Bridging a gap: a serial strip with its middle frame erased
A photocopier crease has wiped out the middle frame of a five-frame Serial Reasoning strip. Frame 1 is a triangle pointing up with one dot inside. Frame 2 is the same triangle pointing right with two dots. Frame 3 is blank. Frame 4 is a triangle pointing left with four dots. Frame 5 is a triangle pointing up with five dots. The four choices for frame 3 are a downward triangle with three dots, a leftward triangle with three dots, a downward triangle with two dots, and a rightward triangle with three dots. One child picks the leftward triangle with three dots. A second picks the downward triangle with three dots but says she 'just counted the dots and guessed which way it should point.' A third child says the strip is broken and pushes it away. Twelve minutes remain in the session and three children are at different points.
1. Derive the missing frame from both sides and show that the two derivations agree.
Read the worked answer
Read the strip left to right first. Between frame 1 and frame 2 the triangle turns from up to right - a quarter turn clockwise - and the dots go from one to two. Now check the right-hand end: between frame 4 and frame 5 the triangle turns from left to up, the same quarter turn clockwise, and the dots go from four to five. Both rules therefore hold along the whole strip, not just at the left end, so neither rule is a local accident.
Left-hand route: frame 2 points right with two dots, so frame 3 points down with three dots.
Right-hand route: undo one step from frame 4, a quarter turn anticlockwise from left, which points down, and one dot fewer, which is three.
Both routes give a downward triangle with three dots.
The agreement matters. With the middle frame erased, a child reading only left to right is extrapolating across a gap with nothing to check herself against; a child who also reads backwards has an internal confirmation. That behaviour is worth noting independently of which choice she marks.
2. Why is the leftward triangle with three dots the predictable error, and what does choosing it tell the teacher?
Read the worked answer
Left is the orientation of the nearest surviving frame, frame 4, and three is the correct dot count from either side. So the child has run the dot rule correctly and filled the orientation slot with whatever she saw last. This is a copying-by-adjacency error, not a random guess.
Note what it rules out: she is not ignoring the strip, and she is not failing to count. The dot count - the more concrete dimension - is doing all the work, while rotation, which requires tracking position in a sequence, is not being tracked at all.
The next probe is to give her the same strip with the dots removed entirely and ask only which way the triangle faces in frame 3, so that counting cannot carry her. If she answers 'down', the rotation rule is present and was being crowded out; if she still says 'left', rotation is the thing to teach, separately from counting.
3. How should the teacher handle the child who says the strip is broken? And how would the item change if frame 5, not frame 3, were the erased one?
Read the worked answer
The refusal is a response to an incomplete stimulus rather than to difficulty. A five-year-old who expects every problem to be a complete picture reads the blank as a defect in the materials. The move is to make the blank legitimate: 'the machine ate one picture and we have to work out what it was,' then start her on the smallest available question - 'what changed between picture 1 and picture 2?' That converts anxiety into a task.
On the second question: erasing frame 5 rather than frame 3 changes the item's character. Frame 3 is bracketed - reachable from frame 2 forward and from frame 4 backward, so the answer can be checked internally. Frame 5 must be extrapolated past the last visible frame with nothing on the right to confirm against, which is strictly harder. It also defeats a heuristic that does no harm in the middle: frame 5 repeats frame 1's upward orientation, so a child who assumes the strip will not repeat itself will eliminate the correct choice.