Figural Series: Three Rules, One Tracked Attribute
A learning specialist is analyzing a grade-7 student's performance on a 16-item figural series subtest. Each item shows four frames of a changing figure and asks for the fifth. The specialist transcribes two representative items in words. Item 12 shows a single polygon whose side count rises by one each frame (3, 4, 5, 6); its fill alternates black, white, black, white; and it rotates 45 degrees clockwise from each frame to the next. Item 9 shows a dot moving one corner clockwise per frame around a ring whose line thickness alternates thick, thin, thick, thin. The student scored 7/16. He was correct on 5 of 5 single-rule rotation items, 0 of 6 dual-attribute items, and 2 of 5 alternation items. His mean time is 38 seconds on items he answered correctly and 96 seconds on items he answered incorrectly; the subtest allows roughly 40 seconds per item. His teacher has requested extended time and wants to know whether that is the right accommodation.
1. For Item 12, state every constraint the correct option must satisfy, then explain what each described distractor would indicate about the student's reasoning.
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Constraints on the answer
- Sides: 3, 4, 5, 6 → +1 per frame → 7 sides.
- Fill: black, white, black, white → alternates → black.
- Orientation: 0°, 45°, 90°, 135° clockwise → +45° per frame → 180° from frame 1.
All three must hold simultaneously. A correct option failing any one is wrong.
Reading the distractors
- 8 sides, black, 180° - he is counting but not computing the increment, or has lost track of the sequence. Suggests no written tracking at all.
- 7 sides, white, 180° - he extracted sides and rotation and missed the alternation. This is the most informative error, because it is genuine partial reasoning and is cheap to fix with a checklist.
- 7 sides, black, 135° - he reused the previous frame's orientation instead of projecting the next increment. This is perseveration, not a rule error, and usually appears when a student stops on the last frame they looked at.
- 6 sides, black, 225° - he continued the rotation correctly but froze the side count, suggesting he is tracking only the attribute that moves most visibly.
Diagnostically, the pattern of distractors chosen separates a student who never modeled the rule from one who modeled two of three rules and stopped checking.
2. Given that wrong answers take 2.5 times as long as right ones, what does that imply about speed versus strategy, and how would you answer the extended-time request?
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The time signature argues against speed as the primary constraint. If time pressure were the problem, errors would cluster on the fast, rushed items and on the last items of the subtest, and correct answers would be the slow ones. Here the opposite holds: 38 seconds on correct items, 96 seconds on incorrect items. He is not being cut off mid-reasoning - he is stalling, scanning the whole display repeatedly and waiting for a pattern to announce itself.
On extended time. Extra time, by itself, is likely to produce more time spent on the same items with few additional correct answers, and it may reinforce the scanning habit. I would not refuse it outright, but I would sequence it: teach a fixed procedure first, then re-evaluate.
Sequencing. Six weeks of strategy instruction with a hard stop at 60 seconds per item, followed by an educated skip and return. Then re-check the time data. If accuracy climbs but he is now leaving items unattempted at the end, time has genuinely become the binding constraint, and extended time becomes a reasonable and defensible accommodation. If accuracy climbs and he finishes, the accommodation was never the issue and the data now show it.
3. Write the scanning routine you would teach and explain specifically how it targets the alternation items he missed.
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Fixed attribute-scan routine
- Name the attributes on the first frame, always in the same order: number of elements, side count, size, fill or shading, orientation, position.
- For each attribute, write the sequence of values across all four visible frames before looking at options - e.g., fill: B, W, B, W; sides: 3, 4, 5, 6.
- Label each sequence as grows, shrinks, alternates, rotates, or stays. Then predict the fifth value.
- Only now read the options.
- Verify the chosen option against every attribute, ticking each one. If any attribute fails, the option is out.
Why this targets alternation. Learners tend to assume a rule must progress - that each frame moves forward to something new. Alternation breaks that assumption, so it is skipped rather than misapplied. Writing the value sequence forces the A-B-A-B shape onto the page, and the explicit label 'alternates' makes it a member of a small recognized set of rule types rather than an unconsidered possibility.
Why step 5 matters. The student's dual-attribute errors show he satisfies the first two attributes that resolve and stops. A written tick-list turns verification into a visible obligation rather than a feeling that the answer looks right.