By RAW, do monks include their ability modifier in the damage roll of their unarmed strikes?

By default, an unarmed strike deals 1 + Strength modifier damage. If a character has one or more levels in Monk, the class’s Martial Arts ability gives them the following benefit (among others):

You can roll a d4 in place of the normal damage of your unarmed strike

Now, is the “normal damage” of the unarmed strike the “1 + Strength modifier” (meaning that a level 1 monk deals just 1d4 damage with an unarmed strike regardless of ability scores) or is it just the “1” (meaning that a level 1 monk deals 1d4 + Strength modifier damage with an unarmed strike, with the option of using Dexterity instead of Strength)?