This figure represents one student's particular classroom behavior during the first twenty days of a hypothetical school year. Let's say the class has a new teacher. A different teacher from the previous year had unwittingly conditioned one of the girls not to raise her hand by constantly reminding her to stop calling out without raising her hand, thus reinforcing her interruptions with attention, and causing it to happen more often. The new teacher studied some behavior analysis techniques and learned how to thoroughly ignore undesired attention-seeking behavior. The girl's interrupting behavior generalizes from the old to the new teacher, but he only recognizes the students who do raise their hands, so he begins extinguishing her calling out responses by saying nothing when it happens.
The chart shows a typical extinction curve. It has a burst, a crest, and a decline. The burst is caused by the lingering effect of the reinforcement from the previous year and the new effect of extinction. At first she "tries hard" to get a reaction, so the behavior increases, but the teacher completely ignores it, so she "gives up trying." The rate of interruption levels off and diminishes to a low level of response. (For actual extinction curves in rats, see Skinner (1938.)
He differentially reinforces a suitable alternate behavior by only calling on her when she does raise her hand. He knows immediate reinforcement works better than delayed reinforcement so he responds soon after she raises her hand. Now she has an acceptable way of gaining his attention.
Next he can modify the rule. Sometimes, during free time, for instance, the class doesn't need to raise their hands. So he traces an outline of his hand onto a blank sheet of paper and colors it green. When he wants them to raise their hands, he tacks the green hand onto the bulletin board and continues calling on students who raise their hands and ignoring those who don't. When the green hand is not up on the board, he can respond when they talk without raising their hands and ignore them when they do raise their hands. They learn to discriminate between the green hand and the non-green hand conditions. The discriminative stimulus, we can say, sets the occasion for hand raising and gains control over their behavior. In the end, they will only raise their hands during the green stimulus if he extinguishes hand raising during the non-green condition.
See the previous post, Don't Reward "Bad" Behavior for more about how a teacher can unwittingly cause undesired behavior in a student.