Most children do narrative story telling without rules or reservation. They (we) can come up with amazing story lines that us 'older' people envy. What happens is we become ossified into the type person we thought we would never become. We are afraid to do some imaginative inputting because someone may laugh at it. Also we don't practice it so we are rusty.
** Additional Thought **
Please read below for my suggestion on how to transition your group to a narrativist style, but take note of of my comment here.
In answering another question (See Here) in this forum I have had one other piece of info I over looked.
Every person is different and games differently for different reasons. Some people will not transition to a strongly narrative style, not because it is bad or they resist it, but because it does not fit their method of experiencing a story. They need a structured method of approaching a problem, or game. The more open-ended type of system doesn't provide them with enough guidelines to make a decision and so they quickly get frustrated with the system. For them it doesn't work as well as something with strong rules adherence. You may have to face the fact that the majority of your group falls into this category and they can't get their heads wrapped around this other style of play. They are not bad because of this they are just not wired to follow that path.
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The trick to transitioning to this type of system is to awaken the inner 8 year-old. We are told make-believe is not for adults, even though we do RPGs and create make-believe worlds, we still don't want to be labeled as immature. So in defense we clam up and let the GM do all the creative work and go along for the ride. Secretly we want to inject our own thoughts, but mostly we opt out and don't say a thing. We do not want to risk rejection.
To awaken the inner child is not all that tricky, it just requires a little planning. The goal is to build trust and acceptance. Once you do this the game will take care of itself.
First - The 'rules-system' you want to use is not really a factor except that you want to do something that the group is interested in. Since you want to kick-start them do not even pick a set of rules or a system. Concentrate on the awakening process for now.
** Addendum Thought Added **
Try this for 30 minutes using your current campaign and characters using the steps below. This would be less threatening and add the cooperative story telling dimension you are looking for. Do this a few times and see if you have success.
** Addendum Thought end **
Next - Move away from the table and into comfy chairs with no distractions. (TV, cell phones, laptops, pads, etc.) All of these are not allowed. They are the biggest crutch and killer of imagination in any session.
Next - Give each player a piece of paper with a name, class/role, and single sentence that describes them. Pick something for each person that they like to play, maybe their favorite class or type of character. They may have a pencil and eraser but no dice.
Next - Have a short paragraph that sets up a location and a problem. Have only the most basic of information.
Now - Throw out a response to this and ask each player one-at-a-time to respond with one sentence what they will do. Your persona should do this too. Expect resistance from your group at this point. If you have 5 people expect only 2 responses, but be sure to ask each person anyway. IMPORTANT -- Make sure to repeat back to each person that responds a restating of what they said. This is called active listening and is the number one way of disarming a person and making them feel valued and accepted. -- This gives them permission to engage the storyline without that 'adult' fear of being called immature. Their input is now considered valuable and acceptable, which are 2 of the key items needed for having fun.
Finally - Weave these statements together into a narrative and speak it back to them. Inject a villain/problem at this point that must be handled. Something that directly conflicts with at least one of the statements made by the group. Make it urgent, something that cannot be ignored and has a benefit. The benefit should advance the story. If someone interrupts at this point, LET THEM. Now you have once again confirmed that input is rewarded and desirable.
After a few rounds you should see something in their eyes or their posture. Make sure on the second or third round to lean forward in your chair and stay there. If someone leans forward they are excited and engaged in what is going on.
People want to be involved in something bigger than themselves and something exciting. If they have permission they will make it that way without you doing much.