You need both. Take 1718. Your understanding of multiplication should tell you that this equals 1010+107+108+8*7. Now your rote learning will allow you to calculate this quickly as 100+70+80+56=306.
and no, my rote learning has not prepared me for that. nothing like that was ever presented to me. i went from multiplication tables to factorisation and never mentally connected the two. as a result i can’t do factorisation in my head at all, despite doing 80% of a master’s in engineering.
Yeah your education failed you. What I am effectively doing is “factoring” 17*18 into (10+7)(10+8), before working out the parentheses, but it’s easier because you only work with numbers and not with x’s. A nice in-between step towards algebra.
yeah that’s what’s so interesting. like obviously i can see the steps with actual numbers but replace with unknowns and it’s 50-50 whether i would be able to do it. and since i work with optimisations every day, i have had to reconstruct this stuff from first principles without a theoretical understanding so i need to go the long way around every time.
You need both. Take 1718. Your understanding of multiplication should tell you that this equals 1010+107+108+8*7. Now your rote learning will allow you to calculate this quickly as 100+70+80+56=306.
you’ll need to escape the asterisks:
\*and no, my rote learning has not prepared me for that. nothing like that was ever presented to me. i went from multiplication tables to factorisation and never mentally connected the two. as a result i can’t do factorisation in my head at all, despite doing 80% of a master’s in engineering.
Yeah your education failed you. What I am effectively doing is “factoring” 17*18 into (10+7)(10+8), before working out the parentheses, but it’s easier because you only work with numbers and not with x’s. A nice in-between step towards algebra.
yeah that’s what’s so interesting. like obviously i can see the steps with actual numbers but replace with unknowns and it’s 50-50 whether i would be able to do it. and since i work with optimisations every day, i have had to reconstruct this stuff from first principles without a theoretical understanding so i need to go the long way around every time.