Three and a half years is too young for fine-motor skills like writing, particularly for boys.
If he were interested and exploring this on his own, that would be one thing... but what benefit do you see to forcing his development faster than his brain and body are growing?
Look around at the adults in your world... can you tell which ones of them learned to write their name at 2 and which learned at 7? While you may be patted on the back for creating a child who can do things before his development enables him, do you have any idea what kind of damage you could be doing?
At one time in Chinese history, it was considered very, very important for very, very young children to be skilled in the art of conversation. To this end, parents spent enormous efforts and resources, and it was largely effective. Children barely past their first year could hold a conversation with ease.
A great flurry of distress arose at the same time... children as old as 3 were not learning to walk.
Everything we impose from the outside on a child's developmental pace has an effect. How long does it take to find out what the effect is? Who knows? Does early-reading focus cause autism? Who knows. They both seem to be coming up in huge numbers simultaneously... and it generally takes huge numbers (like the flat-headed baby problem of putting babies on their backs all the time) to find out what the effects are, that are not random or individual differences.
For sure, making left-handed people write with their right hands causes stuttering --that is: Brain Damage in the verbal processing centre of the brain caused by forced use of the non-dominant hand... it's one of the reasons there are so few people under 60 who stutter, or ever have. It only took 40 or 50 years of tormenting lefties and doing brain damage to untold numbers of children to figure that out.
I despise mommy competitions (whose baby sleeps the longest, whose baby potty trained the earliest, who walked the soonest, who has the first teeth) mostly because those milestones have *nothing* to do with anything mothers do, but also partly because it de-humanizes the child. Did the child naturally potty train without stress? Great! Does it matter at what age that happens? Seriously? Enough to create stress in the child over it?
And, seriously -- in 13 years, when all the kids can do it, the one who wrote his name at 11 months is *not* going to win any prizes for it, because they'll be indistinguishable.
It just does not matter, now or in the long run.
