If you can't grasp conceptually why 8+3=11 then you should just memorize it.
You should memorize it either way.
Imagine if every time you looked at some basic arithmetic, you had to make the choice, am I going to take the time to figure this out and lose my train of thought, or am I going to gloss it over and move on? Imagine having to gloss over 8+3 as "some number in the lowish tens." You might know how to add 8 and 3 conceptually, but to actually work it out would take some extra effort.
I find it amusing that you say "imagine it", since it's like this for me. People think differently :)
I see 8+3 as a number in the lowish tens. If I want the exact result I quickly increment "9-10-11" in my head. Some special cases (0,1,9 and 5+5) are easier.
I guess ability in arithmetic isn't really correlated with ability in calculus, etc., since math has always been my forte.
I'm studying at a japanese university right now and I see the effect of raw memorization daily. It's not pretty. I don't think it's highly underrated.
> ... raw memorization daily. It's not pretty.
> I don't think it's highly underrated.
Raw memorization is dreadfully damaging. Equally, having to add 5 and 8 by counting up is a complete block to other tasks. What's needed is a range of techniques and skills, each assisting the others, and each helping students to get that insight that stops math being a collection of tricks and unmotivated rules, and starts it being a coherent set of principles, facts, tools and techniques.
I think they should start with memorization, and let each individual develop they own heuristics and shortcuts. When those abstract shortcuts are enforced and don't match with the ones a person is already using, it can get confusing.
You should memorize it either way.
Imagine if every time you looked at some basic arithmetic, you had to make the choice, am I going to take the time to figure this out and lose my train of thought, or am I going to gloss it over and move on? Imagine having to gloss over 8+3 as "some number in the lowish tens." You might know how to add 8 and 3 conceptually, but to actually work it out would take some extra effort.
Thus, memorization. It's highly underrated.