Toward A Visually Oriented School Mathematics Curriculum

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Toward a Visually-Oriented School Mathematics Curriculum

Ferdinand Rivera
Toward a Visually Oriented School Mathematics Curriculum Book PDF

Author : Ferdinand Rivera
Publisher : Springer Science & Business Media
Page : 316 pages
File Size : 53,6 Mb
Release : 2011-01-06
Category : Education
ISBN : 9789400700147

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Toward a Visually-Oriented School Mathematics Curriculum by Ferdinand Rivera Pdf

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

Ferdinand Rivera
Teaching and Learning Patterns in School Mathematics Book PDF

Author : Ferdinand Rivera
Publisher : Springer Science & Business Media
Page : 223 pages
File Size : 46,9 Mb
Release : 2014-07-08
Category : Education
ISBN : 9789400727120

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Teaching and Learning Patterns in School Mathematics by Ferdinand Rivera Pdf

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. ​

Mental Models and Their Dynamics, Adaptation, and Control

Jan Treur,Laila Van Ments
Mental Models and Their Dynamics Adaptation and Control Book PDF

Author : Jan Treur,Laila Van Ments
Publisher : Springer Nature
Page : 611 pages
File Size : 51,5 Mb
Release : 2022-01-26
Category : Technology & Engineering
ISBN : 9783030858216

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Mental Models and Their Dynamics, Adaptation, and Control by Jan Treur,Laila Van Ments Pdf

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.

Object Lessons

Caren Holtzman,Lynn Susholtz
Object Lessons Book PDF

Author : Caren Holtzman,Lynn Susholtz
Publisher : Stenhouse Publishers
Page : 229 pages
File Size : 41,9 Mb
Release : 2011
Category : Education
ISBN : 9781571107961

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Object Lessons by Caren Holtzman,Lynn Susholtz Pdf

Uses a highly visual approach to show students and teachers the art in math and the math in art.

Visualizing Mathematics

Kelly S. Mix,Michael T. Battista
Visualizing Mathematics Book PDF

Author : Kelly S. Mix,Michael T. Battista
Publisher : Springer
Page : 378 pages
File Size : 51,9 Mb
Release : 2018-12-07
Category : Education
ISBN : 9783319987675

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Visualizing Mathematics by Kelly S. Mix,Michael T. Battista Pdf

This unique volume surveys recent research on spatial visualization in mathematics in the fields of cognitive psychology and mathematics education. The general topic of spatial skill and mathematics has a long research tradition, but has been gaining attention in recent years, although much of this research happens in disconnected subfields. This volume aims to promote interaction between researchers, not only to provide a more comprehensive view of spatial visualization and mathematics, but also to stimulate innovative new directions in research based on a more coordinated effort. It features ten chapters authored by leading researchers in cognitive psychology and mathematics education, as well as includes dynamic commentaries by mathematics education researchers on cognitive psychology chapters, and by cognitive psychologists on mathematics education chapters. Among the topics included: From intuitive spatial measurement to understanding of units. Spatial reasoning: a critical problem-solving tool in children’s mathematics strategy tool-kit. What processes underlie the relation between spatial skill and mathematics? Learning with and from drawing in early years geometry. Communication of visual information and complexity of reasoning by mathematically talented students. Visualizing Mathematics makes substantial progress in understanding the role of spatial reasoning in mathematical thought and in connecting various subfields of research. It promises to make an impact among psychologists, education scholars, and mathematics educators in the convergence of psychology and education.

Broadening the Scope of Research on Mathematical Problem Solving

Nélia Amado,Susana Carreira,Keith Jones
Broadening the Scope of Research on Mathematical Problem Solving Book PDF

Author : Nélia Amado,Susana Carreira,Keith Jones
Publisher : Springer
Page : 579 pages
File Size : 54,6 Mb
Release : 2018-11-30
Category : Education
ISBN : 9783319998619

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Broadening the Scope of Research on Mathematical Problem Solving by Nélia Amado,Susana Carreira,Keith Jones Pdf

The innovative volume seeks to broaden the scope of research on mathematical problem solving in different educational environments. It brings together contributions not only from leading researchers, but also highlights collaborations with younger researchers to broadly explore mathematical problem-solving across many fields: mathematics education, psychology of education, technology education, mathematics popularization, and more. The volume’s three major themes—technology, creativity, and affect—represent key issues that are crucially embedded in the activity of problem solving in mathematics teaching and learning, both within the school setting and beyond the school. Through the book’s new pedagogical perspectives on these themes, it advances the field of research towards a more comprehensive approach on mathematical problem solving. Broadening the Scope of Research on Mathematical Problem Solving will prove to be a valuable resource for researchers and teachers interested in mathematical problem solving, as well as researchers and teachers interested in technology, creativity, and affect.

Distance Learning, E-Learning and Blended Learning in Mathematics Education

Jason Silverman,Veronica Hoyos
Distance Learning E Learning and Blended Learning in Mathematics Education Book PDF

Author : Jason Silverman,Veronica Hoyos
Publisher : Springer
Page : 220 pages
File Size : 40,9 Mb
Release : 2018-07-20
Category : Education
ISBN : 9783319907901

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Distance Learning, E-Learning and Blended Learning in Mathematics Education by Jason Silverman,Veronica Hoyos Pdf

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.

Mathematics Learning in Early Childhood

National Research Council,Division of Behavioral and Social Sciences and Education,Center for Education,Committee on Early Childhood Mathematics
Mathematics Learning in Early Childhood Book PDF

Author : National Research Council,Division of Behavioral and Social Sciences and Education,Center for Education,Committee on Early Childhood Mathematics
Publisher : National Academies Press
Page : 399 pages
File Size : 40,8 Mb
Release : 2009-11-13
Category : Education
ISBN : 9780309147439

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Mathematics Learning in Early Childhood by National Research Council,Division of Behavioral and Social Sciences and Education,Center for Education,Committee on Early Childhood Mathematics Pdf

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.

Creativity and Technology in Mathematics Education

Viktor Freiman,Janet Lynne Tassell
Creativity and Technology in Mathematics Education Book PDF

Author : Viktor Freiman,Janet Lynne Tassell
Publisher : Springer
Page : 561 pages
File Size : 54,8 Mb
Release : 2018-09-03
Category : Education
ISBN : 9783319723815

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Creativity and Technology in Mathematics Education by Viktor Freiman,Janet Lynne Tassell Pdf

This volume provides new insights on creativity while focusing on innovative methodological approaches in research and practice of integrating technological tools and environments in mathematics teaching and learning. This work is being built on the discussions at the mini-symposium on Creativity and Technology at the International Conference on Mathematical Creativity and Giftedness (ICMCG) in Denver, USA (2014), and other contributions to the topic. The book emphasizes a diversity of views, a variety of contexts, angles and cultures of thought, as well as mathematical and educational practices. The authors of each chapter explore the potential of technology to foster creative and divergent mathematical thinking, problem solving and problem posing, creative use of dynamic, multimodal and interactive software by teachers and learners, as well as other digital media and tools while widening and enriching transdisciplinary and interdisciplinary connections in mathematics classroom. Along with ground-breaking innovative approaches, the book aims to provide researchers and practitioners with new paths for diversification of opportunities for all students to become more creative and innovative mathematics learners. A framework for dynamic learning conditions of leveraging mathematical creativity with technology is an outcome of the book as well.

Informatics in Schools. Curricula, Competences, and Competitions

Andrej Brodnik,Jan Vahrenhold
Informatics in Schools Curricula Competences and Competitions Book PDF

Author : Andrej Brodnik,Jan Vahrenhold
Publisher : Springer
Page : 183 pages
File Size : 47,5 Mb
Release : 2015-09-23
Category : Education
ISBN : 9783319253961

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Informatics in Schools. Curricula, Competences, and Competitions by Andrej Brodnik,Jan Vahrenhold Pdf

This book constitutes the refereed proceedings of the 8th International Conference on Informatics in Schools: Situation, Evolution, and Perspectives, ISSEP 2015, held in Ljubljana, Slovenia, in September/October 2015. The 14 full papers presented together with 3 invited talks were carefully reviewed and selected from 36 submissions. The focus of the conference was on following topics: sustainable education in informatics for pupils of all ages; connecting informatics lessons to the students’ everyday lives; teacher education in informatics; and research on informatics in schools (empirical/qualitative/quantitative/theory building/research methods/comparative studies/transferability of methods and results from other disciplines).

Origins of Mind

Liz Swan
Origins of Mind Book PDF

Author : Liz Swan
Publisher : Springer Science & Business Media
Page : 416 pages
File Size : 55,9 Mb
Release : 2012-12-22
Category : Science
ISBN : 9789400754195

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Origins of Mind by Liz Swan Pdf

The big question of how and why mindedness evolved necessitates collaborative, multidisciplinary investigation. Biosemiotics provides a new conceptual space that attracts a multitude of thinkers in the biological and cognitive sciences and the humanities who recognize continuity in the biosphere from the simplest to the most complex organisms, and who are united in the project of trying to account for even language and human consciousness in this comprehensive picture of life. The young interdiscipline of biosemiotics has so far by and large focused on codes, signs and sign processes in the microworld—a fact that reflects the field’s strong representation in microbiology and embryology. What philosophers of mind and cognitive scientists can contribute to the growing interdiscipline are insights into how the biosemiotic weltanschauung applies to complex organisms like humans where such signs and sign processes constitute human society and culture.

Standards-Based School Mathematics Curricula

Sharon L. Senk
Standards Based School Mathematics Curricula Book PDF

Author : Sharon L. Senk
Publisher : Psychology Press
Page : 515 pages
File Size : 52,5 Mb
Release : 2003
Category : Education
ISBN : 0805850287

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Standards-Based School Mathematics Curricula by Sharon L. Senk Pdf

The Curriculum and Evaluation Standards for School Mathematics published by the National Council of Teachers of Mathematics in 1989 set forth a broad vision of mathematical content and pedagogy for grades K-12 in the United States. These Standards prompted the development of Standards-based mathematics curricula. What features characterize Standards-based curricula? How well do such curricula work? To answer these questions, the editors invited researchers who had investigated the implementation of 12 different Standards-based mathematics curricula to describe the effects of these curricula on students' learning and achievement, and to provide evidence for any claims they made. In particular, authors were asked to identify content on which performance of students using Standards-based materials differed from that of students using more traditional materials, and content on which performance of these two groups of students was virtually identical. Additionally, four scholars not involved with the development of any of the materials were invited to write critical commentaries on the work reported in the other chapters. Section I of Standards-Based School Mathematics Curricula provides a historical background to place the current curriculum reform efforts in perspective, a summary of recent recommendations to reform school mathematics, and a discussion of issues that arise when conducting research on student outcomes. Sections II, III, and IV are devoted to research on mathematics curriculum projects for elementary, middle, and high schools, respectively. The final section is a commentary by Jeremy Kilpatrick, Regents Professor of Mathematics Education at the University of Georgia, on the research reported in this book. It provides a historical perspective on the use of research to guide mathematics curriculum reform in schools, and makes additional recommendations for further research. In addition to the references provided at the end of each chapter, other references about the Standards-based curriculum projects are provided at the end of the book. This volume is a valuable resource for all participants in discussions about school mathematics curricula--including professors and graduate students interested in mathematics education, curriculum development, program evaluation, or the history of education; educational policy makers; teachers; parents; principals and other school administrators. The editors hope that the large body of empirical evidence and the thoughtful discussion of educational values found in this book will enable readers to engage in informed civil discourse about the goals and methods of school mathematics curricula and related research.

A Five-Year Study of the First Edition of the Core-Plus Mathematics Curriculum

Harold Schoen,Steven W. Ziebarth,Christian R. Hirsch,Allison BrckaLorenz
A Five Year Study of the First Edition of the Core Plus Mathematics Curriculum Book PDF

Author : Harold Schoen,Steven W. Ziebarth,Christian R. Hirsch,Allison BrckaLorenz
Publisher : IAP
Page : 423 pages
File Size : 54,8 Mb
Release : 2010-07-01
Category : Education
ISBN : 9781607524151

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A Five-Year Study of the First Edition of the Core-Plus Mathematics Curriculum by Harold Schoen,Steven W. Ziebarth,Christian R. Hirsch,Allison BrckaLorenz Pdf

The study reported in this volume adds to the growing body of evaluation studies that focus on the use of NSF-funded Standards-based high school mathematics curricula. Most previous evaluations have studied the impact of field-test versions of a curriculum. Since these innovative curricula were so new at the time of many of these studies, students and teachers were relative novices in their use. These earlier studies were mainly one year or less in duration. Students in the comparison groups were typically from schools in which some classes used a Standards-based curriculum and other classes used a conventional curriculum, rather than using the Standards-based curriculum with all students as curriculum developers intended. The volume reports one of the first studies of the efficacy of Standards-based mathematics curricula with all of the following characteristics: · The study focused on fairly stable implementations of a first-edition Standards-based high school mathematics curriculum that was used by all students in each of three schools. · It involved students who experienced up to seven years of Standards-based mathematics curricula and instruction in middle school and high school. · It monitored students’ mathematical achievement, beliefs, and attitudes for four years of high school and one year after graduation. · Prior to the study, many of the teachers had one or more years of experience teaching the Standards-based curriculum and/or professional development focusing on how to implement the curriculum well. · In the study, variations in levels of implementation of the curriculum are described and related to student outcomes and teacher behavior variables. Item data and all unpublished testing instruments from this study are available at www.wmich.edu/cpmp/ for use as a baseline of instruments and data for future curriculum evaluators or Core-Plus Mathematics users who may wish to compare results of new groups of students to those in the present study on common tests or surveys. Taken together, this volume, the supplement at the CPMP Web site, and the first edition Core-Plus Mathematics curriculum materials (samples of which are also available at the Web site) serve as a fairly complete description of the nature and impact of an exemplar of first edition NSF-funded Standards-based high school mathematics curricula as it existed and was implemented with all students in three schools around the turn of the 21st century.

Early Algebraization

Jinfa Cai,Eric Knuth
Early Algebraization Book PDF

Author : Jinfa Cai,Eric Knuth
Publisher : Springer Science & Business Media
Page : 624 pages
File Size : 41,7 Mb
Release : 2011-02-24
Category : Education
ISBN : 9783642177354

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Early Algebraization by Jinfa Cai,Eric Knuth Pdf

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.

Eyes on Math

Marian Small
Eyes on Math Book PDF

Author : Marian Small
Publisher : Teachers College Press
Page : 241 pages
File Size : 48,9 Mb
Release : 2012-12-30
Category : Education
ISBN : 9780807753910

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Eyes on Math by Marian Small Pdf

This new book is an exciting follow-up to the authors bestsellers on differentiated math instruction, Good Questions and More Good Questions. Eyes on Math is a unique teaching resource that provides engaging, full-color graphics and pictures with text showing teachers how to use each image to stimulate mathematical teaching conversations around key K–8 concepts. Teachers using the book can download the images for projection onto classroom white boards or screens. The questions and answers will help both students and teachers look more deeply and see the math behind the math!