When I was in junior high, first learning algebra, we learned the laborious rules where you add a three to both sides, or multiply the whole thing by seven, or distributed the "times four" to both sides of the sum in parentheses.

And we went through class exercises to remember them. One day we'd spend the whole time solving equations where you needed to subtract a number from each side to get the answer, the next day one where you had to multiply. Several weeks after that you had to put everything on one side of the equation and then use the quadratic formula.

And after learning enough of these things, I found them happening automatically. I'd copy the equation onto my paper and find that before I was even paying attention to it, I'd subtracted off the extra six, divided both sides by two and there was the answer. When it first happened, it was like magic -- I wasn't thinking about it, my pencil just kept moving until the answer popped out.

Did this happen to everybody, or just to me?
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