Do you agree with the idea the brain processes size by observed surface area?
This is why I ask.
I ask adults to draw a square. Then I ask them to draw a square "Twice as big" as the first.
Almost every time the second square is four times as big as the first.
It is rare that someone diagonally halves the square to create the new square out of the long side of the triangle created inside the original square.
We all learnt from school about square roots yet it seems that adult brains cannot draw simple shapes such as squares "Twice as big".
Is the problem because we all learnt shape from MAB where we are taught "Twice as big" means double?
Are children being confused when one square unit made "Twice as big" suddenly becomes a rectangle 2 unit long?
I understand that MAB is meant to teach place value.
However I wonder if it does so at the expense of proportion?
Would an 'untrained' child believe a root two times root two square is twice as big as a unit square? Or would that child, like an adult, believe a root four times root four square (2x2) is "Twice as big" as a unit square?
My apologies for asking such a simple question. All the childrens' books I have show pictures of half a circle or half a square and so on. I am yet to find a child's math book that retains original shapes when a circle or square is made "Twice as big".
I know there are lots of questions withing this post, yet any simple insights would be appreciated as would direction on any research.