The Emergence Of Mathematical Meaning

Author: Paul Cobb
Publisher: Routledge
ISBN: 9781136486104
Size: 11.50 MB
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This book grew out of a five-year collaboration between groups of American and German mathematics educators. The central issue addressed accounting for the messiness and complexity of mathematics learning and teaching as it occurs in classroom situations. The individual chapters are based on the view that psychological and sociological perspectives each tell half of a good story. To unify these concepts requires a combined approach that takes individual students' mathematical activity seriously while simultaneously seeing their activity as necessarily socially situated. Throughout their collaboration, the chapter authors shared a single set of video recordings and transcripts made in an American elementary classroom where instruction was generally compatible with recent reform recommendations. As a consequence, the book is much more than a compendium of loosely related papers. The combined approach taken by the authors draws on interactionism and ethnomethodology. Thus, it constitutes an alternative to Vygotskian and Soviet activity theory approaches. The specific topics discussed in individual chapters include small group collaboration and learning, the teacher's practice and growth, and language, discourse, and argumentation in the mathematics classroom. This collaborative effort is valuable to educators and psychologists interested in situated cognition and the relation between sociocultural processes and individual psychological processes.

Windows On Mathematical Meanings

Author: Richard Noss
Publisher: Springer Science & Business Media
ISBN: 9789400916968
Size: 10.71 MB
Format: PDF, Docs
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This book challenges some of the conventional wisdoms on the learning of mathematics. The authors use the computer as a window onto mathematical meaning-making. The pivot of their theory is the idea of webbing, which explains how someone struggling with a new mathematical idea can draw on supportive knowledge, and reconciles the individual's role in mathematical learning with the part played by epistemological, social and cultural forces.

On The Emergence Theme Of Physics

Author: Robert Carroll
Publisher: World Scientific
ISBN: 9789814291804
Size: 17.52 MB
Format: PDF, ePub, Mobi
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The book surveys mathematical relations between classical and quantum mechanics, gravity, time and thermodynamics from various points of view and many sources (with appropriate attribution). The emergence theme is developed with an emphasis on the meaning via mathematics. A background theme of Bohemian mechanics and connections to the quantum equivalence principle of Matone et al. is also developed in great detail. Some original work relating the quantum potential and Ricci flow is also included.

Mathematics Education As A Research Domain A Search For Identity

Author: Anna Sierpinska
Publisher: Springer
ISBN: 9789401151948
Size: 20.62 MB
Format: PDF, ePub, Mobi
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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.

Mathematische Reflexion In Der Interaktion Von Grundschulkindern

Author: Cordula Schülke
Publisher: Waxmann Verlag
ISBN: 9783830977865
Size: 20.23 MB
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In dem vorliegenden Forschungsprojekt wird das theoretische Konstrukt einer mathematischen Reflexion mit Bezug auf die besondere epistemologische Natur des mathematischen Wissens entwickelt und spezifiziert. Die zentrale Grundlage stellt eine von Freudenthal (1983) eingebrachte Sichtweise auf Reflexion als 'Standpunktwechsel' dar. Mittels eines Rasters, das auf der Grundlage von Partnerinterviews mit Kindern aus jahrgangsgemischten Lerngruppen entwickelt wurde, werden die fundamentalen Kategorien und Elemente reflexiven mathematischen Denkens fokussiert dargestellt. Gleichzeitig dient das Raster als Instrument zur Analyse von Situationen mathematischer Interaktion und zur Identifikation verschiedener Ebenen mathematischer Reflexion. In den vorgestellten Interviewanalysen wird insbesondere aufgezeigt, wie durch die Anregung reflexiven mathematischen Denkens Lernprozesse im Mathematikunterricht initiiert und intensiviert werden können. Cordula Schülke arbeitet seit 10 Jahren als Grundschullehrerin. Sie war 3 Jahre Stipendiatin der Universität Duisburg-Essen und ist Mitarbeiterin im Projekt EInmaL (Epistemologische Interaktionsforschung mathematischer Lehr-Lern-Prozesse) der Arbeitsgruppe von Prof. Dr. Heinz Steinbring.

The Development Of Mathematics

Author: E. T. Bell
Publisher: Courier Corporation
ISBN: 9780486152288
Size: 16.20 MB
Format: PDF, Mobi
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Time-honored study by a prominent scholar of mathematics traces decisive epochs from the evolution of mathematical ideas in ancient Egypt and Babylonia to major breakthroughs in the 19th and 20th centuries. 1945 edition.