Kant "math"

So in the beginning of the book, Kant talks about analytic and synthetic. Since I am a math major, I found the part on math the most interesting. Kant goes on and describes math a synthetic a priori. I am actually kinda confused by this. To me you can observe math but to really understand it I think you need to have hands on experience. Yes you can believe someone when they say that 1+3=4, but truely, without explaining it, one would not understand why. By showing someone on a numberline (as demonstrated in class) you can say that if you start at 1 and move three more numbers to the positive side, then you will end up at four. Someone could simply remember this equation, but by memorizing it they would not be able to see that 4 - 1=3 or that 4 -3=1. So I am not really sure if i agree with Kant that math is just observed.