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Topic: Research on "Twice as big"
Replies: 19   Last Post: Feb 27, 2011 1:15 PM

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 Jonathan J. Crabtree Posts: 355 From: Melbourne Australia Registered: 12/19/10
Re: Research on "Twice as big"
Posted: Jan 22, 2011 10:15 PM

Thank you all for your input. I really appreciate you putting your minds to this unusual question.

I'm curious about naiive math or intuitive math.

Twice as many involves counting or subitising at its simplest. Twice as long, twice as high and twice as many may be more left-brain measurement.

I remember learning to draw by a technique in which you copy a detailed image. Yet the detailed image is upside-down. The idea (which seems to work) is that the non-numeric right brain then asserts control on the visual processing.

Then the artist turns their drawing the right way up and is delighted to see art!

The alternative is adults will draw the image via measurement and estimation of angle, which results in a bad outsome.

Perhaps twice as big or twice as large relates to size before the left brain and symbols get in the way.

So just as with the square, if I asked adults to draw a circle and then draw a circle twice as big/large they still have no idea what the result looks like, let alone how to draw it.

I believe children think of scale and ratio by comparing relative sizes well before they learn counting. My hypothesis is that you shouldn't need a formula to draw circles or squares approximately twice as big...

So rather than number, I'm wondering about ratios between consistent forms.

A farmer who can't count, may intuit the 'twice as big/large' shape by wondering about how much crop could be sown inside the shape.

A painter might intuit the twice as big/large shape by contemplating how much paint might be need to paint the shape.

A cook might contemplate how much extra dough might be needed to make a pizza twice as big/large.

To me, visual mathematics may be better taught the way people naturally observe the world without symbols and formulae interfering too soon, which is why I'm interested in this area of learning. So while my approaches may not be for everyone, I believe they may help those with either math anxiety or dyscalculia.

As for MAB, it's an acronym for Multi-base Arithmetic Blocks. Perhaps you know them as Cuisenaire or Dienes in the Northern hemisphere.

As it appears there may be no research on this question, I will start surveying adults and children to see if young children are better at estimating 'twice as big/large' an area than adults.

Thank you all again for your interest.

Jonathan Crabtree
Geelong, Australia