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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.
Teaching Elementary Mathematics to Struggling Learners
by Bradley S. Witzel Mary E. LittlePacked with effective instructional strategies, this book explores why certain K-5 students struggle with math and provides a framework for helping these learners succeed. The authors present empirically validated practices for supporting students with disabilities and others experiencing difficulties in specific areas of math, including problem solving, early numeracy, whole-number operations, fractions, geometry, and algebra. Concrete examples, easy-to-implement lesson-planning ideas, and connections to state standards, in particular the Common Core standards, enhance the book's utility. Also provided is invaluable guidance on planning and delivering multi-tiered instruction and intervention.
Teaching for Mathematical Understanding: Practical ideas for outstanding primary lessons
by Tony CottonTeaching for Mathematical Understanding develops the subject knowledge support and practical ideas from Tony Cotton's Understanding and Teaching Primary Mathematics into resources for full lessons. With an emphasis on developing outstanding lessons using a problem-solving approach, this highly practical guide is packed with activities that all trainee and practising teachers can use in the primary classroom. Covering each area of mathematics, every activity offers helpful step-by-step guidance, including teaching and learning objectives; resources; lesson outlines; ideas for differentiation; assessment for learning and key probing questions. Also featured in this text are call-outs to the information contained in the book's companion website, a shared site with a range of relevant resources to support and consolidate your learning. Teaching for Mathematical Understanding is an essential text for all trainee and practising teachers looking for inspiration and guidance towards outstanding mathematics teaching. Companion website features include: Video clips in which primary school teachers demonstrate concepts covered in the book through teaching to a real class PowerPoint presentations which provide support for those using the book as part of a teacher training course updated weblinks to external sites with useful teaching information and resources.
Teaching for Numeracy Across the Age Range: An Introduction (SpringerBriefs in Education)
by Peter Stuart WestwoodThis book provides an introduction to what it means to be numerate, and how numeracy can best be developed and nurtured in children and in adults. It also presents a cohesive coverage of numeracy development from early childhood to adulthood. This book draws on international research and practice to provide a comprehensive overview on the topic. It depicts and draws connections with the National Curriculum in the United Kingdom, the Australian Curriculum, and the Common Core State Standards in the United States. This book identifies skills and concepts involved in achieving functional numeracy, and provides practical advice on effective teaching, learning and assessment. It serves as a valuable guide to educators who teach mathematics in primary and secondary schools, but who are not specifically trained in the subject.
Teaching Foundation Mathematics: A Guide for Teachers of Older Students with Learning Difficulties (nasen spotlight)
by Nadia Naggar-SmithThis fully photocopiable resource will provide essential materials for anyone teaching pre-entry or foundation Maths in secondary schools and further education. Teaching Foundation Mathematics is developed to provide age appropriate material for adult learners with moderate to severe learning difficulties and/or disabilities and for children, over twelve, with special needs. It will also prove useful to teachers training to work with these learners. Thirty ready-to-use lessons are at your fingertips in this book, complete with tutor’s notes, teaching objectives, detailed lesson plans and photocopiable worksheets, where appropriate. The lessons are divided into three areas – number, shape and measure.
Teaching Fractions and Ratios for Understanding: Essential Content Knowledge and Instructional Strategies for Teachers
by Susan J. LamonWritten 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.
Teaching Fractions through Situations: A Fundamental Experiment
by Nadine Brousseau Guy Brousseau Virginia WarfieldThis work presents one of the original and fundamental experiments of Didactique, a research program whose underlying tenet is that Mathematics Education research should be solidly based on scientific observation. Here the observations are of a series of adventures that were astonishing for both the students and the teachers: the reinvention of fractions and of decimal numbers in a sequence of lessons and situations that permitted the students to construct the concepts for themselves. The book leads the reader through the highlights of the sequence's structure and some of the reasoning behind the lesson choices. It then presents explanations of some of the principal concepts of the Theory of Situations. In the process, it offers the reader the opportunity to join a lively set of fifth graders as they experience a particularly attractive set of lessons and master a topic that baffles many of their contemporaries.
Teaching Gifted Learners in STEM Subjects: Developing Talent in Science, Technology, Engineering and Mathematics (Routledge Research in Achievement and Gifted Education)
by Keith S. Taber Manabu Sumida Lynne McClureThis book offers an overview of programmes designed to support the learning of gifted and talented students in STEM subjects, both to allow them to meet their potential and to encourage them to proceed towards careers in STEM areas. The chapters from a range of national contexts report on perspectives, approaches and projects in gifted education in STEM subjects. These contributions provide a picture of the state of research and practice in this area, both to inform further research and development, and to support classroom teachers in their day-to-day work. Chapters have been written with practitioners in mind, but include relevant scholarly citations to the literature. The book includes some contributions illustrating research and practice in specific STEM areas, and others which bridge across different STEM subjects. The volume also includes an introductory theoretical chapter exploring the implications for gifted learners of how 'STEM' is understood and organized within the school curriculums.
Teaching History for the Common Good
by Keith C. Barton Linda S. LevstikIn Teaching History for the Common Good, Barton and Levstik present a clear overview of competing ideas among educators, historians, politicians, and the public about the nature and purpose of teaching history, and they evaluate these debates in light of current research on students' historical thinking. In many cases, disagreements about what should be taught to the nation's children and how it should be presented reflect fundamental differences that will not easily be resolved. A central premise of this book, though, is that systematic theory and research can play an important role in such debates by providing evidence of how students think, how their ideas interact with the information they encounter both in school and out, and how these ideas differ across contexts. Such evidence is needed as an alternative to the untested assumptions that plague so many discussions of history education. The authors review research on students' historical thinking and set it in the theoretical context of mediated action--an approach that calls attention to the concrete actions that people undertake, the human agents responsible for such actions, the cultural tools that aid and constrain them, their purposes, and their social contexts. They explain how this theory allows educators to address the breadth of practices, settings, purposes, and tools that influence students' developing understanding of the past, as well as how it provides an alternative to the academic discipline of history as a way of making decisions about teaching and learning the subject in schools. Beyond simply describing the factors that influence students' thinking, Barton and Levstik evaluate their implications for historical understanding and civic engagement. They base these evaluations not on the disciplinary study of history, but on the purpose of social education--preparing students for participation in a pluralist democracy. Their ultimate concern is how history can help citizens engage in collaboration toward the common good. In Teaching History for the Common Good, Barton and Levstik: *discuss the contribution of theory and research, explain the theory of mediated action and how it guides their analysis, and describe research on children's (and adults') knowledge of and interest in history; *lay out a vision of pluralist, participatory democracy and its relationship to the humanistic study of history as a basis for evaluating the perspectives on the past that influence students' learning; *explore four principal "stances" toward history (identification, analysis, moral response, and exhibition), review research on the extent to which children and adolescents understand and accept each of these, and examine how the stances might contribute to--or detract from--participation in a pluralist democracy; *address six of the principal "tools" of history (narrative structure, stories of individual achievement and motivation, national narratives, inquiry, empathy as perspective-taking, and empathy as caring); and *review research and conventional wisdom on teachers' knowledge and practice, and argue that for teachers to embrace investigative, multi-perspectival approaches to history they need more than knowledge of content and pedagogy, they need a guiding purpose that can be fulfilled only by these approaches--and preparation for participatory democracy provides such purpose. Teaching History for the Common Good is essential reading for history and social studies professionals, researchers, teacher educators, and students, as well as for policymakers, parents, and members of the general public who are interested in history education or in students' thinking and learning about the subject.