What Is Mathematical Proficiency and How Can It Be Assessed
What Is Mathematical Proficiency and How Can It Be Assessed
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什么是数学能力以及如何评估它
DOI：
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发表时间：
2007
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影响因子：
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通讯作者：
A. Schoenfeld
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作者：
A. Schoenfeld
我的重点是第一个问题，因为本书的其余部分主要讨论第二个问题。在本书的引言和第一章中，我指出了这样一个事实：“认知革命”（例如，参见[Gardner 1985]）对理解不同领域的主题产生了重大的重新概念化（另见[NRC 2000]）。从单纯强调知识发生了根本性的转变——学生知道什么？ ——重点关注学生知道什么以及可以用他们的知识做什么。这个想法并不是说知识不重要。显然，一个人知道的越多，使用该知识的潜力就越大。相反，我们的想法是，仅仅拥有知识是不够的；还需要更多的知识。能够在适当的情况下使用它是熟练程度的重要组成部分。数学之外的一些例子可以说明这一点。许多年前，外语教学主要集中在语法、词汇和读写能力上。法语、德语或西班牙语的学生学会了阅读这些语言的文学作品，但当他们访问法国、德国或西班牙时，他们发现自己无法用所学的语言进行有效的交流。同样，多年来以语法教学为重点的英语课程导致学生能够分析句子结构，但不一定能够熟练地以书面形式有效地表达自己。超过
My main emphasis is on the first question, because much of the rest of this volume addresses the second. In the introduction to this volume and in the first chapter, I pointed to the fact that the “cognitive revolution” (see [Gardner 1985], for instance) produced a significant reconceptualization of what it means to understand subject matter in different domains (see also [NRC 2000]). There was a fundamental shift from an exclusive emphasis on knowledge — what does the student know? — to a focus on what students know and can do with their knowledge. The idea was not that knowledge is unimportant. Clearly, the more one knows, the greater the potential for that knowledge to be used. Rather, the idea was that having the knowledge was not enough; being able to use it in the appropriate circumstances is an essential component of proficiency. Some examples outside of mathematics serve to make the point. Many years ago foreign language instruction focused largely on grammar, vocabulary, and literacy. Students of French, German, or Spanish learned to read literature in those languages — but when they visited France, Germany, or Spain, they found themselves unable to communicate effectively in the languages they had studied. Similarly, years of instruction in English classes that focused on grammar instruction resulted in students who could analyze sentence structure but who were not necessarily skilled at expressing themselves effectively in writing. Over the