I recall being forced to memorize the tables by my father at a very young age.

it actually reenforced the multiplicative principles in my head.

In later years, i was required to memorize the tables up through 25 * 25...
it was easier then.

To this day, I know squares that most people find odd... on the tip of my tongue. One's that are hard, I can look at the one above and below and identify the correct one in just a moment.

So I disagree with the memorization being undermining. Math is nothing BUT drilling in order to memorize the concept or property that one is attempting to learn. Indeed, multiplicative properties are far more easy for me to remember now, decades later, than the much more recent trigonometry or calculus that I learned much later.

I can apply pythagorean theorems without blinking, but I have trouble remembering how to find the sides of a triangle from the angles. And I can *never* remember that equation for solving a binomial equation.

Yes, we are rote teaching our children these days, and yes that prhohibits teaching them to *think* for themselves and yes it has been going on for SOOOO long that it's effects are accumulating rapidly...

but multiplication tables aren't necessarily part of the problem. OTOH, ask *anyone* why 2 times 2 is always 4. Just about anyone will stumble allll over that one.