Thirteen Word Cards and One Leftover
During a 20-minute reasoning station, 22 Grade 3 students work in pairs with an identical set of 13 word cards: oak, pine, maple, cedar, robin, eagle, sparrow, wren, trout, salmon, bass, perch, bat. The printed direction reads, 'Make three groups of four. One card will not be used.' Pairs record their groups on one sheet and may not talk.
The teacher's key expects leftover bat, with groups of trees, birds and fish. Results: 9 pairs match the key; 6 pairs build a 'things that fly' group of robin, eagle, sparrow and bat, leave out wren, and keep all four trees; 4 pairs sort by word length and end with groups of six, three and two plus two leftovers; 2 pairs start with plants versus animals and stall; 1 pair leaves out bass, arguing that bass and perch name instruments or actions as well as fish.
The six 'flyer' pairs insist they are right. The station ends in five minutes and the teacher has to decide what to say.
1. Both the keyed arrangement and the six pairs' arrangement appear to satisfy the printed directions. Verify that, then identify the single test that separates them and say whether the printed direction states it.
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Keyed arrangement: trees (oak, pine, maple, cedar), birds (robin, eagle, sparrow, wren), fish (trout, salmon, bass, perch); leftover bat. Three groups of four, one card unused.
The six pairs' arrangement: robin, eagle, sparrow and bat as 'things that fly'; the same tree and fish groups; leftover wren. It also meets 'three groups of four', so the printed text alone does not decide between them.
The separating test is whether the rule holds for every member and only members. It fails for the flyer group: wrens fly, so the rule admits five cards (robin, eagle, sparrow, wren, bat). To keep four, the pairs had to drop a card that satisfies their own rule - an internal contradiction, not a matter of taste. The keyed groups pass the same test: every card in a group is a tree, bird or fish, and no card outside the group is.
The key wins on consistency, not on authority. The printed direction never states that consistency requirement, which is the item's real flaw.
2. The four pairs who sorted by word length produced groups of six, three and two with two leftovers. Diagnose what went wrong and give the one question you would ask them.
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Word length is a property of the printed word, not of the thing named, so the groups are not classifications of living things at all. More decisively, the pairs never checked their work against the constraint: with 3-, 4-, 5-, 6- and 7-letter cards present, no length reaches four cards, so 'three groups of four' was impossible under their rule. Stopping with two leftovers rather than re-sorting shows they were monitoring the words and not the goal.
One question is enough: 'Show me your rule and count how many cards follow it.' Then, 'How many cards does the direction say each group needs?' The second question returns them to the constraint without supplying the answer.
If they still cannot regroup, offer a single entry point - 'Which of these are plants?' - which reveals the taxonomic frame without naming the three groups.
3. Rewrite the printed direction in one or two sentences so that the item still tests classification but no longer admits a rule-consistent alternative.
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Keep the reasoning intact and close the loophole. For assessment use: 'Make three groups of four cards that are the same kind of living thing. One card will not be used.' The word 'kind' signals a class rather than an ability, without handing over the groups.
For teaching, a stronger version names the wrong routes: 'Each group must answer the question What kind of living thing is this? It must not be a group of things that share an ability, a place, or a letter pattern.' That is clearer but removes the discrimination, so it belongs in instruction and not in the scored item.
Also repair a second flaw: bass and perch are homographs, which adds a word-knowledge trap unrelated to classification. Replacing them with carp and herring keeps the item measuring one thing. Finally, print the constraint 'one card will not be used' before the grouping task, not after, so pairs cannot build a five-member group first.