Epistemic Limitations and Precise Estimates in Analog Magnitude Representation
Epistemic Limitations and Precise Estimates in Analog Magnitude Representation
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DOI：
10.1093/acprof:oso/9780190467630.003.0010
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发表时间：
2016-09
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影响因子：
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通讯作者：
Justin Halberda
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文献类型：
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作者：
Justin Halberda
本章重新理解了我们的模拟幅度表示的内容（例如，近似持续时间、距离、数量）。考虑了近似数字系统 (ANS)，它支持被广泛描述为模糊、有噪声且表示能力有限的数值表示。有人认为，这些特征很大程度上是基于误解——所谓的“噪音”和“模糊性”实际上是人们对价值估计的信心的重要认知信号。 ANS 不具有嘈杂或模糊的数字内容，而建议 ANS 具有受认知限制的极其精确的数字内容。对于其他模拟表示也会出现类似的考虑。本章讨论了对 ANS 表示的新理解如何重塑数字的可学习性问题以及儿童必须在数字领域完成的概念变化。
This chapter presents a re-understanding of the contents of our analog magnitude representations (e.g., approximate duration, distance, number). The approximate number system (ANS) is considered, which supports numerical representations that are widely described as fuzzy, noisy, and limited in their representational power. The contention is made that these characterizations are largely based on misunderstandings—that what has been called “noise” and “fuzziness” is actually an important epistemic signal of confidence in one’s estimate of the value. Rather than the ANS having noisy or fuzzy numerical content, it is suggested that the ANS has exquisitely precise numerical content that is subject to epistemic limitations. Similar considerations will arise for other analog representations. The chapter discusses how this new understanding of ANS representations recasts the learnability problem for number and the conceptual changes that children must accomplish in the number domain.