Only after puberty. Children should work out with there own body weight, ie. Erunning, push ups, chins, flexibility, etc. After puberty begins, they can start resistance traing with weights, but following proper supervision.
? strength training? Kids can be taught many healthy skills including strength training as soon as they show interest. The aap and certified trainer organizations recommend all such programs be run by trained individuals & focus on proper technique in the beginning. Such things as power lifting & body building should be avoided until the child reaches skeletal maturity (shaving daily & at final height).