I had a student tell me the other day that he "still doesn't believe that time changes depending on how fast you go".
Because we live in a low-velocity, high-friction world, it is a constant challenge to get teenagers to let go of their misconceptions of how physics works.
Everyone today understands the idea that motion is relative. Galileo first outlined this principle. This is pretty much the idea that if I throw a ball up while I am traveling in a car, it will return to my hand, regardless of the speed of the car. The motion of the car and the motion of the ball are independent. In the car, I see the ball travel straight up and down. Someone on the street will see the ball travel in a curved path, since it is also moving at the same speed as the car. This, in a nutshell, is relativity.
Special relativity (proposed by Einstein in 1905) explains what would happen if the car started traveling really, really fast compared to the guy standing in the street. In 1881, two American scientists, Michelson and Morely, confirmed that light travels at a constant speed. Einstein took this fact to some interesting conclusions. Light always travels at the same speed; so if you gave a flashlight to a guy on a train and a guy standing in the station, both see the light from their flashlight travel at the same speed. Galilean logic tells you that the man on the train should see light go faster, since the speed of the train is being added to the speed of light. But no matter how fast he goes, the light beam will always travel at the same speed away from him.
To keep light at the same speed, distances must shrink and time must slow down for fast moving objects (speed is distance/time).
Lucky for this kid, he doesn't need to believe in time dilation for it to be true. I say "lucky", because if special relativity were not true, his cell phone wouldn't work, and then he'd actually have to do something other than play Plants vs Zombies on a regular occasion.