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Toward A Visually Oriented School Mathematics Curriculum

Author: Ferdinand Rivera
Publisher: Springer Science & Business Media
ISBN: 9789400700147
Size: 74.38 MB
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What does it mean to have a visual representation of a mathematical object, concept, or process? What visualization strategies support growth in mathematical thinking, reasoning, generalization, and knowledge? Is mathematical seeing culture-free? How can information drawn from studies in blind subjects help us understand the significance of a multimodal approach to learning mathematics? Toward a Visually-Oriented School Mathematics Curriculum explores a unified theory of visualization in school mathematical learning via the notion of progressive modeling. Based on the author’s longitudinal research investigations in elementary and middle school classrooms, the book provides a compelling empirical account of ways in which instruction can effectively orchestrate the transition from personally-constructed visuals, both externally-drawn and internally-derived, into more structured visual representations within the context of a socioculturally grounded mathematical activity. Both for teachers and researchers, a discussion of this topic is relevant in the history of the present. The ubiquity of technological tools and virtual spaces for learning and doing mathematics has aroused interest among concerned stakeholders about the role of mathematics in these contexts. The book begins with a prolegomenon on the author’s reflections on past and present visual studies in mathematics education. In the remaining seven chapters, visualization is pursued in terms of its role in bringing about progressions in mathematical symbolization, abduction, pattern generalization, and diagrammatization. Toward a Visually-Oriented School Mathematics Curriculum views issues surrounding visualization through the eyes of a classroom teacher-researcher; it draws on findings within and outside of mathematics education that help practitioners and scholars gain a better understanding of what it means to pleasurably experience the symmetric visual/symbolic reversal phenomenon – that is, seeing the visual in the symbolic and the symbolic in the visual."

Teaching And Learning Patterns In School Mathematics

Author: Ferdinand Rivera
Publisher: Springer Science & Business Media
ISBN: 9400727127
Size: 48.66 MB
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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. ​

Early Algebraization

Author: Jinfa Cai
Publisher: Springer Science & Business Media
ISBN: 9783642177354
Size: 52.27 MB
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In this volume, the authors address the development of students’ algebraic thinking in the elementary and middle school grades from curricular, cognitive, and instructional perspectives. The volume is also international in nature, thus promoting a global dialogue on the topic of early Algebraization.

Mathematics Learning In Early Childhood

Author: National Research Council
Publisher: National Academies Press
ISBN: 9780309147439
Size: 60.99 MB
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Early childhood mathematics is vitally important for young children's present and future educational success. Research demonstrates that virtually all young children have the capability to learn and become competent in mathematics. Furthermore, young children enjoy their early informal experiences with mathematics. Unfortunately, many children's potential in mathematics is not fully realized, especially those children who are economically disadvantaged. This is due, in part, to a lack of opportunities to learn mathematics in early childhood settings or through everyday experiences in the home and in their communities. Improvements in early childhood mathematics education can provide young children with the foundation for school success. Relying on a comprehensive review of the research, Mathematics Learning in Early Childhood lays out the critical areas that should be the focus of young children's early mathematics education, explores the extent to which they are currently being incorporated in early childhood settings, and identifies the changes needed to improve the quality of mathematics experiences for young children. This book serves as a call to action to improve the state of early childhood mathematics. It will be especially useful for policy makers and practitioners-those who work directly with children and their families in shaping the policies that affect the education of young children.

Handbook Of Research On The Psychology Of Mathematics Education

Author: Angel Gutiérrez
Publisher: Sense Publishers
ISBN: 9077874194
Size: 22.54 MB
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This volume is a compilation of the research produced by the International Group for the Psychology of Mathematics Education (PME) since its creation, 30 years ago. It has been written to become an essential reference for mathematics education research in the coming years

A Handbook For Teaching And Learning In Higher Education

Author: Heather Fry
Publisher: Routledge
ISBN: 1317650220
Size: 49.95 MB
Format: PDF, Docs
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This entirely new edition of a very successful book focuses on developing professional academic skills for supporting and supervising student learning and effective teaching. It is built on the premise that the roles of those who teach in higher education are complex and multi-faceted. A Handbook for Teaching and Learning in Higher Education is sensitive to the competing demands of teaching, research, scholarship, and academic management. The new edition reflects and responds to the rapidly changing context of higher education and to current understanding of how to best support student learning. Drawing together a large number of expert authors, it continues to feature extensive use of case studies that show how successful teachers have implemented these ideas. It includes key topics such as student engagement and motivation, internationalisation, employability, inclusive strategies for teaching, effective use of technology and issues relating to postgraduate students and student retention. Part 1 explores a number of aspects of the context of UK higher education that affect the education of students, looking at the drivers of institutional behaviours and how to achieve success as a university teacher. Part 2 examines learning, teaching and supervising in higher education and includes chapters on working with diversity, encouraging independent learning and learning gain. Part 3 considers approaches to teaching and learning in different disciplines, covering a full range including arts and humanities, social sciences, experimental sciences through to medicine and dentistry. Written to support the excellence in teaching and learning design required to bring about student learning of the highest quality, this will be essential reading for all new lecturers, particularly anyone taking an accredited course in teaching and learning in higher education, as well as those experienced lecturers who wish to improve their teaching practice. Those working in adult learning and educational development will also find the book to be a particularly useful resource. In addition it will appeal to staff who support learning and teaching in various other roles.

The Thinking University

Author: Søren S.E. Bengtsen
Publisher: Springer
ISBN: 3319776673
Size: 33.68 MB
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This book reinvigorates the philosophical treatment of the nature, purpose, and meaning of thought in today’s universities. The wider discussion about higher education has moved from a philosophical discourse to a discourse on social welfare and service, economics, and political agendas. This book reconnects philosophy with the central academic concepts of thought, reason, and critique and their associated academic practices of thinking and reasoning. Thought in this context should not be considered as a merely mental or cognitive construction, still less a cloistered college, but a fully developed individual and social engagement of critical reflection and discussion with the current pressing disciplinary, political, and philosophical issues. The editors hold that the element of thought, and the ability to think in a deep and groundbreaking way is, still, the essence of the university. But what does it mean to think in the university today? And in what ways is thought related not only to the epistemological and ontological issues of philosophical debate, but also to the social and political dimensions of our globalised age? In many countries, the state is imposing limitations on universities, dismissing or threatening academics who speak out critically. With this volume, the editors ask questions such as: What is the value of thought? What is the university’s proper relationship to thought? To give the notion of thought a thorough philosophical treatment, the book is divided into in three parts. The focus moves from an epistemological perspective in Part I, to a focus on existence and values in higher education in Part II, and then to a societal-oriented focus on the university in Part III. All three parts, in their own ways, debate the notion of thought in higher education and the university as a thinking form of being.

International Perspectives On The Teaching And Learning Of Geometry In Secondary Schools

Author: Patricio Herbst
Publisher: Springer
ISBN: 331977476X
Size: 60.28 MB
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This book presents current perspectives on theoretical and empirical issues related to the teaching and learning of geometry at secondary schools. It contains chapters contributing to three main areas. A first set of chapters examines mathematical, epistemological, and curricular perspectives. A second set of chapters presents studies on geometry instruction and teacher knowledge, and a third set of chapters offers studies on geometry thinking and learning. Specific research topics addressed also include teaching practice, learning trajectories, learning difficulties, technological resources, instructional design, assessments, textbook analyses, and teacher education in geometry. Geometry remains an essential and critical topic in school mathematics. As they learn geometry, students develop essential mathematical thinking and visualization skills and learn a language that helps them relate to and interact with the physical world. Geometry has traditionally been included as a subject of study in secondary mathematics curricula, but it has also featured as a resource in out-of-school problem solving, and has been connected to various human activities such as sports, games, and artwork. Furthermore, geometry often plays a role in teacher preparation, undergraduate mathematics, and at the workplace. New technologies, including dynamic geometry software, computer-assisted design software, and geometric positioning systems, have provided more resources for teachers to design environments and tasks in which students can learn and use geometry. In this context, research on the teaching and learning of geometry will continue to be a key element on the research agendas of mathematics educators, as researchers continue to look for ways to enhance student learning and to understand student thinking and teachers’ decision making.