I am continuing to think about what it would take to create a robust visualization method for networked systems. If you want the visualization to be a way of teaching, I don’t think it’s enough to simply show nodes and connectors.
My thinking on this topic comes largely from my experience teaching. In essence, teaching is the process of helping someone build their mental network so that they can move fluidly across multiple topics. This is especially true in science, where students need to be able to work with abstract mathematical concepts, experimental measurements and lab results, and a variety of models that explain the behaviors that they observe. This is a difficult and often bewildering task, and many students struggle with knowing where to begin.
One of the perennial problems in an introductory chemistry class is that students come in with very different levels of preparation. Especially in math. To help my students bridge the gap between what they knew and what they needed to know, I tried to make the connections between specific chemistry and math topics explicit in my syllabus. For each chemistry topic, I identified math techniques that students could brush up on, and pointed them to resources that might help.
I did the same in my quantum mechanics class, where the students are more advanced and the connections are even more important.
Essentially, what I was doing in both of these tables was trying to draw the connectors between the math and chemistry nodes, which students often perceive to be completely unrelated. By telling students which math and physics concepts were related to the chemistry we were studying, I hoped to give them a place to start looking when they were confused.
So, did it work? Yes and no. Highly motivated students who just needed to brush up found it useful. Students who were completely lost tended to remain lost. I think that there were a couple of reasons for this. First, I don’t think that many students really took the time to review topics outside of class. Second, even if they did review the topics, the weaker students often weren’t actually able to make the connections between topics, even when specifically told what the two topics were (and often, even if told specifically how they were related).
If you have no idea how two topics are related, simply insisting that there’s a connection probably won’t help. It’s hard for a beginner to see how the ideas from math class apply to what they’re doing in chemistry right now. The perceived relevance of these extra study topics is low, precisely because students can’t see how the two things are related in the first place. The teacher might say that the ideas are connected, and will hopefully work with students to help make connections between the ideas, but simply saying that a is related to b doesn’t do much but cause frustration.
I often thought when teaching that I should make a map of the “network of chemistry” to answer the “when are we ever going to use this?” question that so many students ask. I wanted a real, visual artifact that I could point to show them the mental connections that constitute expertise. But even if I could do it, just showing them a picture of the inside of my brain wouldn’t help.
It’s a little like the guy who loves to name drop when talking about people in a field you know nothing about. When he tells you that Mark used to work with Julie at companyX, his awed tone of voice makes it sound impressive, but beyond that you have nothing to go on. The information doesn’t mean much if you’ve never heard of Mark, Julie or companyX. If you had two of those entities stored in your mental network already, then it might be useful to add the third. But if you have none of them, then knowing that they’re connected to each other somehow probably doesn’t interest you much.
The hyperphysics website attempts to create a web of physics topics to show how they are interrelated. It does a good job of listing off definitions and giving equations for each node, but it doesn’t guide you from a to b. If you just need a quick confirmation that you have the equation right, it’s a useful tool. But for learning things the first time around? Not so much.
What students need to get from one new idea to another is not a lot of name-dropping of things that they don’t know about. A huge list of topics to review isn’t helpful, except to the extent that it gives them a list of search terms to explore and shapes the kinds of questions that they might ask. To really teach requires a story. Instead of saying that “a and b are related,” you need to tell students how a and b are related, and why.
To create a “network of chemistry” that would be effective for a first-time learner, I would need to write a series of nodes explaining each topic, and also a series of interconnected narratives that makes a seamless transition from one topic to the next. Like a gigantic crossword puzzle, the nodes would need to be placed in exactly the right places to overlap with the same idea in another narrative journey. It would be an incredibly difficult project: you’d need to tell every story from every angle so that they converge on a single idea at common points, but you’d have to preserve the continuity when coming at that central idea from different directions. And, you’d have to keep the narrative flow and the structural integrity of each story along the way.
When I talked about this idea with students, I used the metaphor of walking through a forest. In class, we walk on a small collection of well-marked trails. When the students first start to study a particular kind of problem, they cling to just one path and memorize exactly how everything looks along the way, until every rock and tree becomes familiar. And then, mean person that I am, I pick them up and plop them down on another path walking through the same forest, but coming at the same clearing from a slightly different direction. The rocks look different from this angle, and the trees aren’t quite the same, either. There might be something familiar about it, but things are in different places and it’s hard to recognize exactly where they are. They’ve only achieved mastery when they can recognize the same topic from any angle.
Experience is composed of two things: variety, and practice. A student can practice the same problem over and over until it’s completely memorized and have learned nothing. Walking the same path every time only teaches you about the path. To get a sense of the forest, you need to follow different narratives, and learn to see the same thing from different angles. My network of chemistry could simply be a map that shows students how many possible paths there are, but the students still need to walk along the different narrative threads and learn to recognize the forest for themselves.
Most network visualizations do a great job of telling you how many connections exist. They might even magically transport you from one node and plop you down in a completely different place. You might take it on faith that you can get from here to there because I said so, or because it’s on the map. But if you don’t recognize the landscape enough to realize you just passed the clearing you were heading for, you’re still just as lost as before.
Nodes and connectors aren’t enough. Human beings need coherent narratives to get from one place to the next. How do we build these narrative threads into a structure that generates real experience, rather than simply listing off a bunch of meaningless connections? How does a graphic go from name-dropper to story-teller, building out all the detail of how things interrelate, rather than just telling you who’s connected to whom?