A Two-Rule Analogy That Half the Class 'Fail' by Adding a Third Rule
Setting. A resource teacher is building eight analogy items for a kindergarten screening her school runs in September. Item 7 shows a top pair and a bottom pair. Top pair: on the left, a large blue triangle; on the right, a small blue triangle with a black dot in the centre. Bottom pair: on the left, a large yellow square; on the right, a blank answer box. The options are: A, a small yellow square with a dot; B, a large yellow square with a dot; C, a small yellow square with no dot; D, a small yellow square with a dot, tilted 45 degrees; E, a small green square with a dot. On the trial run with 22 children, 11 chose A, 7 chose D, 2 chose B, 1 chose C, and 1 chose E. A colleague argues that item 7 is pitched above the level because it carries two transformations (size drops, a dot appears) instead of one, and wants it replaced with a single-rule item. The teacher has one week before the screening.
1. What is the intended answer, and how far does the response pattern actually support the claim that the seven children who chose D were reasoning rather than guessing?
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Intended answer: A.
Two transformations are licensed by the top pair and nothing else: the figure shrinks, and a dot appears. Shape and colour are unchanged, so B fails on size, C fails on the dot, and E introduces a colour change the pair never shows.
D is wrong but it is a rule-shaped error. A child who picks D has applied both licensed transformations and then added a 45-degree rotation that the example pair does not license. Adding an unsupported rule is a reasoning failure, not a failure to reason.
How strong is the statistical support? With 22 children and 5 options, random responding predicts 4.4 responses per option. D drew 7, and the other three wrong options drew 2, 1, and 1. That skew is suggestive - a guessing child is not more likely to land on the tilted square than on the plain large square - but 7 against an expectation of 4.4 on n = 22 is thin. The honest answer is that the counts are consistent with rule-based reasoning on D but do not prove it. Verification is cheap: re-run three of the seven on a parallel item that has no tilted distractor and see whether the size-plus-dot answer appears.
2. Should item 7 be replaced by a single-rule item as the colleague asks? Decide, and name the one change you would make.
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Keep item 7; place it late in the set and add one single-rule anchor earlier.
The colleague's developmental concern is legitimate - a two-rule analogy is demanding for this age - but 'demanding' is not the same as 'invalid'. An item set needs a range, and eight single-rule analogies would leave the teacher unable to tell a child who reasons well from a child who has simply learned to look for one change.
The number that matters is not 11/22 correct. It is that 18 of 22 children chose an option consistent with at least one of the two licensed transformations (A, B, C, or D), and only one responded to an irrelevant feature (E, colour). That is a working item with a clean error structure.
The single change: leave the stem and the option set alone, and add a parallel item near the front where only the dot appears and size is held constant. That gives you a floor item and turns item 7 into the ceiling item it already is, without discarding a distractor that tells you something.