The long and short of it is, yes, it is beneficial to your child to partake in a weight training program but here are some things to keep in mind when getting your child into a weight training program.
Children are not miniature adults and so you cannot use the same methods on growing children as you can with adults as children are different from adults anatomically, physiologically and emotionally. Children have immature skeletons. Their bones do not mature until age 14 to 22 years old. In girls, exercise during childhood can have critical effects on bone health that can last for their whole lives.
Children are often vulnerable to growth related overuse injuries such as Osgood schlatter's disease. Children have immature temperature regulation systems due to having a large surface area compared to their muscle mass which makes them more susceptible to injury when not properly warmed up.
Children do not sweat as much as adults so they are also more susceptible to heat exhaustion as well as heat stroke. Their low muscle mass and immature hormone system makes it harder for them to develop strength and speed and their breathing and heart responses during exercise are different from an adult's which affects their capacity for exercise.
Now, boys and girls can greatly improve their strength with weight training but as opposed to adults, neurological factors instead of muscle growth factors are mostly responsible for these gains. When considering a program for a child, medical clearance should be obtained first and foremost. The best first approach for designing a program is to establish a repetition range of 8 to 12 and keep the work load appropriate for that range.
Workouts should be spread out to have at least 1 to 2 full days of rest between each workout and the main focus on every exercise performed should be on form and technique, not on weight lifted. Some guidelines to consider are: warm-up and stretching should be done before weight training. Start with light loads and make appropriate adjustments from there. No more than 3 non-consecutive exercise sessions should be done in a week and see that they drink plenty of water before, during and after exercise.
Always remember that if at anytime your child is sick, has an injury of any kind or seems tired or non-energetic, do not have them exercise until you are sure they are better or until they have seen a doctor and have clearance from them.
