notation for fractions can be delayed, conversations between teachers and children can establish important ideas from which formal symbols later will flow naturally. Third, sharing situations can help young children develop whole-number knowledge and can lay foundations for the rational-number system.
The Dollar Game: A Tool for Promoting Number Sense among Kindergartners
Authors: Hoover Holly M.
Published: December 2020

The Dollar Game, a base–ten grouping and trading game, and how a group of kindergarten students reacted to playing the game.
Building a Vision of Algebra for Preservice Teachers
Authors: Stump Sheryl , Bishop Joyce , Britton Barbara
Published: December 2020

Three conceptual approaches to algebra and some corresponding activities that have been used in an algebra course for preservice elementary and middle school teachers at three different universities.
Transition Points
Authors: Caldwell Marion Lee
Published: December 2020

An incentive system to manage classroom behavior based on mathematics skills and concepts. Teachers can adapt “Transition Points” to reinforce their own mathematics curriculum and to encourage behavior that they feel is important in their own classrooms.
Inchworm and a Half: Developing Fraction and Measurement Concepts Using Mathematical Representations
Authors: Moyer Patricia S. , Mailley Elizabeth
Published: December 2020

Children's conceptual understanding, strategic competence, and procedural fluency in mathematics are highly influenced by experiences in the early grades. During these years, many important mathematics concepts, including measurement and rational-number sense, should be a part of children's informal investigations. By informally exploring the same concepts in a variety of ways—with concrete manipulatives, visual models, and abstract representations—first graders can connect their initial youthful notions to sophisticated mathematical thinking.
Math by the Month: Who's on First?
Authors: Larkin Kevin , Perez Kaethe , Webb Darcy
Published: December 2020

The “Math by the Month” activities are designed to engage students to think like mathematicians. The activities allow for students to work individually or in small groups, or they may be used as problems of the week. No solutions are suggested so that students will look to themselves for mathematical justification and authority, thereby developing confidence to validate their work.
Problem Solvers: Decorative Plate Hanging
Authors: Hartweg Kim
Published: December 2020

The goal of the “Problem Solvers” department is to foster improved communication among teachers by posing one problem each month for K–6 teachers to try with their students. Every teacher can become an author: pose the problem, reflect on your students' work, analyze the classroom dialogue, and submit the resulting insights to this department. Every teacher can help us all better understand children's capabilities and thinking about mathematics with their contributions to the journal. Remember that even student misconceptions are interesting and informative.
News from the Net: Thinking Geometrically: Totally Tessellated
Authors: Frederick Betz , Williams Nan
Published: December 2020

Involving students in a hands-on geometry unit is a fun way to finish the school year. The visual aspects of the content can engage students even in the last weeks of school. Once students begin to look at mathematical patterns and relationships, they can extend this thinking to other academic areas such as language arts, science, and social studies.
Investigations: The Mathematical Candy Store: Weight Matters
Authors: Mailley Elizabeth , 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.
Links to Literature: On Time with Arthur
Authors: Pace Renée Denyse
Published: December 2020

The fifteen children in my second-grade class cannot keep their eyes off the screen as they watch an Arthur video. They are completely entranced as they listen to an Arthur book read aloud. Arthur books fly off the shelf during silent reading time. My students love this adorable aardvark; they love him because they can relate to his life experiences. They are approximately the same age as Arthur and they go through the same childhood fears, struggles, and triumphs. So what better book to use to integrate mathematics into literature? Children must make connections between mathematics and realistic situations. When children are taught mathematics in isolation, they might conclude that mathematics occurs only at school and only during the mathematics block of time. They must understand that mathematical situations occur every day, all day, and all around us.
News from the Net: Number Time
Authors: Herrera Terese A.
Published: December 2020

Number Time, located at www.bbc.co.uk/schools/numbertime, is a unique place for young mathematics learners. Developed by the British Broadcasting Corporation (BBC), the site uses interactive animation to help children in pre-K through grade 2 understand and practice number basics. Users will find online games, videos that tell number stories, worksheets for offline work, and support for teachers and parents.
Research, Reflection, and Practice: Writing for an Audience in a Mathematics Methods Course
Authors: Flores Alfinio , Brittain Carmina M.
Published: December 2020

During their first mathematics methods course, many prospective elementary teachers confront their previous conceptions about mathematics and its teaching for the first time. This juncture makes the course important in their evolution as teachers of mathematics. Prospective teachers in a mathematics methods course must develop the ability to reflect on their actions, beliefs, knowledge, and attitudes. Writing in a mathematics methods course fosters reflection in a natural way; it serves as a tool for documentation, analysis, and discussion to help prospective teachers internalize what they learn and reach new levels of comprehension. At the same time, what teachers in training write gives teacher educators a window into their reflection and growth process.
Addressing Parents' Concerns about Mathematics Reform
Authors: Hendrickson Scott , Siebert Daniel , Smith Stephanie Z. , Kunzler Heidi , Christensen Sharon
Published: December 2020

Although NCTM's Standards documents have been around for more than a decade, teachers still frequently encounter resistance when attempting to implement reformoriented instruction and curriculum materials that are aligned with the Standards. Unfortunately, some of the strongest critics of reform are parents. Most have never experienced the type of mathematics instruction that the Standards recommend. The open-ended, conceptually oriented tasks that students bring home are different from their previous experiences and may be confusing. Parents' own anxiety toward and traditional beliefs about mathematics can further heighten their concern about the mathematics their children are now doing.
Balancing Act: The Truth behind the Equals Sign
Authors: Mann Rebecca L.
Published: December 2020

The misconceptions that students have when using the equals sign and a lesson that teachers can use in the classroom to give students the foundation for an accurate conception of equivalency.
What Nathan Teaches Us about Transitional Thinking
Authors: Taylor Ann R. , Breck Susan E. , Aljets Carol M.
Published: December 2020

“This is going to be a very, very, very, very tough question. It is going to take a lot of serious thinking. It is not going to be quick and easy. You are going to have to think about the ones column and the tens. Thirtyfour take away—look what I am going to do to you—sixteen. Now think it out.”
Problem Solvers: Winning Strategy
Authors: Tayeh Carla , Britton Barbara
Published: December 2020

The goal of the “Problem Solvers” department is to foster improved communication among teachers by posing one problem each month for K–6 teachers to try with their students. Every teacher can become an author: pose the problem, reflect on your students'work, analyze the classroom dialogue, and submit the resulting insights to this department. Every teacher can help us all better understand children's capabilities and thinking about mathematics with their contributions to the journal. Remember that even student misconceptions are interesting.
Isn't That Interesting! Reflect and Discuss
Authors: Buschman Larry E.
Published: December 2020

When children solve problems in ways that make sense to them instead of practicing procedures that they have been taught, things can become messy both mathematically and socially. This article examines some of the challenges that teachers and children face when a problem-solving approach is used for mathematics instruction. Additionally, examples are included that demonstrate how mathematical problems can be challenging for both children and teachers in some unexpected ways.
By Way of Introduction: Posing and Solving Problems: The Essence and Legacy of Mathematics
Authors: Contreras José
Published: December 2020

Mathematics, the queen of the sciences, has evolved and continues to evolve because of the frantic and interminable quest of passionate human beings to solve problems that arise within mathematics itself and in the real world. Yes, mathematics is not complete without concepts, definitions, axioms, theorems, proofs, algorithms, or formulas: They are all integral components of mathematics. But problems—posing and solving them—are the heart, the spirit, the essence of mathematics.
Students THINK: A Framework for Improving Problem Solving
Authors: Thomas Kelli R.
Published: December 2020

The results of research about students' and teachers' use of an interaction framework (THINK) to guide group communication about problem solving. Students who used the THINK framework demonstrated greater gains in problem-solving achievement than students who did not use the framework. Teachers reading this article will understand the THINK framework and how to apply it to classroom use.
Bird Station Investigation
Authors: Poth Julie R.
Published: December 2020

How the real-world application of measurement skills within an integrated science unit can strengthen the engagement level of students and improve their critical thinking and problem-solving skills. Teachers learn how to integrate science and math in the classroom to improve students' problem solving skills.
Problem Solvers: Solutions to the Talking Turkey Problem
Authors: Britton Barbara
Published: December 2020

The problem appearing in the November 2005 “Problem Solvers” section, a timely Thanksgiving task, was stated as follows:
Becoming Highly Qualified
Authors: Quigley Kimberly , Gomez Cristina
Published: December 2020

Two years ago, when I learned that even with a college degree and nine years of teaching experience I still needed another mathematics course to become “highly qualified,” I got really scared. What kind of course should I take? For what purpose? Although I am not an expert in mathematics, I knew that taking more courses like the ones I took in college would not help me in my teaching. Other teachers advised me to take one of the lowerlevel mathematics courses at the local community college. These were offered during the summer and were basically a review of eighth-grade prealgebra. This could be an easy way to achieve my goal of becoming “highly qualified.” But I did not see how a course like this would help me become a better teacher.
The Answer Is 20 Cookies. What Is the Question?
Authors: Barlow Angela T. , Cates Janie M.
Published: December 2020

The answer is 20 cookies. What is the question?
Problem Solving in a Structured Mathematics Program
Authors: Buyea Robert W.
Published: December 2020

“Solving problems is not only a goal of learning mathematics but also a major means of doing so. Students should have frequent opportunities to formulate, grapple with, and solve complex problems that require a significant amount of effort and should then be encouraged to reflect on their thinking.”—Principles and Standards for School Mathematics (NCTM 2000, p. 52)
Math by the Month: How Does Your Garden Grow?
Authors: Forrest Kristen , Schnabel Denise , Williams Margaret E.
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.
In My Opinion: Making it Accessible: What U.S. Teachers Should Know about Japanese Mathematics Teaching and Schooling
Authors: Moseley Bryan , Okamoto Yukari
Published: December 2020

Much research has been conducted comparing education in the United States with education in Asian nations, such as Japan, but just how much of this research has been of real use to teachers in the United States? We believe that despite the significant amount of impressive research that has been done analyzing Japanese teaching practices, the manner in which these important findings have been reported to teachers has been largely ineffective. This is unfortunate, because one of the unique strengths of crossnational research is that it provides intact working models of successful practices. Japan is particularly important in this respect because, in many ways, it represents one of the most successful models of constructivist mathematics teaching in the world. We believe that this information is not pursued by U.S. teachers for two general reasons. First, research studies frequently couch results in terms of U.S. deficits. Although we believe these results to be accurate and important, it is difficult for teachers in the United States to compare themselves to teachers in Japan when much of the research that is available makes the persistent lament that U.S. teachers and their students are underachievers. Second, we believe that although important differences exist between Japanese and U.S. school systems (e.g., length of the school year, total time spent on mathematics), the truth is that teachers in both nations have a great deal to learn from each other in terms of the successful practices they use. An unfortunate consequence of the focus on test scores is that school system differences have been mistakenly conflated with teaching practices. This has led to the propagation of several myths about Japanese practices that U.S. teachers tend to cite as evidence of the unsuitability of Japanese practices for U.S. classrooms. We believe that U.S. teachers should separate differences in school systems from differences in teaching practices that could be beneficial to teachers in both nations.
Math by the Month: Geometry and Measurement
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. Geometry (from the Greek words for earth measuring) is the mathematics of measurement, properties of shapes, and relationships of points, angles, surfaces, and solids. This month, students have opportunities to connect geometry and measurement to the world around them. They will find shapes, use area and perimeter to solve problems, explore tessellations, and investigate diagonal lines and lines of symmetry.
Wondrous Tales of Measurement
Authors: Malinsky Marci A. , McJunkin Mark
Published: December 2020

Have you ever considered teaching mathematical concepts through the use of children's literature? One way to begin is to re-create how children learned long ago—elders spinning yarns as twilight deepened, young people caught up in wondrous tales that taught them about their world. To help students make a tactile connection to the experience from long ago, all you need are a skein of yarn and eager students seated in a circle.
Early Childhood Corner: Ladybugs and Lengths: Beginning Measurement
Authors: Tyminski Andrew M. , Weilbacher Monica , Lenburg Nicole , Brown Cindy
Published: December 2020

Measurement is one of five Content Standards promoted by the National Council of Teachers of Mathematics as crucial facets of students' mathematical knowledge (NCTM 2000). Skills and reasoning that develop in association with measurement are applicable in everyday life as well as in many career choices. A significant topic within elementary school curricula, measurement is addressed through the use of investigative activities. Unfortunately, students traditionally struggle with measurement tasks, which points to limited understandings of concepts involved in such tasks (Kamii 2006; Thompson and Preston 2004). Therefore, examining the manner in which measurement is approached within the early elementary classroom is a germane pursuit.
Math by the Month: Math Everywhere
Authors: Brandts Lois , Hoopingarner Tom , Gallego Christine , Saldamando Dora , Tapia-Beltràn Grace , Williams Karolyn
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 your students become familiar with their immediate surroundings and their location in the world through mathematical investigations involving number sense and operations, collecting and representing data, geometry, measurement, logic, communication, representation, and technology.
Links to Literature: Making Sense of Time with A Toad for Tuesday
Authors: Schultz Gilda O.
Published: December 2020

“If you had a whole day to do whatever you wanted, what would you do?” I ask my second-grade students. “What if you had five days?”
Teachers as Lifelong Learners—The Role of Reading
Authors: Coffey David C. , Billings Esther M. H.
Published: December 2020

Why is it so difficult for student teachers to consistently understand, apply, and retain important content from professional literature? They must be taught strategies to read in this specific genre.
Two Thumbs Way, Way Up
Authors: Quinn John , Kavanagh Brian , Boakes Norma , Caro Ronald
Published: December 2020

When fourth graders in an urban district—where standardized testing is traditionally a struggle—learned to peer review and recap their daily mathematics lessons in an easy-to-implement index card format, 100 percent passed the end-of-year assessment, 73 percent at the advanced level.
Ten Is the Magic Number!
Authors: Barker Lindsay
Published: December 2020

How this teacher develops composition of ten with second graders was dramatically reshaped by the 2006 release of NCTM's Curriculum Focal Points.
Research, Reflection, Practice: A Generation of Progress: Learning from NAEP
Authors: Kloosterman Peter , Rutledge Zachary , Kenney Patricia Ann
Published: December 2020

Often referred to as “The Nation's Report Card,” the National Assessment of Educational Progress (NAEP) was designed in the 1960s as a tool for monitoring precollege student performance in various subject areas. The original design included assessment of nine-, thirteen-, and seventeen-year-old students. The first mathematics assessment was completed in 1973 with additional mathematics assessments following at two- to fouryear intervals. In contrast to assessments like the SAT, which are usually taken by college-bound students only, NAEP is given to a sampling of all students across the United States regardless of ability or aspiration. As such, it is the best available measure of mathematics achievement for the nation as a whole (Kenney and Kloosterman 2007).
Why Are Things Shaped the Way They Are?
Authors: Whiten David J. , Whiten Phyllis
Published: December 2020

Why do corn kernels grow in staggered rows? Why are manhole covers always round and honeycomb cells hexagonal? Important geometric concepts are embedded in the shape and design of natural and manufactured objects.
Break the Area Boundaries: Reflect and Discuss
Authors: McDuffie Amy Roth , Eve Norma
Published: December 2020

Understanding the concept of area is a challenge for children. Beyond following procedures with formulas, studying area has been a source of confusion for students at all mathematical levels (Nitabach and Lehrer 1996; Thompson and Preston 2004). In fact, National Assessment of Educational Progress (NAEP) data from fourth and eighth graders suggest that many students have incomplete or superficial understanding of area (Martin and Strutchens 2000). Although students continue to struggle, the 2003 NAEP data shows that performance on area items is significantly improving, which may be due to an increased curricular focus on area concepts and the use of manipulatives and visualization (Blume, Galindo, and Walcott 2007).
From the Classroom: Extra Cheese Wins
Authors: Baker John D. , Bungo Katie
Published: December 2020

Elections are intrinsic to our sense of fairness and are a fundamental part of selecting school or classroom representatives. Furthermore, counting votes and weighing results include mathematics. So, combining democracy and mathematics in interdisciplinary lessons to promote both topics seems quite natural.
Equity for Language Learners: Reflect and Discuss
Authors: Bresser Rusty , Melanese Kathy , Sphar Christine
Published: December 2020

Learn how to focus mathematical language on concepts to accommodate the needs of the 10 percent of U.S. students whose first language is not English.
Investigations: EEK—a cockroach!
Authors: Julien Laurie St.
Published: December 2020

Why would a person who is terrified of cockroaches use them in a math lesson? The idea for this investigation did not occur to me until I read a newspaper article that described Italian scientist Paolo Domenici's research about cockroaches' escape trajectories. In particular, he found that cockroaches have preferred escape trajectories of 90, 120, 150, and 180 degrees from the source of danger (Domenici et al. 2008). Because this real-world information presents a unique problem-solving context for fifth graders to explore angles formed by clockwise and counterclockwise rotations, I overcame my fear of the creatures to develop this investigation.
Fractions and the funky cookie
Authors: Ellington Aimee J. , Whitenack Joy W.
Published: December 2020

A mathematics specialist has great success using a pattern-block configuration to help a small group of fifth graders understand that fractional parts of a whole unit must be equal in size. That's just the way the funky cookie crumbles.
Contemporary Curriculum Issues: An algebraic-habits-of-mind perspective on elementary school
Authors: Goldenberg E. Paul , Mark June , Cuoco Al
Published: December 2020

Although it is necessary to infuse courses and curricula with modern content, what is even more important is to give students the tools they will need in order to use, understand, and even make mathematics that does not yet exist. A curriculum organized around habits of mind tries to close the gap between what the users and makers of mathematics do and what they say (Cuoco, Goldenberg, and Mark 1996, p. 376).
Teaching teachers through justifying activities
Authors: Lo Jane-Jane , McCrory Raven
Published: December 2020

Prospective teachers need not waffle about developing the knowledge required to serve up appetizing justification and problem-solving methods to their elementary school students.
Problem Solvers: Problem: Crack the Code
Authors: Chandler Farrah Jackson
Published: December 2020

Secret codes, puzzles, and ciphers have long held the fascination of children. Unbeknownst to them, such challenges offer the perfect opportunity to apply critical thinking skills and use algebraic reasoning skills. This month, challenge yourself and your students with cryptogram puzzles
Math by the Month: Dressing Up
Authors: Lewis Cathie , Lewis Tom
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 will look to themselves as the mathematical authority, thereby developing the confidence and critical-thinking skills necessary to validate their thinking.