Aizle wrote:
So does that logic continue? Is knowing how to use an abacus even better?
I think you're being intentionally obtuse, here, since you seem to understand the point he's making:
Aizle wrote:
I understand what you're saying. I can appreciate that in order to use a slide rule correctly one needed a bit more understanding.
But to give a serious answer to your question, an abacus and a slide rule perform different mathematical functions (though yes, it is possible to add and subtract with a slide rule, albeit in a circuitous way). You may as well ask if it's better to use a toaster than a blender. That said, using an abacus at least
illustrates the concepts of addition and subtraction better than simply punching in "3 + 5" in a calculator. As well, because most abac..abaci? abacuses?...use denominations (decimal or otherwise), they also arguably require a better understanding of polynomial number systems (... ax^3 + bx^2 + cx^1 + ex^0 ...)
Aizle wrote:
However, I believe that it's not necessarily true that using modern tools indicates that you don't have the conceptual understanding.
I don't believe he ever said it was. Of course someone who punches "3 + 5" into a calculator
may understand the concept behind it, but it is no longer
necessary that they do. He's just refuting your claim that required education correlates with technology. The slide rule and the abacus are both counter-examples of common, low-tech instruments that require more education to use than their higher-tech counterpart.
Which brings us to:
Aizle wrote:
The other question that comes to mind is that is modern tools allow someone to get to the practical answer more easily and perhaps make up for a lesser ability in conceptual understanding, is that necessarily a bad thing?
Well...
Mitch Ratcliffe wrote:
A computer lets you make more mistakes faster than any other human invention in human history ... with the possible exception of handguns and tequila.
Incidentally, even if educational level/quality is rising and technological levels are also rising, that doesn't really establish anything. Under those circumstances, you could just as easily say that educational level correlates well with the number of seconds since Jan. 1, 1970.