bluuebunny/crossref_metadata_2025 huggingface dataset:
Opinions of Pre-Service Classroom Teachers about Academic Controversy Method
Authors: Baydar Aşkın
Published: December 2020

The aim of this study is to determine the opinions of pre-service classroom teachers about academic controversy, from the cooperative learning methods, implemented in social studies teaching course. Using the action research pattern from the qualitative research approaches, the study group for the research comprised 42 preservice teachers in third year attending the primary education department in a state university. Research data were collected from preservice teachers with an interview form asking open-ended questions Responses of preservice teachers to the questions included opinions about the positive and negative aspects of the academic controversy method; whether they would apply this method in future classes and why; and about the contribution of the method to social and individual development of students. Opinions of preservice teachers after implementing the method in the class environment were that the academic controversy method was fun and beneficial for peer teaching; increased in-class interaction, retention of knowledge and self-confidence; ensured effective participation in class, active learning and conflict management; provided democracy education, directed research, taught respect for differences, provided a multidimensional perspective, and reduced the need for authority; and that it developed self-control, self-expression, decision-making and problem-solving skills. Additionally, criticisms mentioned by preservice teachers included causing noise in the classroom, not being appropriate for all class levels, lessons or topics, being difficult to implement in crowded classrooms and that the duration was not sufficient for the implementation.
A Study on APSACS Karachi Zone ESL Teachers’ Notion About Assessment and Its Numerous Employment in English Pedagogy
Authors: Sarwat Samina , Akram Muhammad , Ain Qurat ul , Shahzad Waheed , Iqbal Ashraf , Salman Muhammad Saad
Published: December 2020

Research work regarding to teacher’s cognition, basically, bring into light teachers’ perception, what they know and how they believe. To comprehend teachers’ perceptional structure, it is indispensible as it interlinks to their directional practices in ESL teaching domain. With regards to assessment, teachers’ cognition constitutes a vital and integral research field in two perspectives: understandability of ESL teachers’ belief and practices and their needs in assessments region. This study delves the aim of assessment in ESL classes under four main regimes: (1) summative assessment, (2) formative assessment, (3) students’ self-assessment, and (4) assessment to meliorate teachers’ direction. It also delves to probe ESL teachers’ notions about the assessments’ employment in ESL pedagogy. It also demonstrates that how teachers’ notions interconnect to their KG to HSSC level in teaching English. 35 Pakistani ESL teachers who work at APSACS Junior, Senior and College wings in Karachi Zone. To collect the data, 18-Likert scale questionnaire is employed. Outcomes of study bring out that the participants’ belief on assessment is impregnable on assessments’ employment regarding to formative purposes. On the secondary level, self-assessment procedures and techniques are given significance. From KG to HSSC level, participant teachers have no influence on participants’ assessment predilections. Data collection tool is also a significant contribution to the literature; besides the vital findings it has produced.
Automated Evaluation of Contact Angles in a Three-Phase System of Selective Agglomeration in Liquids
Authors: Schreier Julia , Furat Orkun , Cankaya Murat , Schmidt Volker , Bröckel Ulrich
Published: December 2020

This study aims to an automated evaluation of contact angles in a three-phase system of selective agglomeration in liquids. Wetting properties, quantified by contact angles, are essential in many industries and their processes. Selective agglomeration as a three-phase system consists of a suspension liquid, a heterogeneous solid phase and an immiscible binding liquid. It offers the chance of establishing more efficient separation processes because of the shape-dependent wetting properties of fine particles (size ≤ 10 µm). In the present paper, an experimental setup for contact angle measurements of fine particles based on the Sessile Drop Method is described. Moreover, a new algorithm is discussed, which can be used to automatically compute contact angles from image data captured by a high-speed camera. The algorithm uses a marker-based watershed transform to segment the image data into regions representing the droplet, the carrier plate coated by fine particles, and the background. The main idea is a parametric modelling approach forthe time-dependent droplet’s contour by an ellipse.The results show that the development of the dynamic contact angles towards a static contact angle can be efficiently determined based on this novel technique. These findings are useful for a detailed discrimination of wetting properties of spherical and irregularly shaped particles as well as their wetting kinetics. Also, a better understanding of selective agglomeration processes will be promoted by this user-friendly method.
Bimanual skills and symmetry of upper limb movement in a group of drummers
Authors: Golec Joanna , Sędzielewski Mateusz , Szczygieł Elżbieta , Przybytek Monika
Published: December 2020

Introduction: Hand-eye coordination is essential to carry out daily activities or take part in sports. Developing strong visual-motor coordination is especially important for athletes or musicians who rely on it for their careers.

Goal: This study aimed to evaluate visual-motor coordination in drummers’ upper limbs.

Materials and methods: The study group consisted of 60 men, aged 20 to 30 years (average 24.62 ±2.48). The respondents were divided into two groups, group P consisted of 30 experienced drummers and group N of 30 non-drummers. Standardized tests were employed: Relative Hand Skill test (RHS test) and a plate tapping test.

Results: The RHS test conducted on an original sample demonstrated no significant difference between the P and N group for the dominant limb (p=0.7272) or the non-dominant limb (p=0.3274). A significant difference was observed between the P and N group in the plate tapping test. The difference in the plate tapping test results between the dominant and non-dominant hands was significantly smaller in the P group than in the N group (p< 0.0001).
MOŻLIWOŚCI WYKORZYSTANIA BEZZAŁOGOWYCH STATKÓW POWIETRZNYCH W NADLEŚNICTWIE ŚWIDWIN
Authors: Pastuszka Paweł , Sawicki Paweł
Published: December 2020

One of the fastest developing scientific disciplines in forestry are geomatics and remote sensing. The use of unmanned aerial vehicles deserves a mention. On the example of the Świdwin Forest District the possibilities of using drones in forestry were presented. Unmanned aerial vehicles are mainly used for fire protection, creation of orthophotomaps, checking the health status of stands, monitoring spruce forests and the promotion of state forests.
“Writings of Paraboles”
Authors: McMorran Ciaran
Published: December 2020

This chapter explores how James Joyce interrogates the traditional procedures through which geometric symbols of "perfection and the divine”—including the concept of the infinitely straight line—are first acquired. By referring to Joyce’s early readings of Euclid’s Elements and other geometric texts including the works of Giordano Bruno, it examines how geometry is presented as a traditional system of ideal objectivities in II.2. More specifically, it demonstrates how the schoolchildren’s senseless application of the Wakean classbook’s instructions, and their attempted measurements of the visible world, reflects Bruno’s and Edmund Husserl’s congruent concerns regarding the practice of geometry as a “tradition emptied of sense.” This chapter also sheds light on Joyce’s application of non-Euclidean concepts by referring to his manuscript drafts for II.2, illustrating how non-Euclidean concepts stemming from the works of Bruno and Henri Poincaré are developed within the context of ALP’s curved bodily and terrestrial forms. More generally, this chapter illustrates how Joyce disrupts the univocity of Euclidean symbols by referring to non-Euclidean alternatives, questioning the absolute rectitude (i.e., correctness) of Euclidean geometry. In doing so, it argues, Joyce responds to a history of uncertainty regarding Euclid’s parallel postulate which began over two thousand years ago.
Textual Topography
Authors: McMorran Ciaran
Published: December 2020

This chapter examines how the branching narrative framework of “Wandering Rocks” reflects the structure of the manneristic maze and emulates the nonlinear visual structures which are traced by the characters of Ulysses as they wander through Dublin’s streets. In light of Henri Poincaré’s definition of geometry as “the summary of the laws by which images succeed each other,” it explores how James Joyce presents time presented as the fourth dimension of space in his construction of a textual “picture of Dublin” which follows the movement of wandering bodies. This chapter provides a schema of the narrative network in “Wandering Rocks,” illustrating how Joyce’s textual remapping of Dublin involves the structural emulation of fundamental geometric constructs and related topographical concepts which involve the coincident meeting of lines (as in triangulation, parallax, and the Cartesian coordinate system). In light of the parallactic perspectives which are facilitated by the episode’s branching structure, this chapter demonstrates how the labyrinthine “Wandering Rocks” narrative epitomizes Joyce’s Brunonian perversion of unidirectional rectilinearity on a structural level, disrupting “wider manifestations […] of ‘conceptual and behavioral rectilinearity’” in its nonlinear form.
Brother Singulars
Authors: Feinstein Amy
Published: December 2020

Chapter 2 explores Stein’s use of Arnold’s Hebraism in her first fictions to signal the Jewish morality of her middle-class characters. In 1903, Stein wrote the novella Q.E.D. and the brief first draft of her novel The Making of Americans. In both works, she presents ill-fated romances between ethically-Jewish and more aesthetically-inclined characters. In Q.E.D., she allusively depicts the Jewish identity of her protagonist Adele, who finds herself in a love affair with the aptly named Helen. Adele’s frequent lamentations have biblical roots in texts attributed to the prophet Jeremiah. Stein closes the novella with her characters in a romantic stalemate, but her romance fusing Arnoldian Hebraism and Hellenism as an ideal of Jewish culture had just begun. The affianced couple in the first draft of The Making of Americans espouses Stein’s Arnoldian fusion. The novel’s paterfamilial voice of Hebraism dismisses as “modern” the Hellenic inclinations towards the arts by the young heroine and her fiancé. Similar to Eliot, Woolf, and Joyce, Stein, in her revising of Arnold, imagines the modern writer, her Brother Singular, as one of a plurality of individuals whose typologically Jewish cultural ideals combine the ethical traditions of the Hebrew with the intellectually liberating creativity of the Hellene.
Meat Economies of the Chinese American West
Authors: Sunseri Charlotte K.
Published: December 2020

Cuisine and diet are topics of particular interest to scholars of Chinese communities in the nineteenth-century American West. Many zooarchaeological analyses have identified beef and pork among the main provisions for miners and townsfolk, and this chapter synthesizes archaeological and historical evidence for food access and supply while exploring contexts of socioeconomics and cuisine which likely structured food choices. By focusing on both urban and rural sites to compare access and food choices, the historical evidence of national railroad–based chains of supply for meat products and Chinese food practices in varied living contexts are investigated. Taphonomic marks of centralized processing and redistribution, documented pricing of meat cuts, and patterns of access across the West provide new perspectives on feeding American communities.
Flexible Plant Food Practices among the Nineteenth-Century Chinese Migrants to Western North America
Authors: Popper Virginia S.
Published: December 2020

Plant remains from Market Street Chinatown, San Jose, California, and historical accounts show that Chinese migrants relied on a variety of strategies to obtain plant foods in western North America in the second half of the nineteenth century. They farmed Chinese and European American crops, purchased local and imported foods, and collected wild resources. They faced a diversity of local environmental, social, and economic conditions that required a flexible cuisine and making choices beyond the dichotomy of maintaining a traditional Chinese diet or adopting European American foods.
Multisited Networks
Authors: Yu 余全毅‎ Henry
Published: December 2020

The author considers several themes raised within this volume of essays, including the utility of “transnationalism” as a concept; the importance of connecting multiple sites in order to understand the archaeological record; and considerations of other kinds of evidence such as oral histories, family stories, and memory, rather than archival and archaeological remains. The author suggests considering network theory and the analysis of sites as nodes within complex translocal migration networks, within which migrants circulated and moved objects and ideas as well as their own bodies. Narratives of meaning and desire, particularly concerning social and economic mobility, shaped and fuelled mobility within these networks, where the mobility of knowledge is perhaps the most important object in motion. Intelligence networks moved valuable information and social networks reproduced technologies such as shareholding small businesses, food preservation techniques, and mobilizing trust and credit across distances.
OS COORDENADORES DE ÁREA DO PIBID: PERCEPÇÕES SOBRE O SER PROFESSOR FORMADOR
Authors: Maria Fernandes Nunes Celia , Karine Moura Silva Sales Fernanda
Published: December 2020

Teacher training is a theme that permeates the field of studies in the field of education, as well as educational policies. Among the policies, we highlight the Institutional Teaching Initiation Scholarship Program (PIBID), which consists of an inductive action in the training of teachers aiming to value and improve teacher training. The programis developed in partnership with Universities and Basic Education Schools and involves graduates, supervisors (basic education teachers), area coordinators and teachers who work in institutional coordination and in the management of educational processes (higher education teachers). This article is part of a qualitative research that sought to investigate the relationship between training and teaching practice in theperception of the area coordinators of PIBID / Federal University of Ouro Preto (UFOP). In this article, we will present the analysis of the data collected, through questionnaires and interviews, referring to the category: “What it is to be a teacher and teacher trainer”. Among the perceptions, it was possible to identify that the PIBID / UFOP area coordinators are in permanent training and the PIBID was a possibility of approaching the public school of basic education. The study allowed us to conclude that there is a formative reciprocity among the participants, which as they form. The area coordinators reinforced the conception of knowledge and pedagogical tact in line with the inseparation of theory and practice, the work of the trainer based on dialogue, commitment to public education, teacher training, teaching and learning and the constant reassessment of its own practice.
QUALIDADE DA FORMAÇÃO DE PROFESSORES NA RELAÇÃO COM OS DISCURSOS DA “QUALIDADE DO ENSINO”: EFICIÊNCIA, PRODUTIVIDADE E INCLUSÃO ESCOLAR
Authors: Oliveira Raimundo Nonato Moura , Morais Georgyanna Andrea Silva , Lima Maria da Glória Soares Barbosa
Published: December 2020

What prevailing conception of quality guides the training ofteachers? With this central question, this text, in the light of the meanings of quality of education and teaching in dispute in Brazilian educational policies, analyzes the understanding of the quality of teacher education for primary school, as it has been developing in the last decades. It adopts the historical-dialectic perspective as a research reference, and understands that the ideal of teaching quality, emerged from the interest of dominant groups for the reintegration of education in the economic agenda, in institutionalized initiatives, it brings simplistic theoretical-practical interpretations of teacher training policies to make students' right to quality education effective. The text brings arguments about the importance of understanding the quality of teacher training socially referenced by principles of emancipation and construction of an educational practice for all.
FORMAÇÃO CONTINUADA: A ESCOLA COMO ESPAÇO DE DIÁLOGO E FORTALECIMENTO DOCENTE
Authors: Casagrande Jéssica Luana , Santos Camila de Fátima Soares dos
Published: December 2020

This article discusses the continuing education of teachers, with the school itself as a training space. The objective was to reflect on the conditions and assumptions that underlie this training and the vision of teachers and managers, considering the training practices that are developed. The research was made in a public school, located in a county in the Western region of Santa Catarina. Methodologically, a qualitative approach was made, including bibliographic analysis and application of questionnaires for teachers and managers. The analysis of this study enables to understand the importance of building news conditions for the achievement of this training, in order to assume a space that allows teachers to accomodate their needs and improve educational practices.
SAÚDE MENTAL NA UNIVERSIDADE: A PERSPECTIVA DE UNIVERSITÁRIOS DA PERMANÊNCIA ESTUDANTIL
Authors: Marolla Garcia Luciana , Lucia Messias Fialho Capellini Vera , Lima dos Reis Verônica
Published: December 2020

The way in which university students relate to society emotionally or psychosocially has been gaining prominence in the contemporary world, which has been highlighted in university research, as well as leading universities to look at their students' mentaland emotional health. . The aim of this study was to analyze the opinion of university students of the student stay on how the university could support them in their psychosocial and mental health experiences. To this end, the qualitative and quantitativemethod involved the participation of 140 students, aged between 17 and 24 years, registered at the Technical Center for Psychosocial Care (NTAPS) of Unesp, Campus de Bauru, in 2018, beneficiaries of student allowance. The treatment of the data occurred through the analysis of textual content of the students answers about how the university could support them in their psychosocial aspects. This content was submitted to the textual statistics software, Iramuteq, which, through two analysis techniques, presented a word cloud and an analysis of similarity among the most evoked words in the students' speeches. The word cloud showed graphically that the most cited words were “student”, “university”, “being”, “offering” and “psychological assistance” and the similarity analysis demonstrated the interrelationships between these words. As a result, it was obtained that the students' speeches converge to highlight the importance of psychological assistance during the university period, as part of the student assistance service.
O ESPORTE NA ESCOLA A PARTIR DO CURRÍCULO DO ESTADO DE SÃO PAULO
Authors: Perrud Tardin Heitor , Rogério Romero Luiz
Published: December 2020

The 1980s represented an important period for teaching and learning Physical Education in schools, especially considering methodological aspects and content covered. It can be recognized that changes in methodologies have instrumentalized the movement's practice, however, without highlighting aspects of a pedagogical or critical nature. In this scenario, sport is characterized as a socio-cultural practice and, in the school environment, the form of teaching must be questioned, distancing itself from the reproduction of stereotypes of high performance and alienated training. Thus, it becomes relevant to analyze the approach to sport in the regular educational context. The objective is to analyze the insertion of sport in Physical Education at School for Elementary and High School from the Curricular Proposal of the State of São Paulo. This is a quantitative and qualitative documentary study. A survey of the proportionality of the distribution of topics related to sport and other content approaches was also used. Initially, the systematic reading of the text of the Curricular Proposal of the State of São Paulo was organized. 68 themes were identified to be addressed from the EF to the EM, from the Teacher's Notebooks. Sports, dances, gymnastics, physical abilities were observed; body, health, beauty among others. Thirty themes and content directly related to sport stood out, representing 44% of the total. Sport is predominant content, despite the recognized advances in relation to previous moments, gaps were identified to subsidize the student's global development. It is suggested to propose studies that assist in the educational actions of the teacher in the area and move towards innovation in sports education at school.
Redundant and Flexible Pseudorandom Optical Rotary Encoder
Authors: Miljkovic Goran S. , Denic Dragan B.
Published: December 2020

Optical encoders are mainly used in modern motion servo systems for high-resolution and reliable position and velocity feedback. Pseudorandom optical rotary encoders are single-track and use a serial pseudorandom binary code to measure absolute position. The realization and analysis of such a rotary encoder with advanced code scanning and error detection techniques, as well as an improved redundancy in operation, are presented. A presented serial code reading solution uses two phase-shifted code tracks and two optical encoder modules. So, the realized encoder, hybrid in nature, provides “output on demand” and more or less reliable position information using very efficient error checking. Compared to a standard absolute encoder, this encoder requires a smaller code disc, facilitates installation, has greater flexibility in operation, and is less sensitive to external influences.
Multi-Area Load Frequency Control of Hydro-Thermal-Wind Power Based on Improved Grey Wolf Optimization Algorithm
Authors: Kong Fannie , Li Jinfang , Yang Daliang
Published: December 2020

The mathematical model of load frequency control is established in the interconnected power system of hydro, thermal, and wind for solving the problem of frequency instability in this paper. Besides, the improved grey wolf optimization algorithm (GWO) is presented based on the offspring grey wolf optimizer (OGWO) search strategy to handle local convergence for the GWO algorithm in the later stage. The experimental results show that the improved grey wolf algorithm has a superior optimization ability for the standard test function. The traditional proportional integral derivative (PID) controller cannot track the random disturbance of wind power in the hydro, thermal, and wind interconnected power grid. However, the proposed OGWO dynamically adjusts the PID controller control parameters to follow the wind power random disturbance, regional frequency deviation, and tie-line power deviation.
Gemeinwirtschaft und Gemeinwohl
Authors: Schulz-Nieswandt Frank
Published: December 2020

From a morphological perspective of analysis, what is social economics in its different organisational and sectoral forms and what are its possible roles in the context of capitalism? The controversial debate about commons is one of the key points of interest in this respect. What is the relationship between social economics and both the normative legal regimes of goods and services of general public interest and the idea of social welfare? Its interdependence with the policy of spatial orientation in capital-oriented social policy is very important in this regard.

This interdisciplinary study discusses a broad spectrum of paradigms, approaches, topics and dimensions in relation to this complex field of discourses, while also integrating philosophical questions of fundamental relevance.
Philosophical Inquiry and Psychological Development
Authors: Allen Richard ,   National Philosophical Counseling Association
Published: December 2020

Reasoning can promote psychological development, so even if the role of philosophical counselor is defined strictly in terms of assisting the reasoning of the client, we can expect client-centered philosophical inquiry to yield psychological benefits. The practices of philosophical counseling and psychotherapy permeate one another to some degree while also diverging in characteristic focus. Philosophical counselors are particularly well suited to helping clients think through their situation in the world.
The Future of “Philosophical Counseling”
Authors: Hoffman Eric ,   National Philosophical Counseling Association
Published: December 2020

Beginning from the recognition that “philosophical counseling” is a form of counseling and must acknowledge the extent to which it shares a framework with other kinds of counseling, this article articulates a modest agenda for philosophical counselors and the organizations that represent them. Philosophical counselors may enrich counseling more effectively from the inside, in alliance with other counselors. Respecting the experience and expertise of counselors will help other counselors to appreciate the value philosophy may have for their practice. The general search for allies, who share the sense that philosophy has value for everyday life, may lead, in connection with counseling, to greater involvement of philosophers in training programs for counselors.
A Teacher's Journal: Mathematics and Mother Goose
Authors: Young Cindy , Moulding Wendy
Published: December 2020

Rhyming Patterns can be pictured with mathematical symbols
Promising Research, Programs, and Projects: NCTM / Exxon Education Foundation K-3 Moth Specialist Project
Authors: Witte Bob
Published: December 2020

In 1987 the Exxon Education Foundation began its K-3 Math Specialist Project to improve teaching and learning mathematics at the early elementary school level. The decision to focus on the early grades was prompted by research showing that interest and ability in mathematics tend to decline after grade 3. The purpose of the project was to test whether changing the way mathematics is taught in the early grades would affect children's understanding of, and attitude toward, the discipline in future grades.
Promising Research, Programs, and Projects: Cognitively Guided Instruction
Authors: Chambers Donald L.
Published: December 2020

Cognitively Guided Instruction (CGI) is not a traditional primary school mathematics program. It does not prescribe the scope and sequence of the mathematics to be taught, provide instructional materials or activities for children, or suggest an optimal way to organize a class for instruction.
In My Opinion: Integrating Calculators: How Far Have We Come?
Authors: Reys Barbara J. , Smith Nancy L.
Published: December 2020

The mathematics education community has been recommending the integration of calculators into mathematics curriculum and instruction for nearly twenty years.
Reviewing and Viewing
Authors: Clements Douglas H.
Published: December 2020

Prices on software, books, and materials are subject to change. Consult the suppliers for the current prices. The comments reflect the reviewer's opinions aond do not imply endorsement by the National Council of Teachers of Mathematics.
Early Childhood Corner: Communicating with Young Children in Mathematics: A Unique Challenge
Authors: Schwartz Sydney L. , Brown Anna Beth
Published: December 2020

For prekindergarten and kindergarten children, whose communication skills fall far behind their mathematical understandings, meeting the NCTM's Standard 2: Mathematics as Communication poses unique challenges (NCTM 1989, 26-28).
Classroom Vignette: An Alternative-Assessment Tool
Authors: Walen Sharon B. , Hirstein James
Published: December 2020

How can the upper-elementary or middle-grades teacher create a safe forum for students to discuss mathematics and mathematics attitudes while simultaneously evaluating their progress and achievement?
Links to Literature: Mathematics and Poetry: Problem Solving in Context
Authors: Curcio Frances R. , Zarnowski Myra , Vigliarolo Susan
Published: December 2020

Although many elementary school teachers routinely share poetry with their students to foster an appreciation of language and literature, poetry can also promote the learning of mathematics.
In My Opinion: Timed Tests
Authors: Burns Marilyn
Published: December 2020

Dee Uyeda, a teacher in Mill Valley, California, told her class of third graders that they were going to lake a test. Mrs. Uyeda was interested in the progress the children were making in their mathematics learning.
Investigations: Zoo Mania
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.
News from the Net: Math Fundamentals
Authors: Herrera Terese A.
Published: December 2020

The Math Fundamentals Problem of the Week, located at mathforum.org/funpow, features nonroutine problems to challenge upper-elementary-grade students to think and communicate mathematically. Posted every two weeks during the school year, the problems focus on numbers, operations, and measurement but also may include introductory geometry, probability, and data.
Research, Reflection, Practice: Writing to Reflect in a Mathematics Methods Course
Authors: Flores Alfinio , Brittain Carmina
Published: December 2020

For more than a decade, several authors have highlighted the benefits to students of writing to learn mathematics. Writing is an important component of communication in the classroom. As Principles and Standards for School Mathematics (NCTM 2000) notes, “Writing in mathematics can also help students consolidate their thinking because it requires them to reflect on their work and clarify their thoughts about the ideas developed in the lesson” (p. 61). Teachers probably will not use this tool, however, unless they have had the experience themselves of writing in relation to mathematics. This article presents a brief review of the benefits of students writing to learn mathematics. In the second part of the article, we invite the reader to consider another possible use of writing: as a tool to help preservice teachers reflect on their own growth as they learn to teach mathematics. We discuss some of the benefits that writing has for prospective teachers and present examples of preservice elementary teachers' writing that were collected in several one-semester undergraduate mathematics methods courses that the first author taught. The second author participated as a student in one of the courses. In a second article to be published in this journal, we will focus on the process of writing and writing for an audience.
Early Childhood Corner: Learning about “One”: Units as a Cornerstone for Head Start Mathematics
Authors: Sophian Catherine
Published: December 2020

An important goal of teaching mathematics to young children is to give them a sound foundation for future mathematics learning. Therefore, teachers must identify how the things they teach young children—and the ways in which they teach them—can impact students' ways of thinking about mathematical concepts that will become important in the elementary school years and beyond.
Math By the Month: Algebraic Buffet
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. This month's activities are a feast for the algebraic thinker. The problems focus on patterns and functions. Students move from appe-teasers to dessert, building new knowledge from familiar food-related experiences. These activities incorporate not only various NCTM Content Standards but Process Standards as well.
Early Childhood Corner: Measuring Experiences for Young Children
Authors: Copley Juanita V. , Glass Kristin , Nix Linda , Faseler Alison , De Jesus Maria , Tanksley Sheila
Published: December 2020

“Are you bigger than my teacher?” fouryear- old Jeffery asked his slightly overweight principal on his way to the bus. Responding optimistically, Mrs. Hix said, “Do you mean taller?”
Ideas for Establishing Lesson-Study Communities
Authors: Takahashi Akihiko , Yoshida Makoto
Published: December 2020

Many educators in the United States have recently become interested in lesson study, a professional development approach popular in Japan, as a promising source of ideas for improving education (Stigler and Hiebert 1999). Numerous schools and school districts have attempted to use lesson study to improve their teaching practice and student learning (Council for Basic Education 2000; Germain- McCarthy 2001; Lewis 2002; Research for Better Schools 2002; Stepanek 2001; Weeks 2001).
Math by the Month: Gearing Up for the Summer Games
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.
Promoting Problem-Posing Explorations
Authors: Whitin Phyllis
Published: December 2020

My fourth-grade class had just completed an exploration of pentominoes (polygonal shapes with an area of five square units). Finding all twelve shapes gives children valuable geometric problem-solving practice by highlighting transformations (flips, slides, and turns) and congruence (shapes can be differently oriented, yet congruent). Before moving on to another lesson, I realized that the students might use the same twelve shapes to examine perimeter and area. Eleven of the shapes have a perimeter of twelve units. Only one shape yields a different perimeter, ten units (see fig. 1). The children had limited experience with perimeter and area; I doubted that they understood that shapes with a fixed area could have perimeters of different lengths. Because they were so familiar with the pentominoes, I felt that this material would give them a good opportunity to address these concepts in more detail. Although I did expect them to calculate the perimeters and areas of the twelve shapes, I did not foresee that the children's follow-up discussion would open an opportunity for problem-posing explorations. This article describes my evolving curricular decision making, the children's investigations, and what I learned from this unanticipated experience.
In My Opinion: Top-Ten Ways to Strengthen the Mathematics in Your Classroom
Authors: Lewis Cathie , Schad Brian , Contreras José , Kirschner Vicky , Garnett Cynthia , Taylor P. , Hagelberger Bonnie , Skipper Elizabeth M.
Published: December 2020

Welcome back to yet another exciting school year! Whether it is your first year of teaching or your thirty-first, sometimes we all need a little help before plunging into a new school year. The Teaching Children Mathematics Editorial Panel has assembled a list of activities to strengthen the classroom mathematics program. The ideas range from organizing mathematics materials to working with parents to taking a leadership role in mathematics. We hope our suggestions spark your thinking and planning as you wade into another school year.
Posing Problems from Children's Literature
Authors: Young Elaine , Marroquin Christine L.
Published: December 2020

One of the most important principles in reform mathematics is allowing students to be challenged by mathematics problems (Hiebert et al. 1996). Historically, mathematical problems have required students to apply a known procedure to produce an expected answer. The National Council of Teachers of Mathematics (NCTM 2000) has called for changes in the problems that are typically posed to students, asserting that such problems should instead require students to reason, communicate, represent, problem solve, and make mathematical connections. Posing open-ended, extendable problems allows students to construct their own mathematical learning and understanding by building on previous experiences and making connections among topics and disciplines.
From the Classroom: A Lesson on Logical Necessity
Authors: O'Brien Thomas C. , Wallach Christine
Published: December 2020

This article provides a glimpse into the work of fifth graders (ages 10–11) on a problem involving logical necessity. The research was part of a one-year collaboration between a university professor and his former student, a veteran teacher of twenty-plus years' experience, in an independent midwestern elementary school. The school's curriculum focuses on “teaching for understanding,” and problem solving plays an important role throughout the pupils' experiences. This is one of a series of reports on the various activities that resulted from this collaboration.
Problem Solvers: Making Brownies
Authors: Stump Sheryl
Published: December 2020

The goal of the “Problem Solvers” department is to foster improved communication among teachers by posing one problem each month for teachers of grades K–6 to try with their students. Every teacher can become an author: Pose the problem to your students, reflect on your students' work, analyze the classroom dialogue, and submit the resulting insights to this department. Through contributions to the journal, every teacher can help us all better understand children's capabilities and thinking about mathematics. Remember that even students' misconceptions provide valuable information.
Research, Reflection, Practice: Making the Most of Student Errors
Authors: Lannin John K. , Arbaugh Fran , Barker David D. , Townsend Brian E.
Published: December 2020

Give me a productive error over a boring, mundane, and unproductive fact any day.
Problem Solvers: Solutions to the Cheerio Count Problem
Authors: Tayeh Carla
Published: December 2020

The problem appearing in the December 2005/ January 2006 “Problem Solvers” section was stated as follows:
Research, Reflection, Practice: The Power of Paper–Folding Tasks: Supporting Multiplicative Thinking and Rich Mathematical Discussion
Authors: Turner Erin E. , Junk Debra L. , Empson Susan B.
Published: December 2020

Building understanding of multiplicative relationships is a key goal of mathematics instruction in the upper elementary and middle grades. Multiplicative thinking includes comparing numbers through many processes: multiplication and division (rather than addition and subtraction), ratio, proportions, stretching and shrinking, magnification, scaling, and splitting. Research has shown that multiplicative thinking develops slowly in children, over long periods of time (Clark and Kamii 1996; Vergnaud 1988). Initially, children tend to reason additively about multiplicative situations, and this additive thinking is often resistant to change (Hart 1984). Students need practice with tasks that help develop multiplicative thinking—in particular, tasks that help them recognize and reason about multiplicative relationships.
Problem Solvers: Solutions to the More Than a Guess Problem
Authors: Tayeh Carla
Published: December 2020

The problem appearing in the March 2006 “Problem Solvers” section was stated as follows:
The Empty Number Line: A Useful Tool or Just Another Procedure?
Authors: Bobis Janette
Published: December 2020

A grade 4 mathematics homework question instructed students, “Use the empty number line to solve the following,” causing nineyear- old Emily to respond, “No one should tell me what strategy to use. I should be allowed to make up my own mind!” Emily found it easier to solve some two-digit addition and subtraction computations by splitting them into tens and ones rather than using a strategy that could be recorded on a number line.
Context in Mathematics Learning: Problems and Possibilities
Authors: Lee Ji-Eun
Published: December 2020

One major goal of mathematics educators is to help students become good problem solvers. As a way to accomplish this goal, this article proposes posing problems that encourage students to consider the element of context.
The Day Math and Reading Got Hitched
Authors: Foster Shannon
Published: December 2020

Every teacher has encountered the need for a reteach. On this particular day, I was past the reteach knot on the reteaching rope. I dangled from a solitary string. My bags of tricks, now empty, became dead weight. The dreaded fifthgrade word problem was predicted to win another battle. Its fallen opponents now lay scattered across my desk. Amid the papers lay a dried-up pen whose days of “Great job!” now lay forgotten with the writing of the words “Please see me.” I had failed my students. They deserved better than this. I sat in my puddle of misery and finally decided there had to be something else we could do to get hold of these problems, so I swept the tests into the recycle bin and stalked out the door.
Mathematics and the Learning Cycle: How the Brain Works As It Learns Mathematics
Authors: Zambo Ronald , Zambo Debby
Published: December 2020

Fernando, a third-grade teacher, regularly engages his students in exploring mathematical concepts by providing them with problem-solving activities that build on and extend the knowledge they currently possess. Fernando's class has been working on counting sets of objects and has briefly worked with the idea of equal sharing. Today Fernando poses a problem about pennies in hopes that working on it will enable his students to use the learning cycle to further develop the concept of division.
Assessing Students' Levels of Understanding Multiplication through Problem Writing
Authors: Drake Jill Mizell , Barlow Angela T.
Published: December 2020

Assessing student learning is a very important part of teaching. As teachers, we are continually searching for assessments that give us valid information about what our students are learning. Occasionally, the assessments we use can surprise us with the results they yield.
Research, Reflection, Practice: Algebraic Thinking and Pictorial Growth Patterns
Authors: Billings Esther M.H. , Tiedt Tarah L. , Slater Lindsey H.
Published: December 2020

Dorothy, a second grader at an at-risk school where 87 percent of the students receive free or reduced lunches, watched intently as Mrs. T laid out pattern blocks to create a sequence of figures shaped like people (see fig. 1). When Mrs. T asked Dorothy, “What will the next one look like?” Dorothy replied, “Well, if you wanted to go from [the first person] all the way to four … you would put a head, then the body, hands, then the feet. And then you would put a hat, and another hat, and another one, and another one …. I think that's heavy for a person.” Dorothy thought the hats looked a bit top-heavy; nevertheless, she extended the pictorial growth pattern by correctly building the fourth person (see fig. 1).
Modeling Students' Mathematics Using Steffe's Fraction Schemes
Authors: Norton Anderson H. , McCloskey Andrea V.
Published: December 2020

Each year, more teachers learn about the successful intervention program known as Math Recovery (USMRC 2008; Wright 2003). The program uses Steffe's whole-number schemes to model, understand, and support children's development of whole-number reasoning. Readers are probably less familiar with Steffe's fraction schemes, which have proven similarly useful in supporting children's development of fractional reasoning. The purpose of this article is to introduce some of these schemes. We provide examples of student work accompanied by discussions of how fraction schemes can be used as tools for insight into student reasoning. We hope that teachers will find the schemes useful in understanding their students as mathematicians.
Prove It! Engaging Teachers as Learners to Enhance Conceptual Understanding
Authors: Sweetland Julie , Fogarty Meghann
Published: December 2020

The faculty of an elementary school gathered for a staff development workshop and quickly completed the first mathematics problem assigned by the facilitator: “What is 1/5 × 1/4?” Within a few seconds, every teacher in the room arrived at the correct answer: 1/20. The follow-up question, at first glance, seemed to be equally simple: “How did you get your answer?”
Students Control Their Own Learning: A Metacognitive Approach
Authors: Wieser Ellen T.
Published: December 2020

The Wednesday before a Friday test in my fifth-grade mathematics class brings a flurry of activity as most of my students work cooperatively to review concepts we have covered throughout our fractions unit. I have invited Billy and Maria to the small table at the front of the classroom for some remediation that I know both students need.
Learning to Think and Thinking to Learn
Authors: Kline Kate
Published: December 2020

Encouraging children to think—independently and publicly—is possibly one of any teachers' most challenging and rewarding responsibilities. Young children's less-developed language and listening skills further complicate teachers' work at the early elementary level. Yet, I've been fortunate to work with many teachers who have embraced this challenge and use young children's unique attributes, such as their unmitigated curiosity, to center mathematics teaching on thinking and reasoning.
Math by the Month: Fun on the Farm
Authors: 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 you and your students enjoy the fall season through mathematical investigations involving data collection, number sense and operations, measurement, communication, and representation.
Equity for English Language Learners in the Mathematics Classroom
Authors: Borgioli Gina M.
Published: December 2020

Although English Language Learners (ELLs) quickly acquire basic interpersonal communication skills, most struggle for several years with reading and writing academic content in English (Cummins 1981). In particular, in English-only mathematics classes, children are likely to have difficulty reading and comprehending text, reading word problems, and giving written or oral justifications of their problem-solving strategies in English (Clarkson and Galbrath 1992; Cuevas 1984; Cummins 1984; Moschkovich 2000; Ron 1999). A language barrier should not be mistaken for a learning problem or a deficit. English-speaking peers of ELLs should also avoid assigning them lower social and academic status because of nonnative language skills and perceived inability to perform well on social and academic tasks (Cohen et al. 2004).