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Toward A Visually Oriented School Mathematics Curriculum

Author: Ferdinand Rivera
Publisher: Springer Science & Business Media
ISBN: 9789400700147
Size: 27.61 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: 77.19 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: 18.98 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: 46.12 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: 72.33 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

The Thinking University

Author: Søren S.E. Bengtsen
Publisher: Springer
ISBN: 3319776673
Size: 51.33 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.

Equity In Discourse For Mathematics Education

Author: Beth Herbel-Eisenmann
Publisher: Springer Science & Business Media
ISBN: 9400728123
Size: 42.15 MB
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This book explores the connection between the ways people speak in mathematics classrooms and their opportunities to learn mathematics. The words spoken, heard, written and read in mathematics classrooms shape students’ sense of what mathematics is and of what people can do with mathematics. The authors employ multiple perspectives to consider the means for transformative action with respect to increasing opportunities for traditionally marginalized students to form mathematical identities that resonate with their cultural, social, linguistic, and political beings.

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

Author: Patricio Herbst
Publisher: Springer
ISBN: 331977476X
Size: 33.37 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.

Mathematics Education And Technology Rethinking The Terrain

Author: Celia Hoyles
Publisher: Springer Science & Business Media
ISBN: 9781441901460
Size: 40.17 MB
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Mathematics Education and Technology-Rethinking the Terrain revisits the important 1985 ICMI Study on the influence of computers and informatics on mathematics and its teaching. The focus of this book, resulting from the seventeenth Study led by ICMI, is the use of digital technologies in mathematics teaching and learning in countries across the world. Specifically, it focuses on cultural diversity and how this diversity impinges on the use of digital technologies in mathematics teaching and learning. Within this focus, themes such as mathematics and mathematical practices; learning and assessing mathematics with and through digital technologies; teachers and teaching; design of learning environments and curricula; implementation of curricula and classroom practice; access, equity and socio-cultural issues; and connectivity and virtual networks for learning, serve to organize the study and bring it coherence. Providing a state-of-the-art view of the domain with regards to research, innovating practices and technological development, Mathematics Education and Technology-Rethinking the Terrain is of interest to researchers and all those interested in the role that digital technology plays in mathematics education.