Slab floor breaking up around perimeter

Hello,

I live in a single story home that sits on a concrete slab. While the foundation seems OK, the concrete floor is breaking apart near the perimeter of the house. I would like to repair this so that I can replace the flooring with a product like Pergo.

When I pull out the loose concrete, there appears to be a light layer of insulation underneath, and then more concrete underneath of that.

What is the best way to go about this? Here are some pictures...