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Integrating Research On The Graphical Representation Of Functions

Author: Thomas A. Romberg
Publisher: Routledge
ISBN: 1136476369
Size: 22.17 MB
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This volume focuses on the important mathematical idea of functions that, with the technology of computers and calculators, can be dynamically represented in ways that have not been possible previously. The book's editors contend that as result of recent technological developments combined with the integrated knowledge available from research on teaching, instruction, students' thinking, and assessment, curriculum developers, researchers, and teacher educators are faced with an unprecedented opportunity for making dramatic changes. The book presents content considerations that occur when the mathematics of graphs and functions relate to curriculum. It also examines content in a carefully considered integration of research that conveys where the field stands and where it might go. Drawing heavily on their own work, the chapter authors reconceptualize research in their specific areas so that this knowledge is integrated with the others' strands. This model for synthesizing research can serve as a paradigm for how research in mathematics education can -- and probably should -- proceed.

Using The Mathematics Literature

Author: Kristine K. Fowler
Publisher: CRC Press
ISBN: 9780824750350
Size: 80.48 MB
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This reference serves as a reader-friendly guide to every basic tool and skill required in the mathematical library and helps mathematicians find resources in any format in the mathematics literature. It lists a wide range of standard texts, journals, review articles, newsgroups, and Internet and database tools for every major subfield in mathematics and details methods of access to primary literature sources of new research, applications, results, and techniques. Using the Mathematics Literature is the most comprehensive and up-to-date resource on mathematics literature in both print and electronic formats, presenting time-saving strategies for retrieval of the latest information.

The Nature Of Mathematical Thinking

Author: Robert J. Sternberg
Publisher: Routledge
ISBN: 0805817980
Size: 62.38 MB
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Why do some children seem to learn mathematics easily and others slave away at it, learning it only with great effort and apparent pain? Why are some people good at algebra but terrible at geometry? How can people who successfully run a business as adults have been failures at math in school? How come some professional mathematicians suffer terribly when trying to balance a checkbook? And why do school children in the United States perform so dismally in international comparisons? These are the kinds of real questions the editors set out to answer, or at least address, in editing this book on mathematical thinking. Their goal was to seek a diversity of contributors representing multiple viewpoints whose expertise might converge on the answers to these and other pressing and interesting questions regarding this subject. The chapter authors were asked to focus on their own approach to mathematical thinking, but also to address a common core of issues such as the nature of mathematical thinking, how it is similar to and different from other kinds of thinking, what makes some people or some groups better than others in this subject area, and how mathematical thinking can be assessed and taught. Their work is directed to a diverse audience -- psychologists interested in the nature of mathematical thinking and abilities, computer scientists who want to simulate mathematical thinking, educators involved in teaching and testing mathematical thinking, philosophers who need to understand the qualitative aspects of logical thinking, anthropologists and others interested in how and why mathematical thinking seems to differ in quality across cultures, and laypeople and others who have to think mathematically and want to understand how they are going to accomplish that feat.

Mathematical And Analogical Reasoning Of Young Learners

Author: Lyn D. English
Publisher: Routledge
ISBN: 1135638705
Size: 46.56 MB
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Mathematical and Analogical Reasoning of Young Learners provides foundational knowledge of the nature, development, and assessment of mathematical and analogical reasoning in young children. Reasoning is fundamental to understanding mathematics and is identified as one of the 10 key standards for school mathematics for the new millennium. The book draws on longitudinal and cross-cultural studies, conducted in the United States and Australia, of children's reasoning development as they progressed from preschool through the end of second grade. The multifaceted analysis of young children's development of mathematical and analogical reasoning focuses on individual learners, their learning environments, and the interaction between the two. The multidisciplinary team of authors present multiple perspectives and multiple methodologies, and provide valuable information on organizing and sustaining interdisciplinary and cross-cultural inquiry. Key issues addressed include: *the relationship between mathematical and analogical reasoning; *how changes in children's reasoning relate to the implicit instruction they receive in their classrooms; *analyses of the participating teachers' knowledge, beliefs, and practices with respect to mathematical and analogical reasoning of young learners; and *ways in which we might promote development of mathematical and analogical reasoning in young children. This volume is highly relevant for mathematics educators, researchers in mathematics education, educational psychologists, early childhood teachers, and others interested in mathematical development of young children, in particular, the development of their reasoning processes.

Algebra In The Early Grades

Author: James J. Kaput
Publisher: Lawrence Erlbaum
ISBN:
Size: 48.13 MB
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This volume is the first to offer a comprehensive, research-based, multi-faceted look at issues in early algebra. In recent years, the National Council for Teachers of Mathematics has recommended that algebra become a strand flowing throughout the K-12 curriculum, and the 2003 RAND Mathematics Study Panel has recommended that algebra be "the initial topical choice for focused and coordinated research and development [in K-12 mathematics]." The book provides a rationale for a stronger and more sustained approach to algebra in school, as well as concrete examples of how algebraic reasoning may be developed in the early grades. It is organized around three themes: *The Nature of Early Algebra *Students' Capacity for Algebraic Thinking *Issues of Implementation: Taking Early Algebra to the Classrooms The contributors to this landmark volume have been at the forefront of an effort to integrate algebra into the existing early grades mathematics curriculum. They include scholars who have been developing the conceptual foundations for such changes as well as researchers and developers who have led empirical investigations in school settings. Algebra in the Early Gradesaims to bridge the worlds of research, practice, design, and theory for educators, researchers, students, policy makers, and curriculum developers in mathematics education.

Becoming A Reflective Mathematics Teacher

Author: Alice F. Artzt
Publisher: Lawrence Erlbaum
ISBN:
Size: 17.64 MB
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This revised and expanded edition of "Becoming a Reflective Mathematics Teacher "continues to provide preservice and inservice mathematics teachers with practical ideas for developing and honing reflective and self-analytical skills needed to advance and improve instruction. Ideally suited for use with students who are taking a mathematics methods course or who are student teaching, this activity-oriented, research-based text: *supplies detailed observation instruments that preservice teachers can use when they observe other teachers; *offers reflective activities that provide a structure through which beginning teachers can think about their teaching in an insightful, thorough, and productive manner; and *includes guidelines and instruments for supervisors to use when observing, conferencing with, and assessing beginning or student teachers. All instruments and suggested activities are presented within a highly effective framework for teacher reflection and self-assessment that was developed in the spirit of inquiry-based, learner-centered teaching and is grounded in a cognitive perspective. New in the Second Edition: The first edition of this popular text focused on middle and secondary level mathematics teaching. This edition has been expanded to encompass elementary mathematics education, including new examples from elementary student teachers. Rubrics have been added for the observation report and the portfolio instruments. The text has been updated throughout.

The Origins Of Mathematical Knowledge In Childhood

Author: Catherine Sophian
Publisher: Lawrence Erlbaum
ISBN: 9780805857580
Size: 76.30 MB
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This book examines the origins and development of children’s mathematical knowledge. It contrasts the widely held view that counting is the starting point for mathematical development with an alternative comparison-of-quantities position. According to the comparison-of-quantities position, the concept of number builds upon more basic concepts of equality, inequality, and less-than and greater-than relations, which derive from comparisons between unenumerated quantities such as lengths. The concept of number combines these basic comparative concepts with the concept of a unit of measure, which allows one quantity to be described as a multiple of another. Sophian examines these alternative accounts of children’s developing mathematical knowledge in the light of research: *on children's counting; *on their reasoning about continuous quantities such as length and area; *on the development of the concept of unit; *on additive and multiplicative reasoning; and *on knowledge about fractions. In the closing chapters, Sophian draws out the developmental and the educational implications of the research and theory presented. Developmentally, the comparison-of-quantities position undermines the idea that numerical knowledge develops through domain-specific learning mechanisms in that it links numerical development both to physical knowledge about objects, which is the starting point for the concept of unit, and to the acquisition of linguistic number terms. Instructionally, the comparison-of-quantities perspective diverges from the counting-first perspective in that it underscores the continuity between whole-number arithmetic and fraction learning that stems from the importance of the concept of unit for both. Building on this idea, Sophian advances three instructional recommendations: First, instruction about numbers should always be grounded in thinking about quantities and how numbers represent the relations between them; second, instruction in the early years should always be guided by a long-term perspective in which current objectives are shaped by an understanding of their role in the overall course of mathematics learning; and third, instruction should be directly toward promoting the acquisition of the most general mathematical knowledge possible. The Origins of Mathematical Knowledge in Childhood is intended for researchers, professionals, and graduate students in developmental psychology, educational psychology, and mathematics education, and as a supplementary text for advanced undergraduate courses in cognitive development, educational psychology, and mathematics education.

Books In Print

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Books in print is the major source of information on books currently published and in print in the United States. The database provides the record of forthcoming books, books in-print, and books out-of-print.