Honestly I think it depends on how much new mulch you want to buy
I've done over 'old into new' areas and used all new mulch and done over others using the old mulch as a base and the new mulch on top. Just remove all the mulch that you can first and set it aside, then do your new plantings and decide if you'd like to start fresh or recycle a bit.
I also check my old mulch, if it's infested with bugs, eggs or such then that also helps me make the 'toss' decision.
I also must say hi and welcome
It's wonderful that you are getting to take a landscaping class.