Through The Window Meaning
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Windows on Mathematical Meanings
Author: Richard Noss
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
This book is the culmination of some ten years' theoretical and empirical investigation. Throughout this period, we have come into contact with many who have stimulated our thinking, some of whom belong to the community of Mathematics Educators. Our membership of that community has challenged us to make sense of some deep issues related to mathematical learning, especially the cognitive and pedagogical faces of mathematical meaning making. Alongside this community, we are privileged to have been part of another, whose members are centrally concerned both with mathematics and educa tion. Yet many of them might reject the label of Mathematics Educators. This community has historically been clustered around what is now called the Epistemology and Learning Group at the Massachusetts Institute of Technol ogy. Their work has focused our attention on cognitive science, ethnography, sociology, artificial intelligence and other related disciplines. Crucially, it has forced our awareness of the construction of computational settings as a crucial component of the struggle to understand how mathematical learning happens. We have sometimes felt that few have tried to span both communities. Indeed, an analysis of the references in the literature would, we are sure, reveal that the two communities have often ignored each other's strengths. One reason for writing this book is born of our hope that we might draw together Mathematics Educators and mathematics educators, and assist both communities in recognising that there are insights that might be derived from each other.
The Geometry of Meaning
A novel cognitive theory of semantics that proposes that the meanings of words can be described in terms of geometric structures. In The Geometry of Meaning, Peter Gärdenfors proposes a theory of semantics that bridges cognitive science and linguistics and shows how theories of cognitive processes, in particular concept formation, can be exploited in a general semantic model. He argues that our minds organize the information involved in communicative acts in a format that can be modeled in geometric or topological terms—in what he terms conceptual spaces, extending the theory he presented in an earlier book by that name. Many semantic theories consider the meanings of words as relatively stable and independent of the communicative context. Gärdenfors focuses instead on how various forms of communication establish a system of meanings that becomes shared between interlocutors. He argues that these “meetings of mind” depend on the underlying geometric structures, and that these structures facilitate language learning. Turning to lexical semantics, Gärdenfors argues that a unified theory of word meaning can be developed by using conceptual spaces. He shows that the meaning of different word classes can be given a cognitive grounding, and offers semantic analyses of nouns, adjectives, verbs, and prepositions. He also presents models of how the meanings of words are composed to form new meanings and of the basic semantic role of sentences. Finally, he considers the future implications of his theory for robot semantics and the Semantic Web.
Jeremiah, Lamentations
Among the apostolic fathers, Jeremiah was rarely cited, but several later authors give prominent attention to him. The fathers associated Lamentations with losses and death and saw the book as a description of the challenges that face Christians in a fallen world. In this ACCS volume, readers will gain insight and encouragement in the life of faith as seen through ancient pastoral eyes.