When do you expect to hear back from NSF (DMS)?
The time to hear back on an NSF application is highly variable, both by grant vehicle and for individual applications.  Since most NSF grants are peer reviewed by a panel of academics who also have to meet in person, there's a significant length of time naturally built into the system.

Another part of the delay is that for most programs there are very few applications funded.  As such, even though there may be many clear rejections with relatively fast responses, program managers may end up having a long fight to find sufficient money to accept a project that is right on the boundary of getting accepted.

Still, if you're looking for a number, I have personally never heard of a NSF grant response taking less than 3 months or more than 12 months.