Thinking and Deciding

KNOWLEDGE, THINKING, AND UNDERSTANDING 23
But they refused to apply the formula to new cases, such as a parallelogram depicted
standing on its side, which had not been among the original examples that they had
studied:
They also were given other new cases (which Wertheimer called “A problems”)
that followed the same principle: A rectangle was made into another figure by removing
a piece from one side and attaching it to the opposite side, as shown in the
following diagram, just as a parallelogram can be made into a rectangle by cutting a
triangle from one side and moving it to the other side (without changing A, b, orh).
Some students did indeed apply the formula to such cases, multiplying the base by
the height to get the area, but these same students usually also applied the formula
to other problems showing figures that could not be turned back into rectangles by
moving a piece around (B problems). In sum, learning without understanding was
characterized either by lack of transfer of the principle to cases where it applied or
by inappropriate transfer to cases where it did not apply.