中國家長給小孩講數學常犯的一個錯誤

翎燕 · 發表於 2009-3-12 11:02

一次我小孩做Beestar網上數學練習,一道很簡單的題卻丟了兩分. 仔細看后我認定是Beestar的答案不對.為了小孩這星期能上光榮榜, 我開始和Beestar 辯論. 那個題目大致是這樣的:

Casey』s family visited the Franklin Park Zoo. An 18-foot giraffe there was the tallest animal they saw. Casey was 4.5 feet tall. How many times taller was the giraffe than Casey?
四個選擇是: A. 3, B. 4, C. 5, and D. 6

顯然18除以4.5等於4, 長頸鹿是凱西的4 倍, 就是說長頸鹿比凱西高三倍. 我小孩照我以前講的這個道理選的是A(3倍). 但Beestar的標準答案卻是B(4倍).

在國內小學時, 區分"是多少倍"和"多多少倍"是反覆強調練習過的基本功. 長頸鹿的高度是凱西的4 倍, 就是長頸鹿比凱西高三倍. 如果說長頸鹿比凱西高四倍,那長頸鹿就得是凱西的五倍了(4.5*5=22.5 feet)... 我據此概念和邏輯向Beestar陳述, Beestar 一開始還耐心地解釋, 後來雙方越說越費勁,他們把我搞糊塗了, 我也似乎讓他們感到莫名其妙.

最後我明白了,這是中文和英文語言上的差別. 在英文里"是多少倍"和"多多少倍"竟然是一樣的,沒有區別!! 我至今對此感到奇怪和彆扭. 照此說法,如果我和你一樣高, 難道用英文可以說我比你高一倍嗎?實在是不符合邏輯. 我問過不少老中家長,都有同感.

但Beestar 的解釋是這樣的:

"Taller than" indicates height is the quantity of interest, and that the giraffe's height is greater. "The giraffe is 4 times taller than Casey" then becomes "The giraffe's height is four times Casey's height", i.e. H(g) = 4*H(c)...

In your reasoning, "taller than" implies that the quantity of interest is the subtractive difference, and not the ratio of the two heights.

As with most utterances, the meaning is mostly determined by conventions among the target audience (educated speakers), and not pure logic (which is ambiguous in this case).
Your argument is considered wrong by most experts, though your explanation might be supported by a small percentage of linguistic preivists and pedants.

不管我對此解釋能否接受,我必需接受一個現實,上面這道題只有選B(4倍)才得分. 在美國中小學數學考試中都會如此.所以自己輔導小孩數學的中國家長要當心,別不小心給孩子灌輸了錯誤的概念. 我後來發現這個問題僅限於中國家長. 那些只在美國學校學習的學生從不知道有這回事. 我問過一個父母從不管的ABC高中生, 她覺得我的問題很weird and funny.

雖然我小孩那次沒上光榮榜,發現這個問題也算是收穫不小.