Answer-Key Dispute in a Class V Reasoning Worksheet
While marking a Class V reasoning worksheet over the break, a PRT finds that three of the twenty items are producing disputes. Item 7: 'Statements: All teachers are readers. Some readers are poets. Conclusion: Some teachers are poets.' The key marks it 'follows'. Item 8: 'If TEACHER is written as VGCEJGT, how is PRT written?' The key says 'RTV'. Item 9: 'Pointing to a boy, Meera said, "He is the son of the only daughter of my mother." How is the boy related to Meera?' The key says 'nephew'. Of 42 papers, 31 students wrote 'RTV'; 24 wrote 'follows' for Item 7 while 18 wrote 'does not follow'; 9 wrote 'nephew' for Item 9 and nobody wrote 'son'. The teacher has already told six parents that their child got Item 9 wrong. Papers go home tomorrow, and the same worksheet is scheduled for the other section next week.
1. Work each of the three disputed items independently and state the defensible answer, with reasoning showing whether the key is correct.
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Item 7 - key is wrong; the conclusion does not follow. A conclusion follows only if every situation satisfying both premises also satisfies it. Construct a counterexample: a world in which all teachers are readers, some readers are poets, and no teacher is a poet. Both premises are true there and the conclusion is false, so the argument is invalid. The middle term 'readers' is undistributed in both premises, so nothing forces an overlap between teachers and poets. Correct answer: 'does not follow'.
Item 8 - key is correct. Letter-by-letter: T→V, E→G, A→C, C→E, H→J, E→G, R→T, i.e. each letter shifted forward by two. Applying it to PRT: P→R, R→T, T→V, giving RTV. The 31 students who wrote RTV are right.
Item 9 - key is wrong; the boy is Meera's son. The trap is reading 'daughter of my mother' as 'my sister'. But the phrase is 'the only daughter of my mother', and Meera is herself a daughter of her mother. If Meera has a sister, her mother has more than one daughter, contradicting 'only'; therefore Meera is that only daughter, and the boy - her son - is her son, not her nephew. The word 'only' is doing all the work, and it is precisely what the key ignored.
2. Decide what to do about the marks on Items 7 and 9 and about the six parents already told their child was wrong, given that papers go home tomorrow and the items will be reused next week.
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Guiding principle: a test item that is itself wrong has measured nothing, so no child should be penalised for it - and, importantly, no child should be rewarded for a correct-looking answer produced by a bad key either, because that corrupts the record for the child who reasoned correctly.
Item 9 - the six parents: the school's information was wrong, so it must be corrected first and by the school, not by the child. Re-mark the item, credit 'son', and phone the six parents before the papers reach home - a short factual call: the key was in error, the item has been re-marked in the child's favour, and the reasoning will be explained in class. Do not let the correction arrive inside the bag, where it reads as an unexplained mark change.
Item 7 - mark distribution: the 18 who wrote 'does not follow' were right and were marked wrong; award them the marks. The 24 who wrote 'follows' were following a printed key - for a Class V formative worksheet, do not claw marks back. Practically, mark both responses as credited, record 'item flawed - key corrected' against the item, and write the corrected reasoning on the board. The record shows the flaw; the children are not punished for either the school's error or their own compliance with it.
Before reuse next week: do not reuse Items 7 and 9 in their present form. Correct the key, and replace Item 9 with a version where 'only' is not required, or where 'only' is signposted.
3. Rewrite Item 7 so that exactly one answer is defensible and a Class V child can justify it without knowing formal terms like 'distribution of the middle term'.
Read the worked answer
Rewrite as a counterexample-hunting item rather than a validity-judging item:
'Statements: All teachers are readers. Some readers are poets. Which of these must be true?' (a) Some teachers are poets (b) No teacher is a poet (c) We cannot be sure that any teacher is a poet (d) All poets are teachers
Why this version works:
- The correct option (c) is reachable by drawing two overlapping circles and asking 'must it be so?', which is a Class V operation, not a formal-logic term.
- Options (a) and (b) are the two tempting over-claims, so the item distinguishes 'possible' from 'certain' - the actual skill being tested - instead of rewarding a guess.
- Option (d) catches the reversal error (converting 'some readers are poets' into a claim about all poets).
Classroom follow-up: ask one child who chose (a) to draw a case where teachers and poets do not overlap; the drawing, not the teacher's correction, kills the misconception, and the same drawing technique then transfers to Items 8 and 9.