Sore dancing feet problem...how to solve?

I’ve been doing this dance DVD (Tracey Anderson method) for a few weeks now and I get really sore balls of my feet. I suspect this is normal and one spends a lot of time hippity hoppiting around.

Is the general idea to build up hard skin on the feet to protect your feet from the friction (which is what I presume is causing the pain)? Or should I still be able to keep soft feet (scouring them with pumice stone etc) and just invest in proper expensive dance shoes to protect my feet?

Your professional dancing help and advice would be most appreciated! Thank you x