Tangle and Narrative-Based Learning

Thanks to Tyler Greene for pointing me to worrydream.com. One of the coolest things in a long list of pretty awesome stuff on that site is tangle. It’s a JavaScript library that makes it easy to create interactive documents, so that you can see the sensitivities or effects of whatever the website is trying to explain. This library is a great example of how technology is making it easier to teach and learn (see the examples in the link if you don’t believe me). Most concepts, especially number-based, are really quite simple, but we generally need to understand them first through constructing a narrative. If that narrative can be made more accessible through letting people interact with it, we’ll learn faster and retain concepts better. Here’s an example: I was looking at a calculus textbook recently that “taught” Taylor series (power expansions). For me, the narrative around Taylor series is that I want to start at a point on an arbitrary curve and make an estimate of the y-value of a point just to the right of it. This narrative is sticky, because it the elements of a story, which we’re good at remembering. There’s a motivation; I want that y-value like the Greeks want Helen back. Then, there’s a process that happens to get there; I take derivatives and put them into a series that makes sense in the context of my goals, like the Greeks put together 1000 ships because they had to sail to Troy. It’s easy to remember that I take a first derivative at my starting point and assume to the first order that the next point will be along that line precisely because I know that’s where I want to “go.” The textbook that I was trying to help someone with just gave the formula for a power series, though, and did a very good job of explaining how to plug into it. That’s equivalent to someone telling you without any context that the Greeks launched 1000 ships to attack Troy. In a couple of years, you aren’t going to remember that someone told you that at all, much less that there were ships or how many of them there were.