If you want to train your calves and burn fat, we recommend jump rope over calf exercises. Even better would be if you got seriously into a sport like cycling (not an exercise bike). However, these activities are NOT recommended if you are trying to put on muscle mass; you need those calories for growth.
The calves are one of the hardest working muscle groups in the body, the source of many postural imbalances, the solution to foot and ankle pain and injuries, and of course, very attractive. From the day you start walking, they go to work from sunrise to sunset. It's not impossible to grow them, but understand that a lot of it is based on genetics. Take a look at most NFL players. You will see many with small calves, yet their level of leg strength is far beyond the average human. The point is that calves have a minimal direct effect on strength. They are more of a functional component of our body, responsible for mobility and stability of the foot, ankle, and knee. They play a significant role in the kinetic chain (all joints). Be sure to have a look at the lesson on Ankle Mobility.
Beyond this, the time required to make changes may not be worth your time. Don't go thinking some calf raises are going to make your calves grow like other muscles on your body.
With all of that said, you don't want to ignore the calves and they can be fun to train.
Note: You can add weight using dumbbells, kettlebells, plates, etc., to most of these.
The calf raise movement is known as plantar flexion (stepping on the gas pedal). There are 8 muscles that play a role in plantar flexion. Training bent knee variations will give more emphasis to certain calf muscles. Because the gastrocnemius (the surface calf muscle) crosses the knee joint and contributes to both knee flexion (bending the knee) and ankle plantar flexion, bending the knee places it in a slack position and will reduce its role in calf raises.