A Priori or A Posteriori?

"But though all our knowledge begins with experience, it does not follow that it all arises out if experience." How is it possible to know things before you know things? In terms of sight, I understand that you can know you are seeing before knowing the word for the action. But how does this work with things like math and other such subjects you are not inherently knowledgeable about? Is this statement in favor of the idea of a priori knowledge or is it observations of actions and everyday events that we experience before the introduction of teaching, similar to that of learning the word for seeing? In this case, when you are taught something, you end up learning to associate words with things that you indeed already know, but previously did not have words for. So how does this explain math or science? How do we already know scientific and mathematical things before being taught? Then again when you think about it, if you were to already know things, but learn the words, is it really a priori or is it a posteriori? The whole idea of knowing before knowing is confusing---how is it possible?