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Toward A Visually Oriented School Mathematics Curriculum

Author: Ferdinand Rivera
Publisher: Springer Science & Business Media
ISBN: 9789400700147
Size: 15.47 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: 26.76 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: 58.77 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.

Encyclopedia Of Information Technology Curriculum Integration

Author: Tomei, Lawrence A.
Publisher: IGI Global
ISBN: 9781599048826
Size: 36.44 MB
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As more and more universities, schools, and corporate training organizations develop technology plans to ensure technology will directly benefit learning and achievement, the demand is increasing for an all-inclusive, authoritative reference source on the infusion of technology into curriculums worldwide. The Encyclopedia of Information Technology Curriculum Integration amasses a comprehensive resource of concepts, methodologies, models, architectures, applications, enabling technologies, and best practices for integrating technology into the curriculum at all levels of education. Compiling 154 articles from over 125 of the world's leading experts on information technology, this authoritative reference strives to supply innovative research aimed at improving academic achievement, teaching and learning, and the application of technology in schools and training environments.