Wednesday, May 06, 2009

what lies behind spatial ability and computer ability?

Great comment from alan kay about spatial learning in response to mark guzdial's geek gene post:
Several things to think and read about here. First, Hadamard's "Psychology of Invention in the Mathematical Field" (amazon books link) is one of several non-optional prerequisites for any discussion of these ideas. (These and other careful studies from the past can cut out a lot of mere opinions if people would just read them -- "mere opinions" are the fatal disease of the web ...).

Second, it's worth trying to be a little more subtle in thinking about this issue. For example, is it "spatial ability" that is the actual correlate or is it what *lies behind* "spatial ability" *and* "computer ability". Quite a few of the best minds of the past (including Hadamard, Jerry Bruner, etc.) would say that "a feeling for cause and effect" and "an increased ability to use abstractions for ideas" actually come out of what can be learned first via manual manipulation and visual and other figurative modes of thought. Many of the tests for "spatial ability" are actually as much about "fitting together" as they are relative locations of things.

The notion of "variation" seems non-democratic and even politically incorrect to some, but nature doesn't care about our opinions on anything (this is why it is psychologically difficult to be a scientist). Significant variation exists, even for the most common human traits (like learning language). It would be astoundingly unusual if every child had the same propensities for learning computing. And at a deeper level, it would be astounding if every child had the same propensities for grokking cause and effect relationships and chains of reasoning.

I think a better ploy for general education is to embrace variation by having different strategies for different propensities. For subject x, it's a lucky child who has a lot of pre-wiring for it. But there's no shame for those who don't, to do enough extra skill learning to artificially build scaffolding that wasn't there. I think pedagogy is largely about how to help those who aren't blessed with supreme talents. (And for "great unusual inventions" -- like modern science, math, equal rights, etc. -- almost no humans have a lot of built-in skills (this is why it took thousands of years for them to be invented in the first place!)).

Every musician knows what I'm talking about (because music requires lots of different abilities and it is an extremely rare bird who is pre-wired for all of them -- instead when musicians talk with each other, they will exchange stories of what they had to work at and what came more naturally -- and the areas mentioned as being easy and hard are different for each musician -- but in the end they can all play with each other and create beauty together -- this is not just a metaphor, but a real analogy).

This is generally true for any highly developed field, whether in sports, the arts, or the mathematical sciences. And trying to do a good job with what this really means for pedagogy and curriculum, is certainly one of the most important yet most neglected processes in education.
Notes:

(1) The Hadamard book (google books link) was first published in 1945. Minsky mentions it in The Emotion Machine p. 240 stating that other authors have proposed similar models of thinking (Poincare, Koestler, Miller and Newell and Simon)

(2) Bruner: "doing with images makes symbols" provides a hint as to how to develop an honest children's version of powerful ideas. For instance, etoys (visual programming) is software developed around this concept. Children manipulate icons in a rich virtual environment, one idea is that this might lead to better symbolic or abstract understanding of how the simulations work.

How do we know what a "powerful idea" is apart from subjective assertion? For some ideas about this see non universals

3 comments:

Doug Holton said...

"Quite a few of the best minds of the past (including Hadamard, Jerry Bruner, etc.) would say that "a feeling for cause and effect" and "an increased ability to use abstractions for ideas" actually come out of what can be learned first via manual manipulation and visual and other figurative modes of thought. Many of the tests for "spatial ability" are actually as much about "fitting together" as they are relative locations of things."


There has actually been new research and theoretical work on spatial ability and perception in the past 40 years since Bruner and Hadamard and the like.

In particular it isn't that we learn something first 'via manual manipulation' and then discard that representation for purely visual or abstract representations. The manual manipulation continues to underlie even visual and abstract reasoning as well. This is based on research on embodied cognition, mental imagery, and perception & action.

See for example just one recent paper (there are numerous books on the topic, too):
http://cogprints.org/5780/1/ECSRAP.F07.pdf

Alan Kay said...

Of course, that is what I meant and actually what I did say. In particular, what you say -- that "manual manipulate continues to underlie...." etc. -- is just what Bruner postulated.

There has indeed been new research on spatial ability, etc., but all that I'm aware of in regard to this property simply supports both Bruner and Hadamard.

Cheers,

Alan

Tony Forster said...

Hi, this is an interesting thread for me.

I found "Exploiting mental imagery with computers in mathematics education" and could read a bit with google books (CH1 Dreyfus) http://tinyurl.com/p6d96d

My thoughts:
Constructing mental images is an important mathematical and scientific skill.

They (are typically?)/can be visual rather than linguistic

The images can be (are?) dynamic rather than static, they can include causality.

They are not photocopies, they are vague and fuzzy and contain abstractions of visual images rather than the visual images themselves(maybe we abstract all visual input to process it)

People who are good at thinking mathematically are good at constructing these dynamic visual like images. They are also good at interrogating them, trying "what if" scenarios.

Programming (incl. Etoys, Scratch, GameMaker) draws heavily on the ability to construct and interrogate dynamic "visual like" mental images and for that reason could be expected to increase mathematical and scientific skills.