We just took the first lesson in a Ham Radio class and I realize that getting a Radio Technicians license is a great gateway subject into electrical engineering. It's a bit of math and electronics and a whole lot of fun.
A gateway subject sparks the fire of curiosity into a line of inquiry. People learn faster and better when they are interested in a subject.
There are other educational subject that are gateways to greater understanding.
Cooking gateways into physics, chemistry, biology and mathematics. Alton Brown of Good Eats does a great job of relating cooking to science.
Algebra for higher mathematics. If you have algebra down everything else is pretty easy. We used to complain in our calculus class that the calculus was easy the algebra afterwards was hard, mainly because that was the place we make the most mistakes.
Swimming may be a good gateway to other physical activities, by knowing how to swim you can be confident in water which is a good thing, and is gentle to your body for a workout.
Piano can be the gateway to greater musical talent and appreciation.
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