One of the best things you can do to not only remember but understand concepts in math and science is to create a metaphor or analogy for it—often, the more visual, the better. A metaphor is just a way of realizing that one thing is somehow similar to another. Simple ideas like one geography teacher’s description of Syria as shaped like a bowl of cereal and Jordan as a Nike Air Jordan sneaker can stick with a student for decades.

If you’re trying to understand electrical current, it can help to visualize it as water. Similarly, electrical voltage can “feel like” pressure. Voltage helps push the electrical current to where you want it to go, just like a mechanical pump uses physical pressure to push real water. As you climb to a more sophisticated understanding of electricity, or whatever topic you are concentrating on, you can revise your metaphors, or toss them away and create more meaningful ones.

If you are trying to understand the concept of limits in calculus, you might visualize a runner heading for the finish line. The closer the runner gets, the slower he goes. It’s one of those slo-mo camera shots where the runner is never quite able to reach the ribbon, just as we might not quite be able to get to the actual limit. Incidentally, the little book Calculus Made Easy, by Silvanus Thompson, has helped generations of students master the subject. Sometimes textbooks can get so focused on all the details that you lose sight of the most important, big-picture concepts. Little books like Calculus Made Easy are good to dip into because they help us focus in a simple way on the most important issues.

It’s often helpful to pretend you are the concept you are trying to understand. Put yourself in an electron’s warm and fuzzy slippers as it burrows through a slab of copper, or sneak inside the x of an algebraic equation and feel what it’s like to poke your head out of the rabbit hole (just don’t let it get exploded with an inadvertent “divide by zero”).

In chemistry, compare a cation with a cat that has paws and is therefore “pawsitive,” and an anion with an onion that is negative because it makes you cry

Metaphors are never perfect. But then, all scientific models are just metaphors, which means they also break down at some point. But never mind that metaphors (and models!) are vitally important in giving a physical understanding of the central idea behind the mathematical or scientific process or concept that you are trying to understand. Interestingly, metaphors and analogies are useful for getting people out of Einstellung—being blocked by thinking about a problem in the wrong way. For example, telling a simple story of soldiers attacking a fortress from many directions at once can open creative paths for students to intuit how many low-intensity rays can be effectively used to destroy a cancerous tumor.

Metaphors also help glue an idea in your mind, because they make a connection to neural structures that are already there. It’s like being able to trace a pattern with tracing paper—metaphors at least help you get a sense of what’s going on. If there’s a time when you can’t think of a metaphor, just put a pen or pencil in your hand and a sheet of paper in front of you. Whether using words or pictures, you will often be amazed at what just noodling about for a minute or two will bring.

Metaphors and visualization—being able to see something in your mind’s eye have been uniquely powerful in helping the scientific and engineering world move forward. In the 1800s, for example, when chemists began to imagine and visualize the miniature world of molecules, dramatic progress began to be made. Here is a delightful illustration of monkeys in a benzene ring from an insider spoof of German academic chemical life, printed in 1886.