teach (& teacher)
This sign can use either a double movement or a single movement. A more casual version of the sign starts considerably lower. The more formal version of the sign is done up near your forehead. The double movement indicates "teaching" as a process. For example, I'd use the double movement to convey the concept of "teaching" in the phrase "I enjoy teach(ing)."
I'd do the single movement version of the sign in the phrase, "I TEACH ASL." There is a lot of variety and you will see people doing it either way and meaning the same thing--so don't stress about it.
The sign starts near your head and moves out. Imagine taking information from your head and putting it into someone else's head.
The sign for TEACHER combines one quick movement for teach and then does the "PERSON" sign.
The sign TEACHER starts with both hands held up near the head in somewhat "flattened O" handshapes.
Then both hands move forward about six inches. Then they change into "flat hands" (like "B" handshapes with the thumb alongside--not draped over the palm) and move downward to show a version of the PERSON sign. Thus you have a combination of TEACH + PERSON = teacher. Memory aid: Take information from your head and put it in the other person's head.