Multiple representations for Pattern Exploration with the Graphing Calculator and Manipulatives

Douglas A. Lapp

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Multiple representations for Pattern Exploration with the Graphing Calculator and Manipulatives

机译：使用图形计算器和操作符进行模式探索的多种表示形式

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To teach mathematics as a connected system of concepts, we must have a "shift in emphasis from a curriculum dominated by memorization of isolated facts and procedures and by proficiency with paper-and-pencil skills to one that emphasizes conceptual understandings, multiple representations and connections, mathematical modeling, and mathematical problem solving," according to the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989,125). Too often, educators spend time teaching skills. As a result, little time remains to concentrate on concepts that are essential to understanding mathematics. Students should not be forced to play with symbols on a piece of paper; rather, they should be allowed to play with ideas that lead to conceptual understanding. Manipulatives and technology encourage discovery. Later, some of the desirable skills can be addressed in a remarkably shorter time frame than traditional instruction usually requires (Heid 1992).

机译：要将数学作为一种相互联系的概念系统进行教学，我们必须“将重点从由记忆孤立的事实和程序以及精通纸笔技能为主的课程转变为强调概念理解，多重表示和联系的课程” ，数学建模和数学问题解决”，根据NCTM的《学校数学课程与评估标准》（1989,125）。教育者经常花时间教技能。结果，几乎没有时间集中精力于理解数学必不可少的概念。不应强迫学生在纸上玩符号；相反，应该允许他们玩弄导致概念理解的想法。操作和技术鼓励发现。后来，一些所需的技能可以在比传统教学通常所需的时间短得多的时间内解决（Heid 1992）。

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《Mathematics Teacher》 |1999年第2期|p.109-113|共5页
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Douglas A. Lapp;
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入库时间 2022-08-18 00:46:12

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Reviews: The Study of History: A Bibliographical Guide, the English Idea of History from Coleridge to Collingwood, the Changing Face of English Local History, Arthur and the English: The Arthurian Legend in Medieval English Life and Literature, Enacting Gender on the English Renaissance Stage, Shakespeare's Feminine Endings, Writing the English Republic: Poetry, Rhetoric and Politics 1627–1660, New Stories for Old: Biblical Patterns in the Novel, Catholicism and Anti-Catholicism in Early Modern English Texts, Primogeniture and Entail in England: A Survey of Their History and Representation in Literature, the English Civil War Through the Restoration in Fiction: An Annotated Bibliography, Diana, Self-Interest, and British National Identity, Dryden and the Traces of Classical Rome, between the Ancients and the Moderns: Baroque Culture in Restoration England, Bacchus in Romantic England: Writers and Drink, 1780–1830, Misogynous Economies: The Business of Literature in Eighteenth-Century Britain, the House of Forgery in Eighteenth-Century Britain, the Clothes That Wear Us, An Oxford Companion to the Romantic Age: British Culture, 1776–1832, Domestic Space: Reading the Nineteenth-Century Interior, Victorians in Theory: From Derrida to Browning, the Age of Virtue: British Culture from the Restoration to Romanticism, Woeful Afflictions: Disability and Sentimentality in Victorian America, Women Writers of the First World War: An Annotated Bibliography, the Pub in Literature, British Industrial Fictions, the Insatiability of Human Wants: Economics and Aesthetics in Market SocietyRichardsonR. C., The Study of History: A Bibliographical Guide , 2nd ed., Manchester University Press, 2000, pp. xiv + 140, £40.00.ParkerChristopher, The English Idea of History from Coleridge to Collingwood , Ashgate Publishing, 2000, pp. vii + 244, £45.RichardsonR. C. (ed.), The Changing Face of English Local History , Ashgate, 2000, pp. viii + 218, £45.00.BarronW. R. J. 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机译：可扩展表示的拓扑模式和数据流图的分析

Multiple representations for Pattern Exploration with the Graphing Calculator and Manipulatives

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