優化學習的八五黃金定律

要學會新東西，非得失敗幾回不可。然而，失敗多少回纔算合適？亞利桑那大學牽頭組織研究，最近給出了一個精確答案。

Educators and educational scholars have long recognized that there is something of a “sweet spot” when it comes to learning. That is, we learn best when we are challenged to grasp something just outside the bounds of our existing knowledge. When a challenge is too simple, we don’t learn anything new; likewise, we don’t enhance our knowledge when a challenge is so difficult that we fail entirely or give up.
教育工作者與教育界學者早有共識：學習也講究“最佳擊球點”（高爾夫球、網球等運動中球杆或球拍上的最有效擊球點，也稱甜點或甜蜜區——本網注）。即在需要掌握剛好超出現有知識面的東西時，學習效果最佳。如果挑戰過於輕鬆，我們就學不到新東西；如果挑戰難度過高，我們完全應對不了乃至放棄應對，那就同樣無法拓寬知識面。

So where does the sweet spot lie? According to the new study, to be published in the journal Nature Communications, it’s when failure occurs 15% of the time. Put another way, it’s when the right answer is given 85% of the time.
那麼，“最佳擊球點”究竟在哪裏？《自然·通訊》將刊登的最新研究顯示，15%的失敗率是學習的最優難度。換句話說，能夠回答出來的部分應在挑戰中佔85%的比例。

“These ideas that were out there in the education field – that there is this ‘zone of proximal difficulty,’ in which you ought to be maximizing your learning – we’ve put that on a mathematical footing,” said UArizona assistant professor of psychology and cognitive science Robert Wilson, lead author of the study, titled “The Eighty Five Percent Rule for Optimal Learning.”
這篇研究論文題目爲《最優學習方法的八五定律》。論文第一作者、亞利桑那大學心理與認知科學助理教授羅伯特·威爾遜說：“教育界流行觀念認爲存在‘中等難度區’，在這一區間內學習，效率最高。我們用數學方法進行了驗證。”

Wilson and his collaborators at Brown University, the University of California, Los Angeles and Princeton came up with the so-called “85% Rule” after conducting a series of machine-learning experiments in which they taught computers simple tasks, such as classifying different patterns into one of two categories or classifying photographs of handwritten digits as odd versus even numbers, or low versus high numbers.
威爾遜與布朗大學、加利福尼亞大學洛杉磯分校、普林斯頓大學的研究人員合作做了一連串機器學習實驗，提出所謂的“八五定律”。他們教計算機完成一些簡單任務，例如，把不同的圖形分爲兩類，或者把手寫數字的照片按照數字的奇偶或大小加以分類。

The computers learned fastest in situations in which the difficulty was such that they responded with 85% accuracy.
當研究人員設計的難度讓計算機回答的準確率爲85%時，它們學得最快。

“If you have an error rate of 15% or accuracy of 85%, you are always maximizing your rate of learning in these two-choice tasks,” Wilson said.
威爾遜說：“在二選一這類任務中，錯誤率爲15%或者說準確率爲85%時，學習效率就總是達到最高。”

When researchers looked at previous studies of animal learning, they found that the 85% Rule held true in those instances as well, Wilson said.
威爾遜說，他們隨後考察了以往的動物學習研究，發現“八五定律”同樣適用。

When we think about how humans learn, the 85% Rule would mostly likely apply to perceptual learning, in which we gradually learn through experience and examples, Wilson said. Imagine, for instance,a radiologist learning to tell the difference between images of tumors and non-tumors.
威爾遜說，想想人類的學習特點，通常可能會適用八五定律的大概是知覺學習，它是依靠積累經驗和案例的逐步學習。例如，設想放射科醫生學習區分腫瘤影像與非腫瘤影像。

“You get better at figuring out there’s a tumor in an image over time, and you need experience and you need examples to get better,” Wilson said. “I can imagine giving easy examples and giving difficult examples and giving intermediate examples. If I give really easy examples, you get 100% right all the time and there’s nothing left to learn. If I give really hard examples, you’ll be 50% correct and still not learning anything new, whereas if I give you something in between, you can be at this sweet spot where you are getting the most information from each particular example.”
威爾遜說：“識別腫瘤影像是一件日積月累、越來越拿手的事情，需要經驗，也需要案例。設想有三類案例，分別是簡單案例、高難度案例和中等難度案例。假如案例非常簡單，你永遠全部答對，那就沒有什麼可學的。假如案例難度極高，你只答對一半，那同樣學不到新東西；但如果難度介於兩者之間，那你就會處於‘最佳擊球點’，從每一個案例中學到的東西最多。”

Since Wilson and his collaborators were looking only at simple tasks in which there was a clear correct and incorrect answer, Wilson won’t go so far as to say that students should aim for a B average in school. However, he does think there might be some lessons for education that are worth further exploration.
由於這次只是研究對錯分明的簡單任務，威爾遜並不就此認爲學生應以平均拿到“良”作爲學業目標。不過他確實認爲，這項研究對教育或有啓發，值得深入探討。

“If you are taking classes that are too easy and acing them all the time, then you probably aren’t getting as much out of a class as someone who’s struggling but managing to keep up,” he said. “The hope is we can expand this work and start to talk about more complicated forms of learning.”
他說：“如果課程內容過於簡單，你總能取得好成績，那麼你在這門課上的收穫多半反而不及學業吃力但勉強跟得上的學生。我們希望擴展這項工作，着手研究複雜一些的學習形式。”