About three years ago, I became the national coach of the United States International Math
I was very happy for a day thinking this is very interesting.
But the next day I started to think that maybe I should do something with this.
And I decided that I wanted to focus not only on training an elite group of students but
trying to do as much as I could to boost the baseline mathematics capability in this entire country.
不幸的是 我没有钱 没有人际关系 只有我自己一人
Unfortunately I had no money, no connections and only one person.
确实 我知道的只有数学 算法概论和网络理论
So the only thing I knew was mathematics, algorithms and this probability and network theory.
So after thinking for some time I actually came to an idea which was based on using these
core mathematical areas that I’d been working with to actually build a solution for education
that could be delivered for free on every smart phone.
This is actually the project I’m working on right now called Expii.
Our principle is that actually you could turn that smart phone into a virtual tutor which
automates what a person would get if they hired a tutor.
It wouldn’t be as good as a tutor, but it could get very close.
And if you could deliver a free almost tutor on every smart phone in the United States
你可能会解决掉平等问题 甚至你可能会让每个人 甚至那些生活在
you might solve equity problems, you might be able to allow everyone, even if they live
in a different ZIP Code, to be able to access this tutor, which previously had only been
accessible to people who are quite wealthy.
因为现在聘请一个家庭教师的费用是每小时30美元 20美元 50美元
Because today the cost of a tutor is in the $30 an hour, $20 an hour, $50 an hour depending
on how you look at it.
If you can reduce that to zero dollars an hour you would actually open up this accessibility to everyone.
If we realize that what we’re trying to build is this virtual tutor then you actually, again,
can start to conceptualize. Well，knowledge happens to be all of these concepts linked
together in this network.
那么问题来了 如果你有这个网络 你如何数学化地分析
Then the problem becomes if you have this network how do you mathematically analyze
where a person should go next?
这个问题可以被解决 通过使用概率论和统计学 来找到新的方法去测量
That can be done by using probability and statistics to find new ways to measure how
much each person understands about each concept.
Statistics, because the way that one would measure this is by asking them questions.
The experience someone has is they indicate what they want to learn and then the system
starts to pitch questions at them, questions that they would need to know how to answer
in order to understand what they claim they want to understand.
随着相同问题出现次数的增加 基于人们对问题的回复 这个系统会调整问题的难度
As the questions come, based on people’s responses to the questions, the system adjusts the difficulty
of the questions and where the next questions come from in the same way that a human tutor
adjusts their line of questioning based on whether a person is successful or not successful
at the previous question.
If the student reaches a point where they are hopelessly confused, meaning they don’t
know how to do this question at all, then the system suggests that maybe they could
read some explanations.
As you can see it turns the lesson flow upside down.
这不是先课堂 接着作业 然后考试首先
It’s not that the class comes first and then the homework and then the exam, the first
来临的事情基本上是考试 然后是实践问题 这会适应你的自身情况
thing that comes is the exam essentially, followed by these practice problems, which adapt to
you, followed by the class for anything that you don’t know.
The idea is that this should cure boredom at the high end and also cure confusion at
the struggling end.
I actually started this with a brilliant Carnegie Mellon undergraduate student and then the
two of us built this system together.
But when you start with no resources you need to think of ways to actually generate all
of this content in a way which doesn’t cost enormous amount of resources.
And we took inspiration from Wikipedia.
Our system aggregates all of the questions and explanations that anyone in the world
might want to contribute, uses voting like a website called Quora in order to find out
什么内容是充实的 使用统计学 算法来弄清楚问题
which content is strong, and uses statistics, the algorithms, to figure out what questions
are easy and difficult.
所以 实际上它最终涵盖了所有的内容 变成了现在这个样子
So actually in the end it turns out that it sucks in all of this content, it licenses
it all with the creative commons license like Wikipedia and then puts it all across on a
platform that anyone with a smart phone can use.
So as we keep developing these mathematics and algorithms, our goal is actually to deliver
free education to all of the world using a system that self-organizes in the same way
that mathematics self-organizes from its basic assumptions.