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Teacher Noticing of Pre-service and In-service Secondary Mathematics Teachers: Influences of Teaching Experience, Cognitive Demands, and Teaching Internships on Perception, Interpretation, and Decision-making (Perspektiven der Mathematikdidaktik)
by Anton BastianIn light of increasing demands on teachers and the need to develop teaching-related competences, this book examines the situation-specific skill of teacher noticing in pre-service and in-service secondary mathematics teachers. A video-based test instrument is used to measure teachers’ noticing skills in perception, interpretation, and decision-making from both general and mathematics pedagogical perspectives. The aim is to understand the structure and characteristics of teacher noticing across different groups, as well as the influences of teaching experience and opportunities to learn. Three quantitative studies are conducted: two cross-sectional studies with 457 participants, including master’s students, early career teachers, and experienced teachers, and one longitudinal study with 175 master’s students. The results support the conceptualization of teacher noticing as comprising three facets. They also reveal positive influences of teaching experience on the development of teacher noticing, with in-service teachers outperforming master’s students. However, experienced teachers perform similarly to early career teachers in general and worse in certain areas, suggesting saturation or forgetting effects. The longitudinal study finds that interpretation skills facilitate the development of perception and decision-making, emphasizing the knowledge-based nature of teacher noticing.
A Teacher's Guide to Using the Common Core State Standards With Mathematically Gifted and Advanced Learners
by National Assoc For Gifted Children Gail R. Ryser Susan AssoulineA Teacher's Guide to Using the Common Core State Standards in Mathematics provides teachers and administrators with practical examples of ways to build a comprehensive, coherent, and continuous set of learning experiences for gifted and advanced students. It describes informal, traditional, off-level, and 21st century math assessments that are useful in making educational decisions about placement and programming. Featuring learning experiences for each grade within one math progression, the book offers insight into useful ways of both accelerating and enriching the CCSS mathematics standards. Each of the learning experiences includes a sequence of activities, implementation examples, and formative assessments. Specific instructional and management strategies for implementing the standards within the classroom, school, and school district will be helpful for both K-12 teachers and administrators.
A Teacher's Guide to Using the Common Core State Standards with Mathematically Gifted and Advanced Learners
by Gail Ryser Susan Assouline Susan JohnsenA Teacher's Guide to Using the Common Core State Standards With Mathematically Gifted and Advanced Learners provides teachers and administrators with practical examples of ways to build a comprehensive, coherent, and continuous set of learning experiences for gifted and advanced students. It describes informal, traditional, off-level, and 21st century math assessments that are useful in making educational decisions about placement and programming. Featuring learning experiences for each grade within one math progression, the book offers insight into useful ways of both accelerating and enriching the CCSS mathematics standards. Each of the learning experiences includes a sequence of activities, implementation examples, and formative assessments. Specific instructional and management strategies for implementing the standards within the classroom, school, and school district will be helpful for both K-12 teachers and administrators.
Teachers Have It Easy
by Daniel Moulthrop Henry Louis Gates Dave Eggers Ninive Clements CalegariSince its initial publication and multiple reprints in hardcover in 2005, Teachers Have It Easy has attracted the attention of teachers nationwide, appearing on the New York Times extended bestseller list, C-SPAN, and NPR's Marketplace, in addition to receiving strong reviews nationwide. Now available for the first time in paperback, this groundbreaking book examines how bad policy makes teachers' lives miserable.Many teachers today must work two or more jobs to survive; they cannot afford to buy homes or raise families. Interweaving teachers' voices from across the country with hard-hitting facts and figures, this book is a clear-eyed view of the harsh realities of public school teaching, without chicken-soup-for-the-soul success stories.With a look at the problems of recruitment and retention, the myths of short workdays and endless summer vacations, the realities of the work week, and shocking examples of how society views America's teachers, Teachers Have It Easy explores the best ways to improve public education and transform our schools.
Teachers of Mathematics Working and Learning in Collaborative Groups: The 25th ICMI Study (New ICMI Study Series)
by Despina Potari Hilda BorkoThis open access book is the product of an international study which offers a state-of-the-art summary of mathematics teacher collaboration with respect to theory, research, practice, and policy. The authors – leading researchers and teachers on mathematics teacher collaboration – represent a wide range of countries and cultures. Chapters explore the various forms of teacher collaboration; the diversity of settings and groupings in which mathematics teacher collaboration occurs; the tools and resources that support mathematics teacher collaboration and are the product of collaboration; and the breadth of outcomes of such collaboration. Teachers’ experiences and learning in collaborative settings are represented through their own voices as well as the voices of researchers. Forms and outcomes of collaboration are considered through a variety of theoretical perspectives and methodological approaches. The authors reflect on the policy implications of this work and suggest new directions of research that take into account contextual, cultural, national and political dimensions that impact teachers’ work and learning through collaboration. The book is a valuable resource for researchers, practitioners, and policy makers who are interested in the power of teacher collaboration, and its history and potential for promoting educational innovations and equitable experiences for all teachers and learners.
Teachers' Professional Development and the Elementary Mathematics Classroom: Bringing Understandings To Light (Studies in Mathematical Thinking and Learning Series)
by Sophia CohenThis book illustrates the experiences of elementary school teachers across one year's time as they participated in a teacher development seminar focused on mathematics, and as a result changed their beliefs, their knowledge, and their practices. It explores these experiences as a means of understanding the learning that takes a teacher from a more traditional teaching practice to one that is focused on the ideas and understandings that students and teachers have of the subject matter. The work emerges from and reports on a unique data set from a two-year study of teacher learning that was funded by the Spencer and MacArthur foundations. The teachers, whose work is at the center of this study, were participants in the Developing Mathematical Ideas seminar (DMI), a mathematics teacher development seminar for elementary school teachers. This seminar is one example of intensive, domain-specific professional development. In this seminar teachers study elementary mathematics content to deepen their own understanding of it, they study the development among children of the ideas central to elementary mathematics, and they experience a teaching and learning environment consistent with the pedagogy envisioned by the National Council for Teachers of Mathematics' Principles and Standards for School Mathematics. The seminar is a nationally available teacher development curriculum, thus interested educators can gain access to the resources necessary to offer similar seminars in their own communities. Teachers' Professional Development and the Elementary Mathematics Classroom: Bringing Understandings to Light will be widely interesting to a broad audience, including mathematics teacher educators, teacher education researchers, policymakers, and classroom teachers. It will serve well as a text in a range of graduate courses dealing with teacher cognition/knowledge for teaching, mathematics methods, psychology of learning, and pedagogical theory.
Teaching 6-12 Math Intervention: A Practical Framework To Engage Students Who Struggle
by Juliana TapperThis practical resource offers a classroom-tested framework for secondary math teachers to support students who struggle. Teachers will explore an often-overlooked piece of the math achievement puzzle: the gatekeeping cycles of mathematics and the importance of teachers' own expectations of students. The immediately applicable strategies in this book, developed through the author’s work as a math intervention teacher, intervention specialist, and instructional coach, will give teachers the tools to help students overcome math anxiety, retention struggles, and even apathy. Beginning with a deep dive into the gatekeeping cycles to help teachers better understand their students who struggle, the book then walks teachers through the five-part B.R.E.A.K. it™ Math Intervention Framework: Build Community, Routines to Boost Confidence, Engage Every Student, Advance Your Expectations, Know Students’ Level of Understanding. Educational research, personal anecdotes from the author’s own classroom, and examples from case study teachers are woven into each chapter, leading to clear action items, planning strategies, and best practices that are accessible enough to accommodate all grade levels and schedules. The framework and activities in this book enable teachers to help students overcome math anxiety, create a safe math environment for 6–12 students, and ultimately increase achievement with effective research-based suggestions for working with students who struggle.Find additional resources at www.gatebreakerbook.com.
Teaching and Learning About Whole Numbers in Primary School
by Terezinha Nunes Beatriz Vargas Dorneles Pi-Jen Lin Elisabeth Rathgeb-SchniererThis book offers a theory for the analysis of how children learn and are taught about whole numbers. Two meanings of numbers are distinguished - the analytical meaning, defined by the number system, and the representational meaning, identified by the use of numbers as conventional signs that stand for quantities. This framework makes it possible to compare different approaches to making numbers meaningful in the classroom and contrast the outcomes of these diverse aspects of teaching. The book identifies themes and trends in empirical research on the teaching and learning of whole numbers since the launch of the major journals in mathematics education research in the 1970s. It documents a shift in focus in the teaching of arithmetic from research about teaching written algorithms to teaching arithmetic in ways that result in flexible approaches to calculation. The analysis of studies on quantitative reasoning reveals classifications of problem types that are related to different cognitive demands and rates of success in both additive and multiplicative reasoning. Three different approaches to quantitative reasoning education illustrate current thinking on teaching problem solving: teaching reasoning before arithmetic, schema-based instruction, and the use of pre-designed diagrams. The book also includes a summary of contemporary approaches to the description of the knowledge of numbers and arithmetic that teachers need to be effective teachers of these aspects of mathematics in primary school. The concluding section includes a brief summary of the major themes addressed and the challenges for the future. The new theoretical framework presented offers researchers in mathematics education novel insights into the differences between empirical studies in this domain. At the same time the description of the two meanings of numbers helps teachers distinguish between the different aims of teaching about numbers supported by diverse methods used in primary school. The framework is a valuable tool for comparing the different methods and identifying the various assumptions about teaching and learning.
Teaching and Learning in Maths Classrooms: Emerging Themes in Affect-related Research: Teachers' Beliefs, Students' Engagement and Social Interaction (Research in Mathematics Education)
by Chiara Andrà, Domenico Brunetto, Esther Levenson and Peter LiljedahlThe book presents a selection of the most relevant talks given at the 21st MAVI conference, held at the Politecnico di Milano. The first section is dedicated to classroom practices and beliefs regarding those practices, taking a look at prospective or practicing teachers’ views of different practices such as decision-making, the roles of explanations, problem-solving, patterning, and the use of play. Of major interest to MAVI participants is the relationship between teachers’ professed beliefs and classroom practice, aspects that provide the focus of the second section. Three papers deal with teacher change, which is notoriously difficult, even when the teachers themselves are interested in changing their practice. In turn, the book’s third section centers on the undercurrents of teaching and learning mathematics, which can surface in various situations, causing tensions and inconsistencies. The last section of this book takes a look at emerging themes in affect-related research, with a particular focus on attitudes towards assessment. The book offers a valuable resource for all teachers and researchers working in this area.
Teaching and Learning Mathematics Online
by James P. Howard Ii John F. BeyersOnline education has become a major component of higher education worldwide. In mathematics and statistics courses, there exists a number of challenges that are unique to the teaching and learning of mathematics and statistics in an online environment. These challenges are deeply connected to already existing difficulties related to math anxiety, conceptual understanding of mathematical ideas, communicating mathematically, and the appropriate use of technology. Teaching and Learning Mathematics Online bridges these issues by presenting meaningful and practical solutions for teaching mathematics and statistics online. It focuses on the problems observed by mathematics instructors currently working in the field who strive to hone their craft and share best practices with our professional community. The book provides a set of standard practices, improving the quality of online teaching and the learning of mathematics. Instructors will benefit from learning new techniques and approaches to delivering content. Features Based on the experiences of working educators in the field Assimilates the latest technology developments for interactive distance education Focuses on mathematical education for developing early mathematics courses
Teaching and Learning of Calculus
by David Bressoud Imène Ghedamsi Victor Martinez-Luaces Günter TörnerThis survey focuses on the main trends in the field of calculus education. Despite their variety, the findings reveal a cornerstone issue that is strongly linked to the formalism of calculus concepts and to the difficulties it generates in the learning and teaching process. As a complement to the main text, an extended bibliography with some of the most important references on this topic is included. Since the diversity of the research in the field makes it difficult to produce an exhaustive state-of-the-art summary, the authors discuss recent developments that go beyond this survey and put forward new research questions.
The Teaching and Learning of Statistics
by Dani Ben-Zvi Katie MakarThis book presents the breadth and diversity of empirical and practical work done on statistics education around the world. A wide range of methods are used to respond to the research questions that form it's base. Case studies of single students or teachers aimed at understanding reasoning processes, large-scale experimental studies attempting to generalize trends in the teaching and learning of statistics are both employed. Various epistemological stances are described and utilized. The teaching and learning of statistics is presented in multiple contexts in the book. These include designed settings for young children, students in formal schooling, tertiary level students, vocational schools, and teacher professional development. A diversity is evident also in the choices of what to teach (curriculum), when to teach (learning trajectory), how to teach (pedagogy), how to demonstrate evidence of learning (assessment) and what challenges teachers and students face when they solve statistical problems (reasoning and thinking).
Teaching and Learning Patterns in School Mathematics
by Ferdinand RiveraThis book synthesizes research findings on patterns in the last twenty years or so in order to argue for a theory of graded representations in pattern generalization. While research results drawn from investigations conducted with different age-level groups have sufficiently demonstrated varying shifts in structural awareness and competence, which influence the eventual shape of an intended generalization, such shifts, however, are not necessarily permanent due to other pertinent factors such as the complexity of patterning tasks. The book proposes an alternative view of pattern generalization, that is, one that is not about shifts or transition phases but graded depending on individual experiences with target patterns. The theory of graded representations involving pattern generalization offers a much more robust understanding of differences in patterning competence since it is sensitive to varying levels of entry into generalization. Empirical evidence will be provided to demonstrate this alternative view, which is drawn from the author's longitudinal work with elementary and middle school children, including several investigations conducted with preservice elementary majors. Two chapters of the book will be devoted to extending pattern generalization activity to arithmetic and algebraic learning of concepts and processes. The concluding chapter addresses the pedagogical significance of pattern learning in the school mathematics curriculum.
Teaching and Learning Proof Across the Grades: A K-16 Perspective (Studies in Mathematical Thinking and Learning Series)
by Despina Stylianou Maria Blanton Eric KnuthA Co-Publication of Routledge for the National Council of Teachers of Mathematics (NCTM) In recent years there has been increased interest in the nature and role of proof in mathematics education; with many mathematics educators advocating that proof should be a central part of the mathematics education of students at all grade levels. This important new collection provides that much-needed forum for mathematics educators to articulate a connected K-16 "story" of proof. Such a story includes understanding how the forms of proof, including the nature of argumentation and justification as well as what counts as proof, evolve chronologically and cognitively and how curricula and instruction can support the development of students’ understanding of proof. Collectively these essays inform educators and researchers at different grade levels about the teaching and learning of proof at each level and, thus, help advance the design of further empirical and theoretical work in this area. By building and extending on existing research and by allowing a variety of voices from the field to be heard, Teaching and Learning Proof Across the Grades not only highlights the main ideas that have recently emerged on proof research, but also defines an agenda for future study.
Teaching and Learning Secondary School Mathematics: Canadian Perspectives in an International Context (Advances in Mathematics Education)
by Ann Kajander Jennifer Holm Egan J ChernoffThis volume brings together recent research and commentary in secondary school mathematics from a breadth of contemporary Canadian and International researchers and educators. It is both representative of mathematics education generally, as well as unique to the particular geography and culture of Canada. The chapters address topics of broad applicability such as technology in learning mathematics, recent interest in social justice contexts in the learning of mathematics, as well as Indigenous education. The voices of classroom practitioners, the group ultimately responsible for implementing this new vision of mathematics teaching and learning, are not forgotten. Each section includes a chapter written by a classroom teacher, making this volume unique in its approach. We have much to learn from one another, and this volume takes the stance that the development of a united vision, supported by both research and professional dialog, provides the first step.
Teaching and Learning Stochastics: Advances In Probability Education Research (ICME-13 Monographs)
by Carmen Batanero Egan J ChernoffThis book presents a collection of selected papers that represent the current variety of research on the teaching and learning of probability. The respective chapters address a diverse range of theoretical, empirical and practical aspects underpinning the teaching and learning of probability, curricular issues, probabilistic reasoning, misconceptions and biases, as well as their pedagogical implications. These chapters are divided into THREE main sections, dealing with: TEACHING PROBABILITY, STUDENTS' REASONING AND LEARNING AND EDUCATION OF TEACHERS.In brief, the papers presented here include research dealing with teachers and students at different levels and ages (from primary school to university) and address epistemological and curricular analysis, as well as the role of technology, simulations, language and visualisation in teaching and learning probability. As such, it offers essential information for teachers, researchers and curricular designers alike.
Teaching and Research in Mathematics: A Guide with Applications to Industry
by Parisa FatheddinThis insightful Guide is meant to serve any and all interested in pursuing a career in mathematics education and research. The author’s goal and the book’s theme is to help students and others make a smooth transition to teachers and researchers of mathematics.Part I presents helpful techniques on teaching and conducting research. This innovative book also offers strategies on how to observe from and develop research methods, carry out research, and begin writing research papers. It includes an introduction to LaTeX, the most widely used mathematics typesetting and rendering computer program.Part II introduces some modern research in mathematics in various industries. The aim in is to expose the reader to modern applications and help him/her become acquainted with research papers and how to read and understand them.Authored by a young teacher and researcher, also beginning her career, this book is written by and for young mathematicians. Most graduate students as she experienced, are not given a proper transitory introduction to research and are not taught the "how" in teaching, attending conferences and collaborating. The book is based on the author’s own observations and on techniques she has found effective.Mathematics graduate students and those in related fields will find assistance to help them reflect on and advance their career pursuits. Advisors and mentors might also find useful suggestions here.
Teaching by Design in Elementary Mathematics, Grades 2–3
by Jennifer Stepanek Melinda Leong Linda Griffin Lisa LavelleStrengthen mathematics lessons through collaborative learning with this research-based professional development program. Included are grade-appropriate number and operations topics aligned with the Common Core State Standards.
Teaching by Design in Elementary Mathematics, Grades 4–5
by Jennifer Stepanek Melinda Leong Linda Griffin Lisa LavelleStrengthen mathematics lessons through collaborative learning with this research-based professional development program. Included are grade-appropriate number and operations topics aligned with the Common Core State Standards.
Teaching by Design in Elementary Mathematics, Grades K–1
by Jennifer Stepanek Melinda Leong Linda Griffin Lisa LavelleStrengthen mathematics lessons through collaborative learning with this research-based professional development program. Included are grade-appropriate number and operations topics aligned with the Common Core State Standards.
Teaching Calculation: Audit and Test (Transforming Primary QTS Series)
by Mr Richard EnglishCan you demonstrate a clear understanding of primary mathematics? If you are training to be a primary school teacher you need to have, and demonstrate, a clear understanding of primary mathematics. This companion text to the popular Teaching Arithmetic in Primary Schools enables you to audit your knowledge, skills and understanding, making you more aware of the subject and the areas you need to develop further. It includes: self audits on all areas of calculations, supporting trainees to meet the Teachers' Standards clear links to classroom practice, linking theory with practice advice on next steps for further learning under each chapter If you're a trainee primary school teacher, this resource, along with its companion title will provide you with all the guidance and support needed to develop your Primary Maths subject knowledge and teaching skills. This book is part of the Transforming Primary QTS Series This series reflects the new creative way schools are beginning to teach, taking a fresh approach to supporting trainees as they work towards primary QTS. Titles provide fully up to date resources focused on teaching a more integrated and inclusive curriculum, and texts draw out meaningful and explicit cross curricular links.
Teaching Coding in K-12 Schools: Research and Application
by Therese Keane Andrew E. FluckThis book contains highly effective ways to teach coding and computational thinking skills throughout primary and secondary schooling. It outlines a research informed path for students from birth to 18 years, identifying key skills and learning activities. Based on global perspectives and research at each stage, it outlines how these findings can be applied in the classroom. Teaching coding to students in K-12 has been a skillset that has been debated across educational jurisdictions globally for some time. The book provides examples of schools that are teaching coding to students in engaging and relevant ways, delivering well thought out compulsory curriculums. Additionally, it provides examples of schools where coding is not mandated in the curriculum and is taught in an ad-hoc manner. Through the full discussion of all of these varied examples, the book presents both sides of the serious and ongoing debate in the field as to whether coding should be taught in an explicit way at all. The increasing school of thought that teaching coding is a skill that is already obsolete, and the focus should be on computational thinking is completely examined and presented. In this book, both sides of the argument, as well as the specific, meticulous research underlying each side, are given equal weight. The debate is a serious one and requires a clearly defined thematic response with evidence on all sides of the argument presented rationally. This book does just that. Created by carefully selected authors from around the world, it will be a highly studied research reference.
Teaching Computing: A Practitioner's Perspective
by Henry M. WalkerTeaching can be intimidating for beginning faculty. Some graduate schools and some computing faculty provide guidance and mentoring, but many do not. Often, a new faculty member is assigned to teach a course, with little guidance, input, or feedback. Teaching Computing: A Practitioner’s Perspective addresses such challenges by providing a solid resource for both new and experienced computing faculty. The book serves as a practical, easy-to-use resource, covering a wide range of topics in a collection of focused down-to-earth chapters. Based on the authors’ extensive teaching experience and his teaching-oriented columns that span 20 years, and informed by computing-education research, the book provides numerous elements that are designed to connect with teaching practitioners, including: A wide range of teaching topics and basic elements of teaching, including tips and techniques Practical tone; the book serves as a down-to-earth practitioners’ guide Short, focused chapters Coherent and convenient organization Mix of general educational perspectives and computing-specific elements Connections between teaching in general and teaching computing Both historical and contemporary perspectives This book presents practical approaches, tips, and techniques that provide a strong starting place for new computing faculty and perspectives for reflection by seasoned faculty wishing to freshen their own teaching.
Teaching Data Analytics: Pedagogy and Program Design (Data Analytics Applications)
by Susan A Vowels Katherine Leaming GoldbergThe need for analytics skills is a source of the burgeoning growth in the number of analytics and decision science programs in higher education developed to feed the need for capable employees in this area. The very size and continuing growth of this need means that there is still space for new program development. Schools wishing to pursue business analytics programs intentionally assess the maturity level of their programs and take steps to close the gap. Teaching Data Analytics: Pedagogy and Program Design is a reference for faculty and administrators seeking direction about adding or enhancing analytics offerings at their institutions. It provides guidance by examining best practices from the perspectives of faculty and practitioners. By emphasizing the connection of data analytics to organizational success, it reviews the position of analytics and decision science programs in higher education, and to review the critical connection between this area of study and career opportunities. The book features: A variety of perspectives ranging from the scholarly theoretical to the practitioner applied An in-depth look into a wide breadth of skills from closely technology-focused to robustly soft human connection skills Resources for existing faculty to acquire and maintain additional analytics-relevant skills that can enrich their current course offerings. Acknowledging the dichotomy between data analytics and data science, this book emphasizes data analytics rather than data science, although the book does touch upon the data science realm. Starting with industry perspectives, the book covers the applied world of data analytics, covering necessary skills and applications, as well as developing compelling visualizations. It then dives into pedagogical and program design approaches in data analytics education and concludes with ideas for program design tactics. This reference is a launching point for discussions about how to connect industry’s need for skilled data analysts to higher education’s need to design a rigorous curriculum that promotes student critical thinking, communication, and ethical skills. It also provides insight into adding new elements to existing data analytics courses and for taking the next step in adding data analytics offerings, whether it be incorporating additional analytics assignments into existing courses, offering one course designed for undergraduates, or an integrated program designed for graduate students.
Teaching Early Algebra through Example-Based Problem Solving: Insights from Chinese and U.S. Elementary Classrooms (Routledge Research in STEM Education)
by Meixia DingDrawing on rich classroom observations of educators teaching in China and the U.S., this book details an innovative and effective approach to teaching algebra at the elementary level, namely, "teaching through example-based problem solving" (TEPS). Recognizing young children’s particular cognitive and developmental capabilities, this book powerfully argues for the importance of infusing algebraic thinking into early grade mathematics teaching and illustrates how this has been achieved by teachers in U.S. and Chinese contexts. Documenting best practice and students’ responses to example-based instruction, the text demonstrates that this TEPS approach – which involves the use of worked examples, representations, and deep questions – helps students learn and master fundamental mathematical ideas, making it highly effective in developing algebraic readiness and mathematical understanding. This text will benefit post-graduate students, researchers, and academics in the fields of mathematics, STEM, and elementary education, as well as algebra research more broadly. Those interested in teacher education, classroom practice, and developmental and cognitive psychology will also find this volume of interest.