[Tilted Irish Kilt]

ApplegateRanch :" Also, you said you ‘planted eyes’. How much potato was attached, or was it (common beginner mistake) almost just the eyes?
Were the pieces allowed to callous over before planting?"

Good meaningful questions which get to the 'heart of the matter'.
All cuts on the potato should be exposed to sun to callous over (scab on the cuts).
I like to include at least a 2 by 2 inch piece of the original potato along with the 'eye', and thuroughly calloused by exposure to sunlight.
Potatos are a member of the solanacious family (solar = sun light) as are peppers , tomato , eggplant , etc.
Crop rotation should be practiced so as not to plant solancious plants where other had been planted in the last 3 - 4 years; otherwise there may be pest/disease in the soil.

[ApplegateRanch]

Yeah, 2X2 is good. I usually figure on at least the size of a small egg, and a minimum of 2 eyes.