# Confused at a higher level

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## Concept maps

Posted by Arjendu on March 1, 2008

Towards the end of one of the comps presentations I’ve attended this year, the student said: ‘And now for a concept map, Arjendu-style’. And she laid out the ideas she’d talked about, with links showing which features of the system were crucial for which properties, and which were understood, and so on.

Once or twice a term, on one of those many occasions when I see students’ eyes beginning to glaze over in class, I call for a time-out. We take 10 – 15 mins during which the students stand at the various boards and put their heads together to sketch out the recent ideas they have encountered, while I circulate and chat with them. I do it because I think students get lost in the details and forget the big picture of what they are doing. But also to wake them up. I’ve been doing this in all sorts of classes, including quantum and stat mech. And I was pleased to see that it had at least become part of one student’s thinking style.

At the NSBP conference, Chandralekha’s presentation on cognitive issues and student learning in physics reminded me why I had started doing this. As she said, if you give the same problem to a novice and an expert and ask them to think out loud, you will see a completely different intellectual structure to the approach. For an introductory mechanics problem, for instance, a student will say things like “oh, it’s an inclined plane. I should think about which forces are involved. Wait, is there friction? What about the normal force? What axes should I choose? Oh no, this is a complicated one — there’s gravity and a spring as well.” And so on. An expert will say something like: ‘Hmm, that’s probably best done by a conservation of energy analysis. Ok, which potential energies do I have to track …” And so on. Neither approach misses the point, but the latter constrains you, and focuses you much faster. And you can see this in maps that you can get people to draw. So I figure anything I can do to help people to get from novice maps to expert maps is a good thing. And by making their conceptions explicit, I am able to do this to some extent: At the end of the exercise, I will quickly sketch my own version of the concept map which I hope helps with this transition.

I talked with a colleague about this, and a couple of days later, his wife, who actually leads workshops around the world on teaching techniques sent me an email that I thought worth sharing with the world:

‘[I heard about your conversation about] concept maps – quite a coincidence because just today I was putting together my handouts on concept maps for my upcoming faculty workshops in Taiwan. It is one of the most versatile, useful but seldom used teaching techniques.

I’ve trained faculty in active teaching techniques in Ukraine, Uganda, Oman, Cambodia and now Taiwan – it works in all cultures. I’ve trained only in schools of education and business but in Taiwan I will also be dealing with engineers. Interestingly enough, it was “invented” by a science faculty member at Cornell.

One of the business faculty I worked with in the Ukraine did a great job in combining it with collaborative learning. She had 3 groups of students create a concept map for something in business (I can’t remember what), had them put it on sheets on the walls and then present it to the rest of the class who questioned them about their concepts and they had to explain or revise. There was SO MUCH learning going on …’

And she also sent me a link:
http://cmap.ihmc.us/Publications/ResearchPapers/TheoryCmaps/TheoryUnderlyingConceptMaps.htm

So this post is mostly a reminder to myself to keep using this technique — it’s not just a fun way to wake up students, it seems to have some sound pedagogical theory to back it up!

1. ### Peter Morgansaid

I’ve never been very comfortable with mapping non-visual/non-spatial/non-language ideas to a concept map. I always feel uncomfortably constrained by the need to identify what has to go in the boxes; when I have something in a box, it always seems to be not quite what I want it to be, so I always want to let it out. Of course there has to be some trade-off between holism and detail, and perhaps concept maps are a good way to home in on precision, but I feel more comfortable with linguistic presentation of structure — perhaps it feels more fluid, more needful of and more open to revision. With a linguistic presentation, it seems less difficult to start again from scratch, with fewer visual cues constraining the fresh start, with fresh insight more likely to come fortuitively from the mixing of words.
I have many questions: do you think differently during the revision process when you have already constructed a first draft concept map, in contrast to the revision process when you have a first draft in linguistic (or other) form? Do you find one or the other more constraining? What happens to the internal simmering of ideas when you have a concept map with hundreds of boxes and links? Does the need to reorganize a large concept map periodically become more, or less, difficult than for other methods?
As another method, beyond the linguistic, I find that writing a computer program that does what I thought I wanted it to always teaches me something, largely by putting it into a formal structure. It makes a difference whether the programming language I use is something like C or something like LISP. Whether I’m programming with the intention that other people will be able to understand the program also makes a difference, partly because then the naming of procedures has to be very carefully considered. For some students, I guess the concept maps approach is as foreign to their natural approaches as it is to me (not altogether foreign, I can see its merits, but it somehow doesn’t seem to fit), while others will just start using it as of right. Even for students to whom it is foreign, however, it’s worth making them think using concept maps occasionally, it’s important to see a little of how other people’s heads work, even if ours work quite differently.
A final comment is that the World-Wide-Web is to an extent a (very large) concept map. It is instructive that the less structured search-engine approach to accessing that concept map made the information more usable.
This has developed as I have written. For good or ill, I discarded concept maps as a good way for me a long time ago, so I apologize that my opinions about them are, apparently, somewhat prejudiced.

2. ### arjendusaid

Peter, excellent points all.

Concept maps are another technique for displaying — and therefore in principle, improving — a student’s intellectual grasp of something. It is particularly useful in the early stages of understanding something, to my mind, and gets steadily less useful to the person doing it as the structure gets denser and richer — but still not entirely useless.

It is part of the ‘you don’t truly understand something unless you can convey it to a complete novice’ idea. I do a quick conceptual sketch of my research agenda when trying to recruit research students, for example, and find it a useful exercise for myself, as well. Less so in clarifying things I’ve thought about for a long time, and far more so in talking about recently intriguing issues.

All my classes are punctuated by ‘explain your confusion your neighbor’ moments, by problem-solving moments, and so on. Concept maps are just part of the tool-kit.

3. ### Aphyrsaid

I don’t know about the WWW as a concept map. While both concept maps and the WWW are formally graphs, the key thing for me (as a primarily visual thinker) is that Arjendu’s concept maps are maps as well: they present visual structure, and help put the linear or branching flow of words and equations that we work with most of the time into a more structured representation. I’m a big believer in scalable information presentation, where the interface has meaningful information at different levels. Branching webs and maps help me to identify (at the wide scale) clusters of related items, and at the small scale, the key progression of theories*, and the parts of a model that applied problems draw from.

(*Most physics books I’ve read take you through theories in an order that’s easier to learn, but don’t present how the whole model is built up. Concept maps frequently help me make those connections in class.)

By contrast, the WWW isn’t really represented as a visual map: we interact with it in more of a branching but linear way, kind of like (at least in my mind) a face-to-face conversation. When you’re reading web pages, you’re not really getting visual structure or topology (unless the web site provides you with some), but a flowing dialogue of text.

Anyway, I suppose what I’m trying to say is that because this class works primarily in text and equations, the concept maps (while not the end-all, be-all presentation medium) help me reinforce and organize existing information in a different mode.

4. ### Peter Morgansaid

I agree that the WWW and concept maps both being graphs doesn’t make them directly comparable. It’s not just a question of scale, but it was the question of scale that I was thinking of. Search engines are one way to cope with the explosion of scale that happened after 2000, say, that introduces an entirely new structure that a concept map has no need of because it’s so small. I suspect that it’s not relevant to this, but it’s interesting that Google created a large commercial advantage by taking note of the patterns of links between pages as well as of the textual content.

Concept maps seem to me to work as an aid to understanding only if they can fit on a single piece of paper (Letter size, say), so that the whole structure can be accommodated and processed as visual information; I doubt I could grasp the details of a whiteboard full of tiny scrawls well enough to make significant coherent modifications to the concept map, reliably. Once there’s more detail, the visual side fails to help.

Perhaps the crucial fact here is that arbitrary networks are relatively much more computationally intractable than hierarchies and other restricted networks. Hence, computer programs comprising tens of thousands of procedures and millions of lines can be managed and successfully modified, even if it does take great care, because the relationships are almost all unidirectional. Equally, project timelines with thousands of dependencies can be managed because the timeline restricts the possible relationships (there is software specifically for managing the completion/start dependencies of big projects). I cannot conceive of understanding an arbitary graph that has tens of thousands of boxes and unconstrained relationships well enough to modify it without making mistakes. I think the lesson is that if we want an extensible concept map, we should be careful to restrict the relationships in some way that limits the computational complexity of the network. If we are constructing small-scale structures in the classroom, which will be thrown away in half an hour, anything goes, it’s all helpful, but for the large-scale projects that many students are likely to work on when they leave Olin, be aware of the problems of scaling.

I believe I don’t visualize pages of the Web and the links between them floating in space. I’m not sure that there’s a single way that people do think of this, which I suspect is why, for example, some people can find information on the Web much more quickly than others. I feel almost certain that the more sophisticated strategies for using the web are not at all visual, and I believe that the more sophisticated strategies for handling what could conceivably be presented as very large concept maps are not visual.

I’ve looked again at the very interesting TheoryCmaps link you provided above. I have many reservations, just one of which is the need to ask the “right” questions to get the “right” Cmap. Education is arguably about getting students to understand what the “right” and “wrong” questions are, but there is the not always understood aim that they will then be able to ask better, across-the-current questions, leading to better Cmaps, and make the old Cmaps obsolete.

I hope it’s clear that I’m not saying that Cmaps shouldn’t be used, that they’re no use, whatever, only that I’ve only been able to get them to do significant work for me at the early stages of understanding.

I am suddenly prompted to ask whether anyone here knows, by any chance, where there is a fairly comprehensive “concept map” of historical/conceptual dependencies between interpretations of QM? I saw one in the literature perhaps five years ago, but I’ve lost track of it. Please feel free to be amused at the hypocrisy of this request.

5. ### links round up — 2 « hal’s house of pancakessaid

[…] Concept Maps A reminder from a practicing teacher that concept maps and other “non-traditional” techniques can help students learn. The exchange in the comments is as interesting as the post itself. […]

6. ### agmsaid

Interesting. This is how Georgia Tech’s hyperphysics site is organized to a large extent. It’s really useful when I’m teaching, though the hyperlinks can make things a bit too easy to be disjointed when I’m too tired enough and go “Hey, look at that. Let’s talk about that little thing for a moment.”

7. ### agmsaid

This really helped my students see where they were having trouble with rotational motion. Thanks for blogging about it.