For maintaining an effective discipline in the class, the teacher should

Concept: Classroom discipline is analysed through the authority style a teacher adopts, and that style is located on two independent dimensions — the warmth or responsiveness shown towards learners, and the demandingness or consistency with which limits are held. Crossing the two dimensions gives the familiar typology: low warmth with high demand is the autocratic or authoritarian style, high warmth with low demand is the permissive or laissez-faire style, and high warmth combined with high demand is the authoritative or democratic style.

Concept: Educational psychology further distinguishes compliance from discipline. Compliance is order that is contingent on the teacher being present to enforce it; effective discipline is order that the learner has internalised, so it survives the teacher leaving the room. A stance therefore counts as effective only when it supplies limits that are stable and a relationship that makes the learner willing to own those limits.

Application: The stem asks which stance maintains effective discipline in the class. Applying the two dimensions to the stances offered, only "Deal with them politely and firmly" carries both of them at once — politeness supplies the warmth, firmness supplies the consistent limit. That pairing is the authoritative or democratic style, and it is the combination under which an externally imposed rule is converted into a self-imposed one: the pupil accepts the boundary because it is held consistently and is held by someone who treats him with respect. The answer is therefore "Deal with them politely and firmly."

Contrast: reading each stance offered against the same two dimensions makes the distinction explicit.

• "Allow students to do what they like" supplies warmth or non-interference but no limit at all, so whatever order appears rests on norms the group happens to generate for itself and shifts as the group shifts.

• "Deal with the students strictly" supplies the limit but withholds the warmth, so the order it produces is tied to the teacher's presence and to the expectation of sanction, and it lapses once supervision is withdrawn.

• “Give the students some problem to solve” operates as a preventive tactic: keeping pupils occupied removes idle time within one lesson, but it settles nothing about the standing teacher-pupil relationship that the stem is asking about.

• "Deal with them politely and firmly" supplies both dimensions together, which is why it is the stance associated with self-discipline rather than with supervised compliance.

Cross-check: the same result follows from the definition of effective discipline used above. Remove the teacher from the room in each case — only the stance that has already built a respected and consistently applied limit leaves the class ordered, which is precisely the polite-and-firm combination. Standing classroom-management guidance points the same way: it advises that rules be held in a manner that is firm and respectful at the same time, rather than by strictness alone or by leaving limits unset.