<p>I remember reading somewhere that Feynman. a famous physics, said his mental math skill (including low level calculation) helped him a lot in his work.</p>
<p>My personal experience as an engineering student when I was in college was that, unless you have a good enough calculation skill, you would fail many engineering class. Overly relying on calculator even for simple calculation is never a good idea,IMHO.</p>
<p>When DS was in early elementary school, I originally only paid attention to his conceptual understanding of math concept. Later, I found the school teacher really set a very low standard - it is often the case there was not enough practice. So I started to supplement his math learning material. He did have a short stint with Kumo for less than a year. I found it helped his math test, especially the timed test.</p>
<p>I think many methods from Asia are to ask the student to learn things in tiny baby steps - be it Suzuki method in music or Kumo in lower/intermediate lev math (I think Kumo stopped at differential equation but I think it’s value at that level isimited.) Talking about Suzuki method for learning violin, since these kids started learning so young and sssllloowwlly until each piece is polished before move on, in one year, I heard the top 10 chairs in the all-state orchestra were once trained with that method. The power of intentionally slow-paced learning over more than 10 years. (And the purpose of this learning is really not for achieving excellency in music performance! )</p>
<p>BTW, DS’s private music teacher was suspicious of this method. DS was her first “experiment” with this method. His mother ( not that young) learned it together with him to book 2 or 3. She over practiced in order to catch up with DS (did not sound as great as an old learner) and she ended up needing some physical therapy when she finally stopped playing :(</p>