Date: Mar 10, 2010 6:12 PM
Author: Allan Turton
Subject: FW: 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.
On 10/3/10 1:02 AM, "Mary" <firstname.lastname@example.org> wrote:
> If these remarks are inappropriate please forgive me. I'm diving into the
> middle of a discussion without knowing what's been said except for four
> posts in my email.
> Certainly I have been irritated by the lessons, etc., that do not include a
> square as a rectangle. I do not know whether or when this original, taught
> misconception becomes a handicap.
> My concern is whether you have considered the tendency of young children
> when copying the typical diamond with long axis vertical to exaggerate the
> two sharp points by putting "ears" on them. Also I can remember by own
> frustration by being unable to copy the shape of a holly leaf. Time and
> again I drew scalloped edges, lobes out, which I could see was wrong but
> could not correct. I do not know how old I was, nor do I remember noticing
> when that changed, nor do I know whether this is as typical as the diamond's
> These considerations do seem to be relevant to the problem of appropriate
> shape names for young children.
> Mary Krimmel
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