"When would we ever use that method, since this way is much faster."
This instinctive lean towards the more efficient method did not go unnoticed. I think it would be fair to say that students are always looking for the faster method. It might also be fair to say that students enjoy the 'easy way', as opposed to the 'hard way'. (But I'm not defining either of those terms.)
They are looking for efficiency. This is a very natural mathematical idea within students.
It is highlighted in this video where a Japanese math teacher (at minute 4:23) brings the students back to the pneumonic HA-KA-SE. Fast, Easy, Accurate.
It is the math teachers equivalent to the Olympic slogan, Faster, Higher, Stronger.
Citius, Altius, Fortius
This led me to question whether this HAKASE is a constant consideration in Japanese schooling. Is it standard? In watching more of the video you can hear the students suggesting that the given method might only be easy and accurate, and not necessarily fast.
The lesson is analyzed here by Dan in his ongoing discussion about what he calls the Ladder of Abstraction.
Is this the math slogan we can always make reference to?
How often will I be able to refer back to these 3 words when a student asks, "Why are we learning this?"
And when a student does point out, "When would we ever use that method, since this way is much faster?" I can just agree, unless someone can point out a faster or easier method.
TOO COOL NOT TO SHARE
Gorgeous prime number generator.
It took me a minute to realize what I was looking at but then...ahhhhhh...a beautiful design. Don't miss out on zooming in and out, and speeding it up.