Einav said: Hello!
Our approach so far has involved starting the potatoes in a cup of water until roots and stems develop, and then transplanting them into soil.
Do you mean sweet potatoes? (Ipomoea)
While it can work, I find that sweet potatoes will grow vines without the water.
And... They may well die when moved... I've found them to be a difficult house plant.
Sweet potatoes want warm / hot temps, and plenty of light.
If you are growing in a window, you may want additional light.
On the other hand...
If you are growing 'Irish' taters... (Solanum)
They are cool season plants, and moving into too much heat could have killed them.