{ Better Explained }:
How do you draw an elephant?
- Pencil the structure using ovals, rectangles, and so on
- Ink the final result, taking the lines you want
- Erase the underlying pencil structure, revealing the elephant
…
Is tracing different from drawing? You bet. Tracing is mimicry — we don’t know why a line is there. We just start in one corner and work our way around. Sure, we might make a pretty elephant — but can we draw one with a different trunk? Standing on two hind legs? Probably not.
Math is similar: we “teach” by tracing a student through the steps of a proof. But there’s an underlying pencil structure that was in the mind’s eye of the proof’s author that we’re not seeing. We’re walking the student along the drawing (“Here is the head, here is the trunk, here is the leg”) without show the mindset that created the proof (“The head is an oval, connected to a larger oval for the body; the legs are cylinders, which we smooth out.”).
If we’re lucky, the student generalizes the steps and creates their own pencil structure.
…
Sometimes we create “nice-looking elephants” through trial and error. Later on, we realize there’s a common structure that can simplify future efforts. True learning is about discovering and exploring these structures, not simply generating the pretty elephants.
••••••
OS:
I love Better Explained. I wish they covered more topics, but I feel like I’ve been looking for this my whole life — the intuitive explanation.
Funny; it reminds me of another { 3rd grade story }: besides that it was a group project wherein we had to write something long-ish, the context is irrelevant. The two girls I was sitting with were editing what I’d written, and were trying their hardest to convince me that my paragraph was too long (or too short?) because “paragraphs are 5 sentences long”. Someone had taught them that, without explaining the point that a paragraph depends on how long it takes to convey a thought. A creative writer knows that a paragraph can be a single word or three pages, as necessary.
For the longest time, I inwardly face-palmed thinking about that. Who was to blame? A bad teacher, or students who couldn’t grasp subtleties and abstractions? But… how can I laugh at them now? Truly, my entire mathematical experience (up until recently) has been exactly this way. I’ve been tracing mathematical elephants.
![Above image via { Paint Draw Paint }
“GENERIC PARTS TECHNIQUE” (GPT)
“There will always be a wild and unpredictable quality to creativity and invention, says Anthony McCaffrey, a cognitive psychology researcher at the University of Massachusetts Amherst, because an “Aha moment” is rare and reaching it means overcoming formidable mental obstacles. But after studying common roadblocks to problem-solving, he has developed a toolkit for enhancing anyone’s skills. McCaffrey believes his Obscure Features Hypothesis (OFH) has led to the first systematic, step-by-step approach to devising innovation-enhancing techniques to overcome a wide range of cognitive obstacles to invention.”
…
”I felt that if I could understand why people overlook certain things, then develop techniques for them to notice much more readily what they were overlooking, I might have a chance to improve creativity.”
Psychologists use the term “functional fixedness” to describe the first mental obstacle McCaffrey investigated. It explains, for example, how one person finding burrs stuck to his sweater will typically say, “Ugh, a burr,” while another might say, “Hmmm, two things lightly fastened together. I think I’ll invent Velcro!” The first view is clouded by focusing on an object’s typical function.”
To overcome functional fixedness, McCaffrey sought a way to teach people to reinterpret known information about common objects. For each part of an object, the “generic parts technique” (GPT) asks users to list function-free descriptions, including its material, shape and size. Using this, the prongs of an electrical plug can be described in a function-free way to reveal that they might be used as a screwdriver, for example.
{ e! Science News }
The topic of the above excerpt was mentioned in { one of the links } in my weekly Kurzweil AI feed, and caught my curiosity…
How GPT works
“For each object in your problem, you break it into parts and ask two questions,” explains McCaffrey.
1. Can it be broken down further?
2.Does my description of the part imply a use?”
For example, say you’re given two steel rings and told to make a figure-8 out of them. Your tools? A candle and a match. Melted wax is sticky, but the wax isn’t strong enough to hold the rings together.
What about the other part of the candle? The wick. The word implies a use: wicks are set afire to give light. “That tends to hinder people’s ability to think of alternative uses for this part,” says McCaffrey. Think of the wick more generically as a piece of string and the string as strands of cotton and you’re liberated.
Now you can remove the wick and tie the two rings together. Or, if you like, shred the string and make a wig for your hamster.
[above emphasis, mine.]
That’s excellent, and it’s great that this is being made into software, but surely it isn’t “the first systematic, step-by-step approach to devising innovation-enhancing techniques to overcome a wide range of cognitive obstacles to invention.”
Perhaps the key word there is systematic, because right away I can think of at least 3 other methods/approaches/modes of learning that embody, basically, the idea of getting past “functional fixedness” and seeing that all things are made up of basic parts, which can be broken down… and down again and again — to the subatomic, if you like.
Firstly, I wrote about { “the difference between Montessori and art school” } in July of 2010 — namely, that the Montessori method doesn’t consider using a violin as a “bridge” for your block-city creative, while in art school, we absolutely do. We ask, “Why not?” (and if there isn’t { “a damn good reason why not” }, proceed).
Also, when an artist learns to draw, often s/he first learns to abstract what s/he sees in the world into simpler shapes that s/he then builds on (as pictured above). Seeing in this way is similar to the way one sees if scientifically literate, especially in terms of physics: all things are very basic matter/materials stuck together.
Then, there’s the concept of “thinking wrong”. Essentially, this means including a number of “random” items into the list of elements in a problem, so that those items may allow us to create a more disordered network in our minds, which should synchronize and deliver a solution faster than working from a pre-ordered network. As detailed in this post about { Network Synchronization }.
There’s also a nice, simple explanation of “Think Wrong” at { Project M }.
And what about Edward DeBono? I don’t have his “Thinking Course” on hand to quote, but he offered a systematic approach to creative thinking which also ties in the ideas from “think wrong”.
Simply, the key is to practice dissecting images (and by image I mean any “thing” perceived to be a whole, which may also function in a certain way that’s considered a part of its image — like a candlestick) and realizing their inherent abstractness, and then re-combining those abstract parts into a new whole which will contribute to solving the problem at hand.](http://25.media.tumblr.com/tumblr_m0n3j7VuaL1qa3q7lo1_500.jpg)
