分析了数学知识系统应具有的四要素，指出了现行数学教科书对数学教育的一些片面影响。
Four elements which belong to system of mathematics knowledge are analyzed; some unilateral influences of mathematics teaching material which is using on mathematics education are pointed out.
数学知识系统有几种不同的组织结构：逻辑结构、认知结构、教材结构和教学结构，并且都有多种具体表现形式。
The knowledge system of mathematics has a few different kinds of structure, logic structure, cognitive structure, structure of teaching materials and teaching structure.
传统规范语言的劣势在于，它们是由拥有稳固数学知识的人员使用的，使用它来建模系统很困难。
The disadvantage of the traditional formal languages is that they are used by people who possess a solid mathematical knowledge, but they are difficult to use for a modeling system.
这篇文章主要研究局部坐标系统转换。这个问题涉及的数学知识非常简单，但是很复杂。
This part delves into the local coordinate system transformation. The mathematics of this problem are simple, but elaborate.
他和一个朋友利用数学知识开发了一个在赛马比赛中选拔冠军的识别系统，然后开始推销他们的“马童筛选器”的内部消息传单，但因为无许可证被迫关停。
He and a friend used math to develop a system for picking winners in horseracing and started selling their "Stable-Boy Selections" tip sheets until they were shut down for not having a license.
他和一个朋友利用数学知识开发了一个在赛马比赛中选拔冠军的识别系统，然后开始推销他们的“马童筛选器”的内部消息传单，但因为无许可证被迫关停。
He and a friend used math to develop a system for picking winners in horseracing and started selling their "Stable-Boy Selections" tip sheets until they were shut down for not having a license.
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