Thursday, February 22, 2007

Higher order thinking - a thought experiment

I was challenged by the Connectivism conference to clarify what HOT (Higher Order Thinking) is. I was challenged by the perspective that Higher Order Thinking is not really distinct from other forms of thinking, it just consists of deeper levels of understanding, making more and better connections.

Bloom's Taxonomy helps a little but I suspect Bloom was a writer, a verbal reasoner, not an engineer. His highest level, Evaluate (assess, judge in relational terms), sounds a bit like making connections, it doesn't really ring true for the hard sweat of deep thinking for me.

So I decided to observe deep thinking in the only laboratory I have, inside my own head. To conduct a thought experiment. The big risk here is that we all think differently, we already know that there are verbal and visual thinkers, I'm definitely visual. Does my mental model building hold true for other visual thinkers?

So I decided to observe my thinking and document it. I wanted to analyse deeper thinking, problem solving, the example that came to mind was the truss, I don't know why, nor do I know why it came to me while riding my bicycle.

The word "truss" is stored along with a visual image of a truss, it looks something like this,

except that I can't visualise all the bars at once any more than I can concentrate on them when looking at them now.

I searched my memory for all connections and came up with the words "statically determinate", from that I was able to to retrieve a kind of visual image of a structure where, if you took out one member it would fall apart but if you added another, the braces would fight each other and you wouldn't be able to calculate the forces in the structure. Also the image of the triangle came up as the building block of statically determinate structures.

A visual image of the members being hinged or pinned at the joints came up like this.

Ok it's looking good, there's quite a bit of retrieved data and the problem is, in theory, solvable. But so far there's no higher order thinking, I have been bouncing round Bloom's lower order: 1. Recall data 2. Understand 3. Apply (use). Its all retrieval, making connections, so far.

Now time for the deep thinking, I build an animated visual image of the truss under gravity in my mind. I know it will sag, everything does, this is another connection, data by association. I allow the visual image to sag and observe it, a bit like this:

I observe that the top bars must shorten and the bottom bars lengthen, those visual images trigger the words "compression" and "tension". Yes I think the top bars are compressed and the bottom compressed.

Let's check that, let's run the mental simulation with a top bar removed, it plays in my mind like this.

Yes the top was definitely being compressed.

Now run the mental simulation with the bottom bar removed, it runs like this.

What about the diagonal braces, take one from the middle like this. I imagine it like this.

The structure doesn't know which way to fail, it could twist just as easily either way. I'm thinking that the force in the brace is near zero.

Does this hold for all braces? Try for an end brace like this.

No. So I'm thinking that the forces in the braces are zero in the middle and increase towards the sides. I've got a feeling that they will alternate between tension and compression but this mental simulation is getting taxing and I am at risk of falling off my bicycle.

What have I achieved here? I am satisfied that lower order thinking can be thought of as making connections, as information is recalled and cross checked against other data, checked for consistency, understood.

When the higher order thinking takes place, problem solving, the thinking is qualitatively different. It uses the "virtual serial machine built on top of the hard wired evolved natural predominant parallel processing" of our brain.

Mental models are built, understandings are constructed. The language of constructivism better describes the thinking process. HOT is different.

The simulations were run with sodaconstructor and captured with Cam Studio, then uploaded to Google Video.

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