We must visualize the things we learn in science and math. We cannot just learn words. Here is an example.

 

I asked the students in a geometry class, “Given a square of side 2 feet, what is the area?”

 

Many students jumped up and said the area is length times width.

 

I replied that I never said anything about the length and width, just a side! They were spouting a formula that they memorized, but did not visualize and understand!

 

I then pointed to a square tile on the floor and again asked my question. Finally they realized that a square has length and width equal, and the area is side squared, which is 4 square feet.

 

Think about what is given, visualize the problem, and think of the reply.

 

Continuing with this thought, I asked them what is the area of a cube, side 2 feet.

 

Some replied side cubed, or 8 cubic feet.

 

Wrong! I asked for area, not volume!

 

How many sides does a cube have? I insisted that they visualize the cube and count the sides. There are six sides, and so the area is 6 times side squared, or 24 square feet.

 

Studying physics, we must visualize the operations, that is, the things we are doing in defining the concepts.

 

Studying biology, we must visualize, for example, the parts of a cell. When studying, we have to constantly refer back to the pictures in the book.