The question why people can't draw twice as big or twice as much is interesting to me.
Whether or not the question is unclear may depend on innate thinking styles. That's my hypothesis.
Mathematicians have the right to defend a square twice as big having four times the area and claim the question is wrong.
Children start off in a big and small world. So I'm attempting to work out how best to retain intuitive geometric precision before that ability diminishes.
This is an area of great confusion. Talk to people who sell televisions. When 4:3 went to 16:9 people's big screen televisions presented old shows SMALLER on their bigger screens.
When buying a big screen TV it's never about 4 times the viewing area is it? It's measured on the diagonal.
So yes I know if I tell people to draw a square with the sides twice as wide or twice as high then of course, everyone will make a square four times the area. Similarly if I tell them to draw a square with twice the area they may do better.
Somewhere along the way between big bigger biggest and small smaller smallest, math became the most hated subject amongst our customers.
Attempting to shed light on why, at least to me, does have some worth if the dots of investigation are connected to cognitive styles of students.
Would it help if I did the experiment with circles as well? If so, how would you like my 'twice as big' question asked?
I haven't found any research on this, so while my approach may not be agreed, I am open to suggestions to improve.