bluuebunny/crossref_metadata_2025 huggingface dataset:
AS ESCRITAS DE SI E OS EFEITOS MOBILIZADORES DA FORMAÇÃO DOCENTE EM NARRATIVAS (AUTO)BIOGRÁFICAS
Authors: de Sousa Morais Joelson , Sousa Carvalho do Nascimento Franc-Lane , Divina Ferreira Lima Maria
Published: December 2020

This text is configured as a theoretical-bibliographic research, emphasizing thenarrative (auto) biographical approach to think about the processes of teacher training based on the writings of themselves as contributing to the construction of knowledge, knowledge and transformations that this can provide. We propose to question as a research problem: What are the contributions of the writings of oneself in the teacher education processes woven into (auto) biographical narratives? In view of the above, we weave as objectives of this article: to understand the historical-epistemologicalaspects of the field of (auto) biographical narratives in Brazil; understand the movement of professional teaching training mediated by the narrative writings of themselves, as well as reflect on the contributions of the (self) biographical narratives written in the process of teacher training and professional development. The theoretical-epistemological foundation of this text is based on the principles of the narrative (auto) biographical approach to which we are researchers in this area. The results of the study reveal that the challenge posed in the process of teacher training in the context of a narrative pedagogy, is the adoption of methodological devices in pedagogical practice by teacher trainers, with the use of narrative writings of themselves, which can be undertaken by the trainer himself, in dialogue with students in training, so that they create a culture of writing, and can contribute to their formative process by building knowledge and knowledge necessary for the profession that will accompany them, including, in the professional development of teachers when they are working in the area.
CONCEPÇÃO DE DOCÊNCIA: O QUE PENSAM OS PROFESSORES ALFABETIZADORES DA REDE MUNICIPAL DE ENSINO DE CAMPO GRANDE-MS?
Authors: Miranda de Brito Vilma , Cristina Teixeira Fernandes Rosangela
Published: December 2020

This article showedthe resultsoftheresearchconductedin2018, with the objective of investigating the teaching conceptionofliteracyteachersfromthepolicies continuingeducationdevelopedintheMunicipalEducationNetwork (REME) ofCampo Grande/MS.In this perspective qualitative research was adopted to address and discusspublicpolicies for the training of literacy teachers, going through the laws and programs of federal (PróLetramento and PNAIC) and municipal (Bet on the teacher). Datacollection occurred through semi-structured interviews with literacy teachers in municipal schools in CampoGrande/MS. The research showed that the teaching conception of the literacy teacher who works at REME now understands literacy a graduallearning process, now comprises the learning of literacy articulated with maturity. We also identified the concept of teaching permeated by affection and aptitude, thus tracing a literacy teacher profile. And finally, the conception of teaching based on the need to master systematized knowledge that permeates the literacy process, which allowed us to reflect and discuss the continuing formations offered to REME professorswho centralize discussions in teaching practices to leverage educational indices. It was concluded that there is an urgent need to restructure formations in order to enable discussions that include theory, practice and specificities experienced in the classroom enabling the acquisition of new knowledge and a critical look at the teaching-learning process, providing studies and reflections that articulate and resign the teaching conception of the literacy teacher.
A CONSTRUÇÃO DA AUTONOMIA DO PROFESSOR PRESENTE NAS DIRETRIZES CURRICULARES NACIONAIS DE FORMAÇÃO INICIAL DAS ÚLTIMAS DUAS DÉCADAS
Authors: Andrade dos Santos Tais , Pereira de Souza Filho Moacir
Published: December 2020

Thispaper aims to analyze the curricula of initial teacher training determined by the legislation originating from the National Education Council (CNE), with the outline of the curriculum proposed for the degrees related to the act of teaching in the final years of Elementary and Secondary Education, and aiming to understand the autonomymodels, through the terminations ofthese documents. Typified as documentary research, it was analyzed in a qualitative way, using as methodology the analysis of the content in the following categories: workload, skills and necessary requirements in the documents with the aid of the qualitative analysis software IRaMuTeQ. With Contreras' ideas for the delimitation of the conditions of autonomy as a theoretical reference, the analyzes indicate that the laws are moving towards a reflexive autonomy, with a narrowing of the relationship between theory and practice. However, after these years, the guidelines include training aimed at the knowledge of basic education in a directive and not emancipatory way.
FORMAÇÃO CONTINUADA E A IDENTIDADE PROFISSIONAL DOCENTE
Authors: Maria Albertino Flávia
Published: December 2020

The article is an excerpt from the Master's research, which aimed to identify and analyze the theoretical and methodological assumptions for guiding the proposals for continuing education of teachers, offered by the Municipal Department of Education, in two Elementary Schools I, in a city in the interior of São Paulo and their reflexes in the teaching action. The theoretical contribution was of a historical-cultural nature (Bakhtinian); it is a qualitative investigation, configured as a case study, with documentary analysis and semi-structured interview, involving three teachers, two pedagogical advisors and a director, covering a total of six direct participants. The analysis of the data collected from the documents and the interviews was done through the theoretical process of triangulation, content analysis and semiotic analysis of historical-cultural interpretation (bakhtinian) of the speeches of the interviewed professionals. The results showed that the teacher education process does not occur in a dialogical and ambivalent way, based on cultural development, through interpersonal and intersubjective relationships, as emphasized by the historical-cultural theory. The present research enables a critical-reflexive review of the continuing education practices offered by the researched municipality, and by extension, it may serve as an object of confrontations with other contexts of teacher education in other Brazilian municipalities
JUICIO MORAL DE ESTUDIANTES Y MAESTROS ANTE HECHOS DE VIOLENCIA EN UNA ESCUELA SECUNDARIA PÚBLICA EN MÉXICO
Authors: Fracchia Figueiredo Myriam
Published: December 2020

The objective of the investigation into the violent events in the daily environments of the students of a secondary school in Mexico was to reveal them as part of a training process for their teachers. From the conception that social and school violence are inherent to the social order and are expressed in bodies and things, our interdisciplinary approach was based on a mixed methodology, using qualitative techniques, through observation, pedagogical planning , common reflection and evaluation with teachers, and quantitative techniques, with the preparation and application of an interview of teachers to 429 students of the three grades of secondary school, in the morning and evening shifts, to relieve the network of violence, with emphasis on the school, andthe subsequent creation of a database for its systematization and analysis. This methodological strategy made it possible to unravel the moral judgment of students and adults in correspondence with the acts of violence experienced by the students, which have been mainly fights and beatings, harassment and robbery. Interventions regarding adults, in accordance with school regulations, have been the predominant application of expiatory sanctions, or their inaction, thus adding other forms of violence that express a heteronomous moral judgment. This forces the majority of students to be careful not to fall into provocations from the other minority group, ready to attack them as a way to settle their differences. Also the moral judgment of the students is heteronomous and their proposals to face these facts, to a large extent, coincide with the school regulations. However, a minority group of students proposed, in addition to listening, empathy and dialogue, that they “favor their own behaviors among equals”, which is the law of true cooperation, suggestive for a formative process of adults that facilitates the transition towards a moral judgment of cooperation, for a coexistence of protection and a better teaching-learning process.
Continuity Detection Method in Binary Image Signal
Authors: Hercik Radim , Machacek Zdenek , Koziorek Jiri , Vanus Jan , Schneider Miroslav , Walendziuk Wojciech
Published: December 2020

This paper is focused on a description of a new method of detecting continuities in a binary image. The detecting method is called “Binary Large Object” (BLOB). A new algorithm with other elementary parameters, as processing speed and memory capability, are described here. The developed BLOB method with described algorithms is implemented in MATLAB. The simulation of the algorithms is tested in different conditions, with the time dependences determination. The research results of the computing time or the BLOB memory demand during computation are presented as well. The developed BLOB method is usable as one of the elementary image processing methods of the field detection dependencies in the images, like pattern recognition or OCR algorithm.
Bioeconomy as One of the Key Areas of Implementing a Circular Economy (CE) in Poland
Authors: Marcinek Paulina , Smol Marzena
Published: December 2020

Transformation toward a circular economy (CE) model is one of the main priorities of the European Commission (EC). In the previous years, most of the European countries prepared national documents presenting their possibilities and plans for implementing CE in the country. In Poland, in 2019, the CE roadmap was approved by the government. Bioeconomy was indicated in this document as one of the key areas of CE implementation in Poland. This paper presents a detailed review of the actions needed for the transformation toward the CE model in Poland, and the units responsible for their implementation in the bioeconomy sector. The most important actions include creating conditions for the development of bioeconomy and building local value chains and a raw material base. Moreover, actions in the energy sector and transformation of industry is also indicated. Poland places great emphasis on strengthening cooperation between industry and the science sector, which should contribute to the implementation of innovative solutions in the whole economy, including bioeconomy. Therefore, it is necessary to integrate all activities taken by various stakeholders and the government at the central, regional and local level. A great opportunity to further development of bioeconomy in Poland is large resources of biomass in country. An increase in the biomass usage can positively accelerate the transformation process towards CE. Further efforts are required and planned in this area, based on the directions indicated in the Polish CE roadmap.
NEO Personality Inventory - 3: Recenze metody
Authors: Břežná Barbora , Kovář Dominik
Published: December 2020

NEO–PI–3 představuje osobnostní inventář, jehož účelem je poskytnout kvantitativní popis osobnostních charakteristik jedince. Metoda předpokládá, že rysy osobnosti lze v zásadě shrnout do 5 širších dimenzí. Můžeme říct, že reliabilita a validita metody je obstojná. NEO-PI-3 považujeme za užitečný nástroj, který nabízí jistý rámec pro porozumění osobnosti a vymezených 5 faktorů za jeden z možných způsobů, jak klasifikovat osobnostní strukturu. Zásadní je však kontext použití, detailní znalost jednotlivých subškál a realistický přístup k využití metody.
Examining Job Satisfaction and Organizational Commitment as Motivators of Unethical Pro-Organizational Behavior
Authors: Fulmore Julia A. , Fulmore Anthony L. ,   Philosophy Documentation Center
Published: December 2020

The present study evaluated the relationship between job satisfaction and unethical pro-organizational behavior (UPB), directly as well as indirectly, through organizational commitment. Multidimensional constructs were utilized for job satisfaction and organizational commitment to provide a granular understanding of how these constructs can motivate employees to engage in UPB, which can threaten organizations' success and diminish the public's confidence in organizations. In order to test these relationships, a diverse sample of 617 participants was recruited through the online survey distribution platform Amazon Mechanical Turk (MTurk®) to test the theoretical model using structural equation modeling (SEM). The results indicated that identification, affiliation, and exchange commitment served as intervening variables between growth satisfaction and UPB, while no significant indirect effect of internal work motivation on UPB was found. Implications for research and practice are discussed.
Philosophical Counseling as Psychotherapy
Authors: Mills Jon ,   National Philosophical Counseling Association
Published: December 2020

Contrary to current belief among many philosophers, I attempt to show that philosophical counseling is a form of psychotherapy that is in need of structure and guidance in order for it to prosper as a viable approach to mental health treatment. Methodological approaches are examined including dialectical, solution-oriented, and long-term considerations that comprise the nature of meaning analysis and procedural inquiry. If philosophical counseling is to gain recognition among the helping professions, it will need to embrace a philo-psychological paradigm of theory and practice that emphasizes philosophical eclecicism.
Philosophical Counseling is not a Distinct Field
Authors: Russell J. Michael ,   National Philosophical Counseling Association
Published: December 2020

There is currently a movement advocating “philosophical counseling.” My own development as a philosopher, then a human services professional, then a psychoanalyst, charts how I came to believe that philosophical training was underrated, and training in psychology was overrated, as an appropriate intellectual foundation for psychotherapy. However, these fields are not distinct. Laws governing the practice of psychology are arrogant in their scope, and make virtually everything out to be the practice of psychology. The scope and nature of philosophy isn’t any clearer. The kind of thinking encouraged in psychology is liable to be exactly the wrong sort of thing for training therapists. Unfortunately, philosophers are liable to not be good therapists either. The lack of neat distinctions between philosophical counseling and psychotherapy provides an argument against a monopoly on therapy-like activities by psychologists. On the liberal side this is an argument in favor of freedom of speech, of belief, and trade, for the applied philosopher. On the conservative side, it may also be an argument for certification (as opposed to licensure) for both psychologists and philosophers, in the interest of protecting the vulnerable by promoting truthful self-representation.
Philosophical Counseling and the Interpretation of Dreams
Authors: Raabe Peter B. ,   National Philosophical Counseling Association
Published: December 2020

Philosophers are generally reluctant to say much about the meaning of dreams, especially since Sigmund Freud appropriated the interpretation of dreams as part of psychoanalysis. In this essay I will first review some of the theories of dreams proposed by early philosophers that are now considered largely outdated. I will then critically examine the two powerful theories instituted by Freud and Jung by explaining them and then pointing out their flaws and weaknesses. In response to the failings of these theories I offer a lesser known but more recent theory formulated by Ernest Hartman that is supported by both his own empirical research and that of others. And finally I discuss how this intuitively more reasonable approach can be very helpful to the philosophical counselor whose client wishes to discuss the meaning of her dreams.
Cosmos, Worlds and Republics
Authors: Heuer Wolfgang ,   DePaul University
Published: December 2020

Viruses and pandemics are part of an overarching ecological theme that encompasses not only climate and plants, but all forms and conditions of life. This requires a far-reaching change in perspective. Not only does biodiversity, following Alexander von Humboldt, form a common “cosmos” across the globe, but we humans are also part of it. This natural sphere corresponds to Arendt’s concept of the “world” on the social and political sphere. Cosmos and world take the place of the old irreconcilable separation of nature/barbarism and culture/civilization. Consequently, the threat to cosmos and world does not come from nature but from man-made devastation. Biodiversity and human plurality can only thrive with the principles of environmental/political sustainability.
Investigations
Authors: Lamphere Patricia
Published: December 2020

The “Investigations” depa1tment 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. A basic assumption is that the teacher will facilitate the investigation so as to let students be actively involved in shaping their learning.
Tech Time: Using Technology to Enhance “My Travels with Gulliver”
Authors: Bayliffe Janie , Brie Raymond , Oliver Beverly
Published: December 2020

“Journey in Mathematics: 'My Travels with Gulliver'” is a California state-approved fourth-through sixth-grade unit integrating mathematics, reading, listening, writing, and drawing. The unit is based on the classic story Gulliver's Travels, written by Jonathan Swift in 1726, which describes Gulliver's voyages to Lilliput, the land of tiny people, and Brobdignag, the land of giants. Titania is a land created by the authors of the unit, and Ourland is the students' own classroom. The unit encourages students to explore scaling, measurement, area, and perimeter in a hands-on fashion, such as when Gulliver encounters a carpet peddler.
A Teacher's Journal: Geometry Game
Authors: Ortiz Enrique
Published: December 2020

Geometry is a very important part of the elementary school curriculum. NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) indicates that geometry helps us represent and describe in an orderly manner the world in which we live. Children are naturally interested in geometry and find it intriguing and motivating.
Grade-Number Themes for High-Profile Math
Authors: Barford Judy
Published: December 2020

Many recent professional sources urge us to teach by integrating themes across the curriculum (February 1993 Arithmetic Teacher, entire issue; October 1991 Educational Leadership, entire issue; NCTM 1989).
Newspapers: Connecting the Mathematics Classroom to the World
Authors: O'Connell Susan R.
Published: December 2020

“Students need to sec when and how mathematics can be used, rather than be promised that someday they will use it” (NCTM 1999, 35). The newspaper, as a classroom resource, allows a perfect opportunity to reveal to students the role of mathematics in their lives. When scanning a newspaper, students can find endless applications of classroom-taught skills.
Math by the Month: You Don't Say!
Authors: Chancellor Dinah , Schielack Jane F. , Irvin Barbara B.
Published: December 2020

These activities are designed to speak directly to students by giving them open-ended situations intended to engage their intellect through their interests. Students are encouraged to work on the activities independently, in pairs, or in small groups. No answers are given so that students are encouraged to look to themselves as the mathematical authority, thereby developing the confidence and critical-thinking skills necessary to validate their thinking.
Bilingual Lessons in Early-Grades Geometry
Authors: Flores Alfinio
Published: December 2020

The activities described here are creative, informal, intuitive geometry activities that stress higher-order thinking. The activities were completed by students in twenty-one bilingual classrooms in grades K-3 in a laboratory, hands-on setting.
Math by the Month: Balancing Acts
Authors: Porter Jeanna
Published: December 2020

These activities are designed to speak directly to students, giving them open-ended questions intended to engage their intellect through their interests. Students are encouraged to work on the activities individually, in pairs, or in small groups. No answers are given for the questions so that students are encouraged to look to themselves as the mathematical authority, to develop the confidence and critical-thinking skills necessary to validate their thinking.
Early Childhood Corner: En-chanting, Fascinating, Useful Number
Authors: Schwartz Sydney L.
Published: December 2020

One six-year-old, two four-year-olds, and one three-year-old were playing together using various collections of interlocking blocks and miniature people and animals.
Early Childhood Corner: Authentic Mathematics in the Classroom
Authors: Schwartz Sydney L.
Published: December 2020

Fifteen minutes into the free-choice-center time, children were involved in using materials and developing activities in all the centers in the classroom.
Exploring Size with The Grouchy Ladybug
Authors: Rozanski Kara D. , Beckmann Charlene E. , Thompson Denisse R.
Published: December 2020

The use of the book The Grouchy Ladybug for a mathematics lesson on measurement that integrates language arts and social skills.
Is a Rectangle a Square? Developing Mathematical Vocabulary and Conceptual Understanding
Authors: (Chris) Renne Christine G.
Published: December 2020

Desiring to better encourage students' thinking and conceptual development, a fourth-grade teacher examines classroom discourse and written work during her students' analysis and description of basic geometric shapes.
Collaboration Sites: Teacher-Centered Professional Development in Mathematics
Authors: West Lucy , Curcio Frances R.
Published: December 2020

Imagine an American school system in which teaching is viewed as a scientific endeavor and teachers base their lessons on research, implement them while colleagues observe, and refine them according to what students did or did not understand. This cycle of planning, practice, reflection, and refinement is an example of standards- based teaching and learning. An alternative to the traditional one-stop workshop approach, collaboration-site visits are fledgling efforts toward a teacher-centered approach to professional development and provide an authentic experience of teaching as learning. This article discusses collaboration-site visits, describes a two-day visit to a collaboration site, explains the benefits of participating in such visits that teachers have reported, and offers suggestions for implementing collaboration-site visits to support professional development in mathematics.
Teaching Problem Solving in Mathematics
Authors: Buschman Larry
Published: December 2020

Teachers face many challenges when attempting to teach problem solving to young children. This article examines these challenges from a classroom teacher's perspective and suggests ways to facilitate reform in mathematics instruction.
On the Write Path: Improving Communication in an Elementary Mathematics Classroom
Authors: Anderson Melissa A. , Little Deena
Published: December 2020

The process that teachers used to increase communication during problem-solving investigations. It demonstrates examples of students’ struggles and successes.
A Model for Understanding, Using, and Connecting Representations
Authors: Clement Lisa L.
Published: December 2020

Five different representations and the connections between and among them. The article also describes for teachers how to use multiple representations to support a diverse group of students' mathematical understanding within the mathematics classroom.
Building Responsibility for Learning in Students with Special Needs
Authors: Karp Karen , Howell Philip
Published: December 2020

Ways that elementary school teachers can help students with special needs build responsibility for their own mathematical learning. Includes practical classroom applications for teachers of special needs students.
Supporting Teacher Learning: Mathematical Thinking: Helping Prospective and Practicing Teachers Focus
Authors: Jacobs Victoria R. , Philipp Randolph A.
Published: December 2020

How did Misha solve the problems in figure 1, and what mathematical understandings do her strategies reflect? Misha's written work provides a rich context in which prospective and practicing teachers can discuss issues of mathematics, teaching, and learning. These discussions might include conversations about the similarities and differences between Misha's two strategies, what she must have understood about place value to generate these strategies, and what type of instruction likely preceded and should follow this problem-solving effort.
Early Childhood Corner: Vygotsky and the Three Bears
Authors: Kulczewski Peggy
Published: December 2020

It was 4:30 p.m. and I had just finished straightening up my kindergarten classroom. I let out a sigh. It had been a very long day—the kind of day that leaves you scratching your head and saying to yourself, “Did any learning take place?” I wondered, “Why did Kathy push Tom into the pile of blocks? Why didn't my new center with pattern blocks work for Joey? Luis loved it and he stayed on task. Poor Jennifer—she just started crying when everyone else was counting by 2's.”
Problem Solvers: A Word to the Wise
Authors: Britton Barbara , Tayeh Carla
Published: December 2020

The goal of the “Problem Solvers” department is to foster improved communication among teachers by posing a problem for K—6 teachers to try with their students. Every teacher can become an author: pose the problem, reflect on your students' work, analyze the classroom dialogue, and submit the resulting insights to this department. Every teacher can help us all better understand children's capabilities and thinking about mathematics with their contributions to the journal. Remember that even student misconceptions provide valuable information.
Investigations: Hickory Dickory Dock: Navigating through Data Analysis
Authors: Niezgoda Deborah A. , Moyer-Packenham 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. The tasks invoke problem solving and reasoning, require communication skills, and connect various mathematical concepts and principles. The ideas presented here have been tested in classroom settings.
Assessing Students' Mathematical Problem Posing
Authors: Silver Edward A. , Cai Jinfa
Published: December 2020

Posing problems is an intellectual activity that is crucially important in mathematics research and scientific investigation. Indeed, some have argued that problem posing, as a part of scientific or mathematical inquiry, is usually at least as important as problem solving (Einstein and Infeld 1938; Hadamard 1945).
Early Childhood Corner: ABCs of Early Mathematics Experiences
Authors: Hansen Laurie E.
Published: December 2020

Children begin to develop mathematical thinking long before they enter school. This acquisition occurs in a very natural way as children interact with the environment and their caregivers. Everyday experiences often lend themselves directly to learning mathematics. Planning meals, taking a bath, reading together, playing, and experiencing daily excursions are just a few examples of the daily opportunities children have to count, recognize shapes and numbers, and play with volume and measurement. Nurturing children's natural curiosity about, and aptitude in, mathematics at an early age is of utmost importance. A little encouragement can go a long way. Lozano and Medearis (1997) point out that young children's early experiences should be hands-on and meaningful.
Math by the Month: August 2006
Authors: Forrest Kristen , Schnabel Denise , Williams Margaret E.
Published: December 2020

The “Math by the Month” activities are designed to engage students to think as mathematicians do. Students may work on the activities individually or in small groups, or the whole class may use 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.
Fostering Relational Thinking while Negotiating the Meaning of the Equals Sign
Authors: Molina Marta , Ambrose Rebecca C.
Published: December 2020

How third-grade students developed an understanding of the equals sign and began to use relational thinking as they discussed true/false and open-number sentences. The sequence of instructional activities and children's responses to them are provided.
Understanding the Development of Students' Thinking about Length
Authors: Battista Michael T.
Published: December 2020

Describes assessment tasks and a conceptual framework for understanding elementary students' thinking about the concept of length. Teachers will learn about student difficulties with length and how to differentiate instruction to reach these learners.
Supporting Teacher Learning: Standards-Friendly Lessons in University Methods Courses
Authors: Hart Lynn C.
Published: December 2020

Since the publication of reform recommendations in Curriculum and Evaluation Standards for School Mathematics (National Council of Teachers of Mathematics 1989), many strategies have been used to align teacher practice with the Standards. For example, mathematics educators have examined the impact of coaching in teacher's classrooms (Hart, Najee-ullah, and Schultz 2004), changing curriculum materials (Educational Development Center 2005), using case studies (Barnett 1992), and participating in lesson study groups (Fernandez 2005). Although all these strategies—given the appropriate resources and teacher motivation—can improve instructional practice, many are not easily implemented in a university classroom. Teacher education programs in colleges and schools of education that attempt to facilitate substantial and lasting change in teacher practice, particularly change with preservice teachers, must often find other methods.
Problem Solvers: The Broken Calculator
Authors: Toll Donna , 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.
Investigations: Fraction Action
Authors: Moone Grace , Groot Cornelis de
Published: December 2020

The “Investigations” department features children's hands-on and minds-on explorations in mathematics and presents teachers with open-ended investigations to enhance mathematics instruc tion. These tasks invoke problem solving and rea soning, require communication skills, and con nect various mathematical concepts and principles. The ideas presented here have been tested in classroom settings.
Investigations: Sun Catchers
Authors: Isabelle Aaron D. , Bell Karen N.
Published: December 2020

The “Investigations” department features children's hands-on and minds-on explorations in mathematics and presents teachers with open-ended investigations to enhance mathematics instruction. These tasks invoke problem solving and reasoning, require communication skills, and connect various mathematical concepts and principles. The ideas presented here have been tested in classroom settings.
Deepening Teachers' Understanding of Place Value
Authors: Hopkins Theresa M. , Cady Jo Ann
Published: December 2020

As faculty members of the Mathematics Education Group in the College of Education, Health, and Human Sciences at the University of Tennessee, we are responsible for instructing both preservice and in-service teachers through courses and professional development activities. One topic we address is teaching place value to elementary school students. Teachers' familiarity with the base-ten number system, however, can prevent them from fully comprehending the difficulty these students have when trying to understand the abstract concept of place value. This article presents our evolving lesson in addressing this difficulty.
Mixed Numbers Made Easy: Building and Converting Mixed Numbers and Improper Fractions
Authors: Neumer Chris
Published: December 2020

After several years of observing and interacting with children, I have noticed their struggles with converting mixed numbers and improper fractions. I have tried several types of manipulatives, computer programs, pictures, and algorithm-based activity sheets. Even after being exposed to all these teaching approaches, many students still struggle with these representations. The concept of a mixed number—a whole number paired with a fraction—really boggles students' minds. More so, the idea of an improper fraction—a fraction with a numerator that is greater than or equal to the denominator—is virtually impossible for some fifth graders to grasp. They cannot connect their written algorithms to the concept or explain how they derived their answers. The reason for rewriting their answer in a different form was too abstract for them. Through direct work with my fifth-grade classes over the years, I have developed a new approach that produces great results and a deeper understanding of mixed numbers, improper fractions, and their relationship to each other.
Seeing Students' Knowledge of Fractions: Candace's Inclusive Classroom
Authors: Chick Candace , Tierney Cornelia , Storeygard Judy
Published: December 2020

A fifth-grade teacher describes what she learned from observing two students in her inclusive classroom with different learning styles and kinds of understanding as they solve traditional fraction problems using a clock face.
To Share or Not to Share — How Is the Question!
Authors: Hagen Pamela A. , Hooyberg Terra , Marsden Paul , Simonski Jana , Yuen Gary
Published: December 2020

Can a rich problem-solving task challenge a diverse range of students? How would students across various grade levels, from elementary school to secondary school, respond to the same task? These were the questions five different teachers in different schools wanted to explore in their respective classes, ranging from first grade through ninth grade.
From the Classroom: Shining Light on Multiplication: A Mathematics Lantern Festival
Authors: Bjork Janna L.
Published: December 2020

Sparkling lights fill the night sky. Bright, glowing shapes surround families. It is the night of the Lantern Festival.
Developing Understanding of Fractions through Pattern: Blocks and Fair Trade
Authors: Roddick Cheryl , Silvas-Centeno Christina
Published: December 2020

The design process and implementation of a hands-on unit on fractions in the sixth grade. The unit uses pattern blocks to help students develop conceptual understanding of fractions. Student misunderstandings and outcomes are presented, as well as the teacher's perspective on the impact on her classroom.
One Elementary School's Journey from Research to Practice
Authors: Mathern Donna , Hansen Pia
Published: December 2020

The journey one elementary school took to implement a standards-based mathematics program and increase student achievement by putting research into action, thus causing a school-wide transformation.
Supporting Teacher Learning: Improving Mathematics Instruction through Classroom-Based Inquiry
Authors: Ebby Caroline Brayer , Ottinger Maria Palaitis , Silver Penny
Published: December 2020

Research has shown that learning to teach mathematics for understanding is not simply a matter of learning new pedagogical techniques but rather requires substantial changes in a teacher's knowledge, beliefs, and practice (Putnam and Borko 2000). Preparing teachers to implement reform-oriented curricula requires positioning them as learners and inquirers of mathematical content, student learning, and instructional practice. Ball (1996) asserts that teacher professional development must embrace the uncertainty of practice and reflect a “stance of critique and inquiry—a stance of asking and debating, a discourse of conjecture and deliberation” (p. 506).
Gaining Insights into Children's Geometric Knowledge
Authors: Mack Nancy K.
Published: December 2020

While I was working with a third-grade teacher and his thirty-two students, he turned to me and asked, “Would you work with the children on geometry?” Although I eagerly agreed, several questions raced through my mind: ”I have not had much experience helping children learn geometry and do not know much about their thinking. Will I be able to help these children learn geometry in ways that are meaningful to them? What should third graders learn about geometry? What do the children already know about geometry and the ideas they should learn?” Answers to the latter two questions were especially important in helping the children develop a conceptual understanding of geometry by building on their existing knowledge. This article describes how research on children's geometric thinking used in conjunction with a children's book provided valuable insights into their prior geometric knowledge of the mathematical names and properties of polygons.
Assessing Students' Understanding through Conversations
Authors: Vanderhye Cecilia M. , Demers Cynthia M. Zmijewski
Published: December 2020

In a fourth-grade classroom, the teacher told her students that the area of the rectangle she had drawn on the board was twelve centimeters square. The students knew that one side was three centimeters long, and they were asked to figure out the length of the other sides. One student offered an answer: “The shape looks like a square, so, since all sides of a square have equal length, the other sides must be three inches long.”
What's Your Angle on Angles?
Authors: Browning Christine A. , Garza-Kling Gina , Sundling Elizabeth Hill
Published: December 2020

The word angle may conjure up several thoughts—a corner, two rays and a vertex, or a degree measure. But what about the idea of a turn (a rotation around a fixed point) or of the space between two rays, and what exactly is a degree? Many upper-elementary students have such limited notions of angle that they struggle to provide an appropriate mathematical definition for the term and, instead, describe what we are measuring when we measure an angle. Yet, according to NCTM (2000), students in grades 6–8 must be able to “carefully examine the features of shapes in order to precisely define and describe fundamental shapes” (p. 233). Angle is certainly a prominent feature of shape, so, beginning in the elementary grades, providing students with opportunities to carefully explore the idea of angle is critical for the development of their understanding of geometry. Doing so, however, requires us as teachers to first realize the complexity of the concept of angle. As one sixth-grade student put it, “An angle is a lot more than just degrees.”
Curriculum Focal Points: What's Your Focus and Why?
Authors: Fennell Francis
Published: December 2020

NCTM's Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics (2006) was published a year and a half ago. Anecdotal comments, surveys, and NCTM's documentation of print sales and Web downloads indicate that Curriculum Focal Points is making its way into discussions in boardrooms, schools, school districts, and state departments of education—discussions about the mathematics that is important at particular grade levels.
Research, Reflection, Practice: The Educational Value of Tic-Tac-Toe for Four- to Six-Year Olds
Authors: Kamii Constance , Nagahiro Mariko
Published: December 2020

Do your students like to play tic-tac-toe? If so, do you think of games as time fillers or part of your educational program? In our classrooms, we use this game as a serious educational activity. The purpose of this article is to explain why we value this and similar games and how we use them. We base our opinion on research conducted in Japan (Nagahiro, Kato, and Miyakawa 2003) and the United States (DeVries and Fernie 1990; Kamii 2000; Kamii and DeVries 1996), and our observations in many classrooms.
Early Childhood Corner: I Scream, You Scream: Data Analysis with Kindergartners
Authors: Cook Carolyn D.
Published: December 2020

That students should be able to pose questions, gather data, and represent that data in graphs seems reasonable enough—until you consider that these are the stated expectations for children just four to eight years old! The National Council of Teachers of Mathematics (NCTM) believes young students are capable of these skills and more. NCTM's Content Standard for data analysis and probability outlines what students in prekindergarten through grade 2 should know and be able to do (NCTM 2000).
Using TARGETTS to Create Learning Environments That Support Mathematical Understanding and Adaptive Motivation
Authors: Gilbert Melissa C. , Musu Lauren E.
Published: December 2020

This article focuses on learning environments that support students' mathematical understanding and enhance their adaptive motivation. Drawing on our experiences as teachers and teacher educators, we first describe adaptive motivation. We then introduce TARGETTS, a lesson planning and analysis tool, and describe ways in which teachers can use this tool to highlight specific instructional strategies that support both adaptive motivation and mathematical understanding.
Using Sudoku Bulletin Boards to Teach Mathematical Reasoning
Authors: Buckley Carol A.
Published: December 2020

“Maddening!” “Addicting!” “Can't do it.” “Do it every day.” These are phrases my peers have used in reference to Sudoku puzzles. I enjoy completing Sudoku puzzles but had not previously considered that incorporating them into my instruction would motivate my primary-grades students. After reading “Exploring the Sudoku Challenge” (Wilburne 2006), I decided to offer Sudoku as a student option for the logical reasoning category of a tic-tac-toe instructional strategy. In a tic-tac-toe strategy, three tasks in three different categories are organized to resemble a tic-tac-toe board. Students choose three tasks in a straight line: across, up and down, or diagonally. My students' enthusiasm and curiosity about completing Sudoku were immediately evident.
Aligning Theory with Practice
Authors: Kurz Terri L. , Batarelo Ivana
Published: December 2020

Description of a structure to help preservice teachers get invaluable field experience by aligning theory with practice supported by the integration of elementary school children into their university mathematics methodology course. The framework is described as a model to help others wanting to establish a similar course.
The Goal of Long Division
Authors: Martin John F.
Published: December 2020

Martin describes student thinking that should be developed to facilitate their understanding of answers resulting from division. Keys to this understanding include the role of place value in the quotient and the power of multiples of ten in determining the quotient.
By Way of Introduction: Believing in Change
Authors: Mann Robert
Published: December 2020

The 2008 U.S. presidential campaign featured “change we can believe in,” and the global marketplace and shifting economy have resulted in additional calls for change in many policies and paradigms. Political and economic issues influence education and result in modifications for schools, teachers, and students. Such developments, as well as rapid advances in technology, impact the way we teach and learn mathematics.
Research, Reflection, Practice: What Effective Math Teachers Have in Common
Authors: O'Donnell Barbara
Published: December 2020

Effective teachers integrate problem solving into their mathematics instruction to promote the development of students' mathematical understanding. Students must learn to think critically, reason, and solve difficult, demanding problems as a part of everyday learning events. Teachers often wonder if they are constructing learning environments that ensure such results.
Is Mathematics a Universal Language?
Authors: Whiteford Tim
Published: December 2020

How mathematics is taught in other cultures has a significant impact on how students learn it when joining a U.S. classroom.
A smorgasbord of assessment options
Authors: Bacon Kathy A.
Published: December 2020

Presented with a variety of palatable, inquiry-based, creative learning choices in geometry, this teacher and her fifth graders found tremendous satisfaction in meeting target goals for reasoning skills and taking important “next steps” in learning.
A foxy loxy and a lallapalagram
Authors: Wilson Johnnie B.
Published: December 2020

It is easy to fall into the trap of thinking that teaching mathematics should greatly differ from teaching language arts. The subjects are usually scheduled separately in the school day. Classroom teachers at Munich International School in Starnberg, Bavaria, Germany, did not pay much attention to what language means to learning and teaching mathematics—until their geometry students offered language surprises that reminded their teachers how important language is.
Polygon properties: What is possible?
Authors: Robichaux Rebecca R. , Rodrigue Paulette R.
Published: December 2020

Sorting shapes and solving riddles develop and advance children's geometric thinking and understanding while promoting mathematical communication, cooperative learning, and numerous representations.
Research, Reflection, Practice: Comparison helps students learn to be better estimators
Authors: Star Jon R. , Kenyon Martina , Joiner Rebecca M. , Rittle-Johnson Bethany
Published: December 2020

The ability to estimate is not only a valuable math skill but also an essential life skill. Many adults use estimation daily: when tipping a waitress, determining the cost of a sale item, or converting units. Within mathematics, the ability to estimate is linked to deep understanding of place value, mathematical operations, and general number sense (Beishuizen, van Putten, and van Mulken 1997) and allows students to check the reasonableness of their answers to mathematics problems in a variety of contexts.
From the Classroom: Jump right in
Authors: Piel John A. , Green Michael
Published: December 2020

On opening day at the neighborhood pool, children line up with unbridled enthusiasm after a long winter of inside play. Notice how so many just jump right in and begin swimming without hours and hours of review. How could this be? After all, it has been nine months since their last swim, and what about that “winter lag” we have heard so much about? This scenario should be reminiscent of what teachers face when it is time to jump into a new academic year. Sadly, retention of mathematical knowledge over the “summer lag” is a thorny issue.
Supporting children's problem solving
Authors: Jacobs Victoria R. , Philipp Randolph A.
Published: December 2020

Teachers demonstrated four categories of reasoning when deciding how to respond to students.
Connections: Probability: A Whale of a Tale
Authors: Young Elaine
Published: December 2020

Dear Mr. Blueberry (James 1996) is often used by elementary school teachers to help students learn language arts. In the book, Mr. Blueberry's student Emily writes postcards to her teacher when she finds a whale in her backyard pond over the summer. Mr. Blueberry responds in writing with many reasons why a whale could not possibly live in Emily's backyard. Although this book has long been a favorite for its language arts connections, it also has the potential to introduce probability concepts and vocabulary in the upper elementary school grades.
A new world of mathematical thinking
Authors: Schwartz James E.
Published: December 2020

Use number composition and decomposition to break out of an assembly-line mentality.
A dime @ a time
Authors: Columba Lynn , O'Donnell Patricia , Sanchez Yamil
Published: December 2020

What is the value of a dime these days? Quite a lot, actually! This month, a dime gets you a dozen entertaining challenges. Have fun exploring the math that can be found a dime @ a time.