How old is your child? Depending upon the age of your child, this might be behavior that is typical of the age or it might signal an underlying problem. If your child is in preschool, I would talk with your child's preschool teacher about their perceptions and recommendations. Some of this is certainly age-appropriate at this age.
However, if your child is in elementary school, there is a little more cause for concern. Similarly, I would approach your child's teacher and ask for their advice.
Regardless, your child may be eligible for free testing through the school or school district (if they are in preschool). However, there generally needs to be some kind of referral (or you can request it of the special eduational administrator). I have included a link to a sample letter requesting the evaluation below.
anoniem - the member who asked this question - selected this as the best answer posted by another Education.com member.
from a fellow member
In first grade, it is common to see students transpose letters and numbers in writing. You may even see students call out a d when they see a b on flash cards or other letters. The letters you've mentioned seem to be the most common and also includes q.
It's not anything you should be worried about, it is just something that you will want to practice with your child. Through practice, this will improve but even later, you may still see occasionally that your child will write a letter backwards (it is common). As far as left side or right side-again is just a matter of practice. I've seen teachers place stickers on one hand or another to indicate which to use. To make it simple for your child, for instance, if he is right handed, remind him that how he can remember which is which, is he writes with his right hand or vice versa.
I've included a couple links for you, the first is a worksheet for left/right practice and the second is to a site where others have the same concerns as you. It mentions that it is very common with children to do just as you have described and especially with boys, it also mentions that boys may continue this until age 9 easily. If your child was showing signs of dyslexia, there would be many other indications that your teacher would have most likely have noticed.
Children with midline crossing problems generally have mixed hand dominance or were late establishing a hand dominance, have difficulty with drawing diagonals, often split crossing their "t" at the top and have visual spatial issues such as reversing numbers and letters. You may want to have an occupational therapist take a look at your son since he is still struggling with his number and letter writing. There should be an occupational therapist who consults with his school if he is in public school. A good book to read about this is Sensational Kids by Lucy Jane Miller, OTR.
The letter b, p, d, all consist of a stick and a ball, its just their orientation ie: spatial awareness. Most children especially these days, have no experience in spatial awareness, due to sedentery life style.
Physical activity will help, with this, your body needs to experience going up and under, across , etc.. some teachers also however like to teach b and d together> however this is not advisable.
if you put your left hand thumb up and close your fist, your hand will make the letter b, and the right hand will make the letter d, , then you can associate the b, with the left hand, and d with the right hand. I hope this makes sense. :) like the other members have stated, this is a common problem.