Kant- Synthetic a priori

At first Kant explains that there are a variety of judgments that are possible of a synthetic a priori. He then carries on about how Hume and other philosophers find it is quite difficult to discover them. In order to make a connection between two ideas, there needs to be some sort of experience in which the ideas are linked. Meaning, it would be impossible to have both a priori and synthetic. Kant believes that math, especially geometry is a priori. For example, 7+5=12 is synthetic. In conclusion math is a synthetic and a priori judgment. I would have to say that I disagree with this because math isn’t something that we are born knowing. It cannot be considered a priori.
We are taught mathamatics in school through use of objects, therefore making links to numbers. We are using separate ideas to relate to one, therefore not making math a priori.