## [Editorial] Teaching Math, Singapore Style [NYT060918, A26]

**【社論】數學教學，新加坡風格（紐約時報06年9月18日, A26）**

那些在數學和自然科學教育方面勝過美國的國家具有一些共同點︰他們將公立學校學生該學甚麼和甚麼時候學納入了國家優先考慮中。他們也花費了大量精力來確保每間學校都擁有能夠明確達至國家教育目標的高水準教學。但由於地域差異，相比之下這些國家會存在一個非常之不穩定的標準和測試係統。我們也同樣不可幸免地會受到教學風尚的影響。

其中一個最為臭名昭著的風尚源於二十世紀八十年代晚期。當時許多學校背離了需要操練和解答的傳統數學教學模式，而這種有時被戲稱為〞模糊數學〞的方法，居然讓孩子們在甚至不學習基本乘除運算的情況下對問題進行任意猜想。這樣下來對高階數學的掌握是不可能了。這種新的數學教學方法如諺語所說地一樣，「見高不見遠」，自然引起了不少非議。

很多人將這一不幸事件歸咎於在一九八九年由一個權威機構－全美數學教師理事會－所作的一篇報告。學校團體將其中的建議認為是反對機械式學習的號召。而就在上個星期，這個理事會自我矛盾地推出了重視各年級基本知識學習的新建議。

根據這個新（也許該叫舊）計劃，學生們將需要再次通過基本知識的學習－加減乘除之類－以打好基礎為七年級的代數學習作準備。這一新的改進被看作是對像新加坡一樣的國際數學強國靠攏。

鑑於我們國家常年抗拒從國外引入更優的教學方法，參照新加坡的計劃令人期待。但是想咬這個改進成功得話我們還必須先做一些事情。

首先，美國有必要中止讓非專業人士來教授大多數數學和自然科學課程的悲慘狀況，或是讓這些人先認真地學一學。

我們也需要解決當前學術成果的標準和衡量湊合了事的情況，並確保每個地方的學生都可以同時得到高水平的老師和高質量的數學和自然科學課程，就像預期目標中的一樣。

只有免為其難地進行這些基本而又關鍵的改革，我們纔可以繼續在信息經濟時代的國際競爭中不輸給那些我們不得不面對的對手。

**[Editorial] Teaching Math, Singapore Style [NYT060918, A26]**

The countries that outperform the United States in math and science education have some things in common. They set national priorities for what public school children should learn and when. They also spend a lot of energy ensuring that every school has a high-quality curriculum that is harnessed to clearly articulated national goals. This country, by contrast, has a wildly uneven system of standards and test that varies from place to place. We are also notoriously susceptible to educational fads.

One of the most infamous fads took root in the late 1980’s, when many schools moved away from traditional mathematics instruction, which required drills and problem solving. The new system, sometimes derided as "fuzzy math," allowed children to wander through problems in a random way without ever learning basic multiplication or division. As a result, mastery of high-level math and science was unlikely. The new math curriculum was a mile wide and an inch deep, as the saying goes, touching on dozens of topics each year.

Many people trace this unfortunate development to a 1989 report by an influential group, the National Council of Teachers of Mathematics. School districts read its recommendations as a call to reject rote learning. Last week the council reversed itself, laying out new recommendations that will focus on a few basic skills at each grade level.

Under the new (old) plan, students will once again move through the basics – addition, subtraction, multiplication, division and so on – building the skills that are meant to prepare them for algebra by seventh grade. This new approach is being seen as an attempt to emulate countries like Singapore, which ranks at the top internationally in math.

All these references to Singapore are encouraging, given this country’s longstanding resistance to the idea of importing superior teaching strategies from abroad. But a few things need to happen before this approach can succeed.

First of all, the United States will need to abandon its destructive practice of having so many math and science courses taught by people who have not majored in the subjects – or even studied them seriously.

We also need to fix the current patchwork system of standards and measurement for academic achievement, and make sure that students everywhere have access to both high-quality teachers and high-quality math and science curriculums that aspire to clearly articulated goals.

Until we bite the bullet ton those basic, critical reforms, we will continune to lose ground to the countries with which we must compete in the global information economy.