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It's important to distinguish between what you memorized as part of a rote process as a child as part of your formal education process versus what you have remember as part of your lifetime of experiences. And if your own personal first exposure to multiplication tables was being made to memorize them, you are probably going to think that's the only way to do it.

For example, most adults would probably the ones they use the most often memorized without any formal education. People use halves, quarters, doubles, and quadruples all the time, so the brain creates shortcuts for those.

Personally my older sister taught me the principles of multiplication and division a couple of years before I encountered them in elementary school. So I had already started to think of it as like... A nested adding function. And also using the algebraic properties (communicative, distributive, associative... I'm probably forgetting some of their names) helped me to understand the numbers and their relationships. So memorizing that 10x means you move the decimal place, but then extrapolating that so that n x 5 = n x 10/2 , which is often easier. Or that n x 9 = (n x 10) - n. So memorizing not the results, but the process.

So when I got to 2nd grade and they started teaching multiplication tables my experience was different from my peers. They would hand out sheets of multiplication problems for the class to do quietly, and at first I was about average: faster than the kids who weren't trying, but slower than the ones who had begun to memorize the table. But I was less prone to the errors that other kids would make: mixing up 6's and 9's or 1's and 7's because they look similar, for example. And I quickly got faster than them, especially when we expanded beyond aingle-digit tables. It also helped me in the process of learning division: when we on from just leaving remainders as an R# to actually writing out decimals or using fractions. My peers would get tripped up trying to divide a number that did not fit nearly into the tables they had memorized. Then they introduced exponents, which a lot of people struggled with but for me was the next logical step to take (although my sister probably showed them to me earlier too).

And even today I totally break out the calculator app or even spreadsheet app on my phone. Not for help with the algebra, but to make a record and make sure that I'm including everything I need to. If I were in the grocery store trying to predict what my end cost will be at checkout, it's much more likely I would get it wrong from missing an item, missing a promotion, or not knowing enough about sales tax eligibility than from any algebraic mistake.