Do a Barbarian's different damage resistances stack or just overlap?

Question

I have a player who recently joined my current game who thinks he only takes ¼ damage from bludgeoning, slashing and piercing damage. He claims that the resistance granted by barbarian rage stacks with the resistances from the Totem of the Bear. I believe that the Bear Totem just expands his resistances to all damage types excluding psychic, but doesn't give him double resistance to bludgeon, slashing and piercing damage.

Relevant passages:

PHB, page 48, under "Rage":

You have resistance to bludgeoning, piercing, and slashing damage.

Page 50, under Totem Spirit "Bear":

Bear. While raging, you have resistance to all damage except psychic damage. The spirit of the bear makes you tough enough to stand up to any punishment.

So does the Bear Totem Spirit give double resistance against the bludgeoning, slashing and piercing damage for ¼ damage received or not?

Answer 1

The reference you're looking for is on page 197 of the Player's Handbook, under, naturally enough, Damage Resistance and Vulnerability. Specifically the third paragraph states:

Multiple instances of resistance or vulnerability that affect the same damage type count as only one instance.

So the Bear Totem Barbarian still takes half damage from bludgeoning, slashing, or piercing attacks.