Not every parent has the joy of hearing their child say mama and dada (or any special name) at a young age. For some of us, we wait
years. My husband and I only had to wait 27 months, which is not bad compared to some waits. Our daughter was diagnosed about that same time with dyspraxia, also known as apraxia. Verbal apraxia is a speech disorder that is not outgrown, but is overcome. Apraxic children struggle with speech, despite intelligence, because of a disconnect between the brain and mouth. (Apraxia can also affect the entire body, making movement awkward for children.)
Of course, not all children with a limited vocabulary have a speech disorder. Most just have a delay, and for many children it is mild. Our son was like this. Our children had four years of therapy (age 15 months- 4.5 years for our daughter and about six months total for our son at age 2). People often ask me for tips, and thanks to a fabulous therapist who taught our daughter well and helped me to be "mommy therapist," I learned a lot!
I am not a trained speech-language pathologist. I am just a mom who was willing to work hard to help my children's speech development. Below are ideas that helped my children, but every child is different. If you are concerned about your child's speech, especially if they are over the age of two, I would suggest getting an (often free) evaluation through your state's early intervention program. It can't hurt, and then you would know if you child is actually behind or on target. Below is a combination of what we learned to help our apraxic child and our speech-delayed child.
Sign Language
By teaching your child a few important signs, your child will be able to pair movement to the specific word. Communication is the goal, and sign language enables communication. Speech will follow.
(I was shocked at how quickly my daughter learned a word approximation for the word help after teaching her the sign. It was within a day or two, and at that point she was not even capable of saying mama or dada.)
Label Everything
When the parent gives a name for everything from apple to zoo, it increases the child's mental vocabulary. At some point the mental vocabulary will become spoken, but it is a slow process. By giving a name to every day objects and activities, you will soon be able to know what interests your child most.
Add a Word
Once your child has a word
or word approximation in his or her vocabulary, have him put two familiar words together to get what he wants.
"More, please."
"More milk."
"Dad, up."
At first just have your child repeat one word at a time, but model the two words together. When you take the time to request your child add a word, make sure you require him to say each word. Eventually, you can require that the two words be used together in one sentence before giving the desired item. Eventually, add a third word , but remember this is much more difficult!
"More play, please."
You might also consider spending time teaching a new phrase. If a child has mastered a two or three word phrase to make desires known, think about what else could be taught.
"I want milk."
"I want milk, please."
Books, Songs, Crafts

Though not all children love books or music, both can increase a young (AND older) child's vocabulary. In our home, we have found that songs are especially helpful for toddlers. Even if a young child only sings the "O" out of E-I-E-I-O, it's still singing and repeating. More can come later.
For older children, I have been amazed at the way my four year old is aware of language in books and music. Just in the past few days she has asked what
curious, chowder, and
dam mean. Even younger children can learn A LOT from books and music! It really expands their world!
Parent-led crafts can also be a great way to encourage speech. We created a
ABC Speech book (pictured) and have shared
various speech crafts/activities. Please, please remember that just because a child is not capable of speech (especially after age 2), they are still capable of learning colors, shapes, numbers, and
letters.
"THAT"
Though our son is nearly three years old, he will often request something by saying, "I want that." At times he has a word for the object of his desire, and other times he does not. I attempt to ask him to tell me what "that" is each time he uses the word. If he doesn't have the word, I model it and ask him to repeat it.
Purposeful Play
Our SLP really modeled well how to have parent-guided play. She never stopped talking or singing the entire hour she played with our daughter. Purposeful play, to me, is just when I, as the parent, spend time with my child playing. During this time, I have expectations and lead the play (instead of my child). During purposeful play to encourage speech, don't allow the child to have access to all the toys you are playing with. For example, if you are playing with a farm set, the animals/farmers/machinery may be playing hide-and-seek. Until your child asks for them (by sound, word/word approximation, or sentence depending on what s/he is capable of) they stay hidden. Once your child has them, the animal can help count, find colors, or even just practice sounds or words.
I don't think that is a very adequate description of purposeful play, because it is best to see it in action. We learned so much from our SLP, and much of our daughter's overcoming apraxia probably had to do with purposeful play.
This same theory can be used at meal times to request things like cups and bowls, forks and spoons. Let your child choose the color (you model first) of the item in question. Name the items on his or her plate. You can even choose a snack or meal time when your child is not in control of the food. Instead, she needs to ask for mmm/muh/more with each bite. Remember, it's whatever she is capable of doing.
Articulation
It's hard when you can't understand what a child is saying when they actually want to talk. When our son first started talking, it was suggested that we use short, clearly spoken sentences. If we knew what he was saying, we would model it clearly and slowly, as well. We still model for him, but now that he is speaking a lot, we can't correct him all the time. Instead, we just choose certain times of the day (maybe meal time or play time) when we will model correctly and ask him to repeat it back to us.
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Remember, this is just what was helpful for us, and I am not an SLP. It's also a combination of what we did with our son and daughter. Honestly, with our apraxic daughter some things were skipped altogether due to the way she blossomed near her third birthday (with minimal speech prior to that). Our son's issues were mild, so our treatment of his speech problems were not intensive. However, we still thought about speech expectations throughout the day to help him become a better communicator.
If you find this information helpful, please let me know. If you can add to the conversation (because I really did limit myself) please share in the comments, too.