The news for /k/ and /g/ correction is bad and good. The bad news is that they can be difficult sounds for the child to acquire at the sound, consonant-vowel, vowel-consonant and word levels. The good news is that once the child is able to use the sounds in single words, she take off and quickly integrate the sounds into conversation without much difficulty. I have found that, only on occasion, does the child need to be prodded to use the sounds at the conversational level.
There is a pretty good chance that someone has tried to help the child say those sounds and wasn’t successful, so now it’s your turn to try. If the you are the first person to try to help the child, you are lucky because you won’t have to undo what others have tried. Either way, trying to get a child to say /k/ and /g/ can be tough process and requires patience because the going can be slow.
I’d like to start out by saying that I never ask the child to say /k/ and /g/ outright. I don’t even mention those sounds at the beginning because there is a good chance they have tried and failed before. There is some sort of negative Pavlovian response a child has if she believes I will ask her to say /k/ or /g/. Moreover, if I ask him/her to say the sounds or mention them, she later may refuse to cough or throat clear and say she cannot because she suspects I will want her to say /k/ or /g/. (I cannot explain this phenomenon. It is just something I have observed time and again.) If that happens, I will need to resort to desensitizing the child and convincing her to try the cough or throat clear.
I start out by asking the child to cough. Then I ask her to cough with her mouth wide open. If the child resists coughing, a throat clearing or guttural monster sound may work instead. I ask the child how a cough, throat clearing or guttural monster makes her throat feel inside when produced (scratchy, rough, tickly, etc.). I ask the child to place her hand on his throat and tell me what she feels when she coughs/throat clears (throat moves, vibrates, tickles, etc.).
I stay with the cough/throat clear until the child is able to easily produce it upon request. Next, I add in the vowel so that the child repeats cough (pause) vowel sound. If you prefer, you can start with vowel (pause) cough. Over time, I reduce the pause time in small increments. We do this task again as I switch the vowel. I gradually (this can happen in a few minutes or sessions) shape my cough to sound less like a cough and more like a /k/ or /g/. Once again, I don’t want the child to think that I want her to say /k/ or /g/. Then the day comes when I make the leap. I present the model, mouth wide open, with the phoneme + vowel and ask the child to make his/her sound like mine. Instruct him/her to keep his/her mouth wide open. When the child is successful, I make a big deal about it and only then do I tell him/her that he/she just said the (/k/ or /g/) sound. I repeat this for each consonant and vowel (or vowel and consonant) combination. I move the child on to words when she can repeat each combination using the phoneme.
The word level can continue to be tricky because the child may revert to his usual production of the word. Therefore, I prefer to separate the consonant from the rest of the word with a pause, as I described above. It may take less time now to eliminate the pause. If it doesn’t, I remain patient, but determined. I will move the child on to word pairing (come case, keep cane, etc or pick back, sick Rick, etc.) if the pause is still there but slight. Eventually, the child will get it and say the words without a pause. After all, it requires less effort.
There are a group of what I call tricky words. These words contain /t/ or /d/ and /k/ or /g/. Some of these common words are: dog, cat, goat, coat, tag, gate, kite, take, get and duck. I deal with these words separately and in two ways. First, I have the child produce the CV pause C (“do” pause “g”). Again, I reduce the pause over time. I also use contrastive word pairs and their pictures. Thus, I have a picture of a goat and tote placed before the child. I point to each picture, model and the child repeats my model. Eventually, I expect the child to be able to produce the correct word for the picture on his/her own.
I hope these tips help you tackle those stubborn /k/s an /g/s.