Learning Mathematics: Constructivist and Interactionist by Leslie P. Steffe, Heide G. Wiegel (auth.), Paul Cobb (eds.)

By Leslie P. Steffe, Heide G. Wiegel (auth.), Paul Cobb (eds.)

The first 5 contributions to this unique factor on Theories of Mathematical studying take a cognitive standpoint while the 6th, that by way of Voigt, takes an interactionist standpoint. the typical topic that hyperlinks the six articles is the point of interest on scholars' inferred reports because the place to begin within the theory-building method. This emphasis at the meanings that items and occasions have for college students inside their experiential realities should be contrasted with techniques during which the target is to specify cognitive behaviors that yield an input-output fit with saw habit. it is very important notice that the time period 'experience' because it is utilized in those articles isn't constrained to actual or sensory-motor adventure. A perusal of the 1st 5 articles shows that it comprises reflective reports that contain reviewing earlier task and waiting for the result of power task. additionally, via emphasizing interplay and conversation, Voigt's contribution reminds us that non-public reports don't come up in a vacuum yet as a substitute have a social element. In taking a cognitive viewpoint, the 1st 5 contributions study the professional­ cesses in which scholars conceptually reorganize their experiential realities and therefore build more and more subtle mathematical methods of realizing. The conceptual buildings addressed by way of those theorists, ranging as they do from fractions to the elemental Theorem of Calculus, point out that experiential techniques to mathematical cognition are attainable in any respect degrees of mathematical improvement. even supposing the authors use diverse theoretical constructs, numerous extra commonalities should be discerned of their work.

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T: 1990, "Constructivism, phenomenology, and the origin of arithmetic skills", in L. P. Steffe and T. ), Transforming Children's Mathematics Education: International Perspectives, Lawrence Erlbaum Associates, Hillsdale, NJ, pp. 62-75. Papert, S: 1980, Mindstorms: Children, Computers, and Powerful Ideas, Basic Books, New York. : 1962, Play, Dreams and Imitation in Childhood (Translated by C. Gattegno and F. M. Hodgson), W. W. Norton & Company, New York. 29 134 LESLIE P. STEFFE AND HEIDE G. : 1980, ''The psychogenesis of knowledge and its epistemological significance", in M.

1981, "An attentional model for the conceptual construction of units and number". Journal for Research in Mathematics Education 12(2), 83-94. : 1983, "Learning as constructive activity", in J. C. Bergeron and N. ), Proceedings of the Fifth Annual Meeting of PME-NA, Universite de Montreal, Montreal, Canada, pp. 41-63. : 1989, "Constructivism in education", in T. Husen and N. ), The International Encyclopedia of Education, Pergamon Press, Oxford, pp. 162163. A. 30 JERE CONFREY AND ERICK SMITH EXPONENTIAL FUNCTIONS, RATES OF CHANGE, AND THE MULTIPLICATIVE UNIT ABSTRAcr.

Perhaps because of its common use, percent has developed several context-specific idiosyncrasies, especially when used as a unit in a rate relationship. ' We would answer that percent is a multiplicative unit. 5. Magnification. Although magnification as a multiplicative unit is similar to proportion/similarity, magnification is generally used to indicate segmentation relative to different perspectives on the same object whereas proportional similarity is used to indicate a relationship between separate objects, such as the chambers of a nautilus, or of changes in a single object over time (see Fig.

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