this post was submitted on 12 Dec 2023
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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).