On Saturday, when I derived some area formulas, a junior high school student said in regard to the formula for the area of a triangle: “Oh! That’s why there’s a 1/2!”
Poor kid. She’s had teachers too incompetent in and careless of reasoning to address the precious, budding reasoning in student’s minds by showing something so simple as the fact that a triangle is half a parallelogram, which has the same area as a rectangle, which can be measured by unit squares.
Reasoning out the formula is not difficult to show nor hard to grasp.
She’s had to suffer with learning area formulas — and no telling what else — based on authority and on the premise that she cannot understand.
She needs a more rational education.
She is having to merely memorize facts given her by an authority and in an unintegrated, non-logical manner, causing her to be impaired in judgement and in achieving goals.
She should be trained to use the complex, powerful machinery of her mind so she can live her life and make her way in the world.