A Volume in The Montana Mathematics Enthusiast: Monograph Series in Mathematics Education Series Editor Bharath Sriraman, The University of Montana The name of Zoltan P. Dienes (1916-) stands with those of Jean Piaget and Jerome Bruner as a legendary figure whose theories of learning have left a lasting impression on the field of mathematics education. Dienes' name is synonymous with the Multi-base blocks (also known as Dienes blocks) which he invented for the teaching of place value. He also is the inventor of Algebraic materials and logic blocks, which sowed the seeds of contemporary uses of manipulative materials in mathematics instruction. Dienes' place is unique in the field of mathematics education because of his theories on how mathematical structures can be taught from the early grades onwards using multiple embodiments through manipulatives, games, stories and dance. Dienes' notion of embodied knowledge presaged other cognitive scientists who eventually came to recognize the importance of embodied knowledge and situated cognition - where knowledge and abilities are organized around experience as much as they are organized around abstractions. Dienes was an early pioneer in what was later to be called sociocultural perspectives and democratization of learning. This monograph compiled and edited by Bharath Sriraman honors the seminal contributions of Dienes to mathematics education and includes several recent unpublished articles written by Dienes himself. These articles exemplify his principles of guided discovery learning and reveal the non-trivial mathematical structures that can be made accessible to any student. The monograph also includes a rare interview with Dienes in which he reflects on his life, his work, the role of context, language and technology in mathematics teaching and learning today. The book finds an important place in any mathematics education library and is vital reading for mathematics education researchers, cognitive scientists, prospective teachers, graduate students and teachers of mathematics.

This book provides an insightful view of effective teaching practices in China from an international perspective by examining the grades 7-12 mathematics teacher preparation in the Shandong province of China. It is an excellent reference book for teacher educators, researchers, reformers, and teaching practitioners. A qualitative research approach, involving in-depth interviews with purposive sampling of ten grades 7-12 award-winning mathematics teachers, was chosen to conduct the study. The participants are from the Shandong province and have been awarded recognition for his/her achievements in teaching grades 7-12 mathematics by the different levels: school, district, city, province, or nation; and his/her students have achieved high average scores in college entrance exams or in high school entrance exams among the classes at the same grade level. Data analysis revealed the following findings: first, grades 7-12 mathematics teachers from the Shandong province of China were prepared to teach through pre-service training, in-service training, and informal learning. The pre-service training can be characterized as emphasizing formal mathematics training at advanced level. The in-service training is integrated with teacher collaboration and teaching research, and has the characteristics of diversity, continuity, and orientation toward teaching practice. The in-service training also stimulates teachers to conduct selfdirected learning. Second, the award-winning grades 7-12 mathematics teachers are identified by the following characteristics: they are passionate about mathematics and share their passion through teaching; they actively take part in teaching research through application of teaching research in the classroom, collaboration with peers, and systematic lesson preparation; they apply technology into teaching; and they take an active role in teaching research in order to expand their professional opportunities. Based on the findings of this study, the following conclusions were reached: pre-service training and in-service training are both necessary processes for mathematics teachers to build up their knowledge base for effective teaching. Pre-service training is just a starting point for the teaching profession. In-service training, integrated with teacher collaboration and teaching research should be a continuous activity that is a part of a teacher's everyday life.

A volume in Research in Mathematics Education Series Editor Barbara J. Dougherty, University of Mississippi This volume investigates the evolution of the geometry curriculum in the United States over the past 150 years. A primary goal is to increase awareness of the nature of the current geometry curriculum by investigating the historical, mathematical and pedagogical influences that it has sustained since its inception. Given the limited access to first-hand accounts of the enacted geometry curriculum during the past 150 years, the book relies on textbooks to provide a record of the implemented curriculum at any given point in time and on policy documents and journal articles to provide insight into the prevalent issues and arguments of the day. The book is organized in a chronological sequence of ""notable events"" leading to discernable changes in thinking about the geometry curriculum over the past century and a half-roughly the extent of time during which geometry has been taught in American schools. Notable events include important reports or commissions, influential texts, new schools of thought, and developments in learning technologies.These events affected, among other things: content and aims of the geometry curriculum; the nature of mathematical activity as construed by both mathematicians and mathematics educators; and, the resources students are given for engaging in mathematical activity. Before embarking through the notable events, it is necessary to consider the ""big bang"" of geometry, namely the moment in time that shaped the future life of the geometry curriculum. This corresponds to the emergence of Euclidean geometry. Given its influence on the shape of the geometry curriculum, familiarity with the nature of the geometry articulated in Euclid's Elements is essential to understanding the many tensions that surround the school geometry curriculum. Several themes emerge over the course of the monograph, and include: the aims and means of the geometry curriculum, the importance of proof in geometry, the role of visualization and tactile experiences, the fusion between solid and plane geometry, the curricular connections between geometry and algebra, and the use of motion and continuity. The intended audience would include curriculum developers, researchers, teachers, and curriculum supervisors.

Web 2.0 technologies, open source software platforms, and mobile applications have transformed teaching and learning of second and foreign languages. Language teaching has transitioned from a teacher-centered approach to a student-centered approach through the use of Computer-Assisted Language Learning (CALL) and new teaching approaches. Engaging Language Learners through Technology Integration: Theory, Applications, and Outcomes provides empirical studies on theoretical issues and outcomes in regards to the integration of innovative technology into language teaching and learning. This reference wok discusses empirical findings and innovative research using software and applications that engage learners and promote successful learning, essential tools for educational researchers, instructional technologists, K-20 language teachers, faculty in higher education, curriculum specialists, and researchers.

Take a Stand! (grades 9-12) helps teens develop critical thinking skills by examining debates on issues directly relevant to their lives (that you won't find in most classroom materials). Each chapter: Covers an important topic relating to electronics, sex, mental health, and relationships. Presents a question for debate, such as "Should kids choose their own religion?" and "Is it possible to love more than one person?" Shows how each issue might arise in an ordinary teen conversation. Presents and explores two or more opposed answers to philosophical debates. Encourages high school students to develop their own positions while learning to appreciate other perspectives. Throughout the book, the chapter contributors-all current or recent teens themselves-highlight key definitions, quote compelling sources, and diagram the central arguments. Each chapter includes discussion questions to guide arguments, as well as helpful sidebars and illustrations to increase comprehension. Perfect for inspiring classroom discussion of topics that matter to today's teens. Grades 9-12

This book stems from the 2019 meeting of the UNESCO UNITWIN international network for Arts Education Research for Cultural Diversity and Sustainable Development. It presents scholarly, international perspectives on issues surrounding arts education and sustainability that addresses the following questions: What value can the arts add to the education of citizens of the 21st century?; What are the challenges and ways forward to realize the potential of arts education in diverse contexts? The book discusses empirical research and exemplary practices in the arts and arts education around the world, presenting sound theoretical and methodological frames and approaches. It identifies policy implications at national, regional and global levels that cut across social, economic, environmental and cultural dimensions of sustainable development.

180 Days of Spelling and Word Study is a fun and effective daily practice workbook designed to help students improve their spelling skills. This easy-to-use second grade workbook is great for at-home learning or in the classroom. The engaging standards-based activities cover grade-level skills with easy to follow instructions and an answer key to quickly assess student understanding. Each week students learn 10 words, focusing on spelling rules, patterns, and vocabulary. Watch students become better spellers with these quick independent learning activities.Parents appreciate the teacher-approved activity books that keep their child engaged and learning. Great for homeschooling, to reinforce learning at school, or prevent learning loss over summer.Teachers rely on the daily practice workbooks to save them valuable time. The ready to implement activities are perfect for daily morning review or homework. The activities can also be used for intervention skill building to address learning gaps.

Written in a user-friendly, conversational style, the fourth edition of this groundbreaking text helps pre-service and in-service mathematics teachers build the comfort and confidence they need to begin talking to children about fractions and ratios, distilling complex ideas and translating research into usable ideas for the classroom. For two decades, Teaching Fractions and Ratios for Understanding has pushed readers beyond the limits of their current understanding of fractions and rational numbers, challenging them to refine and explain their thinking without falling back on rules and procedures they have relied on throughout their lives. All of the material offered in the book has been used with students, and is presented so that readers can see the brilliance of their insights as well as the issues that challenge their understanding. Each chapter includes children's strategies and samples of student work for teacher analysis, as well as activities for practicing each thinking strategy, designed to be solved without rules or algorithms, using reasoning alone. The fourth edition of this popular text has been updated throughout and includes new examples of student work, updated artwork, and more. As with previous editions, an equally valuable component of this text is the companion book MORE! Teaching Fractions and Ratios for Understanding (2012), a supplement that is not merely an answer key but a resource that provides the scaffolding for the groundbreaking approach to fraction and ratio instruction explored here. MORE! includes in-depth discussions of selected problems in the main text, supplementary activities, Praxis preparation questions, more student work, and templates for key manipulatives.

A volume in Advances in Music Education Research Series Editors Linda K. Thompson, Lee University and Mark Robin Campbell, SUNY at Potsdam Research Perspectives: Thought and Practice in Music Education calls attention to various theoretical and methodological aspects within the expanding field of research in music education. Perspectives presented in this volume offer readers a host of ideas and practices that range from international and historical to empirical and philosophical. Of special interest is a set of invited essays. Collectively, these essays illuminate our understanding of the peer review process, the importance of artistic vision in research and education, and the notion of complementarity - a recognition of the validity of diversity of thought and practice in music education research. The studies in Part 1 of Research Perspectives include early childhood musical development, an international comparison of early childhood preservice teacher knowledge and skills, and a psychohistoric examination of developmentally appropriate practice. Part II is comprised of studies focused on psychometrics of motivation, and professional development of practicing music educators. This volume is a significant addition to the libraries of Colleges of Education and Schools of Music, as well as an important reference for music scholars and educators, researchers, and graduate students who are concerned with advancing both the scope and quality of research in the study of music teaching and learning.

Curriculum materials are among the most pervasive and powerful influences on school mathematics. In many mathematics classes, student assignments, the questions the teacher asks, the ways students are grouped, the forms of assessment, and much more originate in curriculum materials. At the same time, teachers have considerable latitude in how they use their curriculum materials. Two classes making use of the same materials may differ markedly in what mathematics content is emphasized and how students are engaged in learning that content. This volume considers a variety of research tools for investigating the enactment of mathematics curriculum materials, describing the conceptualization, development, and uses of seven sets of tools. Mathematics education researchers, curriculum developers, teacher educators, district supervisors, teacher leaders, and math coaches will find insights that can improve their work, and guidance for selecting, adapting, and using tools for understanding the complex relationship between curriculum materials and their enactment in classroom instruction.

A volume in Research in Mathematics Education Series Editor Barbara J. Dougherty, University of Mississippi This monograph reports on an analysis of a small part of the mathematics curriculum, the definitions given to quadrilaterals. This kind of research, which we call micro-curricular analysis, is often undertaken by those who create curriculum, but it is not usually done systematically and it is rarely published. Many terms in mathematics education can be found to have different definitions in mathematics books. Among these are ""natural number,"" ""parallel lines"" and ""congruent triangles,"" ""trapezoid"" and ""isosceles trapezoid,"" the formal definitions of the trigonometric functions and absolute value, and implicit definitions of the arithmetic operations addition, subtraction, multiplication, and division. Yet many teachers and students do not realize there is a choice of definitions for mathematical terms. And even those who realize there is a choice may not know who decides which definition of any mathematical term is better, and under what criteria. Finally, rarely are the mathematical implications of various choices discussed.As a result, many students misuse and otherwise do not understand the role of definition in mathematics. We have chosen in this monograph to examine a bit of mathematics for its definitions: the quadrilaterals. We do so because there is some disagreement in the definitions and, consequently, in the ways in which quadrilaterals are classified and relate to each other. The issues underlying these differences have engaged students, teachers, mathematics educators, and mathematicians. There have been several articles and a number of essays on the definitions and classification of quadrilaterals. But primarily we chose this specific area of definition in mathematics because it demonstrates how broad mathematical issues revolving around definitions become reflected in curricular materials. While we were undertaking this research, we found that the area of quadrilaterals supplied grist for broader and richer discussions than we had first anticipated. The intended audience includes curriculum developers, researchers, teachers, teacher trainers, and anyone interested in language and its use.

Second language (L2) pronunciation has become increasingly visible as an important area of L2 teaching and research. Despite the growing number of resources available focused on L2 pronunciation, technology in L2 pronunciation has received much less attention. While technology has been an enduring strand of L2 pronunciation research, it has also been somewhat inconspicuous. Indeed, research has examined a wide variety of technologies such as language-learning platforms, speech visualization software, and Automatic Speech Recognition. Despite the abundance of research, it can be difficult to gain a full sense of work in this area given the lack of a comprehensive and consolidated resource or reference. This book endeavors to fill that gap and make L2 pronunciation technologies more visible by providing teachers and researchers an introduction to research in a wide variety of technologies that can support pronunciation learning. While working to introduce practitioners to numerous technologies available, it also dives into the research-basis for their use, providing new studies and data featuring a wide variety of languages and learning contexts.

Sixteen teachers. Sixteen journeys. All on a quest to become outstanding teachers of writing. All taking different paths to acquire and hone those skills that make a teacher effective. From kindergarten to college, teachers are faced with the daunting task of instilling the art of writing in their students. From creative writing to research, the art of writing incorporates the writing process to create the inking of our thinking. These 16 teachers from across the nation have traveled a long and arduous path to seek and to reach for the methods and strategies that will make them successful writing teachers. This is their stories.

Why has the 6+1 TRAIT model had such a tremendous impact on writing instruction? Because it works. It allows teachers to pinpoint students' strengths and weaknesses in ideas, organization, voice, word choice, sentence fluency, conventions, and presentation, and focus instruction. Now Culham turns her expert eye to our youngest students. Like her groundbreaking guide for grades 3 and up, her new book contains scoring guides, sample papers, and focus lessons for each trait, but framed to address K-2 teachers' needs For use with Grades K-2.