I am happy that DSO do many mathematical calculations: this, however, also has a sad dark side, that is, machines replace our brains.

Very true; you have the right attitude.

If you don't understand the mathematics and the concepts, then the arithmetical calculations are pointless - and probably misleading. Just using a convenient tool without understanding is cargo cult science or voodoo magic.

If we look at modern children, they no longer make any mental calculations, they use the cellphone calculator ...

Not necessarily true.

When my daughter was being taught arithmetic (~2000), I was impressed that they were no longer taught "the single true way" to do, for example, multiplication.

I was taught the times tables up to 12 (because there were twelve pence in one shilling!), and beyond that it was the long multiplication algorithm.

My daughter was taught to visualise the numbers and how they fitted together, so that she could break a particular calculation into

*whichever* simpler calculations were helpful. Thus 20*18 might be decomposed into 2*2*100-2*20. That gives a better "feel" for numbers than the simple algorithm, and enables mental "sanity checking".

OTOH, using calculators for normal operations is sensible; why do work that is better done by machines -

*provided* you

*do* understand what the machines are doing, and that what they are doing is

*sensible*.