The “numbers” (rationals, mainly) definitely have a “shape” in my mind, at least up to 800 or so. When I do simple arithmetic I feel like I simply glance over to the right place and “see” the answer.
I remember as a child trying to draw the shape of the number “line” (it curls and twists) and being surprised that I was unable to do so.
This has never seemed to have given me any advantage or disadvantage in learning more complex maths than one gets in primary school. But since so much arithmetic is done in numbers less than 100 (or scaled down to that range) it does make a lot of things easier.
I remember as a child trying to draw the shape of the number “line” (it curls and twists) and being surprised that I was unable to do so.
This has never seemed to have given me any advantage or disadvantage in learning more complex maths than one gets in primary school. But since so much arithmetic is done in numbers less than 100 (or scaled down to that range) it does make a lot of things easier.