A Six-Mark Gain That Was Really an Eleven-Mark Absence Problem
The headmaster of a government high school wants to know whether the activity-based mathematics programme piloted in Class VIII B worked. Terminal examination data are placed before the staff: Section A (n = 40, no programme) has a mean of 62 with SD 14; Section B (n = 40, programme) has a mean of 68 with SD 6. Section B was taught by a teacher with twelve years of experience; Section A by a first-year contract teacher. Twenty-six children of Section B come from families of government employees; Section A draws largely from a nearby colony. Six children of Section A were absent for the examination and were entered as zero. At the staff meeting the headmaster announces that the programme raised results by six marks and proposes extending it to all sections. A teacher objects and is told that the data are clear. Separately, the headmaster wants to run a small action research project and asks for guidance on records and analysis.
1. Assess the claim that the programme raised results by six marks, using the means, the standard deviations, the coefficient of variation and the treatment of absentees. State what can and cannot be concluded.
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The absentee arithmetic alone overturns the claim. Section A's total is 40 × 62 = 2480. Six of those forty scored zero. Among the 34 who actually sat, the mean is 2480 ÷ 34 = 72.9. So the recorded section mean is depressed by about eleven marks purely by the scoring convention. That is nearly twice the six-mark effect being celebrated. If absentees had been excluded and reported as a separate n, Section A's mean of those who appeared would exceed Section B's 68.
The spread matters as much as the mean. Coefficients of variation: Section A = 14 ÷ 62 = 22.6%; Section B = 6 ÷ 68 = 8.8%. Section B is homogeneous; Section A is widely spread. A low mean with a high SD usually means one subgroup is being left behind rather than the whole class being weak, and a low SD in B is consistent with a selected or more homogeneous intake, not necessarily with better teaching.
Significance is not causation. The standard error of the difference is √(14²/40 + 6²/40) = √5.8 ≈ 2.41, giving t ≈ 2.5. The gap is unlikely to be chance, but it is entirely explainable by teacher experience, parental occupation, locality and absenteeism.
Conclusion. The defensible statement is: Section B scored higher and was more tightly clustered. The claim that the programme caused a six-mark gain is not supported, and scaling it up on this evidence would be a mistake.
2. Redesign this as a feasible action research study within one school year, specifying the records to be maintained and how absentees, ethics and the bottom quartile will be handled.
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Design. Use a pre-test and post-test with the same paper in two sections, and rotate: the same teacher teaches both sections, using the programme in one for a term ABAB, so that teacher effect and programme effect are separated. Match children on the previous year's mathematics marks before comparing gains. Compare mean gain per child, not the class mean alone, and report the bottom quartile separately, since that is where the pilot's claim is weakest.
Records. A one-page register per child with pre-test, post-test, attendance and item-wise scores; a dated field diary of what was actually taught and any deviation; samples of children's written work for each unit; a photograph-free log of materials used; the absentee list with dates.
Absentees. Decide and state the rule in advance: report both the number enrolled and the number who appeared, and never enter a zero for an absent child in an analysis of teaching effect. If a child misses a test, record the score as missing and analyse on complete cases, noting how many were dropped.
Ethics and feasibility. Inform parents and the SMC; ensure no section is denied the better method beyond one term; keep children's names out of any circulated report; keep the whole study inside existing periods so it does not draw on instructional time.
Output. A single page shared with staff and the MEO: question, method, result, limitation, next step.