Kant: How is Pure Mathematics Possible

Kant's main argument for why pure mathematics is possible seems to be based on the idea that time and space, the concepts which mathematics, specifically geometry are based on those that are understood intuitively. He calls these concepts a priori meaning that it comes before experience. So does this mean that it can be understood without the use of the senses, or better yet, an experience involving the senses? He claims, "a priori can never concern any other things than objects of our senses." Perhaps I'm not understanding correctly, but I cannot figure out how something can come before sensuous experience, and yet is only understood through the senses. Is he saying that we know about space and time intuitively without the use of our senses, yet we understand them only through experiences of our senses of objects that lie within them?

I am also confused as to how a priori such as time and space relate to his claim that "we can know objects as they appear to us (to our senses), not as they are in themselves." Is he claiming that we "just know" about concepts like time and space, yet it is impossible for us to "just know" about the true nature of an object? Instead we only understand an object through the perception of it that we have gathered from experiences of it through our senses?