全部7亿人，我们连一个简单的数学现实。
All 7 billion of us are connected by a simple mathematical reality.
“数学现实”原则、“数学化”原则和“再创造”原则是弗赖登塔尔数学教学原则的核心。
The ideas of Virtual life of Math, Mathematization, and Recreation, are the core principals of the Math teaching and learning theory of Freudenthal.
全球经济也无法容忍美国劳动人口的读写、数学和科学能力越来越弱的现实。
Nor is the global economy forgiving of an American workforce with increasingly weak literacy, math and science abilities.
由四名学生组成的小组制作一个视频，说明一个数学问题及其在现实世界中的应用。
Teams of four students make a video illustrating a math problem and its real-world application.
但是每一位热衷于使用数学对现实世界建模的工程师都知道，模型只是模型。
But every engineer, enthusiastically using mathematical models of the real world, knows the model is just that, the model.
数学计算降临了，人类行为的现实却被人遗忘了。
Mathematicstakes over, and the reality of human action loses out.
由于头脑愚笨并遭现实物质世界打击，孤独症患儿的头脑常常更乐于接受数学、符号和代码等虚拟领域。
Clumsy and overwhelmed by the physical world, autistic minds are often far more comfortable with the virtual realms of maths, symbols and code.
数学计算降临了，人类行为的现实却被人遗忘了。
Mathematics takes over, and the reality of human action loses out.
在现实中，计算机科学家经常使用的数学，跟上面所列的数学仅有很小的重叠。
The math computer scientists use regularly, in real life, has very little overlap with the list above.
如果数学是对纯理念王国的感知的话，那么研究数学就需要让自己的大脑以某种方式抵达现实世界之外的某地。
If mathematics is the perception of this realm of pure ideas, then doing mathematics requires our brains to somehow reach beyond the physical world.
同事笑话他的观点，但狄拉克坚持己见：数学太和谐了，必然会反映在现实中。
His colleagues mocked the idea, but Dirac stuck to his guns: the maths was so harmonious that reality had to reflect it.
在这些例子中，类的对象与现实世界(或者至少是数学世界)中的一些实体都有显著的对应关系。
In each case there is an obvious correspondence between the object and some entity in the real world (or at least a mathematical world).
数学是研究现实生活中数量关系和空间形式的数学。
Mathematics is the study of quantitative relationship between real life and space form of math.
新里程不同教室有用在不同领域的学习，不同的重点：现实生活，感官，语言，数学，艺术，音乐，自然科学。
Classrooms are designed with different areas of learning, each with its own focus: practical life, sensorial, language, mathematics, geography, art, music, science, history and nature study.
弄清这些问题对于新课标下的数学教学改革具有重要的现实意义和参考价值。
Clarify it has important realistic meaning and reference value that these questions mark the reform in education of mathematics under to the new lesson.
其实，接受非学校教育的孩子即使没有经过正规的数学课训练，也很容易通过现实生活知识来培养其数学能力，或者很容易赶上那些接受正规培养的同龄人的数学水平。
Often unschoolers with no formal training in math acquire mathematics through real world applications or can catch up with formally instructed peers easily.
所以研究学习迁移的规律对实现我们的数学教学目标具有非常现实的意义。
Therefore the research study migration rule to achieve our mathematics teaching goal to have the extremely realistic significance.
看到这几句话还能勉强理解，这不就是当年数学家对麻子女友的一句“你脸上的小数点真可爱”的现实版本嘛。
"See these words can barely understand, this is not the mathematician to pockmarked girlfriend sentence" you face a decimal point is really cute "version of reality."
第二章，笔者从理论依据和现实意义两方面，论述了实施数学课堂活动教学的可行性和必要性。
Chapter two: From theoretical basis and practical significance, interpreted feasibility and necessity of mathematics classroom activity teaching.
现代精神疾病神经影像技术表明，只有可以通过影像扫描看到和数学化计算的现象才具有现实意义。
Modern psychiatric neuroimaging suggests that only phenomena that may be seen and mathematically computed throughout the scan are real.
旁白：人们相信这个完美的数学模型能够应用于不那么完美的现实世界。
NARRATOR: People believed this perfect mathematical model could be applied in a less-than-perfect world.
在现实中，计算机科学家经常使用的数学，跟上面所列的数学仅有很小的重叠。
The math computer scientists use regularly in real life has very little overlap with the list above.
数学思想是人脑对现实世界的空间形式和数量关系的本质的反映，是思维加工的产物。
Mathematical thought is the reflection of quantitative relations and spatial forms of reality in human brain, and it is the thought processing product.
数学并不会使人脱离现实世界，恰恰相反，数学牵引着现实，让人更加接近现实，让现实更加清晰。
Mathematics does not make people out of the real world, on the contrary, mathematics leads the reality, let people more close to reality, let the reality more clearly.
最后从工程角度提出了有现实意义的软件测试框架，并从数学上证明了该框架的有效性。
Finally the article puts forward software test frame with practical significance from engineering point of view, and gives a mathematical proof for.
数学法则只要与现实有关的，都是不确定的；若是确定的，都与现实无关。
As long as the laws of mathematics are related to reality, they are not certain; if it is determined, it has nothing to do with reality.
利用现代教学手段进行数学教学具有深刻的现实意义。
It is full of deep and realistic significance to conduct mathematics teaching making use of modern medium.
数学法则用在现实中是不确定的，确定的时候，又不能用于现实。
As far as the laws of mathematics refer to reality, they are not certain; as far as they are certain, they do not refer to reality.
数学法则用在现实中是不确定的，确定的时候，又不能用于现实。
As far as the laws of mathematics refer to reality, they are not certain; as far as they are certain, they do not refer to reality.
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