When Answers Are Instant, Thinking Matters More
I once watched a student forget the formula for the area of a trapezoid.
That could have been the end of the problem. They did not have the formula, so they did not have the answer.
But instead of stopping, they began to rebuild the shape. They split it into pieces they understood — a rectangle, a triangle on one side, another triangle on the other — and used the areas they did know to work out the area they had forgotten.
It was slower than remembering the formula, but far more interesting.
That moment has stayed with me because it captures something important about mathematics....
