[RPG] How to create an introductory D&D encounter intended for teaching the rules

Start with pre-made Characters

By which I don't mean generic characters that could be in any fantasy story, but by creating a character specifically for each of your children. These characters should be based around the characters from movies and TV shows they each seem to be drawn most toward. It's not the perfect fit that character creation is, but it can let you leap over the hurdles that character creation presents to a new player and let your children get right into the game. Your child's statement about it feeling exactly like a movie is what you want to most emulate.

Use essentials classes only, specifically MBA focused ones

Essentials classes (the Knight, the Slayer, the Warpriest for example) are built around having strong class features (always on) vs. making choices between how to use encounter and daily powers to most benefit the party. They work best in Heroic Tier (levels 1-10) and are strong classes that do not require as much optimization as the AEDU classes do. more importantly they focus on what are iconic archetypes both within and without of D&D. The Knight and the Slayer for example are both actually sub-classes of the traditional fighter. The first wears heavy armor and is all about protecting his friends while the second is about dealing as much damage as possible to monsters.

Use inherent bonuses

One of the best rules options you can take advantage of is inherent bonuses. Found in Dungeon Master's Guide 2, p. 138. as well as the Dark Sun Campaign Guide Book, p. 209 (where it was expanded) inherent bonuses take the place of magic items for the purposes of system math. At set levels the characters will gain +1, +2 etc. to their to hit rolls, damage rolls, and their defense stats. Magic items are still compatible in that their properties, item attacks, and bonuses to crit damage remain, but their mathematical bonus does not stack with inherent bonuses. Whichever bonus is largest is used.

Focus on the story and the adventure, adjudicate their actions to fit

If you were playing 4e with adults I would wholly say to depend upon the use of the powers their characters have and play the system as-is. However this may be a difficult pill for your children to swallow all at once (there are plenty of adults on the internet that can't handle 4e's separation of fluff, the descriptions and lore, from crunch, the hard rules themselves). When your children's turns in combat come up or they are making decisions out of combat ask them what they want their character to do and then based on their answer formulate what their character would do mechanically and then walk them through what their character does. This way you can introduce and have them take over parts of the rules at 1 piece at a time.

A brief preface: if you've been trying for years to teach a topic to multiple different people, it's likely the problem isn't with your students. Teaching is actually rather difficult and it's worth learning some pedagogical techniques.

At the end of the day, there are a number of pedagogical traditions you can draw upon. Here, we will touch on three of them: mimesis, granularity, and system mastery. Before we begin, however, it's worth noting that you should confirm that they actually want to learn these topics. While classrooms have a number of positive and negative reinforcement techniques built in (loss of social status for not complying with norms, validation from grades, social expectations of learning, goal-fulfillment, etc..) hobby games do not have that same structure. Therefore, the only basis for engagement is voluntary pre-commitment. Try to differentiate "saying yes because polite" from "saying yes from general interest." Different social groups consider declining an invitation to be some level of taboo, and will therefore not decline, despite not being in the least interested.

Consider figure one by Boyd and McConville: without a common mutuality of concern and shared social experiences, there is no comprehensible explanation of the activity.

Rule-complexity is actually the least worry about teaching RPGs. Much of what forms a role-playing game is a tradition of play stretching back to the originators of the game. There are cultural expectations and touchstones that are so deeply embedded in our social tradition that they do not bear comment. Simple RPGs, by their very nature, assume more of those traditions. As a gedankenexperiment, try imagining explaining why playing "golf" is fun. "You hit the ball, then you chase the ball." There are a whole bunch of social expectations and experiences bound up in the game of Golf that are actually quite difficult to explain.

Pedagogical technique 1: Mimesis

Humans are creatures that are actually remarkably good at mimicry. We learn our first language by mimicking the sounds of our parents [citation needed] (I'm so not getting into neural-encoding of languages or anything like that here.). Therefore, review the recorded let's plays in this answer, find ones in genres that interest your group, and spend an evening listening to them and discussing.

It is critical to choose genres that your players already have experience in. It is too much to teach the common genre conventions of a given domain of fiction and other things. The point of mimesis is to expose, as novel, only the things that are the topic under discussion. Therefore, try to get favourite books of your group, and find a system that exposes the conventions of the modal genre, Avoid universal systems for now, as they load more of the cognitive work onto the players. This topic is worthy of a well specified game-recommendation question in its own right.

Once you've found the system, and found the favourite books of your group, your objective will be to game in those books. You will, effectively, be engaging in collaborative fan-fiction. This shortcut is useful: originality is great for people who understand the domain. Until then, stick close to your source material.

Again, here, the objective should be to find recorded games that match your desired system and genre. You can recommend listening to these individually, or listen communally as a group. Be prepared for very low compliance for individual assignments: very few people "like" doing homework on things that they're being socially pressured into doing [citation needed].

By listening to these games, and then by discussing these games as a group after the listen, you're not asking your putative players to act. What you're doing is building their background knowledge of the actions expected in an RPG in a zero-risk environment. In these discussions, beware confirmation bias. Ask them to explain what's happening in games to you. Figure out what they're getting and what they're not getting. Make sure to provide positive and negative feedback here: it's important to validate learned concepts as well as correcting mis-learned ideas.

Pedagogical technique 2: Granularity.

Consider the idea of Granularity Hierarchies. Consider the idea of driving. When driving a car, the first time, there are so many things to keep track of: the state of cars on the road, inputs via the front window, the side windows, the rear side windows, the rear-view mirror, the side-mirrors, road noise, the dashboard, people screaming at you to stop!, etc...

After driving for a while, all of those different "tasks" are grouped up into the task called "driving" and become mostly automatic, reducing the cognitive load of driving and allowing for new, more difficult tasks like "where am I now?" and "where am I going?"

There is a rough hierarchy of task difficulty. Mastery of basic tasks is required before advancing into moderately advanced tasks. Die-rolling has a huge number of assumptions bound up into the task, and isn't actually a very good place to start. Get a "RPG board game" to get the idea of characters working on tasks with a chance of failure. Once they have the idea of "hey, this is a 20 sided die, and I should add this number and compare against this other number." then move into simple vignettes in the chosen game system. If they all read Harry Potter, for example, maybe start with "you're trying to avoid Finch's cat while sneaking through the halls" and use that as the basis for teaching action success and failure. While I don't believe this level of granularity is normally necessary, the main reason it's not necessary is because there tend to be few new role-players in any given group, given the level of difficulty you've been reporting, it's likely worthwhile to go back to basics.

Again, make sure to verbalise your own mental procceses when running your side of the screen. "I'm doing this because of this, that, and the other thing. I'm offering you Y, because you did X." By chunking the rules into small chunks, you can test mastery of those chunks before "zooming out" and playing the game.

Pedagogical technique 3: System mastery

At the end of the day, your players will have to learn the rules. Give them the books for the system you've identified, one that matches their genre expectations and one that doesn't presume on too much implicit knowledge. Then ask them to commit to reading goals before the next meeting. At the next meeting discuss what they have read and the implications on the game of that chapter.

So long as it's not pure homework, and you're using the other techniques actively at the same time, expecting them to read the books and remember the rough rules of the game is not too much to ask. It's not your job to be the book: that's the book's job. If they aren't willing to read a long book, find a shorter (but well articulated game) that does what they want. (Again, that's likely in our game-recommendation section already.)

Conclusion:

You can lead a horse to water, but you can't make them drink. Assuming your players are actually wanting to learn, the common theme is to have multiple distinct learning elements that your players can engage in. It's not your job to teach the entire social tradition of RPing. Set up a venue where they can be guided to recorded games, can practice task activities, and can get help in understanding the readings. If they don't engage, just enjoy playing board games and don't force the issue.