Not sure exactly what your control issues are…
It looks like your students are using traditional and omni-directional wheels, powered by one motor per side to power their bot. This kind of drive system (like the claw bot) is used in tanks and skid steers. It is not really suited for quick, precise movement. A fast bot using this system would likely be hard to control.
As to the bevel and differential gears, there is a lot of depth here. Maybe this info will help some…
Bevel gears are simply meant to allow 2 gears, mounted at right angles, to mesh. They change the direction of the motion, but as vex iq bevel gears are all 18-tooth gears, they do not really help with gear ratio by themselves.
Bevel gears, however, are very useful in differential gears. Differentials allow one drive motor to power two wheels that (because of the diffetential) can rotate at different speeds. This makes handling and cornering smoother by allowing the inside wheel to spin slower than the outside wheel during a turn.
Likewise, the differential can shift power between the two linked output wheels. When one is under load, power will automatically transfer to the one under less load. Look up Apalrd in the vex iq forum; he has some excellent examples of differentials in use.
They can even be used to allow 2 motors to power the same wheel, indepently or in combination. Differentials are very versatile and can certainly help with handling/control of fast bots. May take a little research, but we encourage that!
I would start by looking at the example images on the vex iq product page for diffetentials. You might also want to search the Web and this forum for even more examples.
Attached (first 3 photos) are pics of another application that I built. Three motors and three differentials were used. Each motor turned its corresponding differential at a different speed. (2:1, 1:1, and 1:2) The power was transferred through all three by the small 12-tooth gears linking the entire system to create a kind of transmission. Only two wheels (opposite / diagonal) are actually powered, but the differentials allowed that power to “shift” between wheels as needed.
By powering each motor seperately, I got three speeds. When multiple motors were powered in combination, forward and reverse, I got the torque of multiple motors and even more speeds. Slow and powerful, to very fast!
The last photos are of a more traditional AWD vehicle similar to Apalrd’s. Not very fast, but it does use diffetentials.