Toward a Visually-Oriented School Mathematics Curriculum

2011-01-06 Education

Author : Ferdinand Rivera
Release : 2011-01-06
Genre : Education
Kind : eBook
Book Rating : 148/5 ( reviews)

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Book Synopsis Toward a Visually-Oriented School Mathematics Curriculum by : Ferdinand Rivera

Download or read book Toward a Visually-Oriented School Mathematics Curriculum written by Ferdinand Rivera. This book was released on 2011-01-06. Available in PDF, EPUB and Kindle. Book excerpt: 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

2014-07-08 Education

Author : Ferdinand Rivera
Release : 2014-07-08
Genre : Education
Kind : eBook
Book Rating : 127/5 ( reviews)

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Book Synopsis Teaching and Learning Patterns in School Mathematics by : Ferdinand Rivera

Download or read book Teaching and Learning Patterns in School Mathematics written by Ferdinand Rivera. This book was released on 2014-07-08. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematics Learning in Early Childhood

2009-12-13 Education

Author : National Research Council
Release : 2009-12-13
Genre : Education
Kind : eBook
Book Rating : 064/5 ( reviews)

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Book Synopsis Mathematics Learning in Early Childhood by : National Research Council

Download or read book Mathematics Learning in Early Childhood written by National Research Council. This book was released on 2009-12-13. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mental Models and Their Dynamics, Adaptation, and Control

2022-01-26 Technology & Engineering

Author : Jan Treur
Release : 2022-01-26
Genre : Technology & Engineering
Kind : eBook
Book Rating : 219/5 ( reviews)

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Book Synopsis Mental Models and Their Dynamics, Adaptation, and Control by : Jan Treur

Download or read book Mental Models and Their Dynamics, Adaptation, and Control written by Jan Treur. This book was released on 2022-01-26. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces a generic approach to model the use and adaptation of mental models, including the control over this. In their mental processes, humans often make use of internal mental models as a kind of blueprints for processes that can take place in the world or in other persons. By internal mental simulation of such a mental model in their brain, they can predict and be prepared for what can happen in the future. Usually, mental models are adaptive: they can be learned, refined, revised, or forgotten, for example. Although there is a huge literature on mental models in various disciplines, a systematic account of how to model them computationally in a transparent manner is lacking. This approach allows for computational modeling of humans using mental models without a need for any algorithmic or programming skills, allowing for focus on the process of conceptualizing, modeling, and simulating complex, real-world mental processes and behaviors. The book is suitable for and is used as course material for multidisciplinary Master and Ph.D. students.

Reshaping School Mathematics

1990-02-01 Education

Author : National Research Council
Release : 1990-02-01
Genre : Education
Kind : eBook
Book Rating : 872/5 ( reviews)

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Book Synopsis Reshaping School Mathematics by : National Research Council

Download or read book Reshaping School Mathematics written by National Research Council. This book was released on 1990-02-01. Available in PDF, EPUB and Kindle. Book excerpt: The United States must restructure mathematics educationâ€"both what is learned and the way it is taughtâ€"if children are to develop the mathematical knowledge and skills they will need to be personally and professionally competent in the twenty-first century. Joining the recent reports that have opened a national dialogue on these issues, Reshaping School Mathematics focuses discussion on essential ideas that transcend details of current curricula or assessment results. It examines changing perspectives on the role of mathematics in society and changing practice in the use of technologyâ€"particularly calculators and computersâ€"in mathematics education.

Popular eBooks

Toward a Visually-Oriented School Mathematics Curriculum

Teaching and Learning Patterns in School Mathematics

Mathematics Learning in Early Childhood

Mental Models and Their Dynamics, Adaptation, and Control

Reshaping School Mathematics

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