Or, you could just know the number. When I was a kid, we were drilled with the multiplication tables up to 12 X 12, until it’s all system 1 and you just know the product. To pass, we had to undergo an oral test where we were given a bunch of multiplications up to 12 X 12 and had to answer them immediately without pencil or paper.
This frees your mind for contemplating higher level issues, without having to waste time multiplying single digit numbers.
In my opinion, if a student is still having to calculate 7*8 in a grade higher than maybe grade 3, someone has failed in teaching that kid. The value of having basic operations committed to system 1 is tremendous. It makes everything that comes after much easier, as well as day-to-day arithmetic.
One of the problems with modern education, in my opinion, is that students are passed forward in grades without mastering the stuff in the current grade. This is especially bad for math, because the knowledge builds on itself. If you keep advancing with major holes in your ability, it just feels like math gets harder and harder as the years go on, and some students come to believe that they just aren’t good at math, when in fact the school system just failed them.
This effect is much worse in poorer schools, where the gaps in learnjng are larger. There are high schools in cities like Baltimore and Chicago where only a handful of students outmof hundreds graduate with minimal proficiency in math, science, and English. I believe there are a few high schools where none of the graduating class in high school were proficient in one or more core subjects.
If this was about skin color and not economic circumstances or family issues or terrible schools, we’d see the same results among black students in good schools. We don’t. And the white kids in the terrible schools would do better. They don’t.
The idea that this is a race issue is a nice deflection away from the failed schools and failed governments in cities like Detroit, Baltimore, New York, etc.