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播放视频

美国奥林匹克教练的独特数学教学法

This U.S. Olympiad Coach Has a Unique Approach to Math

I think that the biggest problem with math is a branding issue
我认为数学最难的是人们给它的“标签”
where people think that math is rote, boring and about memorization.
人们认为数学枯燥无味 需要死记硬背 还得记性好
If you ask me what math is,
你要是问我什么是数学
I’ll say math is actually the distilled heart of thinking.
我会说数学实际上是思考时提炼出的核心
It’s logic.
它是逻辑
It’s thinking about ways that if something was true, then something else is always true.
数学在思考“假定一件事为真 那另一件事也为真”这类的方法
And as you learn how to assemble these chains of logic,
当你学会如何连接逻辑链
you can use that skill for anything.
你就可以用这个技巧去解决任何事
So actually my real goal is to help build the world to be a more thinking place.
所以我真正的目的是帮助世界有更多的思考者
The man in front of the class is no ordinary math teacher. This is so good.
这位站在讲台上的老师不是普通的数学老师 “谢谢夸奖”
And the kids in the chairs are no ordinary students.
椅子上的孩子们也不普通
They are the U.S. team for the International Math Olympiad,
他们是国际数学奥林匹克竞赛的美国小组成员
the best high school math minds in the country.
是美国数学头脑最好的高中生
My angle as a coach
我呢 是一个教练 但我的目标
is actually a little bit different from what some people might expect.
实际和人们期待的有些许不同
I actually don’t optimize for whether or not the team will win
实际上 我为的并不是这个小组赢不赢得这场
in this particular competition that’s coming up.
即将到来的特别的竞赛
This is a conversation I actually had
这是我和美国数学协会
with the executive director of the Mathematical Association of America
执行董事的一次对话
when I was picked to take this role as a coach.
当我被提拔为教练时
The goal is to not only teach skills that could be useful in this contest,
我的目的不单单是教学生比赛中可能用到的技能
but to also show how the math that they’re working on could be used later to do other things,
还要展现出他们所学的数学可以在其他事情上也能用到
and also to talk about some of the other skills that one might need besides mathematics.
另外还要分享一些不仅限于数学学科用得到的技巧
The biggest difference between a math competition problem and a textbook problem
数学竞赛和书中习题的最大不同点在于
is that in the textbook problem
书上的习题
you’re supposed to already have been taught how to solve it.
是已经教过怎么去解的
That’s actually why it’s a textbook problem.
这就是书本习题
Whereas a math competition problem is specifically selected
而数学竞赛中的题是经过特殊筛选的
based on the ingenuity of the problem
基于技巧的题
and the hope that you won’t know how to solve it when you see it.
当你遇见这种题型时你不知道怎么解
And actually that’s why I think everybody benefits
这就是为什么我说每个人都能
from playing with math competition problems.
从数学竞赛题型中受益
They teach you how to invent new ways to think about challenges.
这些题会帮助你发现新的思考机会
and the kinds of challenges we face in this world today are not textbook problems.
所以现在我们面临的某些挑战并不是书本习题
Well, right now, we’re dealing with COVID.
现在 我们正与新冠作斗争
If that was a textbook problem, we’d be done by now.
假如它是书本习题 我们现在就可以解决它
And so the real purpose of everyone engaging in these math contest problems
所以你看 每个人参加数学竞赛的真实目标是
is so that people can get a chance to exercise that creative muscle
可以取得机会去锻炼创新“肌肉”
when it comes to creating analytical ideas.
尤其谈到创造性分析想法时
Honestly, the task of improving math education is hard.
说实话 完善数学教育这项任务很艰巨
I have the utmost respect for the people who are working on this all the time.
但我对这些正在为此而努力的人们抱有极大的期待
But if I could make a few suggestions,
但如果要我提供一些建议的话
I would actually suggest to focus on having people spend more time
我会建议人们花更多时间
thinking about how they might come up with an idea
思考如何想出好主意
on how to solve the problem.
以及怎么解决难题
As opposed to having students
而不是让学生们
be used to the idea that someone else is going to show them what to do,
习惯去用别人教过的方法
and then they’re just going to copy it.
不然他们只会照搬
That’s actually what I do in my own teaching.
我自己教学生时就沿用这个原则
I actually don’t want to show students what to do and have them copy.
我真的不愿意给学生示范怎么解决问题 并让他们照搬
I want to bring them along to help them also discover
我一直想带给他们的是帮他们发现
the reason why you should multiply those two numbers
为什么两个数要相加
is because of something that you came up with.
原因他们就自己去找
My favorite aspect of being a coach
成为一名教练 我最喜欢的一方面
is the opportunity to see people who are so much more talented than me
是有机会看到比我更有天赋的人
and to know that the future is bright.
还有就是未来可期
That gives me the optimism to keep carrying forward in life.
那真的是给了我乐观心态去期待生活

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视频概述

这位美国奥林匹克数学教练是怎样训练数学天才们的?数学的本质是什么?书本上的题与数学竞赛有什么区别?该怎样让人主动思考解决问题呢?

听录译者

杨麦丝

翻译译者

张查查

审核员

审核员ZIYU

视频来源

https://www.youtube.com/watch?v=MsskCxQ4sks

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