讨论了日常生活中的数学证明。
This paper discusses the mathematical proofs in everyday life.
中学是一个重要的年龄段，因为学生有足够的数学能力来解决高级问题，但他们还没有真正决定他们在生活中想做些什么。
Middle school is an important age because students have enough math capability to solve advanced problems, but they haven't really decided what they want to do with their lives.
20 - 21《CognitioninPractice：Mind,Mathematics,andCulture inEveryday Life》在实践中认知：心智、数学和日常生活的文化是关于这个观点的一本有趣的参考书。
(p. 20-21) the book Cognition in Practice: Mind, Mathematics, and Culture in Everyday Life is an interesting reference for this viewpoint.
不像数学，在科学里我们不能有绝对的肯定。但是在日常生活中，我肯定不会担心手机会给我的健康带来什么威胁。
In science, unlike math, we can't have absolute certainty, but in the scheme of things, this is not a health risk I would be concerned about at all.
从一个通过编程说出“数学课很难”的芭比娃娃到一个能够分析句子语法但拒绝回答“四分之三的一半是多少”的首相，数学恐惧症在生活中处处可见。
From Barbie dolls programmed to say "math class is tough" to ministers of state who will parse and analyse a sentence but refuse to answer "what's half of three-quarters?", maths-phobia is everywhere.
在后来的生活中我才意识到从数学、科学和逻辑问题上归纳出这种态度并应用于日常生活是如此的有用。
It was only later in life that I realized how helpful it is to generalize this attitude beyond math, science, and logic problems and into the realm of practical daily existence.
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.
我们将看到这个悖论在实际生活中的重要性，“Charles Doering博士说。”Charles Doering博士是密歇根大学的数学家。
"The importance of the paradox in real life remains to be seen," said Dr. Charles Doering, a mathematician at the University of Michigan, who is familiar with the research.
父母可将数学融入在生活中，随时教导幼儿认识电话、电梯或月历上的数字，幼儿对数字就能更加了解。
Parents can incorporate mathematics into daily life by teaching their child to recognize numbers on the telephone, in the elevator or on a calendar for more practical and concrete understanding.
数学在我们的日常生活中是不可避免的。
评论家们说上海数学的教学模式已经变成一种“应试教育”，学生们只会在考试中拿高分，但是他们对数学知识在实际生活的应用能力还是比较欠缺的。
Critics say Shanghai maths becomes a kind of 'teaching to the test', meaning pupils do well in exams, but are not prepared to adapt their knowledge to everyday situations.
就数学规律能涉及现实生活中而言，他们是不确定的，就他们的确定性来说，他们就不能涉及到现实生活中。
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.
在城市生活垃圾系统决策中，常常需要确定合适的目标或规划，而模糊数学决策法是有效的定性方法之一。
Suitable objective or a plan is often determined for systematic decision of urban domestic refuse, and fuzzy mathematics decision method is one of the effective qualitative methods.
数学在日常生活中是非常重要的。
从一个通过编程说出“数学课很难”的芭比娃娃到一个能够分析句子语法但拒绝回答“四分之三的一半是多少”的首相，数学恐惧症在生活中处处可见。
From Barbie dolls programmed to say "math class is tough" to ministers of state who will parse and analyse a sentence but refuse to answer "what's half of three-quarters?"
数学教学活动之外的调查研究，也多是渗透在幼儿园内其他各科教学、一日生活、游戏活动中的研究。
Investigation and research outside of the Mathematics teaching activities also mostly penetrate in the research of other subjects, daily life and games activities in kindergarten.
像大多数学龄前儿童一样，5岁的Sid喜欢观察研究日常生活中的现象和事件。
Like most preschoolers, 5-year-old Sid loves to observe and investigate objects and events that are part of daily life.
正是我的父亲最初激发了我对于数学的渴望，并且将我带进这个迷人的世界。我也开始探索生活、精神和宇宙万物中的规则。
It was my father who initially inspired my aspiration in mathematics field and introduced me into this glamorous world and the search for order in life, mind and the universe.
数学作为一种思维工具，在各个学科领域和社会生活的各个方面中，发挥着越来越重要的作用。
Mathematics as a thinking tool play an increasingly important role in various disciplines and all aspects of social life.
数学作为一种思维工具，在各个学科领域和社会生活的各个方面中，发挥着越来越重要的作用。
Mathematics as a thinking tool play an increasingly important role in various disciplines and all aspects of social life.
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