The official explanation given by Beestar.org is

The ratio between the red marbles and the white marbles was 3:1 at the beginning. After 24 red marbles were removed, the ratio was 9:4. So the number of removed red marbles represented (3-9/4) = 3/4 of the white marbles. Hence the number of white marbles was 24 ÷ (3/4) = 32.

這個方法看起來挺簡單.但在美國的小學生中能想出此邏輯的很少(比我一開始想象的少得多).各位家長請如實地交流一下,你的孩子自己想出此解法了嗎?據我對周圍中國家長小孩的觀察,我估計大概是這樣:

Assuming the child is a fifth or sixth grader in US.

The child solved the problem correctly by himself (not guessing): top 5%

The child solved the problem correctly with some hint from parent: top 10%

The child could not solve the problem, but eventually understood the parent's thorough explanation and could apply it to similar problems: top 30%

The child mostly understood parent's explanation, but could not apply the logic to solve similar problems: top 50%

The child found the solution too hard to understand despite explanations: top 70%

Neither the child nor the parent could solve the problem: the rest.

我小學五年級時是班上的數學尖子.象這樣的題見多了.做起來小菜一碟. 我想現在國內好小學的五年級學生應有一半能解這樣的問題. 但在美國我們的孩子雖已在班上數一數二,可實際上與我們以前和現在國內的學生水平差得很遠. 我們的孩子都很聰明, 但在學校學到的數學真是太少了. 如果他們象周圍老美那樣跟着學校上, 等走上將來更全球化的社會, 他們絕不是中國印度那些 sharp kids的對手. 我自己很忙,不可能整天教小孩數學,只能找幾個好的program, 讓孩子多參與. 盡力而為了.