The "slow jam" can work but it probably should be in a smaller group. The most important thing a musician can learn is how to function in a group. It has been my experience that many accomplished soloists don't function well in a jam. Here are my suggestions.

1. Encourage the new person to memorize songs, chords and lyrics, and not rely on printed material as soon as possible.
2. Encourage the new person to listen closely to the musical dynamic taking place in the gathering and contribute simply. Most people in a jam session who have been playing a while tend to overplay as well.
3. Keep the focus. If there is someone taking a lead, that's where it should be.
4. Remind the group that if they accomodate new people by playing a little simpler and sometimes softer, they will be rewarded by musical values.
5. Keep the "egos" at bay. They belong on a solo stage not in a group that's trying to make music.
6. Encourage participation by suspending all criticism and judgement of them.
7. Encourage them to take the lead in the group occasionally by offering a song that they have learned (by heart) or making a suggestion as to what song should be played.
8. Encourage them to get together with other people outside of the jam session to work up numbers or to just hang out and pick.
9. For those who have a proficiency on a particular instrument, they might try playing a new instrument which puts them on a beginning level. This way they not only have more empathy for the beginners but will develop a new skill along with them. (I have been playing bass in some of the classes I teach).
10. Don't try to be too ambitious with song material. Stick to the tunes that have fewer chords and lend themselves to a group sing.

Frank Hamilton