Hi S.,
I am a speech therapist and thought I would throw my two cents in. At 3, our little guys and gals brains are having soooo many thoughts that it is difficult for their month (which is motorically still developing) to keep up with all that they want to get out. So stuttering/stammering at this age is VERY normal as the other moms have said.
However, you do need to be very conscious of two things...1) if it persists past the age of 5 (not 3rd grade!!) they you should get them enrolled in speech therapy through the school system. The reason this is, is that there are certain stuttering patterns that reveal if the child needs intervention or not...and the earlier the better! Although pediatricians are very knowledgeable in a variety of areas, unless they have had specific history in studying stuttering patterns, they may not be the best authority! If you wait till 3rd grade and you do have a true stutter, then you have missed out on 3 years of therapy and there is usually a self esteem issue that goes along with it!
2) does your family have a history of stuttering (typically a male on either side of the family). If there is a history of stuttering, then you really want to monitor it!! It is hereditary!! 1% of the population stutters and out of that there is a fair percentage that "recovers" from it by the age of 8. But again, if your child is not in that percentage then you have missed out on a significant amount of therapy.
I hope that you don't find this too overwhelming. Please feel free to contact me if you have any question!
Sincerely,
~A. E., M.A. CCC-SLP