几个星期前，我请这个博客的读者给我寄来一些关于自我指导学习数学的故事。
Several weeks ago I invited readers of this blog to send me stories about the self-directed learning of math.
一个组织收集的信息显示，在巴基斯坦，五年级有一半的儿童不懂基础数学，也不会用他们的语言阅读故事。
Information gathered by an organization shows half of all Pakistani children in the 5th grade do not understand basic mathematics and cannot read a story in their language.
在（纪录片）开头，袁的三个孙女回忆了她们祖父的故事，并提到祖父最关心的是她们的英语和数学学习。
In the opening parts, Yuan's three granddaughters recalled stories about their grandfather and said that he mostly cared about their English and math studies.
然而，我的课题留下了多少秘密，这是很令人吃惊的：有多少数学故事仍然没有结果，或者读起来就像看密电译文一样。
It is striking, however, how much of my subject remains a mystery: how many mathematical stories are still without endings, or read like texts that have yet to be deciphered.
其中大部分的故事来自非学校教育的家长，根据他们的观察，描述孩子们学习数学的情形。
Most of the stories came from unschooling parents who described math learning that they observed in their kids.
巴特沃斯博士讲述了一名从出生便有数学障碍的年轻人查尔斯的故事。
Dr Butterworth tells the story of Charles, a young man with lifelong mathematical difficulties.
如此震动心灵的故事，解释了为什么这本薄薄的小书恰是对某些著作的一剂对症解药，因为多数学者研究档案后往往拿出令人望而却步的成果。
Such moving stories explain why this slim book is just the right antidote to the often daunting studies most scholars produce after working in the archives.
在《量子力学的奇妙故事》（戈瑟姆书籍，2010）一书中，Kakalios试图通过无障碍，几乎不涉及数学的方式解释这一科学上最复杂的课题，使读者能同时了解量子力学和它的贡献。
Kakalios sets out to tackle both tasks in The Amazing Story of Quantum Mechanics (Gotham Books, 2010), an accessible, mostly math-free treatment of one of the most complex topics in science.
数学论文和小说都是讲述一个故事以展显复杂的思想，但是数学论文只用小说词语和符号的一小部分数量就完成这件事。
Both a mathematics article and a novel are telling a story and developing complex ideas, but a math article does the job with a tiny fraction of the words and symbols of those used in a novel.
用故事的形式描述一个数学问题，是其他可以可以帮助孩子理解数学关系的方法。
Something else that can help children understand number relationships is to have a math problem described in the form of a story.
数独的故事开始于1783年，当时一名瑞士数学家里恩哈。优勒发明了“拉丁方块”。
Sudoku's story begins in 1783 when Leonhard Euler, a Swiss 11 mathematician, invented "Latin 12 Squares."
数学论文通常只讲述更大更长的故事中的一个片段。
A math article usually tells only a small piece of a much larger and longer story.
这个故事里的小男孩在学校成绩不好，无论是语文还是数学他都不擅长。
The story of the little boy doing well in school, whether he was not good at mathematics or languages.
这种故事性和隐喻性的教育，既可以运用于叙事性较强的语文、历史教育等方面，也适用于逻辑性较强的数学教育等方面。
The storical and metaphorical education can be applied to narrative subjects such as language and history education as well as logical ones such as maths education.
发生在我出生之前的这个故事，使我想起了我的母亲是多么的不平凡，并且她也是一位有天赋的数学家。
This story—which happened before I was born—reminds me how extraordinary my mother was, and isalsoa gifted mathematician.
发生在我出生之前的这个故事，使我想起了我的母亲是多么的不平凡，并且她也是一位有天赋的数学家。
This story—which happened before I was born—reminds me how extraordinary my mother was, and isalsoa gifted mathematician.
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