Thanks Walter. It would be nice if everyone would start off with the more general classes as we seem to do it with everything else when kids are young. With two children under 4 in my house I am constantly explaining general classes and introducing specifics only as the need arises: ?This is a dog. This is another type of dog. This is yet another dog and another. That small one is called a Chihuahua - they look kind of like big rats, don?t they? But they?re actually dogs.? They get it pretty easily, just as Doug Clements suggests.
But when it comes to geometric shapes in classrooms or in story books we?re rather let down. The ?end-points? are nearly always used - I?ve yet to see a page in a story book that has ?rhombus? at the top of the page and pictures of squares and non-rhombuses underneath. They?re using the class name for only part of the class of ?rhombus?. Therefore, only non-square rhombuses get attached to the label.
I just can?t help thinking that if we had ?end-point? names then we could at least work with whatever approach seemed best. If the research tells us to start with specifics and work towards generalities then we could do so without any confusion. I?ve done this with my 4 year old - she understands at a basic level that squares and oblongs are both types of rectangles because the corners are all the same size and that?s what makes rectangles special. Similarly, if the research tells us to start with generalities and work towards specifics we could do that too, knowing that once we hit the ?end-points? we can say, without any conflict, that ?this type of rectangle is an oblong? and ?this type of rectangle is a square?.
Thanks for reminding me of the circular frames for orientation - such a simple idea to implement. I think it?s a related issue but only part of the problem. Orientation and prototypical examples are easily fixed, but if you have an imprecise label for multiple examples you?re still stuck when it comes to naming things. At the other extreme is over-specification as Michael De Villiers showed in his ?Extended Classification of Quadrilaterals? - I certainly don?t expect us to get to that level of labelling for kids aged 3-15, but at least it shows that it is possible to assign labels to very specific end-points.