中国家长给小孩讲数学常犯的一个错误

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中国家长给小孩讲数学常犯的一个错误
一次我小孩做Beestar网上数学练习,一道很简单的题却丢了两分. 仔细看后我认定是Beestar的答案不对.为了小孩这星期能上光荣榜, 我开始和Beestar 辩论. 那个题目大致是这样的:

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?
四个选择是: A. 3, B. 4, C. 5, and D. 6

显然18除以4.5等于4, 长颈鹿是凯西的4 倍, 就是说长颈鹿比凯西高三倍. 我小孩照我以前讲的这个道理选的是A(3倍). 但Beestar的标准答案却是B(4倍).

在国内小学时, 区分"是多少倍"和"多多少倍"是反复强调练习过的基本功. 长颈鹿的高度是凯西的4 倍, 就是长颈鹿比凯西高三倍. 如果说长颈鹿比凯西高四倍,那长颈鹿就得是凯西的五倍了(4.5*5=22.5 feet)... 我据此概念和逻辑向Beestar陈述, Beestar 一开始还耐心地解释, 后来双方越说越费劲,他们把我搞糊涂了, 我也似乎让他们感到莫名其妙.

最后我明白了,这是中文和英文语言上的差别. 在英文里"是多少倍"和"多多少倍"竟然是一样的,没有区别!! 我至今对此感到奇怪和别扭. 照此说法,如果我和你一样高, 难道用英文可以说我比你高一倍吗?实在是不符合逻辑. 我问过不少老中家长,都有同感.

但Beestar 的解释是这样的:

"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.

不管我对此解释能否接受,我必需接受一个现实,上面这道题只有选B(4倍)才得分. 在美国中小学数学考试中都会如此.所以自己辅导小孩数学的中国家长要当心,别不小心给孩子灌输了错误的概念. 我后来发现这个问题仅限于中国家长. 那些只在美国学校学习的学生从不知道有这回事. 我问过一个父母从不管的ABC高中生, 她觉得我的问题很weird and funny.

虽然我小孩那次没上光荣榜,发现这个问题也算是收获不小.