愉快學習的迷思

近年常強調愉快學習，以致很多人都認為這是最理想的學習模式。當然，學習得愉快固然是好，但只顧愉快而忘記了學習有時也須刻苦的話，就只會一事無成。為甚麼現代的人這麼容易忘掉前人的傳統智慧：刻苦是成功的必經階段。

美國新近的教授數學方法 New Constructivist Math Program，受到強烈反對就是一個好例子。

http://www.lit.net/orschools/everydaymath2.htm

其中我最認同的引述如下：

The Department of Education arrived at these programs at the recommendation of an ‘Expert Panel’ consisted of ......, and a list of public school officials and some education-related companies. Not a single active research mathematician or scientist was included in the panel. The panel's ‘expert opinion’ is not shared by the mainstream practicing mathematicians and scientists.

After this endorsement, university research and academic mathematicians became very concerned about the impact of its watered down approach toward teaching math on students’ ability to do math and science when they enter college. The concern was led by ... {a long list of math Professors in the top Universities in US} ... This resulted in an open letter led by them addressed to Secretary Riley, U.S. Secretary of Education in 2000, and supported by 200 top mathematicians and scientists, including four Nobel laureates, and two Field Medalists (the top honor in the field of mathematics).

A new pedagogy for teaching the new curriculum has emerged and according to Professor Wu of UC/Berkeley, the main features of the new teaching approach are:

1. An over-reliance on the so-called constructivist educational strategies (kids come up with the principals themselves by trial-and-error)
2. Misuse of technology (using calculators most of the time)
3. De-emphasis of drills and the role of memory in some texts (such as emphasis on not having to memorize the multiplication table)
4. An over-emphasis on the ‘fun’ component of learning without mentioning hard work.

The bottom line of the new approach is that 2000 years of mathematical discovery are to be abandoned in favor of self discovery through trial and error and observations made based upon a few simple concrete examples. No general principals are derived, proved and extrapolated. Several key skills are not learned. The devastating effects of not covering some key mathematical concept and skills are not apparent until the students enter college and pursue a science or engineering related curriculum where concepts and skills learned in grade schools become the back bone of the skills needed to do further work.

Originally, the emergence and adoption of the new math teaching was an attempt to bridge the gap between higher achieving students and minority students. The goal was very noble and ambitious. The program was aimed at the lower achieving population with the goal of reducing their math phobia. The new Constructivist math curriculum has been adopted in several school districts, and is gaining popularity, especially after the NSF expert panel identified the mentioned ‘exemplary’ programs. If they are so lacking in rigor why are they so popular? I believe part of the reason lies in the feedback from the teachers, students and parents themselves. First, students regard the hands-on activities ‘fun’. Of course it is fun when you are learning not by ‘dull rote memorization’ and drills but by hands-on manipulations, and ‘discovery’. Parents like it because they see how much their kids start to enjoy math lessons! The approach taken by the new curriculum is also ‘politically correct’ in that it emphasizes using real-world problems, which has been the main criticism of the traditional teaching of mathematics, in that many find it being irrelevant to the real world situations. The bottom line is that all these are fine and dandy, but the real evaluation criteria should be the students’ performance on standardized math tests, and their degree of preparation and success in taking math courses in a college environment. From two major studies this is not so.

我不是教育家，但我是一個十分喜愛數學，而且對數學是一個十分有觸覺的人。我認為用這種 New Math Program 教下一代肯定”死硬”！我相信所有精通數學的人都會認同我的講法，只有那些不懂數學的教育家才會支持這種 New Math Program。當然，若果背後的意識形態是要 no child left behind，我就無話可說。但必然的結果是 no child race ahead, 因為 every child left behind！

記憶在學習的過程中有其非常重要的地位。腦袋裡空空如也，甚麼資料也沒有，如何思考？分析力是透過把一些已知的事物，在心中不斷仔細思量鍛鍊出來的。

我們現在是站在巨人的肩頭上（Isaac Newton名句），不可能每一個人都花時間重新發現一切。當然，我們必須有敏銳的心靈去發掘萬事萬物的根本原理，和其中所要求的嚴謹思考模式，but in real life, deriving/operating everything from "first principle" is very inefficient and impractical.

問題是選擇甚麼去記，和怎樣才是最有效的記憶方法。九因歌當然要背！

我們不是要放棄愉快學習，但我認為愉快學習只是手段，作為幫助提起興趣，絕不應迷失本來的方向。學習的動力來自多方面，一個真正懂得學習的人絕對不會因為一時枯燥而放棄學習！

"Genius is one percent inspiration and ninety-nine percent perspiration."
- Thomas Alva Edison