神級數學題 9成人都答錯！

elbar

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？

小寶貝兒

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?

cow

題目指明用estimation作答會較好.

shadeslayer

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。

shadeslayer

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.

shadeslayer

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.

cow

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

shadeslayer

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.

shadeslayer

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。

cocokan2004

"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.  

Cheeselover

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

Yanamami

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

shadeslayer

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.

1234ats

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
..............