Ignoring the attention-getting behavior of hyperactive children can be a helpful tool to classroom teachers because often the frequency of the misbehavior will decrease and even stop. What operant conditioning process does this technique utilize?

The operant conditioning process which such technique utilizes is known as Extinction.

Explanation:

Extinction is said to have occurred when a previously learned behavior disappears simply because it is not being reinforced or entertained by someone or something else.

Taking an example from the question, the children in the classroom get the attention of their teacher by being hyperactive. However, when the teacher chose to ignore such attention-getting behavior from the students, they gradually become less hyperactive and in extension, less misbehaving.

It would eventually get to the point which they no longer crave for attention by misbehaving. When that happens, extinction is said to have occurred.