I have only previously made flash games, using MovieClips and such to separate out my animations from my game logic. Now I am getting into trying my hand at making a game for Android, but the game programming theory around separating these things still confuses me. I come from a background of developing non game web applications so I am versed in more MVC like patterns and am stuck in that mindset as I approach game programming.

I want to do things like abstract my game by having, for example, a game board class that contains the data for a grid of tiles with instances of a tile class that each contain properties. I can give my draw loop access to this and have it draw the game board based on the properties of each tile on the game board, but I don't understand where exactly animation should go. As far as I can tell, animation sort of sits between the abstracted game logic (model) and the draw loop (view). With my MVC mindset, it's frustrating trying to decide where animation is actually supposed to go. It would have quite a bit of data associated with it like a model, but seemingly needs to be very closely coupled with the draw loop in order to have things like frame independent animation.

How can I break out of this mindset and start thinking about patterns that make more sense for games?