The graphical illustrations mathematics teachers use enable students to learn geometry more easily by providing them with an intuitive understanding of geometric concepts, which makes it easier to acquire the ability to manipulate symbols for the purpose of calculation. Illustrating algebraic concepts graphically would be equally effective pedagogically, even though the deepest mathematical understanding is abstract, not imagistic. The statements above provide some support for each of the following EXCEPT: a. Pictorial understanding is not the final stage of mathematical understanding.
b. People who are very good at manipulating symbols do not necessarily have any mathematical understanding.
c. Illustrating geometric concepts graphically is an effective teaching method.
d. Acquiring the ability to manipulate symbols is part of the process of learning geometry.
e. There are strategies that can be effectively employed in the teaching both of algebra and of geometry.