Two rules, one missing tile: scoring Item 3 in a Pattern Completion booklet
Ms. Okafor runs a 20-minute small-group session with four kindergartners. Each child works through a booklet of six Pattern Completion items. Item 3 shows a 3-by-3 floor of tiles with the bottom-right tile missing. The rule is a Latin square: every row and every column holds exactly one red tile, one blue tile and one yellow tile. Shape runs the other way - every tile in a column has the same shape, so column 1 is all squares, column 2 all circles, column 3 all triangles. The answer choices are all triangles except one yellow square, and they include a red triangle, a yellow triangle and a yellow square. Two children choose the red triangle and one chooses the yellow square. A fourth child chooses correctly but cannot say why. Time is nearly up and Okafor has to decide what each child actually understands before the group moves on to the next subtest.
1. Item 3 constrains the missing tile in two separate ways. Walk through the checks Okafor should expect a child to make, and state the correct choice.
Read the worked answer
The item carries two rules, and they govern different attributes.
- Colour rule: every row and every column contains exactly one tile of each colour. Reading row 3 across, the two filled cells show two different colours, so only the third colour is legal. Reading column 3 down returns the same colour - that is a confirmation of the same rule, not a third rule.
- Shape rule: shape is constant down a column, so column 3 fixes the shape as a triangle, irrespective of what row 3 contains.
Answer: the yellow triangle.
The judgement being tested is not 'can you see a pattern' but 'can you hold two constraints and let each one govern a different attribute.' A child who checks only the column sees 'triangle', notices that most choices are triangles, and then picks a colour by preference - which is exactly why the red triangle attracts so many responses. The yellow square is the mirror error: colour rule run, shape rule dropped.
2. The red-triangle child and the yellow-square child each got half the item. Are these the same error, and how should Okafor probe each?
Read the worked answer
They are different errors and point to different remediation.
The red-triangle child ran the shape rule (column 3 is the triangle column) and then abandoned the colour rule. That is a rule-selection failure under load: one dimension held, the other dropped. The yellow-square child did the reverse - colour correct, column shape ignored - which is typical of scanning left to right along the row and never looking down the column.
Probe by isolating the dimensions. Cover columns 1 and 2 with a card and ask only 'what shape must go here?' Then cover rows 1 and 2 and ask only 'what colour?' A child who answers both correctly in isolation but fails them combined is not missing the concepts; the item is measuring how much constraint she can hold at once, and that is worth recording separately. A child who fails the isolated questions has not acquired either rule, and Item 3 sits above her entry point.
3. The fourth child's answer is correct but unexplained. What may Okafor legitimately conclude, and what should she avoid concluding?
Read the worked answer
Very little from this item alone.
Avoid concluding that the child reasoned through both rules. The item is reachable by elimination: with three triangles offered and only one of them yellow, a child who notices the singleton colour arrives at the right answer without ever running the shape rule.
Equally, avoid concluding she guessed. On a nonverbal test a correct answer is a correct answer, and children of this age routinely apply a rule they cannot put into words; the absence of an explanation is not evidence of a lucky mark.
The way to settle it is transfer, not interrogation. Give a second item with the same architecture but the attributes swapped - shape varying along the row, colour constant down the column - and see whether the child re-reads the grid or repeats her previous answer pattern. If she transfers, credit the reasoning. If she does not, she has learned one item, and the booklet total should be read as a count of solved items rather than a measure of rule use.