This poor old thing was is pretty bad shape, especially the lower row and edge. I did both repair patching on the worst places, and a goodly amount of conservation backing and stitching where rips and tears were less dense. You can see both in this photo:
In the following photo, taken with flash rather than the natural lighting up there in the first photo, the patch fabric contrasts more clearly with the original fabric. You can see the new bottom border and the places that were patched on the blocks. The top border is also new fabric.
Finding good patching fabrics was kind of surprising. This may have originally been an actual red and actual white quilt, but now it surely is more of a rust and tan. Check out the fabric comparisons below. The red is the great fabric I found that usually goes perfectly with late 18th and early 19th century reds. You can see how well that fabric worked when I repaired a fun redwork Peter Pan quilt.
Here's how I supported and stitched the rips.
The fabric you can see inside the rip is the backing of the quilt. This quilt has no batting.
I cut a rectangle of the rust fabric to slip inside the tear and give support to the old fabric. The corners are rounded to help them not buckle while the inset is being slipped inside the tear. (This ended up being a bit too long, and I cut it a bit off one of the short ends while I was working.)
I use a small, dull poker to help put the inset underneath and smooth it out, a flat toothpick for example. The fabric is very weak and brittle, so this part has to be done very slowly and carefully.
Here's the stitching in progress. I use a herringbone stitch. Be sure the stitches go into the inset so the tension isn't borne by the weak, old fabric. Keep the knots in the new fabric, again to protect the old fabric from further tearing. If you're working on a quilt with batting, you can do this technique just the same, and your stitches can go down into the batting as well.
Here's the finished repair.
Here's another variation of the schoolhouse block, this one used just once in a quilt celebrating America and her institutions. The story of this entire quilt is at a previous post.