Even though Amphetamines are stimulants, and it certainly seems unusual to treat a hyperactivity disorder with stimulants, they actually have a calming effect on children with ADHD. What is also of concern is side effects, dependency, and other possible long-term issues. Hopefully most parents are also using other types of methods along with medicine to help their child. The over diagnosis of this condition is also something to be cautious of.
The primary basic rationale for using the stimulant amphetamine for treating ADHD is that such treatment accords with all the academic literature on the subject of ADHD and its treatment. One related controversy is that the literature presents no alternatives because none have been considered.
The strange thing about treating this type of disorder is that patients can react so differently to a medication than the logical response might seem. Patients with ADHD react completely differently to a stimulus that those without the disorder. Their brain chemistry is different than others and a stimulus will actually calm rather than excite. There are other modes of treatment such as changes in the diet, daily routine, or other medications. Most doctors do not arbitrarily prescribe amphetamines anymore. There was a time when this was common place. Now that we understand the risks and side effects better, it is no longer standard practice to simply write a prescription without exploring other options first. For some people, their ADHD greatly impacts their daily life. If ADHD goes untreated in children, it can lead to delays in their education and greatly impact their development. Medications are sometimes needed to allow children and adults with severe ADHD to have healthy, productive lives.
You might be interested to note that other stimulants are also recommended for children with ADHD. For example, instead of using amphetamines which of course are serious medication, coffee can be taken by children because of the caffeine and the way that it acts as a stimulant. It can help children calm down.
It's important to note that most physicians, families and educators try very hard to not make "extensive" use of amphetamines without justification. My experience has been that most care providers are very cautious about prescribing medications, particularly with very young patients, and will start with a very low dose and increase it in small increments as needed, based on observed response to the medication.
Apparently amphetamines are used in the treatment of ADHD because they improve concentration and help to calm people suffering from this condition. Apparently they help people to focus better. Treatment of psychological conditions with drugs seems to make a good deal of sense, since it can be argued that psychological conditions are ultimately chemical conditions. Of course, the whole science of studying brain chemistry is very much in its infancy, and it will probably be a very long time before we develop treatments that are highly effective and entirely safe (if the latter goal is even attainable).
Here's a link that may be helpful to you: http://www.nida.nih.gov/infofacts/adhd.html