A question about a recipe: Three Onion Chowder with Parsleyed Oyster Crackers

I have a question about the ingredient "russet potatoes, peeled and cut into 1/2 dice" on the recipe "Three Onion Chowder with Parsleyed Oyster Crackers" from thirschfeld.

Should the potato be pre-cooked, or will the diced potato cook in the pot after you add it in? I wasn't sure as it seems like they go in late in the recipe. Should they be a fairly small dice? Thanks!