Three year olds are not learning by the month. They are putting concepts together and linking words. Here is a good development chart for three year olds.
Use pronouns I, you, me correctly
Is using some plurals and past tenses
Knows at least three prepositions, usually in, on, under
Knows chief parts of body and should be able to indicate these if not name
Handles three word sentences easily
Has in the neighborhood of 900-1000 words
About 90% of what child says should be intelligible
Verbs begin to predominate
Understands most simple questions dealing with his environment and activities
Relates his experiences so that they can be followed with reason
Able to reason out such questions as "what must you do when you are sleepy, hungry, cool, or thirsty?"
Should be able to give his sex, name, age
Should not be expected to answer all questions even though he understands what is expected
As long as you know he can hear and understand you, don't worry. He'll get it. Just make sure while you're doing things like taking a bath and other things you chat with him "We're gonna clean your arms now, cleaning your arms. Do you want to clean your arms