Building a three-week remedial schedule against a hard teacher-supply constraint
Class X has 120 students. Diagnostic tests flag 90 as weak: 50 need Mathematics only, 40 need Science only, and 30 need both. The principal has promised, in writing to the parents' committee, that every flagged student will get four remedial sessions in each subject needed across three weeks. Constraints: there is one usable slot per day, 4:00 to 5:00 p.m., for six days a week, and the last bus leaves at 5:15. Rooms are one laboratory with 24 seats and two classrooms with 40 seats each. Mathematics teacher A is free Monday, Wednesday and Friday; teacher B on Tuesday, Thursday and Saturday; each is capped at four sessions a week. The Science teacher is free Monday to Thursday, normally four sessions a week, but is on board-practical duty for two of those slots from week 2 and is on external evaluation duty for the whole of week 3. Sessions in different rooms may run in parallel.
1. Test the promise against the constraint. Compute the Mathematics and Science session capacity over three weeks and state whether the commitment can be met, showing your arithmetic.
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Convert the promise into seat-needs, then into sessions.
Demand. Students needing Mathematics = 50 + 30 = 80. At four sessions each, Mathematics seat-needs = 320. Students needing Science = 40 + 30 = 70. At four sessions each, Science seat-needs = 280.
Mathematics supply. Teachers A and B are each capped at four sessions a week and between them cover all six days, so 8 sessions a week × 3 weeks = 24 sessions. At 40 seats in a classroom, capacity is 960 seat-slots against 320 needed. Mathematics is comfortably feasible, and there is spare room to run Mathematics in the laboratory on days it is free.
Science supply. Week 1: 4 sessions. Week 2: 4 minus 2 board-practical slots = 2 sessions. Week 3: 0. Total 6 sessions. At 24 laboratory seats, capacity is 144 seat-slots against 280 needed. Shortfall = 136 seat-slots, and no Science at all in week 3.
Verdict: the Mathematics part of the written promise is deliverable; the Science part is not, and cannot be made deliverable by scheduling cleverness. The commitment needs renegotiation with the parents' committee in week 1, not in week 3.
2. Give a workable weekly pattern for week 1 and state exactly which constraint fails in week 2, what you will do, and what you will tell the parents' committee.
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Week 1 pattern. Monday: Science in the laboratory (24 seats) plus Mathematics with teacher A in classroom 1 (40). Tuesday: Science plus Mathematics with teacher B. Wednesday: Science plus Mathematics with A. Thursday: Science plus Mathematics with B, since A is not free but the laboratory is. Friday: Mathematics with A in classroom 1 and Mathematics with A again is not allowed under the cap, so run one Mathematics session and use the second room for a supervised practice hour with no teacher input. Saturday: Mathematics with B plus supervised practice. That gives Science 4 sessions (96 seats) and Mathematics 6 taught sessions plus two practice hours.
Week 2 failure. Science drops to 2 sessions because two of the teacher's four slots go to board practicals. Science seats fall to 48 for the week, against 70 students × 4 sessions = 280 needed overall.
Response: do not cancel Science. Convert the two board-practical slots into a whole-class demonstration that the Science teacher's practical batch prepares and that class teachers supervise using a printed sheet - this is legitimate because the board practicals are themselves Class X Science content. In week 3, when the Science teacher is away, hand Science to the two Mathematics teachers as a data-and-graphs unit using the Science practical results, which serves both subjects.
Message to the committee: Mathematics as promised; Science reduced to intensive blocks in weeks 1 and 2 plus supervised work in week 3, with the reason (board practicals and evaluation duty) stated plainly and the revised hours given in writing.
3. A parent complains that only "weak" students are being called and that his daughter, who is not on the list, is being denied teaching. How do you respond, and what does this reveal about how the list was built?
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Respond on the merits, and treat the complaint as a signal about the diagnostic, not as a nuisance.
The list was built from a single diagnostic test with a cut-off, and a cut-off always creates a hard edge: a student at 34 marks and one at 32 are treated completely differently. That is a property of the instrument, not of the students' needs, and the parent has identified a real design flaw.
Immediate response: explain the criterion openly, show the daughter's diagnostic script, and state what she needs. Then make the remedial sessions open-door for the last 15 minutes and add a weekly stretch task for students above the cut-off, so the remedial hour is not perceived as a punishment class. Never describe students publicly as weak; use "students who need more practice on these topics".
What it reveals: the diagnostic tested one paper at one time and ignored classwork, attendance and teacher judgement. The fix is to build the list from two sources - the diagnostic and the subject teacher's topic-wise record - with a review after two weeks so a student can enter or leave the list. Report to the committee on how many students moved in and out, which is the honest measure of whether the cut-off was doing any work.