This photo is one of the most popular in my entire collection, so I thought I'd give proper credit to the source for one thing, write a blurb, and add it to a few groups.
I came across this post from the kotaku team, which seemed to help explain what 'The Little Professor' did.
Basically the thing just displayed math problems in tiny red numbers and you had to input the answer. After going through a set it would give you your score. The whole thing was sound free as well.
There seem to be several available on EBAY at any given time.
same model as above from the National muesum of american history link
a bad shot from the computer museum link