BOX 3.4 Finding the Area of a Figure
The understanding method encouraged students to see the structural relations in the parallelogram, for example, that the parallelogram could be rearranged into a rectangle by moving a triangle from one side to the other. Since the students knew how to find the area of a rectangle, finding the area of a parallelogram was easy once they discovered the appropriate structural relations.
In the rote method, students were taught to drop a perpendicular and then apply the memorized solution formula.
Both groups performed well on typical problems asking for the area of parallelograms; however, only the understanding group could transfer to novel problems, such as finding the area of the figures below.
or distinguishing between solvable and unsolvable problems such as
The response of the “rote” group to novel problems was, “We haven’t had that yet.”
SOURCE: Based on Wertheimer (1959).