In my experience teaching science and math, I've found this sort of analogy to be of limitted utility. It is often possible to get a whole class on board with the story and understanding the "rules" and able to come to the right conclusions. They're thrilled. Then you try to bring up the more abstract version and connect it and you get blank stares. Some kids make the connection quickly, but they tend to be the ones that wouldn't have needed the story version in the first place.
I have found that people who understand a topic well often mistake frameworks of understanding that they come up with after they understand for good ways to teach the concept to people who don't yet understand. It's like people think, "Oh I get it! Here's the big picture!" And they explain it that way. But the big picture they came up with was the result, not the cause, of their understanding.
I have found that people who understand a topic well often mistake frameworks of understanding that they come up with after they understand for good ways to teach the concept to people who don't yet understand. It's like people think, "Oh I get it! Here's the big picture!" And they explain it that way. But the big picture they came up with was the result, not the cause, of their understanding.