Search Results for patterns-in-teaching-and-learning-of-maths

This highly illustrated book draws together the wide variety of studies in the learning of mathematics undertaken by the Pattern in Mathematics Research Group at the University of Leeds.

Author: Anthony Orton

Publisher: A&C Black

ISBN: 9781847144560

Category: Education

Page: 246

View: 312

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This highly illustrated book draws together the wide variety of studies in the learning of mathematics undertaken by the Pattern in Mathematics Research Group at the University of Leeds. Their purpose has been '... to provide structure and support to ... studies of children's perception, conception and use of pattern in learning mathematics'. Set up in 1992, they have embraced work across the whole curriculum, and through all the years of compulsory schooling. As each chapter of this book relates to a different study that was undertaken, the reader can dip in and select relevant material. At the same time, the editor has ensured continuity and progression, allowing the book to be approached as a whole: the early chapters are concerned with very young children; subsequent chapters deal with the primary and middle age ranges, and later ones relate to secondary school work. With individual chapters relating to number, algebra, shape, graphic relations and probability, this new volume provides guidance for teachers of pupils of all age groups. Patterns in mathematics are of immense importance; this book relates pattern to the teaching of mathematics through all years of school. Practical and original, it is closely tied to the National Curriculum. It is a source of new ideas for mathematic teachers at all levels.
2004-10-01 By Anthony Orton

This book discusses the learning and teaching of geometry, with a special focus on kindergarten and primary education.

Author: Ewa Swoboda

Publisher: Springer

ISBN: 9783319442723

Category: Education

Page: 50

View: 690

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This book discusses the learning and teaching of geometry, with a special focus on kindergarten and primary education. It examines important new trends and developments in research and practice, and emphasizes theoretical, empirical and developmental issues. Further, it discusses various topics, including curriculum studies and implementation, spatial abilities and geometric reasoning, as well as the psychological roots of geometrical thinking and teacher preparation in geometry education. It considers these issues from historical, epistemological, cognitive semiotic and educational points of view in the context of students' difficulties and the design of teaching and curricula.
2016-09-09 By Ewa Swoboda

Stages in the history of algebra with implications for teaching. Educational Studies in Mathematics, 66, 185–201. Kleinberg, J. (2011).

Author: Ferdinand Rivera

Publisher: Springer Science & Business Media

ISBN: 9789400727120

Category: Education

Page: 216

View: 586

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This 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. ​
2014-07-08 By Ferdinand Rivera

Guess my X and other techno-pedagogical patterns: toward a language of patterns for teaching and learning mathematics. In T. Schümmer & A. Kelly (Eds.), ...

Author: Yishay Mor

Publisher: Springer

ISBN: 9789462095304

Category: Education

Page: 338

View: 698

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These are challenging times in which to be an educator. The constant flow of innovation offers new opportunities to support learners in an environment ofever-shifting demands. Educators work as they have always done: making the most of the resources at hand, and dealing with constraints, to provide experiences which foster growth. This was John Dewey’s ideal of education 80 years ago and it is still relevant today. This view sees education as a practice that achieves its goals through creative processes involving both craft and design. Craft is visible in the resources that educators produce and in their interactions with learners. Design, though, is tacit, and educators are often unaware of their own design practices. The rapid pace of change is shifting the balance from craft to design, requiring that educators’ design work become visible, shareable and malleable. The participatory patterns workshop is a method for doing this through engaging practitioners in collaborative reflection leading to the production of structured representations of design knowledge. The editors have led many such workshops and this book is a record of that endeavour and its outcomes in the form of practical design narratives, patterns and scenarios that can be used to address challenges in teaching and learning with technology.
2014-05-08 By Yishay Mor

This reflexive relationship between these structures of interactions and student actions and learning is central to the issues explored in this book, alongside the implications these may have for teachers' practice, and students' learning.

Author: Jenni Ingram

Publisher: Oxford University Press

ISBN: 9780192640109

Category: Mathematics

Page: 304

View: 948

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Classroom interaction has a significant influence on teaching and learning. It is through interaction that we solve problems, build ideas, make connections and develop our understanding. Patterns in Mathematics Classroom Interaction describes, exemplifies and considers the implications of patterns and structures of mathematics classroom interaction. Drawing on a Conversation Analytic approach, the book examines how the structures of interactions between teachers and students influence, enable, and constrain the mathematics that students are experiencing and learning in school. In particular, it considers the handling of difficulties or errors and the consequences on both the mathematics students are learning, and the learning of this mathematics. The various roles of silence and the treatment of knowledge and understanding within everyday classroom interactions also reveal the nature of mathematics as it is taught in different classrooms. Examples of students explaining, reasoning and justifying as they interact are also drawn upon to examine how the structures of classroom interaction support students to develop these discursive practices. The approach taken in Patterns in Mathematics Classroom Interaction enables the identification of not only what structures exist and pervade classroom discourse, but also how these structures influence teaching and learning. It is the understanding of how these structures affect students' experiences in the classroom that permits the use and development of practices that can support students' learning. This reflexive relationship between these structures of interactions and student actions and learning is central to the issues explored in this book, alongside the implications these may have for teachers' practice, and students' learning.
2021-03-01 By Jenni Ingram

In fact, it might be advisable to begin the teaching of mathematics with the study of patterns, even prior to the introduction of numbers.

Author: Ana Helvia Quintero

Publisher: World Scientific

ISBN: 9781783268665

Category: Mathematics

Page: 292

View: 283

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The methods for teaching mathematics usually follow the structure of mathematics. The problem with this is that the structure of mathematics took centuries of elaboration to develop and is not the same as how one originally experiences mathematics. Based on research of how mathematics is actually learned, this book presents an innovative approach for teaching mathematics that will engage pupils and can have lifelong benefits for how they take on board more advanced mathematical topics. Math Makes Sense! makes use of the realistic mathematics education (RME) philosophy, which bridges the gap between informal mathematics learning (such as in day-to-day life) and more formal teaching in school. Many real-life situations as examples for learning are included, as well as different mathematical and logic puzzles that will stimulate learning and foster understanding. The ideas presented are not confined to one national curriculum and so can be helpful worldwide to teachers/ instructors (both in practice and those still in training), private tutors, homeschooling parents, and educational researchers. Contents:PrefaceAcknowledgmentsAbout the AuthorsFostering the Learning of MathematicsConstruction of Concepts and Mathematical InterpretationsNumberingAddition and SubtractionMultiplication and DivisionFractions, Decimals, and PercentagesMeasurementExploring SpaceProbability and StatisticsPatterns, Relations, and FunctionsThe Joy of PuzzlesTechnology: A Tool for Analysis and InterpretationAssessmentConcluding Remarks Readership: Teachers, trainee teachers, researchers interested in mathematics education, homeschool parents, and parents with children in primary/ elementary school. Key Features:This book is grounded on solid mathematics learning research, as well as on the authors' own observations in the classroom, and so combines theoretical knowledge with practiceWritten in an accessible mannerGives educators ideas which they can easily implement in the classroom
2016-03-02 By Ana Helvia Quintero

This book is an essential purchase for any professional who wishes to embed creative approaches to teaching in their classroom.

Author: Linda Pound

Publisher: Routledge

ISBN: 9781317511267

Category: Education

Page: 196

View: 708

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This new and updated edition of Teaching Mathematics Creatively offers a range of strategies to enable trainee and practising teachers to take an innovative, playful and creative approach to maths teaching. It promotes creativity as a key element of practice and offers ideas to involve your students and develop knowledge, understanding and enjoyment. Exploring fresh approaches, this text explains the role of play in bringing mathematics alive for children and teachers alike. It identifies the power of story-telling in supporting mathematical thinking, examines cross-curricular teaching, and allows you to plan for teaching creatively. Imaginative ideas, underpinned by the latest research and theory, include: Learning maths outdoors - make more noise, make more mess or work on a larger scale Everyday maths - making sense of the numbers, patterns, shapes and measures children see around them Music and maths – the role of rhythm in learning, and music and pattern in maths Giant maths - how much food do you include on a giant shopping list? Stimulating and accessible, with contemporary and cutting-edge practice at the forefront, Teaching Mathematics Creatively includes a wealth of innovative ideas to enthuse teachers and enrich maths teaching. This book is an essential purchase for any professional who wishes to embed creative approaches to teaching in their classroom.
2015-04-24 By Linda Pound

Patterns are widely recognised as the foundation of mathematics.

Author: Marina Marie Papic

Publisher:

ISBN: OCLC:271251667

Category: Mathematical ability

Page: 354

View: 342

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For example, how might mathematics teacher educators learn to recognise energetic learning? Are there any patterns linked to when a new label or category ...

Author:

Publisher: BRILL

ISBN: 9789004424210

Category: Education

Page: 430

View: 954

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This fourth volume addresses teacher educators’ knowledge, learning and practice with teachers/instructors of mathematics. It provides practical, professional and theoretical perspectives of different approaches/activities/programmes to promote effective teacher education practice, with valuable implications for research.
2020-12-15 By

The National Council of Teachers of Mathematics has established curriculum standards for early childhood math skills.

Author: Lily Erlic

Publisher: Teaching and Learning Company

ISBN: 9780787733759

Category: Education

Page: 19

View: 871

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The National Council of Teachers of Mathematics has established curriculum standards for early childhood math skills. Preschool Math features creative, developmentally appropriate activities that directly address these standards. These activities encourage interaction and communication, and feature healthy food themes, ready-to-use reproducibles and fundamental mathematical concepts. Give children a foundation for learning that will pave the way for future confidence and success in mathematics. It's as basic as 1-2-3!
2009-09-01 By Lily Erlic

... patterns,2 a typical subject matter of school algebra.3 Her pedagogical approach4 for teaching using hybrid environments for mathematics learning ...

Author: Jason Silverman

Publisher: Springer

ISBN: 9783319907901

Category: Education

Page: 220

View: 137

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This book builds on current and emerging research in distance learning, e-learning and blended learning. Specifically, it tests the boundaries of what is known by examining and discussing recent research and development in teaching and learning based on these modalities, with a focus on lifelong mathematics learning and teaching. The book is organized in four sections: The first section focuses on the incorporation of new technologies into mathematics classrooms through the construction or use of digital teaching and learning platforms. The second section presents a wide range of perspectives on the study and implementation of different tutoring systems and/or computer assisted math instruction. The third section presents four new innovations in mathematics learning and/or mathematics teacher education that involve the development of novel interfaces’ for communicating mathematical ideas and analyzing student thinking and student work. Finally, the fourth section presents the latest work on the construction and implementation of new MOOCs and rich media platforms developed to carry out specialized mathematics teacher education.
2018-07-20 By Jason Silverman

Author: John Costello

Publisher: Taylor & Francis

ISBN: 0415049881

Category: Mathematics

Page: 191

View: 541

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1991 By John Costello

Written for both trainees and practitioners working with children aged 0 to 8 years, including those studying for Early Years and Early Childhood degrees and those on Primary PGCE and Primary Education courses, this book offers mathematical ...

Author: Helen Taylor

Publisher: SAGE Publications Limited

ISBN: 1446253325

Category: Education

Page: 280

View: 312

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'What a super book! It is absolutely packed with practical ideas and activities to help you love maths, and love teaching and/or learning it. It certainly helps to develop an enthusiasm for a subject most adults tend to say "I'm no good at..."' - Early Years Educator ‘A wonderful book, packed with practical ideas and activities to help all students love maths.’ - Jo Boaler, Professor of Mathematics Education, Stanford University Fostering an enthusiasm for mathematics in young children is a vital part of supporting their mathematical development. Underpinned by subject and pedagogical knowledge, case studies and research-based perspectives, the authors provide clear guidance on how to support young children's learning and understanding in an effective and engaging way. Contemporary approaches to developing essential mathematical learning for young children are explored, including: play, practical activities and talk for mathematics outdoor learning understanding pattern counting, calculation and place value measures and shape problem solving and representing mathematics assessment working with parents. Written for both trainees and practitioners working with children aged 0 to 8 years, including those studying for Early Years and Early Childhood degrees and those on Primary PGCE and Primary Education courses, this book offers mathematical subject knowledge and teaching ideas in one volume. Helen Taylor is Course Leader of PGCE Primary Part-time Mathematics at Canterbury Christ Church University. Andrew Harris is Course Leader of PGCE Modular Mathematics at Canterbury Christ Church University.
2013-11-19 By Helen Taylor

This study described how and why a Korean elementary teacher taught mathematics as he did.

Author: Cheong-soo Cho

Publisher:

ISBN: OCLC:44999092

Category: Korean teachers

Page: 754

View: 493

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This study described how and why a Korean elementary teacher taught mathematics as he did. Specifically, the study sought to describe his beliefs about the teaching and learning of mathematics and relate them to patterns of classroom interaction and norms. An ethnographic inquiry guided the study of one third grade 10-year veteran teacher over three months in Korea. Through participant observation, the researcher observed Teacher Lee's teaching paying special attention to the mathematics lessons for one class of 45 students daily Monday through Saturday. Formal and informal interviews were used to collect data on the teacher and 17 of his students as well as other teachers (such as four teachers in the third grade), two principals, two mothers, and three beginning teachers. In addition to participant observation and interviews, a variety of documents were also collected, including newspapers, articles from journals, test items used in the teacher's classroom, daily worksheets, curriculum guide book, mathematics textbook, the school's newspaper. All videotapes and audiotapes were transcribed for inductive analysis. The analysis generated six major themes of the teacher's beliefs about the teaching and learning of mathematics and how those beliefs impacted the interactions and norms: (a) behave orderly, think freely; (b) teaching mathematics with understanding; (c) manipulative activities and games; (d) discourse-oriented teaching practices; (e) mathematical tasks; and (f) professional development. The teacher's beliefs about the teaching and learning of mathematics were closely related to the interaction patterns and classroom norms. This close relationship implies that identifying interaction patterns and classroom norms may shed light on understanding teachers' beliefs and teaching practices. The teacher's study group activity was a major professional development factor in promoting the consistent relationship. Implications and recommendations included (a) the need for more study of classroom norms and interactions as practical knowledge of teaching mathematics, (b) the need for investigating the effect of a study group to support teacher change, (c) the importance of the relationship between pedagogical content knowledge and teachers' beliefs, and (d) the need for more study of classroom management for teaching mathematics using understanding and discourse as an instructional strategy.
2000 By Cheong-soo Cho

Teaching and Learning Mathematical Problem Solving: Multiple Research Perspectives. ... Pattern in the Teaching and Learning of Mathematics.

Author: Barmby, Patrick

Publisher: McGraw-Hill Education (UK)

ISBN: 9780335229260

Category: Education

Page: 232

View: 781

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This book addresses the particular areas of mathematics within the primary curriculum that teachers find difficult to teach and in which children struggle to achieve.. .It begins with introductory sections on how children learn mathematics and is then organised on a subject area basis, dealing with the teaching of particular maths topics. Key topics addressed include rounding and measuring, means and medians, fractions, negative numbers, commutative and associative laws in number operations, and shape and space. .Within each chapter, the authors examine the themes of representing, reasoning and communicating, drawing out both the subject knowledge and ways of teaching each topic. A reference section for studies drawn upon is provided at the end of each chapter.....
2009-09-01 By Barmby, Patrick

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.

Author: Chiara Andrà

Publisher: Springer

ISBN: 9783319492322

Category: Education

Page: 292

View: 748

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The 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.
2017-05-03 By Chiara Andrà

The research and development of mathematics teaching was based on the ... we can identify basic patterns of teaching and learning and derive well-founded ...

Author: Marcus Nührenbörger

Publisher: Springer

ISBN: 9783319435428

Category: Education

Page: 43

View: 978

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This ICME-13 Topical Survey reviews the state-of-the-art by first exploring the roots and scope of design science. Second, it presents two examples of current design science projects that focus on substantial learning environments including a student and a teacher perspective. Subsequently, the book elaborates on how empirical research can be conceptualised within design science. Lastly, it explores developments in design science from a national and international perspective, while also discussing current trends in design research. Within the German-language tradition, considering ‘mathematics education as a design science’ primarily draws on the works of Wittmann. The core of this approach constitutes designing and investigating learning environments that involve substantial mathematics.
2016-07-26 By Marcus Nührenbörger

This book focuses on issues related to mathematics teaching and learning resources, including mathematics textbooks, teacher guides, student learning and assessment materials, and online resources.

Author: Lianghuo Fan

Publisher: Springer

ISBN: 9783319732534

Category: Education

Page: 377

View: 158

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This book focuses on issues related to mathematics teaching and learning resources, including mathematics textbooks, teacher guides, student learning and assessment materials, and online resources. The book highlights various theoretical and methodological approaches used to study teaching and learning resources, and addresses the areas of resources, teachers, and students at an international level. As for the resources, the book examines the role textbooks and other curricular or learning resources play in mathematics teaching, learning, and assessment. It asks questions such as: Could we consider different types of textbooks and roles they play in teaching and learning? How does the digitalization of information and communication affect these roles? What are defining features of e-textbooks, and how could we characterize the differences between the traditional textbooks and e-textbooks? As for the teachers, the book discusses the relationships between teachers’ individual and collective resources, and the way in which we could model such relationships. Specific questions addressed are: What is the role of teachers in developing textbooks and other teaching and learning materials? What are the relationships between resource designers and users? What are the consequences of these changing roles and relationships for the teaching of mathematics, and for teacher knowledge and professional development? As for the students, the book explores how students, as well as their teachers, interact through resources. It raises and addresses questions such as: What are the effects of modern ICT (particularly internet) on students’ use and the design of resources? How do changing patterns of use and design affect student behaviour, learning, and relationships to the subject of mathematics?
2018-02-13 By Lianghuo Fan

When asked about learning and understanding mathematics, people often reply ... The approach to learners' error patterns is a unique feature of this book.

Author: Helene J. Sherman

Publisher: Waveland Press

ISBN: 9781478639138

Category: Education

Page: 264

View: 753

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Highly regarded by instructors in past editions for its sequencing of topics and extensive set of exercises, the latest edition of Abstract Algebra retains its concrete approach with its gentle introduction to basic background material and its gradual increase in the level of sophistication as the student progresses through the book. Abstract concepts are introduced only after a careful study of important examples. Beachy and Blair’s clear narrative presentation responds to the needs of inexperienced students who stumble over proof writing, who understand definitions and theorems but cannot do the problems, and who want more examples that tie into their previous experience. The authors introduce chapters by indicating why the material is important and, at the same time, relating the new material to things from the student’s background and linking the subject matter of the chapter to the broader picture. Building proficiency in learning mathematics by tailoring instruction to students’ specific misconceptions and learning needs is the backbone of this indispensable text, written for K–8 pre- and inservice teachers, as well tutors. An important theme is that long-term retention is based on a strong conceptual foundation of numeracy and on a well-designed learning environment. Each chapter deals with a different mathematics topic, including whole numbers, fractions, decimals, as well as time and money. Chapters also include examples of error patterns and specific, well-defined strategies and activities for diagnosis, prescription, and remediation. New to this edition is a chapter devoted to English language learners. The complexities of language barriers are delineated along with reasons that students struggle with learning English and mathematics at the same time. An audio file of common mathematics terms translated from English into most-often spoken languages by ELLs can be accessed at www.youareamathperson.com. Outstanding features: • Response to Intervention (RTI) model underpins discussions of differentiating instruction. • Mathematics content reflects components of the Common Core State Standards Initiative for Mathematics and the National Council of Teachers of Mathematics’ Principles and Standards for School Mathematics. • Case studies and student examples promote a sound understanding of learners’ varied cognitive, behavioral, and physical needs. • Discussion questions challenge readers to think more deeply about the application and utility of concepts related to the error patterns. • Step-by-step directions for interactive instructional classroom games and activities are provided to extend and enrich teaching and learning.
2019-03-07 By Helene J. Sherman

A Teaching Handbook Steve Chinn, Richard Edmund Ashcroft ... (1999) Pattern in the Teaching and Learning of Mathematics. London. Cassell.

Author: Steve Chinn

Publisher: John Wiley & Sons

ISBN: 9781119159988

Category: Education

Page: 360

View: 580

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A seminal handbook in the field for more than 20 years, this new and updated edition of Mathematics for Dyslexicsand Dyscalculics contains the latest research and best practices for helping learners with numerical and mathematical difficulties. Provides a complete overview of theory and research in the fields of dyslexia and dyscalculia, along with detailed yet pragmatic methods to apply in the classroom Contains enhanced coverage of place value and the role of the decimal point, why fractions can challenge a developed logic for arithmetic, and the complexity of time along with new material on addressing anxiety, fear, motivation, and resilience in the classroom; and links to new resources including standardized tests and recommended reading lists Written by two mathematics teachers with 50 years of teaching experience between them, much of it in specialist settings for students with specific learning difficulties Offers effective teaching strategies for learners of all ages in a structured but accessible format
2017-01-18 By Steve Chinn

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