Quote Originally Posted by HoreTore View Post
ONLY after the reasoning behind is fully understood.
But this is kind of interesting: it is easy to see what you mean with multiplication (even though the example is actually quite flawed because once you move on from positive integers the logic breaks down, and it ought to crash hard in your first year of any technical study worth its salt); however how do you explain this with division?

Multiplication can be defined inductively (which I guess you are doing: letting the kids consider it repeated addition) even if it is really not, but division offers no such explanation that stands up to even casual scrutiny.

Children should never memorize the multiplication table, for example, until they have understood what multiplication is. But after you understand it, yeah, there's no harm in memorizing it.
Nah they should just look up the logs and do the addition.

Seriously though, from a “understanding” point of view if you understand what you are doing when fiddling with logs you inherently understand multiplication. So I do think the log method is better than just summing values from memorised tables, occasionally forgetting to “carry over” (or whatever it is called in English?) those extra values and getting the wrong answer out.