Myopia (nearsighted, shortsighted) vision normally means that when relaxed and looking at a distant object, your sons eye is elongated enough that the focal point of light entering the eye is in front of the retina. Being myopic 1.00 diopter is very low, but do expect changes. Your son is quite young and his eyes may continue to change up until around age 20. Progressive myopia at his age is not unusual.
Remember that being myopic means that you can see near objects quite well, but things distant are somewhat out of focus. With a small refractive error like 1.00 diopter, your son may be able to see adequately without corrective lenses around the house, at the dinner table, or with other tasks that do not require precise vision on objects at distance.
There are a few who believe that the use of corrective lenses will cause myopia. Thus far there is scant evidence that there is any truth to this theory. The same is true for exercises like the Bates Method. When you look for scientific data that prove these theories, you will find that there is none...but there are believers.
Since you posted in a forum about refractive surgery, the answer to the question if LASIK or similar surgery may be appropriate for your son is a resounding NO! There have been a few cases of juvenile LASIK, but these were for extreme circumstances where refractive error was so bad that it threatened natural development of vision function. In my opinion your sons refractive error is very small and the potential risk of LASIK or something similar for a developing eye makes surgery absolutely out of the question.
Ask in about 13 years and the answer may be different.
Glenn Hagele
CRSQA
http://www.USAEyes.org
I am not a doctor.