Mrs. Olinski is able to discipline Jared and Ham effectively because she has developed the confidence to respond strongly against the boys' attempt to disrupt the class. Troublemakers like Jared and Ham act out because they want attention, and by embarrassing them in front of the class, Mrs. Olinski regains her rightful control. It is evident from the body language of the students how the focus of their respect changes after the belching incident. As Ham and Jared walk to the front of the room after first being challenged by Mrs. Olinski, their "smiling faces (lift) and (tilt) toward (them) like...sunflowers as they follow the sun across heaven". After Mrs. Olinski puts the boys in their place, no one "smile(s)...or even (makes) eye contact with (them)" as they return to their seats (Chapter 6).
Mrs. Olinski hasn't always been able to be such an effective disciplinarian. In this, her first year back in teaching after having been rendered a paraplegic in an automobile accident, she has tended to be a little tentative in her approach to her class. Hamilton Knapp in particular has been taking complete advantage of Mrs. Olinski's situation, putting her on the spot by pretending he cannot see what she's written on the board while knowing that she cannot write any higher from her wheelchair, and by cruelly writing the word "CRIPPLE" on the board when she is out of the room. Recognizing her predicament, the Souls resolve to "give her some support...give her a lift", and through the friendship and kindness she finds with them at Sillington House, Mrs. Olinski develops the "chops" to assert herself as a teacher and earn the respect of even the most malicious of troublemakers (Chapter 4).
You will have to decide for yourself whether you have ever seen this strategy work in the classroom. Think of a time when a classmate has tried to undermine a teacher's authority by clowning around, and remember how the teacher handled the incident, and what the result was.