Friday, March 11, 2016

Model-making & Mathematics

All of life in a body is spent making correspondence with models that only exist in the mind.

I can only write with this pen because in my mind, there is an idealized structure that is "pen and paper". 

Each action we make is modelled first within this internal world, fashioned piece by piece since our first conscious thought.

As I look about me most of what I perceive first took its form within a human mind. Only the trees outside the window deny a totally mind-made world.

In this way, we can see how marvellous the human mind is, for even if the pen I have is unlike any other I have seen or used, my model is flexible enough to accept this as a "pen".

Analogously, we attempt to pigeonhole all objects and circumstance into our marvellous internal world. 

As an infant, we encounter new situations frequently. As an adult, it is sometimes hard to cope with change. This is why "a childlike" way of looking at the world is so much more adaptive. Recent attempts at teaching organized, non-linear thinking attempt to cultivate that childlike flexibility of the mind (non-judgemental brainstorming).

Mathematics is the most organized study of the model-building mind.

This is, of course, a very abstract study however; and is difficult for people not acquainted with self examination of their innate model-building abilities.

Perhaps this is a potential area for instruction to aid in building math skills. If we can train people to be aware of their daily application of models, they might become more inclined to see mathematics, not as an odious chore, but as the most natural of studies.

Traditional mathematics is, of course, tied into an elaborate language system.

Learning the language is the later, secondary concern, however. You could not teach a human language before they had been able to live in the culture and develop an internal scaffold system on which to hang the labels, which is exactly what language is ~ a set of labels for mind-models.

For too long, the teaching of mathematics has taken place in a vacuum where few models exist and little or very weak scaffolding is built.

We cannot expect to put a newborn child in a dark, quiet room, fed intravenously or with tasteless, textureless food, and expect them to emerge at age eighteen reciting Shakespeare!

So with the language of model-building.

The joy of mathematics is the common model that it allows us. It is as if we could all be connected by telepathy, so that each could show their models to all others. Mathematics is the "standardized model kit".


  1. Observing a child do it's job which is trying to make sense of our senseless world, is a fine way of jolting us out of our stagnant thought patterns.

    1. Absolutely Coline! Understanding that has made being a teacher, and a grandparent too, so much richer.