教育王國

標題: 神級數學題　9成人都答錯！ [打印本頁]

作者: elbar 時間: 15-11-18 10:18 標題: 神級數學題　9成人都答錯！

撰文 : TOPick編輯

以下數學題，你可以解答嗎？

卡露蓮星期一看了28頁書，星期二再看了103頁，她星期二是否比星期一多讀了75頁書嗎？為什麼？

驟眼看，答案理應是「103-28=75」。

但如果你是這樣想的話，就絕對大錯特錯了！

早前有美國網民上載了一張照片至Facebook，小孩的答案正正是「103-28=75」，不過卻給老師打了一個大交叉，要扣一分。

為何答案被扣分？

原來這條題目是美國「共同核心課程」（Common Core States Standards Initiative）的題目，須採用「估算法」來計算。

按「估算法」來計算，需要把題目中的103及28，四捨五入為100及30，答案應該是「100－30＝70」，而非用準確的數值103及28來計算。

老師批改後指出正確答案應是70。相片來源：facebook

有家長再收到老師批改的功課後，將該題數學題拍照放上facebook，結果引起網民一片嘩然。

不少家長認為答案是「顛倒黑白」、「不合常理」、「非常荒謬」，又質疑「難倒要我的女兒寫下錯的答案嗎？」甚至將矛頭直指現行的教育制度，認為有必要進行改革。

不少家長認為答案非常荒謬。相片來源︰facebook

其實不止外國的小朋友功課考起家長，香港很多小學的功課同樣是神級題目。不知道這一條題目又能否考起各位香港家長呢？

作者: Spectra666 時間: 15-11-18 10:44

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作者: 小寶貝兒 時間: 15-11-18 11:35

其實我唔係好理解咩係美國既共同核心課程....... 有高手可以解在下疑惑嗎?

作者: cow 時間: 15-11-18 13:39

題目指明用estimation作答會較好.

作者: Spectra666 時間: 15-11-18 14:54

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作者: shadeslayer 時間: 15-11-18 15:10 標題: 回覆：神級數學題　9成人都答錯！

這題目關鍵係問句：

Is 75 a reasonable answer and why?

即係答案係一個 Yes or No，followed by an explanation. 如果要知準確答案，可以問 how many more pages did she read on Tue compared to Mon?

這題目如果學生答案係100-30=70 不加解釋，也是錯。所以唔係 round up or down, or how many significant figures 的問題。

Also "Reasonable" means vague, not precise.

This is a question to test students approximation but arithmetic calculation.

假設課堂有教 Approximation，我比較撐老師。

作者: Spectra666 時間: 15-11-18 15:46

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作者: shadeslayer 時間: 15-11-18 16:28 標題: 引用：+本帖最後由+Spectra666+於+15-11-18+15:51

原帖由 Spectra666 於 15-11-18 發表
本帖最後由 Spectra666 於 15-11-18 15:51 編輯

Well, it is clear to me the question "Is 75 a reasonable answer?" is a cue that the question is not testing arithmetics, it is testing approximation. The student answer clearly did not use approximation.

Of course if one interprets the question in a different way, then the answer is different.

作者: shadeslayer 時間: 15-11-18 16:39 標題: 引用：Quote:原帖由+Spectra666+於+15-11-18+發表

原帖由 shadeslayer 於 15-11-18 發表
Well, it is clear to me the question "Is 75 a reasonable answer?" is a cue that the question is not ...

Is the cue too subtle? Is the question poorly written? Probably.

作者: Spectra666 時間: 15-11-18 17:40

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作者: cow 時間: 15-11-18 18:38

應該係教緊estimation. 所以應該用estimation方法。
≈ 105 - 30
= 75

作者: shadeslayer 時間: 15-11-18 20:00 標題: 引用：Quote:shadeslayer+發表於+15-11-18+16:28+

原帖由 Spectra666 於 15-11-18 發表
Not really.
我們不清楚這條數是給那一年級的學生，但從撰文者所描述「小孩的答案正正...」，及那手寫答案 ...

The key question is:

"Is 75 a reasonable answer?" sufficient cue for students to take the question as a approximation question?

Your answer is No, it is not cue for an approximation question. It should be taken as a arithmetic question.

My answer is May be sufficient, but is definitely subtle.

Perhaps our difference is not that great.

作者: Spectra666 時間: 15-11-18 20:31

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作者: Spectra666 時間: 15-11-18 20:35

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作者: shadeslayer 時間: 15-11-18 20:57 標題: 引用：Quote:shadeslayer+發表於+15-11-18+20:00+

原帖由 Spectra666 於 15-11-18 發表
我左睇右睇都冇法理解
"Is 75 a reasonable answer?" 是任何cue for students to take the question as a a ...

我地都係中文人，對英文了解有分別好正常。

作者: cocokan2004 時間: 15-11-19 00:33

本帖最後由 cocokan2004 於 15-11-19 00:38 編輯

"reasonable" = 合理, " 只要解釋得"合理",就可以係GOOD ANSWER. 75點可能唔合理呀? ESTIMATE 既技能好易明, 考來都多鬼如. 又其HK人, 去一次旅行用幾銀, 飲一餐喜酒洗幾錢. 星期日全家出動玩一日要幾錢, 即刻ESTIMATE到啦. 如真的玩ESTIMATE又真係淺到難易接受.

作者: Cheeselover 時間: 15-11-19 07:44 標題: 引用：+本帖最後由+cocokan2004+於+15-11-19+00:3

原帖由 cocokan2004 於 15-11-19 發表
本帖最後由 cocokan2004 於 15-11-19 00:38 編輯

"reasonable" = 合理, " 只要解釋得"合理",就可以係 ...

I can say that again. Reasonable means sound judgement, based on good sense or able to reason logically. The question asks student whether 78 pages more than last day is reasonable or not. Let's look another question, 8 - 5. 3, >0 or

作者: Yanamami 時間: 15-11-19 08:49

死！我以為Carol係Tue讀左103頁，即Mon+Tue共讀了131添……

作者: shadeslayer 時間: 15-11-19 09:51 標題: 引用：Quote:原帖由+cocokan2004+於+15-11-19+發

原帖由 Cheeselover 於 15-11-19 發表
I can say that again. Reasonable means sound judgement, based on good sense or able to reason logica ...

But the trouble is more than the interpretation and meaning of "reasonable", the western dads and mums also felt that the question is somewhat misleading or wrong.

作者: 1234ats 時間: 15-11-19 09:51

The question asks for a reasonable answer.

75 is not only a reasonable but also an absolute correct answer.
And "because 103-28=75" is factually correct thus is a valid explanation.

There is no way that the student's answer is wrong.

If the teacher wants to test the concept of estimation, the question should be "reasonable estimate" instead of "reasonable answer".

Even if the question asks for reasonable estimate, the teacher's explanation is incomplete as the round off precision is not stated.

round off to the nearest integer: 103-28=75
round off to the nearest even number: 104-28=76
round off to the nearest multiple of 5: 105-30=75
round off to the nearest multiple of 10: 100-30=70
round off to the nearest multiple of 100: 100-0=100
round off to the nearest multiple of 1000: 0-0=0
..............

作者: shadeslayer 時間: 15-11-19 09:55 標題: 引用：The+question+asks+for+a+reasonable+answe

原帖由 1234ats 於 15-11-19 發表
The question asks for a reasonable answer.

75 is not only a reasonable but also an absolute correc ...

"Reasonable estimate" sounds better.

In estimation, the rounding off "is" not precise. And no need to be precise.

作者: 1234ats 時間: 15-11-19 10:07

shadeslayer
In estimation, the rounding off "is" not precise. And no need to be precise.
-----------------------------------------------------------------------------------------
I'm not sure about that. How about approximation? Does the rounding off for approximation has to be precise?

Just for the sake of argument, if rounding off for estimate can be arbitrary chosen then 103-28=75 should also be a correct estimate because it is based on rounding off to the nearest integer.

作者: Cheeselover 時間: 15-11-19 10:08 標題: 引用：Quote:原帖由+cocokan2004+於+15-11-19+發

原帖由 Cheeselover 於 15-11-19 發表
I can say that again. Reasonable means sound judgement, based on good sense or able to reason logica ...

Don't know why my message was lost in transmission. Whatever, 8 - 3, the answer could be 5, >0 or

作者: caa 時間: 15-11-19 10:12

This kind of questions obviously aim to trick the kids. Why can't the question be set as "Is 70 a reasonable answer?" I can't figure out what purpose the teacher wants to achieve thru this question other than to discourage the kids.

作者: shadeslayer 時間: 15-11-19 10:17 標題: 引用：shadeslayerIn+estimation,+the+rounding+o

原帖由 1234ats 於 15-11-19 發表
shadeslayer
In estimation, the rounding off "is" not precise. And no need to be precise.
----------- ...

I think the essence of approximation is rounding an awkward number to a number close enough to the original number but is much easier to handle arithmetics. There is no rule in terms of rounding to how many significant figures, or integer, or even numbers, etc. everybody may have slightly different views.

103 -> 100 easy to understand
106 -> ? For this I would still use 100. You may be different.

作者: cow 時間: 15-11-19 10:24

Dear Parent/Guardian,

Many times in real life, an exact answer is not needed and an estimate will do......The rules for “rounding” that you may have learned in school are
purposely not taught at this level [grade 2]......

for example, to estimate 84 – 39, you could think 84 – 40 = 44.

This subtraction is easy to do mentally because the second number (40) has been converted to the closest multiple of ten. Note that converting the first number to a multiple of 10 (80 – 39) does not make the subtraction easier.
http://www.nthurston.k12.wa.us/c ... in/1439/2_LH_M9.pdf

作者: cow 時間: 15-11-19 10:27

Using Compatible Numbers to Estimate Answers

Mathematicians sometimes estimate answers to addition and subtraction problems
by using compatible numbers. Compatible numbers are numbers that work
well together. If a pair of numbers is easy to add or subtract, those numbers are compatible. For example:

Tonio collects sports cards. He has 17 football cards and 26 baseball cards. About how many cards does he have in all? About how many more baseball than football cards does he have?
17 is close to 15
26 is close to 25
15 + 25 = 40, so he has about 40 cards in all.
25 – 15 = 10, so he has about 10 more baseball than football cards.
http://www.sw.wednet.edu/site/ha ... eName=EstAddSub.pdf

作者: shadeslayer 時間: 15-11-19 11:59 標題: 引用：Using+Compatible+Numbers+to+Estimate+Ans

原帖由 cow 於 15-11-19 發表
Using Compatible Numbers to Estimate Answers

Mathematicians sometimes estimate answers to addition ...

These references actually support what I said in my earlier posts.

作者: cocokan2004 時間: 15-11-19 18:45

如果全班90%小朋友都識答, 我5會話出題有問題囉. 如果大部份人都錯就係出錯問題或老師根本無教過ESTIMATION. 無講清楚佢直家唔想玩MATHS, 玩ESTIMATION.

你問我你有109元, 拿走12元. 我用0.1秒找到PRECISE答案. 但你話一定要用ESTIMATION, 我反而要用幾秒去ROUND UP. 條題簡單到ESTIMATE唔到. 玩得ESTIMATE, 應該係出一些題目是"找ESTIMATE 答案快過PRECISE答案".

作者: hkpapa852 時間: 15-11-20 16:41

本帖最後由 hkpapa852 於 15-11-20 17:12 編輯

cocokan2004 發表於 15-11-19 18:45
如果全班90%小朋友都識答, 我5會話出題有問題囉. 如果大部份人都錯就係出錯問題或老師根本無教過ESTIMATIO ...

如果話問緊"estimation"既答案, 但個"estimation"太準確而當錯, 根本就唔合理

Estimation係估計, 但估計都可以係準確, 所以答75一定唔可能話錯.

要話錯, 只能話個學生唔應該以calculation by exact figures既方式去解釋個答案.

作者: frederickw 時間: 15-11-21 14:27 標題: 引用：Quote:原帖由+Spectra666+於+15-11-18+發表

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作者: shadeslayer 時間: 15-11-21 16:02 標題: 引用：Quote:原帖由+shadeslayer+於+15-11-18+發

原帖由 frederickw 於 15-11-21 發表
有趣的是, 我完全唔明點解你覺得 there is a cue that the question is testing approximation.

剩睇條題 ...

As I said this is interpretation of English and English is not precise, especially by people like us, non native speakers. I had that feeling, you may not. I have given my reasons before and I am not going to repeat.

歡迎光臨教育王國 (/)