學生問栗，讀數學有甚麼用。她們認為，日常生活中，只要懂得加減法便成，為何中學課程要她們讀三角幾何，甚至微積分？
學生的問題，栗子妹想了很久，最後得出一個結論：數學科的內容或許不實用，但學科培養的解難態度，卻是人人終生受用的。
數學科的證明題目，培養學生的邏輯思維，讓他們明白，凡事要講理據，也要按步就班，不能一步登天。
數學題有難有易，易的計得輕鬆，難的卻吃力不討好，但是否計錯一次便放棄？在栗看來，數學題不過是人生難題的縮影。
解答數學題，往往有多個辦法，令栗想起「條條大路通羅馬」。發覺這個方法計不下去？不要緊，還有方法乙方法丙方法丁在等著呢！只要肯嘗試，總有成功的一天。
回到問題本身：為甚麼課程教授的東西，一定要有用？如果事事以實用行先，不如去讀工業學院，或是職業先修班吧！
Dull people will find most things not useful. Bright people, on the other hand, will find use for most things. My $0.02.
回覆刪除[版主回覆12/09/2009 20:18:00]Raymond: 這兩天我都在想，到底 dull people 跟 bright people 有甚麼差別呢？不是智力的差異，而是對人生的態度吧？我一直相信，就算再平平無奇的東西，只要肯花心思，也會發掘出趣味來的。
從前我都是討厭數學的一員，但因為不服輸，死讀爛讀，最終都讀出成績來，期間更發現計數的樂趣。可惜現在講求速食，新一代都沒我們那一代的能耐了...
關於一門學問是否有用，我認同堅的看法，那是要經過時間的洗禮才會曉得的。
(長氣了，請見諒 )
我想現在學生的思想較為"現實"做任何事講求有無用﹗其實數學課亦是鍛鍊人生不怕失敗勇於嘗試的精神，終身受用。可惜是他們看不出來﹗
回覆刪除[版主回覆12/09/2009 20:20:00]愚：我覺得另一位博客說得對，是大人的現實，影響了小孩的價值觀。他們看不出來屬正常，但身邊的大人，有沒有跟他們解釋呢？
I'm one of the dull ones, by Raymond's standards. I have to agree with your student. I think the most basic elementary geometry has some practical use. Trigonometry has no use unless you're wish to be an engineer. Calculus is useless, in my view. After the 4 basic binary operations, calculus gives you two more, to use solely for doing advanced maths and statistics. Elementary algebra, maybe up to some simple word problems, has some practical applications. Some basic statistics, like simple probability, and terminology like mean and median, perhaps standard deviation and correlation coefficient, may have some use in everyday life.
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I really see nothing useful in anything more advanced than the above.
[版主回覆12/09/2009 20:24:00]Teacher: I agree with you that most of the advanced math is of very little use in daily life. But I am still grateful that I have learnt something useless. The subject really improves my logical thinking.
BTW, have I told you that I hate statistics? I would rather do calculus than explaining central tendancy to my students ...
My friend once asked me why did we bother going to college and study. Bill Gates and many other richest people never graduated from college. It took me a while before I can answer him. If you look at a bell curve, some people will be very lucky and some will be very unlucky but for most of us that are in the middle, we need to prepare ourselves so when an opportunity present itself we can take advantage of it. You never know what you will need in life. The only truth is the more you know, the more you know you don't know. Some knowledge may not have any direct application but there are always indirect use for them. I noticed a lot of people are not able to see the similarity in different field and area and therefore can't apply the knowledge that they already have. 吾識變通 If an elevator first stop is the 8th floor and you are going to the 6th, most people will just walk up but isn't it better to walk down from the 8th floor? Sorry for the winded reply.
回覆刪除[版主回覆12/09/2009 20:31:00]堅: Thank you for your sharing 至真呀!
I really like your point about preparing ourselves for upcoming opportunities. People today are too realistic. They only want to grab the benefits in front of their eyes.
On 吾識變通, I guess you must have known some bookworms like me ? There are so many smart people in the workplace that only few people cannot adapt themselves to the changing environment. (我咁蠢都識喎, 其他人又點會唔識？ )
學生之所以「現實」，不就是因為大人現實﹖
回覆刪除[版主回覆12/09/2009 20:33:00]對。想起來也不能怪學生，因為自己都係超現實的人...
中西史所學內容多數人做嘢用不上(我例外). 但係咪無學習價值?
回覆刪除[版主回覆12/09/2009 20:37:00]這點提得好 ！讀中學的時候，只知道自己不討厭讀歷史，但就沒發覺學習歷史的重要性。希望現在知道不算太遲
Whoa, I didn't know my comment comes across as so judgemental. It's supposed to be just a smart-ass quip. Teacher, I largely agree with you what constitute "useful math", assuming one's not a specialist of course.
回覆刪除堅 , I think Bill Gates is a special case. He's so brilliant that staying in college were just going to waste his time!
回覆刪除Raymond, you are anything but judgemental. I was just rolling with your quip
回覆刪除正確和積極的態度才是最重要的。
回覆刪除[版主回覆12/09/2009 20:38:00]說的是，但若然大人事事都以實用為先，試問小朋友又點可能會培養到正確和積極的態度呢？
Central tendency? You mean the Central Limit Theorem?
回覆刪除As I get older, I find even things like philosophy, sociology, and history are interesting. When I was in college, these were the electives that we had to take and most of us thought they were a waste of time. Who is going to use them? It is not important as F=ma. I also notice human has only one point of view and that is their own. We often project ourselves on to other. Most of mine friends are Engineers and we think in a certain way we thought that is the only logical way and everyone should think that way because we all did. It turns out it was only because my universe was too small. After I got into Fashion Design, the people are totally different. What make sense to me don't make any sense to them. Their train of thought is different. That is why we can have so much debate on everything from global warming to what is best for our children.
回覆刪除[版主回覆12/13/2009 07:14:00]堅：I have similar experience too. I only thought history was an interesting subject but I didn't realize the importance of it. (However, I never think of F=ma as important.)
I once wanted to be a fashion designer, but I knew that I did't have what it takes, so I gave up and focused on translation.
On different train of thought, my 六婆 is a designer, and we makes a lot of 雞同鴨講 scenes.
堅 , I have similar experience too as I got older. Science and engineering give us skills to make life more comfortable, but philosophy and sociology give us opportunity to become better people, to know what's the right thing to do. Both sides are very important, hence the importance of a broad and balanced education.
回覆刪除[版主回覆12/13/2009 07:16:00]插句嘴：從前學府還會說全人教育，現在全都要培養未來英才，沒空理會閣下的人格是否健全了
After being an Engineer and Fashion Designer, I think science is much more creative. Science make dream comes true. Anything you can dream of is possible there is no limit at all!. Initially, I thought physical law must be obey we can't over come gravity. And there should be no limit in Fashion, who is to say what is good or bad? Maybe in haute couture or junior and anything else is dictated by sales and no one have the gut to break out the box. Look at the advance in genetic, medicine, hand held device, and knowledge of the universe so many things that were someone's wild dream and they are coming true and helping us advance as a species.
回覆刪除[版主回覆12/20/2009 08:21:00]You're right about the dream comes true thing, 堅. The advance in genetic and medicine is really impressive.
I believe everything has its constraints, and the ultimate one is money! In HK, it is said that 'no money, no talk', and it's true.
If you have a great idea, you can get a lot of money. Look at Yahoo and then Google! The amount of money that Google is making is beyond anyone's dream... The next great idea could be in genetic, battery technology, and many other. I think there is a sense of freedom of the mind that the West still has an advantage over the East. American was always a dreamer without any constraints. A sense of any constraints can be overcome and not letting it block your imagination. Don't just ask why but also why not. I think the advantage came from without culture and tradition.
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