It's a well-known fact here that mathematicians can't do calculations. I've had professors in class ask the class to do very simple calculations for their complex examples for them. (Or they get it wrong. A lot.)
The driving factor for mathematics is laziness. I didn't even memorize the basic multiplication table (1-10) for a long time, but I remembered some shortcuts (like multiplying stuff by 9 was easy) and got by.
The multiplication table really bothers me. It's considered to be the least a child can learn in elementary school. And kids that haven't learned to do math mentally just memorise it like a poem. I really don't think this is the correct approach.
We teach multiplication as an algorithm based on breaking the problem into single-digit pieces. If you're trying to learn that algorithm, and you keep needing to figure out what all the pieces are, you won't be able to follow along with the bigger picture. It would be like trying to write an essay, but having to look up the spelling for each word in the dictionary... it would take you a lot longer, and be much more of a struggle. Instead, you memorize the pieces, and then later can focusing on understanding how all of those pieces fit together.
I feel a bit bad for not memorizing it, to be honest. Not sure if there is any other way for learning to multiply?
How do you "understand" that 6x 8 = 48?
With bigger numbers, then you can apply a system. And as I mentioned I also "cheated" a bit with the basic table. For example I would have remembered that 5 x 8 = 40 and then calculated 6 x 8 = 5 x 8 + 6 in my head, because the multiplications for 5 are easy (half the other factor x 10 +/- 5). But there might not be a cheat for every point in the table?
You can learn to better comprehend a quantity or amount. So you understand that 6 * 8 is larger than 2 * 8, and then understand that it is actually 3 times that. Another approach would be to always think of multiplication as condensed summation, so 6 * 8 = 8 + 8 + 8 + 8 + 8 + 8 = (8+8) + (8+8) + (8+8) = 32 + 16 = 48. I would let my kid write out the summation and apply an analytical approach rather than memorising it blindly. I guess you have to memorise it eventually, but a lot of kids are lost if they fail to recollect the answer.
