First,

The blanks used for zinc cents are plated. Stripping the copper plating through reverse plating is a common school experiment. (Reversing the anode and cathode will strip the copper quickly.) This experiment is commonly combined with a potato battery. It's a fun, safe and cheap experiment, and happens in middle schools all the time.
Your coin is reverse plated. Look next to the rim on the reverse, and you will see a small trace of the remaining copper.