Group Improvisation: A Pep Talk

Wanna get better at improvising? Wanna be able to capture more of that New Orleans polyphonic style?
Your brass band has gotta jam…
…even if everyone is open to soloing over a tune that you all know or are learning.  That’s awesome, but it’s a different experience from jamming/group improvising.
In group improvising, you don’t have to sustain a creative statement over the whole form of a tune.  Instead, you can find a short figure that you can repeat, or find notes that sound good as sustained “pads”, etc.  You’re contributing to the overall texture of what’s happening.
Group improvising in a jam setting offers an opportunity to experiment (because it’s not, generally, a performance) with what works for you and what doesn’t, all the while other people could potentially be doing the same thing (and not staring at you while you do it!).  It’s an opportunity to stick with a musical context for longer than the chorus of your solo and try out some things.  It’s also an opportunity to combine this exploration with listening to what others are doing and working from there (i.e. responding).  Often in soloing we approach it as creating a melody over the given harmonic/rhythm context but this is only one kind of improvisation.  Also, you could be so concerned with what you’re doing that you don’t listen to the degree that you’re capable of.  That’s a skill that takes time and practice.
Part of learning to improvise is taking the initiative to do so.  It’s intriguing when musicians who want to improvise don’t do so on a regular basis in their own practice sessions.  Even while alone and unaccompanied (which I HIGHLY recommend).  Or along with favourites records (also, recommended and probably more obvious).  And now there are lots of materials available for private practice, e.g. recorded accompaniments specifically designed for this purpose (which I’m sure you all know).
So, why is there a hesitance?  My feeling on it is that people are generally concerned with “I don’t know what to play”, seeking “right answers” to this challenge.  It can become more complicated as one develops other skills (including, ironically, technique adequate to the task) but also decreasing self-confidence/increasing fear: the “mistake” factor.  This can happen at an early age sadly, but speaks to how we generally learn music in our Western education system.  I could go on…
Group improvising offers a solution to this challenge AND it’s integral to the style of street band music (or “second line” music) that many of us practice.
It’s also fun, individually rewarding PLUS it will ultimately help with how to arrange tunes: it can give a band more flexibility in what can happen (duets, section playing, etc.).
I’m not necessarily suggesting jamming with “no structure” – although I do think there’s a place for that, too. Rather, someone can introduce a riff (not unlike some of the stuff we street band players already play as basslines to our pieces) and that we collectively improvise around it.
Part of our practice – part of the “lineage” – includes improvisation (with a strong emphasis on the collective to boot) and it’s worth spending more time on it. In my experience, the only time that band members get “to practice” (loosely) their improv skills, is when it comes time to solo on a tune.  It’s not enough, in my opinion, if members want to be better improvisers and better able to play creatively as a collective.
Even if one’s primary goal is to learn tunes and not be a jam band per se, working a little bit regularly on group improvisation in the manner I suggested is not mutually exclusive but rounds out the practice nicely.