Structuring Error and Experimental Variation as Distribution in the Fourth Grade
Structuring Error and Experimental Variation as Distribution in the Fourth Grade
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四年级的结构错误和实验变异的分布
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
Leona Schauble
中科院分区：
文献类型：
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作者：
A. Petrosino;R. Lehrer;Leona Schauble
人类似乎有一种天生的分类和概括倾向，这些活动对于我们理解世界至关重要（Medin，1989）。然而，无论如何描述物体和事件，它们的可变性至少与它们的相似性一样重要。在《欢乐满屋》中，斯蒂芬·杰伊·古尔德通过他选择的章节小标题“作为普遍现实的可变性”（1996 年，第 38 页）巧妙地阐明了这一点。 Gould (1996) 进一步指出，对自然系统进行建模需要考虑其可变性。现在大众媒体和专业媒体都广为人知的一个例子（例如，Weiner，1994）描述了随着环境在相对较短的时间内波动，喙形态上看似微小的变化如何导致不同种类加拉帕戈斯雀的比例发生巨大变化。了解生物体和物种内部以及之间的变异性是掌握“多样性”等大概念的核心（NRC，1996）。然而，由于其核心地位，学校教学中对可变性的重视程度很低。学生们几乎没有获得任何概念工具来推理变异性，即使有，这些工具充其量也只是初级的。通常，这些工具仅包含一些统计数据的简短介绍（例如，用于计算平均值或标准差），很少关注更全面的数据建模。也就是说，学生通常不会参与允许他们提出问题、考虑与问题相关的衡量标准和属性的质量，然后继续构建数据并对他们的问题进行推断的环境。数学思维和学习，5(2&3), 131–156 版权所有 © 2003，Lawrence Erlbaum Associates, Inc.
Humans appear to have an inborn propensity to classify and generalize, activities that are fundamental to our understanding of the world (Medin, 1989). Yet, however one describes objects and events, their variability is at least as important as their similarity. In Full House, Stephen Jay Gould neatly drove home this point with his choice of a chapter subhead: “Variability as Universal Reality” (1996, p. 38). Gould (1996) furthernotedthatmodelingnaturalsystemsoftenentailsaccountingfor theirvariability. An example now widely familiar from both the popular and professional press (e.g., Weiner, 1994) is the account of how seemingly tiny variations in beak morphology led to dramatic changes in the proportions of different kinds of Galapagos finches as the environment fluctuated over relatively brief periods of time. Understanding variability within and between organisms and species is at the core of grasping a big idea like “diversity” (NRC, 1996). Yet, given its centrality, variability is given very short shrift in school instruction. Students are given few, if any conceptual tools to reason about variability, and even if they are, the tools are rudimentary, at best. Typically, these tools consist only of brief exposure to a few statistics (e.g., for calculating the mean or standard deviation), with little focus on the more encompassing sweep of data modeling. That is, stusdents do not typically participate in contexts that allow them to develop questions, consider qualities of measures and attritubutes relevant to a question, and then go on to structure data and make inference about their questions. MATHEMATICAL THINKING AND LEARNING, 5(2&3), 131–156 Copyright © 2003, Lawrence Erlbaum Associates, Inc.