All classrooms are equal but are some more equal than others?
As I trot and jump through respected maths dictionaries, trusted resource books and ‘gold standard’ websites, I keep catching my hooves on something.
It’s a triangle, an isosceles triangle.
I read the definitions for this triangle and start shaking my head.
Faulty Maths Alert Ahead!
You see an isosceles triangle is universally defined as a triangle with 2 equal sides and 2 equal angles with 1 line of symmetry. ‘Fun’ definitions portray a few of the triangles like this:
This is just one example of the faulty maths out there.
The isosceles triangle tends to be drawn in exactly the same way with the base resting on the horizon and ‘two equal legs’ above it. Now I think this is erroneous and dangerously so.
I was taught (and teach today) that an isosceles triangle is a trigon with at least two congruent sides and angles.
Note the ‘at least’ part of the definition there. This is an inclusive definition.
So that makes an equilateral triangle a special case of an isosceles triangle because it has three equal sides, three equal angles and three lines of symmetry (the other special isosceles trigon is the isosceles right angled triangle). Of course, not all isosceles trigons are equilateral.
Is it worth getting worked up about?
If you love maths and the precision of maths then yes, it certainly is especially as so many previous exam papers have got it wrong in their mark schemes and guidance.
Imagine the scene: the question asks you to draw an isosceles triangle so you do. Your isosceles triangle just happens to be a special one, it’s an equilateral triangle. It’s marked incorrect and you miss out on a higher level by one mark.
It’s worth making a case for. There might be quite a few backdated miscarriages of justice buried away worth digging up.
So, there we have it. In most classrooms the incomplete definition is trotted out without a second thought.
Some classrooms really are more equal than others.
Maths curricula, publishers, examining boards and pedagogues have a huge responsibility to get it right. At least Mark Ryan does in Geometry for Dummies.
My feeling is that we need to redefine what an isosceles triangle is and upgrade our books and teaching before things get messy. What do you think?