Concept maps and pointers

How do humans store knowledge? The prevailing theory is that at some abstract level, similar ideas are linked together. This mental map, or graph in CS lingo, is a network of all concepts (nodes) that are connected in different ways. Current research explores the “distance” between nodes by way of reaction time, but the model is old enough to be mentioned in Godel, Escher, Bach. Regular readers of this blog (both of you) know that I’ve mentioned that book (post still forthcoming) a few times already. If you don’t know much about it, your mental map is pretty sparse:

But the author has quite a different picture of the concepts in his book:

From "Godel, Escher, Bach" by Douglas Hofstadter, Figure 70 (detail).

This is a roundabout way of saying that the same words mean different things to different people. The book’s title is a pointer to (or name of) a place in the network (which I’ve highlighted in purple) but the network itself is very different. The same label points to different content. So the punchline for education is this: don’t teach pointers, teach the network.

A curriculum is a checklist of pointers. A teacher may think he has failed if his students say, “yeah, I took a whole class on object oriented programming, but somehow I missed exactly what that was.” (True story.) The good news is that, even if the student can’t define the phrase, she still knows what it means on some deeper, murkier level. Being unable to give that concept a name and adding it fully to her mental map is merely the missing capstone. If instead she was able to recite a textbook definition (“an object is an instance of a class”) but not have any idea what she was saying, she’d pass a multiple choice test having learned absolutely nothing.

The ideal situation, of course, is for the student to be able to recite the definition knowing exactly what she’s saying. That is, to have both a map and set of pointers that line up with society’s. A shared, standardized vocabulary is what makes communication possible, but only among people with similar networks. Done properly, adding pointers/labels/names to concepts (instead of concepts to names) doesn’t feel like crushing creativity but rather a welcome organizational tool that opens up opportunities for more learning and communication.

This discussion opens a window into the way the mind works. Anything is easy once it’s learned, because the network is already built and it’s only a matter of accessing it (finding the right pointer), which is how summaries and aphorisms work. Forgetting occurs when the brain loses the pointer to a concept (a memory leak in CS terms), and such information is not erased, merely misplaced. Sights or smells can evoke otherwise inaccessible memories by providing pointers the conscious brain has forgotten.

But I digress. The takeaway message is teach concepts and a deeper understanding of the material, rather than a bunch of jargon with no meaning behind it.


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