I stumbled upon a couple of sites today that verify the name of the school that was kitty-corner across the road where Ole Finnestad, wife Caroline and family lived.
The school was located in Lee County, Alto Township, Northwest Section 12 on Woodlawn Road on the southeast side of the intersection.
The School was called the Finnestad (or Carlson) #135.
Here is a photo from the Lee County Historical Site.
Correction (April 12, 2013) below:
The School can be found on the following plat map of Alto township by locating Section 12: