We engineers are good at math, not necessarily because we are smart, but because we learned math differently others. Most of the population are verbal thinkers, but we are predominately visual. Visual thinkers can skip the reading in a physics textbook, focus on the figures and images, and then better understand the mathematical manipulations. Engineers do not memorize formulas, they internalize them and play with them by altering one variable in their heads. We can see a pendulum in our head while changing the length of the string. Then we can recognize that the period of a pendulum is independent of the mass and solely dependent on the length. We can see the formula and the swinging at the same time. This is very different from another student who might need to memorize the formula and be able to follow a procedure to solve a particular problem. Visual thinkers can have full intuitive understanding, which has obvious advantages over the verbal thinker in fields such as engineering. I suspect that some people do mathematic only by following procedures, while others really understand it by taking the concepts further beyond just following established procedures. When math becomes procedural, it becomes boring and uncreative. Those who claim that they are bad a math say so because they have trouble visualizing the representation of it. Engineers are able to visualize equations as physical representations within the mind.
Engineers are visual or non-verbal thinkers in general. Not only do we represent physics in our minds, we are also able rotate static objects to understand them better. Our engineering designs live in our minds a spatial objects and we can enter our projects whenever we demand. We certainly are not talking to ourselves, we are seeing the thing in our mind. In Eugene Ferguson's book, Engineering and the Mind's Eye (Ferguson 1992), he quotes Richard Feyman (1988) when he discovered the difference between a visual thinker from a verbal one:
I said, "Thinking is nothing more than talking to yourself."
"Oh yeah", Bennie said, "Do you know the crazy shape of a crankshaft in a car?"
"Yeah, what of it?"
"Good. Now tell me: how did you describe it when you were talking to yourself?
So I learned from Bennie that thoughts can be visual as well as verbal.
Research by child development theorist Linda Kreger Silverman indicates that less than 30% of the population strongly uses visual/spatial thinking (Silverman 2001). According to Silverman (2001), "Visual/Spatial learning is the common phenomenon of thinking through visual processing using the part of the brain that is emotional and creative to organize information in an intuitive and simultaneous way." It is the ability to mentally manipulate two and dimensional figures in the brain. Engineers tend to be good at this.