Why is it that students find it easier to calculate the area of triangle ABC but will have difficulty calculating the area of triangle DEF? Middle school students even believe that it’s impossible to find the area of DEF because the triangle has no base and height!
That knowing the invariant properties that makes a triangle a triangle (or any geometrical shape for that matter), is not an easy concept to learn is illustrated by this conversation I had with my 4-year old niece who proudly announced she can name any shape. The teacher in me has to assess.
Thinking about how a four-year old could possibly think of these meaning of the shapes made me ask: If four-year olds are capable of thinking this way then why do we think that there are students who can’t do math or doubt the idea that algebra is for all?