Any KUMON students out here?

Ignoring the fact that there are very young inventors, and secondary school students who can come up with original ways to prove theorems, or even to discover them; the practice of using exercises to train yourself into calculating within thinking sticks with you through your life if you believe that the increased calculating ability does.

This is an entire culture as I have mentioned several times already, and is the prime reason why oriental students, despite the exceptional academic performance, are not creative nor critical.

Really? Terence Tao (Field's Medal winner, youngest full professor at UCLA, etc), the Chinese IMO team, and most recently, Yitang Zhang, who published a very important paper in Number Theory.

It's completely wrong to say that "oriental students...are not creative nor critical".

With regards to the thread, I did go to KUMON for a few months and while it improved my arithmetical ability, I'm not sure it helped me in terms of actual mathematical ability, because the focus is on speed and accuracy (which are certainly helpful, but can also be harmful if you don't stop to think a problem through).

Terence Tao is an Australian who went to Princeton.

Yitang Zhang is an American who went to Purdue University.

See the problem? Both western educated. I've already said earlier I was talking about the education not the race.

By limiting yourself to recite that 5+3 must be 8, you are limiting yourself to indeed think in only one way of it. You could've dug deeper and questioned why 5+3 would be 8 but you didn't.

I believe you were talking about the culture, and both of those mathematicians were certainly influenced by an "oriental" culture through their parents. Additionally, Zhang was educated in the Chinese system and did his undergraduate degree in Peking. You also haven't accounted for the Chinese IMO team.

Do you expect a typical GCSE / A Level student to pull out the Peano axioms and prove why 5+3=8? Heck, even 1+1=2 took around 300 pages to prove in Principia (and even that was assuming addition is suitably defined.)

For mathematical creativity and problem solving skills, I agree that Kumon isn't really very effective, but for improving your arithmetical and numerical skills in specific situations, 'mindless repetition' is pretty much the only thing you can do.

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The Chinese IMO team has nothing to do with the academic field of anything. The same way how University Challenge doesn't tell you who the best academics are.

You don't just get the culture from your parents, and your parents certainly don't dictate most part of your educational experience. His schools didn't teach it that way, his university didn't teach it that way. That was more than enough.

A few years of schooling could be enough to inspire someone to be better, especially when it's a doctorate in America. And I don't know how the Chinese system was like when Zhang was young, but it definitely still wasn't to the extreme of Kumon drilling.

IMO problems require creativity; that is a fact. This proves that the Chinese system doesn't entirely deprive students of creativity. I wouldn't compare it to University Challenge.

If someone is educated for 21 years in one system from birth, I doubt that an Amercian PhD would somehow erase the influence.

As well as this, I believe that the Japanese Maths curriculum is very much proof-based, so it's not all rote learning.

God Kumon was awful. Just lots of drilling, an insult to knowledge systems.

Would you mind writing out your steps? I'm having trouble coming up with a plausible set of steps that results in x^2-x+3.

Yoh, you like hate hate their guts , I met someone like you in Kumon too lol - actually lotsa boys like you - the girls kinda click more. But I like the drilling part, it seems a good description - I feel they can be a bit stressful at times.

I think you have to be quite self-motivated for Kumon to benefit you. (After all, doing practice in pretty much anything takes some willpower to get started, if nothing else.)

I think you have to be quite self-motivated for Kumon to benefit you. (After all, doing practice in pretty much anything takes some willpower to get started, if nothing else.)

Here is a photo of how I did the sum. But I didn't simplify it cos I just wanted to see if my beginning steps are correct. Thanks again for the help...

The bit after the second equals sign is wrong. (Substitute x=1 to see that it's not equal to the bit after the first equals sign.) Do you see why? (Hint: $\frac{a}{b} \not = \frac{b a}{b}$.)

No, I don't get it , maybe I'm just too silly haha!

When you went from $\dfrac {x+1}{x-2}$ to $\dfrac {(x+1)(x-2)}{x-2}$, you changed the question.

You're essentially saying something like this:

$\dfrac {3}{4}$ = $\dfrac {3 \times 4}{4}$

Do you see why that is wrong? What would you have to do to keep the $\dfrac {3}{4}$ the same?

LOL I do, thanks. But where did they get the 3 from in the answer?

Firstly notice that they haven't changed the numerator, they've just rewritten it:

$\dfrac {x+1}{x-2}= \dfrac{(x-2)+3}{x-2}$

The form they've changed it into is more useful in terms of getting the algebraic fraction into a different form.

Now they've split it up like this:

$\dfrac {x-2}{x-2} + \dfrac {3}{x-2}$

The denominator is the same, so they haven't changed the numerator - it's still equal to $\displaystyle {x+1}$

That easily simplifies into:

$1 + \dfrac {3}{x-2}$

Does that make sense?

Oh God, I feel silly .
I understand the entire thing, but I still don't understand where is the 3 coming from? How did they get 3?