Figural Classification With More Than One Defensible Odd One Out
During a figural-classification trial, a student sees four figures and is asked to choose the one that does not belong. Figure 1 is a large square containing a small shaded circle. Figure 2 is a large square containing a small unshaded circle. Figure 3 is a large square containing a small shaded triangle. Figure 4 is a large circle containing a small shaded square. The answer key identifies figure 4 as the odd one out. A student, Nia, chooses figure 2 and explains, 'It is the only one where the inside shape is white instead of shaded.' The examiner must decide how to score Nia's response and what to do with the item. The district requires that classification items have a single defensible answer, and the examiner is also compiling a bank of items for next year. Nia has strong spatial reasoning but often notices details the key ignores.
1. Inventory the attributes of the four figures and identify at least two defensible odd-one-out answers, including the key's.
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Attributes:
- Fig 1: outer square; inner shaded circle.
- Fig 2: outer square; inner unshaded circle.
- Fig 3: outer square; inner shaded triangle.
- Fig 4: outer circle; inner shaded square.
Defensible answers:
- Fig 4 - the only outer circle (key's rule).
- Fig 2 - the only unshaded inner shape.
- Fig 3 - the only inner triangle.
- Fig 4 also - the only inner square.
A valid classification needs one criterion shared by three figures and violated by one. Here several criteria qualify, so the item is not unidimensional.
2. The key says figure 4. Nia chooses figure 2 with a clear reason. How should the examiner score and document this?
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Nia's rule is valid: figures 1, 3, and 4 all have shaded inner shapes; figure 2 is the only unshaded one. She should not be marked wrong. Because the district requires a single defensible answer, the item should be flagged and either discarded from scoring or scored as correct for any well-justified choice. Document the flaw: shading and inner-shape type were allowed to vary along with outer shape. Her response is evidence of detail detection, not a reasoning deficit.
3. Revise the item so that only figure 4 is defensible, preserving the intended outer-shape rule.
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Hold all attributes constant except outer shape. Example: Fig 1 large square with small shaded circle; Fig 2 large square with small shaded circle; Fig 3 large square with small shaded circle; Fig 4 large circle with small shaded circle. Now only the outer contour varies, so figure 4 is uniquely odd. Check that size, inner shape, inner shading, and orientation are identical across all four. If the item is meant to test outer-shape classification, no other attribute should be free to vary.