Knee walls are often found in Cape Cod-style homes or Bungalow ( Chicago ) style homes.  They are vertical surfaces that typically use drywall or paneling to create a finished look inside a room. These rooms are often used as bedrooms around Chicago, and sometimes as home office playroom or workout space. 

The knee wall is sometimes load-bearing to support the horizontal sloped rafters. The purlin is a horizontal beam along the length or a roof, resting on main rafter and supporting the common rafter boards such as a knee wall. 

This assembly makes it hard to cool in summer and hard to keep from wasting heat and creating mold and condensation in the rafters from heat escape in winter. This also creates a drafty colder first floor in winter due to heat escape at a faster rate than traditional attics. 

In either method of insulation, it is essential to air seal the seams of the interior/exterior framing ( see photo) to prevent drafts and air movement between the interior conditioned air and exterior weatherized air.