My little brother started Suzuki cello lessons when he was four years old, and the private lessons were only fifteen minutes long! Even then, I remember that his attention span fell far short. So yes, like the pp, I think that private lessons are premature at this age.
The local Suzuki teacher has some violin students as young as 3, but even though she is very good about changing things up in rapid succession to keep the child interested and very experienced with teaching preschoolers, it must be a very rare child with an attention span long enough to be able to benefit from violin lessons at the age of 3. And that's for a stringed instrument. Percussion instruments may very well be different, as the pp suggests.
I do have three ideas that you can pursue.
1. I would suggest that you and your husband take a few drumming lessons yourself. You can learn some basics.
2. I would search youtube for some brief 3 or 4 minute videos in which drumming instructors give some quickie introductory pointers aimed at beginning students.
3. I would pay drumming teachers for consultations, without your child present, to help you brainstorm ideas of brief activities that you could do with your child.
Then, you can modify what you learn into VERY SHORT duration activities and have your child do them for a minute or two.
You know, things like clapping exercises (to practice rhythm) that you and your child can do together for a couple minutes while waiting in line at the store.
Or you could demonstrate syncopation for a minute or two while driving around town on errands.
Then, another time, you could give your child a pencil and see if your child can mimic from you the correct hand position to hold the drumstick. (I assume that there is a right way and a wrong way, but I don't actually know what it is because I don't know anything about drumming.)
Or maybe you can have your child chant different words to learn different rhythms, like the Suzuki classic miss-is-ip-pi-hot-dog.
Or maybe you could have your child learn to sing the melody of the old standby song from the musical Westside Story (http://www.youtube.com/watch?v=Qy6wo2wpT2k) "IIIII like to BE in a-MEriCA" to learn how to switch back and forth between triplets and eighth notes.
If you just think creatively (perhaps in consultation with a music teacher), you can think of all kinds of quick short fun things that teach your child some basics of rhythm without your child even realizing it.
Instead of a lesson, per say, I think at this age it is more effective to insert what I guess you could call Teachable Seconds. If you change it up constantly, never make it last longer than a couple of minutes, and spread them out throughout the week, then it will stay fun.
Edited by emilysmama - 11/11/11 at 6:58am