"The essence of mathematics is in universal methods for solving all problems in a particular class of problems. Use of “hacks”/”tricks” is a replacement of mathematics by cheap surrogates. Hacks/tricks can work at a certain level, but frequently obstruct students’ progress at the next level of learning of mathematics."

I would have to agree with the article.

I tried to learn the Trachtenberg system [1] a while back. I thought it would be a simple and fun thing to do. Maybe it's just my brain but I couldn't wrap my head around all the different rules for simple multiplication. Rather than speeding up my mental arithmatic it slowed it down considerably. In the end I gave up, feeling a little bit more stupid than when I started.

[1] https://en.wikipedia.org/wiki/Trachtenberg_system

What are you classifying as a hack? I've always enjoyed the trick for squaring numbers ending in 5. You take the number(s) before the last 5 and multiply it with the number above and add 25 to the end,

So for 4545, you do 45, which is 20 and add 25 to the end, giving 2025.

That's a fun one because it's quicker to do it in your head than it is to type it into a calculator.