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You need training in the symbols and in the manipulation of those symbols to work out mathematical problems.
你需要對這些符號以及運用這些符號解開數學難題的訓練。
Even something as basic as counting has to be taught. Formal mathematics is not something that little children can do naturally.
即使簡單如數數這樣的事情都必須被教授。形式數學不是小孩子天生就能做的事情。
And it wasn’t even part of human culture until a few thousand years ago.
直到幾千年前，它甚至都不是人類文化中的一部分。
Well, it might be interesting to ask the question: are these two abilities linked somehow?
提出下面這個問題也許很有趣：這兩種能力在某種程度上有聯系嗎？
Are people who are good at approximating numbers also proficient in formal mathematics?
擅長近似數字的人也會精通形式數學嗎？
So, to find out, researchers created an experiment designed to test ANS in 14-year-olds.
于是為了弄清真相，研究人員創造了一個設計用來測試14歲孩子的ANS的實驗。
They had these teenagers sit in front of a computer screen. They then flash a series of slides in front of them.
他們讓這些青少年坐在一個電腦屏幕前，然后在他們面前快速放映了一系列圖片。
Now, these slides had varying numbers of yellow and blue dots on them.
這些圖片上有不同數量的黃色和藍色圓點。
One slide might have more blue dots than yellow dots, let’s say...six yellow dots and nine blue dots.
一張圖片上的藍點也許比黃點多，比如有6個黃點，9個藍點。
The next slide might have more yellow dots than blue dots. The slide would flash just for a fraction of a second.
下一張圖片上也許黃點比藍點多。這些圖片會在零點幾秒內閃過。
So you know, there was no time to count the dots. And then the subjects would press a button to indicate whether they thought there were more blue dots or yellow dots.
所以沒有時間可以數這些圓點。然后這些實驗對象會按一個按鈕表明他們認為圖片上的藍點更多還是黃點更多。
