Re:DragonBox: Algebra beats Angry birds
by dbaupp on Wednesday June 13, 2012 @11:21AM
(#4106381)
I 100% agree that having symbol manipulation is required for deeper understanding and learning.
In my experience, being able to quickly and (fairly) reliably move symbols around in one's head makes futher learning much easier and faster, as one can follow proofs and explanations intuitively without feeling the need to work through each step laboriously to justify it.
As a simple example, being able to see the steps that were used to go between
(x - 1)^2 - 2 = 0
x = 1 +- sqrt(2)
at a glance gives one a higher "maths-learning" bandwidth, since one spends just the 3 seconds it takes to read those lines, instead of the extra 30 seconds physically doing the working.
(And, on a slightly different note, having some basic facts memorised like (for example) "d/dx sin(x) = cos(x)" is a little like the difference between data in L1 cache and that just in RAM. However, this doesn't mean that one should not understand why, or not be able to rederive it in a flash by drawing a diagram or whatever.)
In my experience, being able to quickly and (fairly) reliably move symbols around in one's head makes futher learning much easier and faster, as one can follow proofs and explanations intuitively without feeling the need to work through each step laboriously to justify it.
As a simple example, being able to see the steps that were used to go between
at a glance gives one a higher "maths-learning" bandwidth, since one spends just the 3 seconds it takes to read those lines, instead of the extra 30 seconds physically doing the working.(And, on a slightly different note, having some basic facts memorised like (for example) "d/dx sin(x) = cos(x)" is a little like the difference between data in L1 cache and that just in RAM. However, this doesn't mean that one should not understand why, or not be able to rederive it in a flash by drawing a diagram or whatever.)