Monday, August 13, 2007

Higher order thinking - a thought experiment

This is a repost of a blog of mine from February, which has been in draft till now:

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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9 Comments:

Anonymous Daniel Livingstone said...

There is a good (long!) video with Brian Beckham - an academic, physicist and games programmer that I found via the MS UK academic blog:
here.

There are a number of examples included where he explains some of the connections and (HOT?) thinking behind many of the techniques he uses and has developed (particularly in the second half)

I think you might like the video.

Wednesday, August 15, 2007 9:24:00 PM  
Blogger Tony Forster said...

Thanks for the video. Now I'm really happy I didn't spend too much time trying to create a racing car simulation.

The video shows how game making can be a really good way to learn physics. Ive added it to my collection of learning physics through games http://del.icio.us/tonyforster/physics

Though a racing car simulation may be beyond school students, simulations of speed and acceleration, parabolic motion, planetary motion and mass spring damper are definitely within their scope, see for ideas http://schoolgamemaker.rupert.id.au/samples3/

I hope that a student will prove me wrong and write a car simulation. Given a relevant and authentic challenge and the right tools, students can really surprise you with their achievements.

Thursday, August 30, 2007 9:20:00 AM  
Blogger Bill Kerr said...

I'm still suspicious of the term "higher order thinking". I think what we call HOT just arises from more fluency at the lower level thinking. As LOT become automated then HOT becomes enabled

Why chose this sort of thought experiment? ie. one where you keep the pieces in your head? Actually, would things have changed, become clarified, when you put it down on paper (the google images)?

The idea with constructionism is to use external events to assist in the building of (alleged) internal structures - a distributed cognition. I'm thinking that you might have chosen an in your head introspection because somehow you think that is more evidence for HOT? I'm not sure why it would be.

eg. I can play blindfold chess but that just arises from a high level of fluency about chess patterns, I'm not sure that it's really special in terms of cognition, even though most people can't do it

The introspective techniques you have used have been analysed by cognitive scientists. I don't fully understand it but it might be worth check out these links to:
phenomenology
Heterophenomenology

Monday, September 24, 2007 9:53:00 PM  
Blogger Tony Forster said...

Bill writes "Actually, would things have changed, become clarified, when you put it down on paper (the google images)?"

You cannot run the simulation on paper, or not well. It has to run in your head or on a computer.

and "The idea with constructionism is to use external events to assist in the building of (alleged) internal structures - a distributed cognition. I'm thinking that you might have chosen an in your head introspection because somehow you think that is more evidence for HOT? I'm not sure why it would be."

My intention was to examine the internal structure which may be assisted by external supports like pencil and paper.

Friday, November 09, 2007 5:17:00 PM  
Blogger Tony Forster said...

More support for the idea that comprehension and problem solving involves the building of mental models. That better thinkers are able to construct more detailed and robust mental models and better able to interrogate them.

In the literary domain, the Event Indexing Model describes such mental models.

So whether thinking visually or verbally, its still model building

Thursday, February 14, 2008 7:33:00 AM  
Blogger Tony Forster said...

If Event Indexing Model says: situations conveyed in narratives are connected in memory along five dimensions time, space, protagonist, causality, and intentionality.

How are mental models of text based problems indexed? When you build a mental representation of a complex problem space, eg the ethics of cloning, what dimensions are used? How do good problem solver's mental models differ?

Thursday, February 14, 2008 10:59:00 AM  
Blogger Tony Forster said...

“runnable mental model”
http://tecfa.unige.ch/perso/mireille/papers/Betrancourt_Chassot08.pdf

Thursday, February 14, 2008 1:51:00 PM  
Blogger Tony Forster said...

"Kyllonen and Shute (1989) have proposed a taxonomy that represents the spectrum of internal states with which cognitive psychologists are concerned. Their taxonomy begins with simple propositions (e.g., stating that Japan sells more electronic products than any other nation), proceeding through schema, rules, general rules, skills, general skills, automatic skills, and finally, mental models (e.g., analyzing the potential of a trade war between Japan and the United States based on an analysis of balance of trade trends). The latter type of knowledge seems particularly important because mental models are the basis for generalizable problem-solving abilities (Halford, 1993)."

http://tinyurl.com/2598ob

Thursday, February 14, 2008 6:48:00 PM  
Blogger Tony Forster said...

not as original as I thought. see http://www.cs.utexas.edu/~novak/symp92.html which talks about this truss example as a "gedanken experiment" (thought experiment?)

Sunday, May 24, 2009 9:06:00 PM  

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