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Multiple representations (mathematics education) : ウィキペディア英語版 | Multiple representations (mathematics education) Multiple representations are ways to symbolize, to describe and to refer to the same mathematical entity. They are used to understand, to develop, and to communicate different mathematical features of the same object or operation, as well as connections between different properties. Multiple representations include graphs and diagrams, tables and grids, formulas, symbols, words, gestures, software code, videos, concrete models, physical and virtual manipulatives, pictures, and sounds. Representations are thinking tools for doing mathematics. == Higher-order thinking == Use of multiple representations supports and requires tasks that involve decision-making and other problem-solving skills.〔S. Ainsworth, P. Bibby, and D. Wood, “Information technology and multiple representations: New opportunities – new problems,” Journal of Information Technology for Teacher Education 6, no. 1 (1997)〕〔B. Moseley and M. Brenner, Using Multiple Representations for Conceptual Change in Pre-algebra: A Comparison of Variable Usage with Graphic and Text Based Problems., 1997, http://eric.ed.gov/ERICWebPortal/contentdelivery/servlet/ERICServlet?accno=ED413184〕〔http://www.pictorialmath.com/updates_downloads/PresenterGuide.ppt〕 The choice of which representation to use, the task of making representations given other representations, and the understanding of how changes in one representation affect others are examples of such mathematically sophisticated activities. Estimation, another complex task, can strongly benefit from multiple representations 〔http://continuities.wordpress.com/2010/04/25/sharing-multiple-representations-of-systems〕 Curricula that support starting from conceptual understanding, then developing procedural fluency, for example, AIMS Foundation Activities,〔http://www.youtube.com/watch#!v=4c5SunC5Lbs〕 frequently use multiple representations. Supporting student use of multiple representations may lead to more open-ended problems, or at least accepting multiple methods of solutions and forms of answers. Project-based learning units, such as WebQuests, typically call for several representations.
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