Item Analysis and a Parent Demanding a Grade Change
Ms. Ramos taught a five-day unit on fractions to 40 Grade 5 learners and gave a 50-item test. She analyzed three items using the upper 27% (11 learners) and lower 27% (11 learners). Item 12: 32 of 40 answered correctly; 10 of 11 upper and 2 of 11 lower were correct. Item 19: 22 of 40 correct; 7 upper and 4 lower correct. Item 25: 0 of 40 correct. The school requires a 75% passing grade computed as (raw score ÷ 50) × 100, with no transmutation. One learner, Ana, scored 36/50; she missed all five items on adding dissimilar fractions but earned full marks on every other objective. Ana's parents ask that she be allowed a special project to raise her grade to 78, and the principal privately asks Ms. Ramos to "consider the parents."
1. Compute the difficulty and discrimination indices for Items 12, 19, and 25, and decide whether to retain, revise, or reject each. Show your reasoning.
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Formulas used: difficulty p = (number correct) ÷ (total); discrimination D = (proportion correct in upper group) − (proportion correct in lower group), using the 27% groups of 11.
Item 12:
- p = 32/40 = 0.80 (easy)
- D = 10/11 − 2/11 = 8/11 = 0.73 (very high)
- Decision: retain. A high p is not automatically a flaw if the item tests a prerequisite skill that must be secure. D = 0.73 means strong learners reliably out-perform weak ones, so the item is measuring something real; it just is not discriminating across a narrow band. Keep it for coverage, but do not count on it to spread scores.
Item 19:
- p = 22/40 = 0.55 (moderate)
- D = 7/11 − 4/11 = 3/11 = 0.27 (marginal)
- Decision: revise. Difficulty is ideal, but marginal discrimination usually means the distractors are not working as intended (implausible options, two defensible answers, or a reading-load problem). Inspect which wrong options were chosen and rewrite them before reusing the item.
Item 25:
- p = 0/40 = 0.00; D = 0/11 − 0/11 = 0.00
- Decision: investigate, then most likely reject. On a four-option item the probability of all 40 learners guessing wrong is (0.75)^40, which is vanishingly small - so this is not simply "a very hard item." Search for a miskeyed answer, an ambiguous stem, or content never taught. Never enter a zero-difficulty item into the item bank without diagnosis.
Overall reasoning: difficulty and discrimination answer different questions - how many got it right versus whether the item separates the prepared from the unprepared. Only D tells you whether the item is functioning as a measure, and that is why Item 12 survives while Item 25 fails.
2. Should Ana receive the special project to reach 78? Decide, and justify using principles of grading and professional ethics.
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Decision: no grade-changing project; yes to targeted reteaching and reassessment of the weak objective - provided the same option is open to every learner.
1. The arithmetic. 36/50 = 72%, and 75% of 50 = 37.5, so she is short of the passing mark by roughly one to two points. This is a borderline case, not a hopeless one, which is exactly the kind of case where teachers are tempted to bend rules.
2. What the score profile says. Ana's errors are not scattered. They are entirely concentrated on one objective (adding dissimilar fractions), and she scored full marks on every other objective. A grade is a summary of achievement across objectives, but the pattern here is diagnostic: the weak skill was apparently not learned well by at least one strong performer, which raises a question about the instruction on that objective, not just about Ana.
3. Why an unrelated project cannot fix the grade. A grade must be valid - it should mean "this learner has achieved these objectives." A special project on other content would raise the mark without changing what Ana can or cannot do, so the 78 would be meaningless. It would also violate fairness: the same offer must be available to the other learners who fell short, or the rule has been applied differently to a family who asked.
4. What to do instead. Reteach dissimilar fractions to Ana (and any others with the same error pattern), then give a comparable short reassessment on that objective. If policy permits reassessment for mastery, the new evidence legitimately updates the grade - the change is earned, not negotiated.
5. Responding to the principal. Agree with the concern for the family while separating two requests: helping Ana learn the skill (fully supported) versus assigning a mark she has not demonstrated (not supportable). Document the diagnostic pattern and the reteaching plan in writing. The teacher's duty is to the learner's actual competence, and to consistent standards for all 40 learners - not to the comfort of the office.