models and modeling perspectives a special double issue of mathematical thinking and learning volume 5 mathematical thinking learning

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Models And Modeling Perspectives

Author : Richard A. Lesh
ISBN : 9781135484262
Genre : Education
File Size : 62. 19 MB
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This special issue of Mathematical Thinking and Learning describes models and modeling perspectives toward mathematics problem solving, learning, and teaching. The concern is not only the mature forms of models and modeling in communities of scientists and mathematicians, but also the need to initiate students in these forms of thought. The contributions of this issue suggest a variety of ways that students (children through adults) can be introduced to highly productive forms of modeling practices. Collectively, they illustrate how modeling activities often lead to remarkable mathematical achievements by students formerly judged to be too young or too lacking in ability for such sophisticated and powerful forms of mathematical thinking. The papers also illustrate how modeling activities often create productive interdisciplinary niches for mathematical thinking, learning, and problem solving that involve simulations of similar situations that occur when mathematics is useful beyond school.

Mathematikunterricht Im Kontext Von Realit T Kultur Und Lehrerprofessionalit T

Author : Werner Blum
ISBN : 9783834823892
Genre : Mathematics
File Size : 81. 38 MB
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​Mathematikunterricht aus verschiedenen Perspektiven zu betrachten und wissenschaftlich zu untersuchen, erweitert die Sicht auf das Lernen und Lehren von Mathematik. In dem Buch werden vier große Bereiche beleuchtet, die insbesondere die jahrzehntelangen Forschungsfelder von Gabriele Kaiser kennzeichnen: mathematisches Modellieren, sprachliche und kulturelle Einflüsse auf das Mathematiklernen, Lehrerprofessionsforschung sowie Theoriebildung in der Mathematikdidaktik. Zu diesen Bereichen haben national und international ausgewiesene Expertinnen und Experten Beiträge geleistet, um Gabriele Kaiser aus Anlass ihres 60. Geburtstags zu ehren. Das Buch enthält aktuelle Ergebnisse empirischer Untersuchungen und theoretische Perspektiven in Bezug auf einzelne Aspekte des Wirkens der Jubilarin.

Advanced Mathematical Thinking

Author : Annie Selden
ISBN : 9781135478384
Genre : Education
File Size : 69. 39 MB
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First Published in 2005. Routledge is an imprint of Taylor & Francis, an informa company.

Mathematics Education As A Research Domain A Search For Identity

Author : Anna Sierpinska
ISBN : 9789401151948
Genre : Education
File Size : 80. 71 MB
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No one disputes how important it is, in today's world, to prepare students to un derstand mathematics as well as to use and communicate mathematics in their future lives. That task is very difficult, however. Refocusing curricula on funda mental concepts, producing new teaching materials, and designing teaching units based on 'mathematicians' common sense' (or on logic) have not resulted in a better understanding of mathematics by more students. The failure of such efforts has raised questions suggesting that what was missing at the outset of these proposals, designs, and productions was a more profound knowledge of the phenomena of learning and teaching mathematics in socially established and culturally, politically, and economically justified institutions - namely, schools. Such knowledge cannot be built by mere juxtaposition of theories in disci plines such as psychology, sociology, and mathematics. Psychological theories focus on the individual learner. Theories of sociology of education look at the general laws of curriculum development, the specifics of pedagogic discourse as opposed to scientific discourse in general, the different possible pedagogic rela tions between the teacher and the taught, and other general problems in the inter face between education and society. Mathematics, aside from its theoretical contents, can be looked at from historical and epistemological points of view, clarifying the genetic development of its concepts, methods, and theories. This view can shed some light on the meaning of mathematical concepts and on the difficulties students have in teaching approaches that disregard the genetic development of these concepts.

Finite Mathematics Models And Structure

Author : William J. Adams
ISBN : 9781469107349
Genre : Mathematics
File Size : 44. 28 MB
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Still another book on finite math? Why? Hasnt everything that should have been said been said? No, I would argue. The shortcoming that troubles me most about the books I am familiar with is their failure to provide perspective on what math technique and the use of technology can do for us and its limitations. This can only be addressed through vigorous and sustained use of the mathematical modeling perspective, which is a hallmark of this books exposition. A point continually stressed is that reaching a mathematical answer to a problem is not the end of the story. It is in a sense the end of a chapter, but the next chapter is concerned with questions about whether and how the mathematical answer should be implemented. Also addressed is the question of what to consider when more than one answer is obtained for a problem.

Emerging Perspectives On Gesture And Embodiment In Mathematics

Author : Laurie D. Edwards
ISBN : 9781623965556
Genre : Education
File Size : 62. 55 MB
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The purpose of the book is to establish a common language for, and understanding of, embodiment as it applies to mathematical thinking, and to link mathematics education research to recent work in gesture studies, cognitive linguistics and the theory of embodied cognition. Just as in past decades, mathematics education experienced a "turn to the social" in which sociocultural factors were explored, in recent years there has been a nascent "turn to the body." An increasing number of researchers and theorists in mathematics education have become interested in the fact that, although mathematics may be socially constructed, this construction is not arbitrary or unconstrained, but rather is rooted in, and shaped by, the body. All those who engage with mathematics, whether at an elementary or advanced level, share the same basic biological and cognitive capabilities, as well as certain common physical experiences that come with being humans living in a material world. In addition, the doing and communicating of mathematics is never a purely intellectual activity: it involves a wide range of bodily actions, from committing inscriptions to paper or whiteboard, to speaking, listening, gesturing and gazing. This volume will present recent research on gesture and mathematics, within a framework that addresses several levels of mathematical development. The chapters will begin with contributions that examine early mathematical and protomathematical knowledge, for example, the conservation of volume and counting. The role of gesture in teaching and learning arithmetic procedures will be addressed. Core concepts and tools from secondary level mathematics will be investigated, including algebra, functions and graphing. And finally, research into the embodied understanding of advanced topics in geometry and calculus will be presented. The overall goal for the volume is to acknowledge the multimodal nature of mathematical knowing, and to contribute to the creation of a model of the interactions and mutual influences of bodily motion, spatial thinking, gesture, speech and external inscriptions on mathematical thinking, communication and learning. The intended audience is researchers and theorists in mathematics education as well as graduate students in the field.

Journal For Research In Mathematics Education

Author :
ISBN : UCR:31210024496679
Genre : Mathematics
File Size : 49. 14 MB
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Investigating Mathematics Teaching

Author : Barbara Jaworski
ISBN : 9781135716110
Genre : Education
File Size : 38. 51 MB
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Barbara Jaworski addresses a number of questions that are central to research on reform in mathematics education today. In this volume she attempts to chart critically yet honestly her own developing ideas as she undertakes a several-year-long enquiry into mathematics teaching and gives a very personal account of her developing conceptions, conjectures, thoughts and reflections. The author accounts for her research both genetically and biographically, simultaneously restructuring the development of her ideas and giving a rigorous, critical and reflective account.

Das Denken Von Kindern

Author : Robert S. Siegler
ISBN : 9783486806427
Genre : Psychology
File Size : 38. 37 MB
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Bis in die jüngste Vergangenheit blieb uns der Zugang zu vielen der interessanten Aspekte des Denkens von Kindern verwehrt. Philosophen haben sich Jahrhunderte lang darum gestritten, ob Säuglinge die Welt als "strahlendes und dröhnendes Durcheinander" sehen oder ganz ähnlich wie ältere Kinder und Erwachsene. Erst mit der Entwicklung aufschlußreicher experimenteller Methoden in den vergangenen Jahren wurde die Antwort deutlich. Sogar Neugeborene sehen bestimmte Aspekte der Welt recht klar und mit 6 Monaten ähnelt die Wahrnehmung von Säuglingen der von Erwachsenen. Dies und andere Erkenntnisse über das Denken von Kindern sind Gegenstand dieses Buches.

Dissertation Abstracts International

Author :
ISBN : STANFORD:36105121673219
Genre : Humanities
File Size : 37. 14 MB
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