This is a very common speech impediment. My daughter actually just "graduated": out of speech therapy after working on her "r" sound. I can tell you what she did in her therapy and it is easily done at home, as that is where most of her practice took place.
You will need to first determine if she is capable of making the "r" sound and in which situations she cannot make the sound. You can do this just by having her repeat different words and different sound combinations. For example, some kids can say it at the beginning of a word or when followed by a specific vowel. Start there, then work into "r" being at the end of a word. Don't forget to move into words where "r" is in the middle or comes after another consanant.
Words to try:
raw, race, rest, real, rink, rice, root, row, rule, run
corn, care, car, war, wear
tomorrow, current, sorrow
Then move into combinations like green, grandma, grin. grass, crab, crow, crown, crystal
My daughter had a problem with all of them, but more so with the combination words. They all sounded like a "w".
So, what to do about it? Train the muscles in the back of the mouth and throat to make the sound. Two common ways that this is done are 1) to make a car screaching sound like the brakes. "rrrrrr". If that doesn't work, then move to a gutteral growl. Teach them the difference between the sound they are making and the correct sound by forming their lips in a way that they show their teeth (much like if you were going to bite someone - nice example, huh?) rather than puckering them. Do this intensely once a week. Play a game and before they get their turn in the game (any board game works), they have to say a word correctly. The reward is their turn. Don't be so specific and perfect that the game isn't fun. Reward baby steps! Anything better than the sound they are making is progress. Now, pick 4 or 5 words that are particularly difficult for them to say. On the other 6 days that you don't do the game have them say each of those words, reminding them to show their teeth or growl. Only go through the words 1 time each day because you don't want them to get frustrated or not want to do it (you can do the game more often, in which case you'd do both the game and this suggestion.)
It will take a LONG time, but you will see baby steps. You will need to do a lot of reminding, because some of this is simply forming a new habit. Sometimes I have my daughter repeat what she is saying 3 or 4 times until she says it right. Usually it only takes a reminder now, though. You canwork on a cue, like touching your throat or touching the top of your head or something that will remind them in public rather than saying something out loud, which will embarass your daughter. Nine year olds are starting to get self-conscious and don't want a public display. They may not even like doing it at home, so work out a reward that works (a dime or quarter a day, or candy if you are not opposed to that.) We just did a high-five each time she got it right.
With your daughter & Smockity's being 9, they have had a LONG time of those muscles being lazy and this also being a bad habit. It may take longer than the 5 months that my daughter took and it takes consistency of doing this every day.
If they are not even able to make a gutteral "r" sound using their throat, there may be a physical concern that should be discussed with a professional. I don't know what those concerns would be because it didn't apply to us. Your pediatrician can refer you for speech services through private companies like Easter Seals if you don't want to go through your local school district. Easter Seals was great for us! (Insurance coverage varies depending on your provider and the diagnostic code.)
Keep in mind that we have all different accents and tones of voices in our country. Mangling the "r" isn't detrimental to survival. Sometimes it takes a child getting old enough to become aware of it themselves (teenager) and willing to self-correct. So don't despair! Keep it positive and encouraging and just work with her and she'll probably come around within a year (if you're consistent.) My daughter took just less than 6 months and she still makes it as a "w", but she is capable of "r" and with reminding she will switch it, so it just takes A LOT of practice.
I'm not placing blame in anyway. I will just say that "baby talking" to babies and kids doesn't help. They repeat sounds they hear. That is my primary arguement against Elmo. Sesame Street was so much more educational 35 years ago! Keep that in mind when talking with your kids and other people's kids.
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