請教數學問題

petline

lillymarie 發表於 12-12-9 08:43
有本書作者給予一些guidelines for effective algebra study, 以下是我覺得可以參考的幾點：

1。starting  ...

都係基本學習習慣姐。日做日清，緊密跟進。
但係用ahead schedule 呢一招真係可以令學生谷底反彈，先教一次令佢上堂易 d 聽得明，信心返左黎，學生士氣同正面動機會好好多，但家長/老師就要花多d功夫啦。

lillymarie

petline 發表於 12-12-9 09:05
都係基本學習習慣姐。日做日清，緊密跟進。
但係用ahead schedule 呢一招真係可以令學生谷底反彈，先教一 ...

我現在認為囝囝的問題，是他做數做得不夠，同時他學校教的又太淺。其實老師給他的題目，他說“10秒”就做完。有時解釋給他聽，他說明白，但做題時就喊不明白，因為不懂得用返他之前話明白的規則。
小朋友怕悶怕重覆，若 algebra 必需靠多做多練才能掌握得好， 這就是考家長的地方。

ANChan59

lillymarie 發表於 12-12-9 09:30
我現在認為囝囝的問題，是他做數做得不夠，同時他學校教的又太淺。其實老師給他的題目，他說“10秒”就做完 ...

有些小朋友做數是用"腦"做，好此電腦運作 - 不斷"Trial and Error"，然後出答案，快而準，不一定用我們傳統數學學習模式。低年級問題不大，到高年級較難找到他的出錯地方，就算成績優異都是隱憂，因為跳步驟都會被扣分。跟老師或CP商量如何處理。

laorenjia

所以拆完後面要寫負，好似新年派例是，屋(括號) 內每個細路 (數字) 都有一封。

I like your 派利是 method. However, you are more biased to "how" instead of "why". In a class of students, there are always one or two who are not only curious about "how" but also about "why". I was slow in mathematics (I gather I still am). I was always the last one in class to understand what the teacher taught, but I hated most was when the teacher told me that I did not need to know why yet. The beauty of maths is that with just a couple axioms, you can almost construct the whole mathematical palace youself step by step. Unlike other subjects such as chemistry or physics, there are nothing in primary and secondary school maths which cannot be traced back to those few axioms.

We learn distributive law in primary school; we learn operation of negative numbers in F1. With both, we can understand why the brackets are removed this way. Of course, we need your 派利是 method to remember the rule.

lillymarie

我大囝正正就是想知道why, 他說若不明白怎能記住？
不過，我們暫時把這問題放下，上網找到一本教algebra的免費書，由pre-algebra學起。

cstchan

lillymarie 發表於 12-12-7 20:07
和大囝計數，a - (b - c) = a - b + c.他不明白為何會是 “+ c"
我自己數學鈍只靠背書”負負得正“， 但囝 ...

試試跟孩子用以下情景來計算 10 - (2 + 1) 和 10 - 2 - 1︰

籃子內有10個橙。媽媽打算給哥哥2個橙、弟弟1個橙。

情況一︰媽媽先把2個給哥哥的橙和1個給弟弟的橙放在膠袋內才取走分給兩兄弟，所以籃內剩下 10 - (2 + 1) 個橙。

情況二︰媽媽先取2個橙直接給哥哥，然後再取1個直接交給弟弟，所以籃內剩下 10 - 2 - 1 個橙。

拆括號等於不用膠袋，所以括號內所有數值前的正負號都要倒轉。

其實在 a - (b - c) = a - b + c 中，不是單單由 -c 變 +c，還有 +b 變 -b！

cstchan

lillymarie 發表於 12-12-9 07:08
a(b - c) = ab - ac

我看書這似乎是一個規則（distributive rule），講了幾次，囝囝仍說不明白，但又講不出不明白甚麼。睇書話algebra要多做題目才能明白當中概念，所以接下來會讓囝囝多做algebra的題目。

至於乘法分配性質，可以考慮計長方形面積，先以 a(b + c) = ab + ac 較容易理解︰

ab + ac 是用來計算兩分別「長b闊a」和「長c闊a」的長方形面積總和。

因為兩個長方形有相同的闊，所以可以合成一個「長(b+c)闊a」的長方形，其面積可直接以 a(b + c)來計算。

laorenjia

cstchan 發表於 12-12-11 23:07
試試跟孩子用以下情景來計算 10 - (2 + 1) 和 10 - 2 - 1︰

籃子內有10個橙。媽媽打算給哥哥2個橙、弟弟1 ...

Your analogy works fine with 10 - (2 + 1). Can you think of one for a - (b - c) as well?

cstchan

laorenjia 發表於 12-12-12 17:34
Your analogy works fine with 10 - (2 + 1). Can you think of one for a - (b - c) as well?

Again, we can consider a basket with 10 oranges.

At first, mother would like to give 2 oranges to her son.  So she picks up 2 oranges and puts them into a plastic bag.  However, she changes the idea and would like to give 1 orange to her son.  So she takes out 1 orange and put it into the basket again.  The number of oranges in the basket will be 10 - (2 - 1) where (2 - 1) is the number of oranges in the plastic bag.

If there's no plastic bag, then mother will pick up 2 oranges to her son.  When she changes her mind, she will get back 1 from her son and put it back into the basket.  The number of oranges will be 10 - 2 + 1.

nadal

回復 laorenjia 的帖子

The proof is easy.

a - (b -c)
= a + c - (b - c + c)                 (effectively this is just moving both numbers along the number line)
= a + c - (b - 0)
= a + c - b

Done.

cellon

interesting...

lillymarie

原帖由 Annie123 於 12-12-13 發表
負負得正 is a rule that students learn when they learn multiplication of negative numbers.
And this ...

the maths his school taught was super simple, hasn't taught multiplication or division of negative numbers yet. In fact, he is probably a year ahead of his school.

The number line concept is good enough for him.

Now we focus on pre-algebra first, just to make sure he won't miss any important concepts.

lillymarie

原帖由 cstchan 於 12-12-11 發表
本帖最後由 cstchan 於 12-12-11 23:15 編輯

this is good, I'll try it when we come across the problem again.

lillymarie

原帖由 cstchan 於 12-12-11 發表
本帖最後由 cstchan 於 12-12-11 23:15 編輯

I'll try this one too.

sell2japan

petline 發表於 12-12-9 09:00
work定係唔work，係要睇學生feedback，唔係口講，不如等結果說話吧。

我教了十幾年數，只知道 algebra 要 ...

「靠模仿同慣性去做」的確如此

1234ats

楼主提出的问题已有很多网友提供不同的解释方法。

但我觉得这些很基本的数学观念问题应该在学校里解决，而不应留给家长或补习社解释。为何学生遇到不明白时不发问？为何老师没有更好渠道了解学生是否真的明白？似乎大家都普遍接受由补习老师教导学生，那学校老师的角色又是什么？
我问过一些需要补习的学生为什么老师教完也不懂，几乎清一色的答案都是不明白老师讲什么，问也没用。

为何芬兰学生放学后不需要补习而我们家长却要花金钱精力做就这么多补习天王？

我不是埋怨谁，只是觉得我们今天的教育模式对一部分学生是非常无效和低效率的，教育界好应多思考这问题。

lillymarie

老師在課堂上只能照顧到大多數學生的進度。要拔尖補底就靠自己了。