And thank you, Allan, for realizing that my post was well-meant.
In my recollection, the ears really do look like animal ears, rather like donkey ears, and that is what child psychologists called them. Have you seen them? I think they showed when a child (perhaps about two?) was too young to have been exposed to any shape discussions. Still, one asked the child to copy a drawing; I doubt that it was ever spontaneous. I do not know whether the tendency was much investigated, whether the orientation of the figure could be changed for a similar result, how sharp the angle had to be, what other developmental signposts it correlated to, etc. Worth looking into? Maybe.
The holly is something I've neither heard of nor seen, except in myself. Like you, though, I'm well aware of mirror imaging, have seen many examples of entire names and of indivdual letters and numerals. Lower-case b-d confusion is ubiquitous and notorious. Old and childish, I notice that I am increasingly unsure of left-right, especially when something is upside-down. An example is table setting. At least experience has taught me to be wary, think carefully. I've had no experience with observance of paper-folding, believe I'm in the 90-95% group.
You're certainly right about square-rectangle distinction being a non-issue for most people. I find the spatial approach fascinating, surely productive. I've just made models of a triangular dipyramid and a rhombohedron (hope I have the names right), intend to make more and play with them.
A possibly illustrative aside: I attended a workshop where students were developing and testing alternative, green life-styles. A couple were working on a complicated mechanism for powering a sewing machine with a stationary bicycle. They were unaware of the original treadle Singer I learned to use as a girl. My ingenious electrical-engineer father eventually rigged up my mother's machine to run on electricity! Even interest in Dutch-style windmills is returning, along with the most advanced new designs.
And thank you for posting to the Math Forum, too.
- ----- Original Message ----- From: "Allan Turton" <email@example.com> To: "Mary" <firstname.lastname@example.org>; <email@example.com>; <firstname.lastname@example.org> Sent: Wednesday, March 10, 2010 3:03 PM Subject: Re: Inclusive and exclusive definitions... again!
> Thanks Mary. I'm not sure what you mean by the "ears" - I'm guessing you > mean that they extend the acute angles even further than what they had > drawn > originally. I guess they might have been exposed to the idea that a > diamond > must be "pointy", rather than a diamond must have equal sides. > > The holly leaf difficulty is something I've not seen. Perhaps it's related > to how some people, some of the time, do things as reflections. For > example, > I've noticed that some young children will suddenly write their name > backwards, sometimes with the letters reflected too, sometimes not. I've > also noticed that in groups I do paper-folding with, maybe 5-10% of > children > and adults will do all the steps as a mirror image even when the > instructions are right in front of them. For example, they fold the > top-left > corner instead of the top-right corner. > > As for when not including squares as rectangles becomes a problem, there > are > a couple of instances I can think of, but mostly confined to the classroom > environment. One is in testing situations where knowledge/ignorance of > square-as-rectangle can trip up students on badly chosen test items. The > second is when students are trying to establish relationships between > shapes > to see the value of class inclusion. Outside of school, knowing a square > is > a type of rectangle seems to have almost no value except at trivia nights. > Perhaps this is why curriculum writers can't be bothered getting it > right - > people function extremely well without knowing any different. > > Allan > > P.S. If this email doesn't get through to the email list (as happened with > the ones to and from Walter) I'll post yours and mine at the Math Forum if > you don't mind.