Redirected: Why are teachers so quick to have students use u-substitution?

[Ishuda]

What is simplified is actually completely complicated to others.

I personally like the form: \(\displaystyle \dfrac{{y - x}}{{ xy\sqrt[3]{y}-xy\sqrt[3]{x} }}\). What can be simpler?

Here is a question which is in no way meant to be argumentative.
Why are teachers so quick to have students use u-substitution?
I find that rather than helping students, it actually discourages the recolonization of pattern.
Mathematics is the science of pattern.

I thought the question was interesting enough to make a new thread about it instead of an appendage to another thread.

I tend to agree in one sense but in another it, at least in part, requires that 'pattern recognition' capability to pick the proper u and, most of the time it just seems to make problems simpler and 'easier' to work [and I am a lazy fellow].

For example, use the question here and suppose I wasn't yet quite comfortable with
u³ \(\displaystyle \pm\) v³ = (u \(\displaystyle \pm\) v) ( u² \(\displaystyle \mp\) uv + v²)
It is 'easier' [I don't have to write those pesky exponents] to perform the long division
\(\displaystyle \frac{u^3\, -\, v^3}{u\, -\, v}\)
than
\(\displaystyle \frac{u\, -\, v}{u^{\frac{1}{3}}\, -\, v^{\frac{1}{3}}}\)

Oh, and about your answer. Personally I agree

 

[Deleted member 4993]

I personally like u-substitution because that helps me recognize pattern and helps me explain to others quickly.