In few days ago, we came across a math question on Alec’s assignment that goes something like this in Chinese…
“A has $4000 and B has $3200. How much more does A have compared with B in term of a fraction.” The model answer was later found to be 1/4.
Before M and Alec found out about the model answer, while they all new the absolute difference is $4000-$3200 = $800, they were boggled with the calculation as to which amount should be used as the denominator (divider) for calculating the difference in terms of a fraction.
For some reasons, M had asked mom before I knew about this. By the time mom asked me, she had already forgotten whether the question was about “how much less does B have compared with A” or “how much more does A have compared with B”; yet she remembered all the numbers including the model answer since the assignment had already been marked and returned to Alec.
What’s troubling me was that everyone seems to be trying to find the mechanics for calculating this kind of questions in that, everyone, including Alec’s private math tutor, were more concerned with which “position” of the number is situated within the question is to be memorized for future references as the number to be used as the denominator for the calculation! However, that’s doesn’t explain why it should be used though.
The problem surfaced when mom had forgotten and had mixed up the orientation of the question, and mistakenly said it was “how much less does B($3200) have compared with A($4000)” with the model answer being 1/4. That’s prompted me insisting that either she had the question wrong or the model answer is wrong.
Mom said that she had deduced it but had forgotten in which position the amount is situated within the question that should be used as the denominator. However, she said, if the question was “how much less does B($3200) have compared with A($4000), with the model answer being 1/4, that would be the amount in the “first position” within the question that should be used as the denominator. She continued that I should double check with the question and model answer, determine which orientation the question was, find out which position is the amount that works out to that model answer, that’s the position that should be told to Alec to be memorized as the denominator for future questions!
Like I said, that does not explain why. Yet everyone seems to have that same idea.
Over the next couple of days, while I kept forgetting to ask M what the actual question was, I insisted upon mom that there was something wrong with that. My reason is, since we are “comparing the first person’s amount with the amount of the second person”, then it should be the second person’s amount that should be used as the denominator to be used to calculate the answer, not because whether it is situated in the first position or the second position of the question.
My way of thinking was, even though admittedly I had forgotten exactly how this kind of question was to be calculated, since the later person’s amount is used to be compared with, then we are taking about a fraction related to the person’s amount. So, if the question were how much less does B ($3200) have compared with A ($4000), then the calculation should be (A-B)/A and the answer would have been 1/5 rather than 1/4. Since we already knew the answer is 1/4, then there must be either something wrong with the question or the model answer is wrong.
I then showed mom that, assuming the model answer of 1/4 is correct, and if we rephrase the question “how much less does B have compared with A” to “if B is 1/4 less than A’s $4000, how much does B have”, then the absolute amount of B would be have worked out to be $3000 instead of the said $3200. That is why I think there is something wrong with the whole thing. Had the question been “how much more does A have compared with B ($3200) in terms of a fraction”, then 1/4 would make A has $4000 which coincides with that amount given.
Finally, a check with the assignment revealed that I was right. The question was indeed “how much more does A($4000) have compared with B($3200)” and the answer was 1/4.
The whole point is, rather than understanding the question and calculating the answer in order to learn mathematics, people are more concerned with how to memorize a quick way to find an answer that matches the model answer in order to get a higher mark. So when the model answer were incorrect, than no one would have noticed it and continue to solve other questions in the wrong way. Then the mathematical questions became just a bunch of number crunching practices rather than something to could be applied to solve real world problems. And that is one of the main problem of local education!
WhaUSay?!