just remove the quotes
phone.map[phone.type] = {type:'cell', provider:'Verizon', num:'1234567'};
Because you are using strings in your example this may not apply but be aware that if you use instances of custom types as Map key...
The keys of a `HashMap` must have consistent [Object.operator==]
and [Object.hashCode] implementations. This means that the `==` operator
must define a stable equivalence relation on the keys (reflexive,
anti-symmetric, transitive, and consistent over time), and that `hashCode`
must be the same for objects that are considered equal by `==`.