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I played math games with my grandkids for pocket change. Get it right, I give them a dime. Get it wrong, they give me a dime. It's cost me at least $100, but they can now accurately do basic math in their heads almost instantly. My grandson went from failing math to excelling in the subject. He can do math faster than using a calculator.
Examples?
We use an electronic timer. Started with adding single digit numbers. He needs to provide answers before the timer goes off. Right answer adds a dime, but wrong answers or no answer before time expires subtracts a dime. Identified the numbers he had trouble with. We play until he's taken a couple dollars from me. I always let him win a couple dollars to keep up the interest. Lowered the time until it was down to a second.
Most math is learning and applying a technique. But there is no technique or formula for adding/multiplying single digit numbers - it's all memory. That's what I did with my grandkids, and it frees them to learn the techniques without struggling with the basics.
Not to be a naysayer, but there ARE techniques for single digit multiplication and addition. In fact, it's utilizing some basic principles, like the transitive property.
You can always always breakdown mathematics into smaller bits, like 9+8=(9+1)+7=17, or 7*6=(5+2)*6=30+12=42.
You could even do counting! 1+3 => 1...2,3,4 => 4. Or 3*4 => 3,6,9,12 => 12. There's lots of shortcuts!
Aren't those all still based on basic addition and multiplication? If you don't know 2+2=4, breaking down 2*3 into 2+2+2 doesn't help.
Memorization is about speed. Knowing 3*4=12 is much faster than 3+3+3+3.
If you can't break down something, memorizing the answer only teaches you the answer to those problems. Each piece of mathematics is a building block that can be used to help understand another part. You are skipping past the part of why 2+2=4 because it seems forthright and immutable. But, memorizing that means that there may come a time when 2+2 isn't equal to 4, and without the knowledge of how to get there, could you then solve for 2*3?
This seems silly (and maybe a little abstract), but it's meant more as an example to show why knowing how to break things down could solve bigger problems later on. Learning multiple ways to solve a problem can be really helpful!
It's really just meant to show that it can be broken down, not that it is faster (because it isn't).