Figural Analogies: When the Answer Is Two-Thirds Correct
A grade-6 student completed a 14-item figural analogy subtest. Each item presents a pair of figures, A and B, and a third figure, C, and asks for the figure that relates to C as B relates to A. The examiner transcribes one item. Figure A is a small black square with a white dot in its upper-left corner. Figure B is a large white square with a black dot in its lower-right corner. Figure C is a small black triangle with a white dot in its lower-left corner. The student scored 6/14. Of his 8 errors, 6 were options that satisfied exactly two of the three transformations in the stem, and 2 applied the transformations in the reverse direction, as if mapping B onto A. When asked, he said: 'I look at what changed and then do the same thing.' He was surprised to hear that six of his answers were only partly right, and he asked how he is supposed to know when two answers both look like they work.
1. State the complete rule for the transcribed item and explain what each of four candidate answers would reveal about his reasoning.
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Transformations from A to B
- Size increases: small → large.
- Figure fill and dot fill swap: black figure with white dot → white figure with black dot.
- The dot moves to the diagonally opposite corner: upper-left → lower-right.
Applied to C, the answer must be a large white triangle with a black dot in the upper-right corner.
What each option means
- Large white triangle, black dot upper-right - correct; all three applied in the right direction.
- Large white triangle, black dot lower-left - size and color applied, dot not moved. He stops after the two most visually obvious changes.
- Small white triangle, black dot upper-right - color and dot applied, size not. He is tracking the small local change and missing the global one.
- Large black triangle, white dot upper-right - size and dot applied, color not. He may be treating 'black' as a fixed property of the shape rather than a transformable one.
Each option isolates one dropped transformation, so the choice identifies which attribute he does not inspect. That is much more actionable than the aggregate score.
2. Six of eight errors were partially correct. Explain what that pattern implies about guessing versus systematic partial-rule application, and what it predicts about instruction.
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With four options, random guessing would produce roughly one in four correct and would scatter wrong choices across the three distractors without structure. That is not what happened. Six of eight wrong answers each satisfied exactly two of three transformations. The probability of that clustering by chance is very low, and the distractor design - each wrong option violating exactly one attribute - is built to detect precisely this pattern.
The reasonable inference is that he reliably detects most of the transformations and then stops once an option looks plausible. This is a verification failure, not a rule-detection failure. His own account supports it: he looks at what changed, then looks for something that does the same thing, and accepts the first match.
Prediction. Because the transformations are already being perceived, instruction aimed at the check step should produce a fast, visible gain - often within a few sessions - and should not require rebuilding his reasoning from scratch. That is a different prognosis from a student who sees no transformations at all, whose progress would be slower and would depend on attribute naming and comparison first.
Caveat to check first: confirm that the two reverse-direction errors are not a separate difficulty with the A-to-B arrow. Direction and verification are different fixes.
3. He asks how to decide when two answers both seem to work. Give the decision rule you would teach.
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Start by reframing the question: both answers cannot fully work, or the item would be broken. One of them satisfies the whole rule and one satisfies part of it.
Full-rule test
- List every feature that changed between A and B - shape-adjacent features like size, fill, outline, count, and position/orientation of any internal element.
- Write each change as a sentence: size goes up; fills swap; the dot crosses to the opposite corner.
- Check the candidate against each sentence in turn, same direction. One failure eliminates it.
- Prefer the option that changes nothing beyond what the stem requires. Extra changes are not neutral; they are unsupported.
When the stem is genuinely ambiguous. Occasionally only one feature changes and two options are consistent with it. Then apply parsimony: the simplest rule that accounts for all the observed change, and no gratuitous additions. Do not import a rotation or a color change from a previous item.
Habit to build. Say the rule out loud in one sentence before touching the options, and verify after choosing. His six partial answers came from choosing without verifying; the rule does not need to be more sophisticated, it needs to be audited.