"Knowing" and "Understanding" (1)

"Understanding" refers to a state beyond simply "knowing."
Even those students who can respond correctly when instructed to say the formula for the area of a trapezoid cannot use it correctly when they must actually find the area. For example, when the orientation of the presented trapezoid is changed, they may mistake the hypotenuse as the base.
Such students may "know" the formula of the area of a trapezoid, but it cannot be said that they "understand" it. The goal of mathematics education in Japan is, of course, "understanding."

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