Four Votes for the Distractor: Judging a Part–Whole Analogy
A tutor runs a 50-minute verbal session for six students preparing for the analogies subtest. Items are timed at 90 seconds and scored right-or-wrong, with no partial credit. On item 7 - PEDAL : BICYCLE - the group splits 4–2. Four students choose 'oar : rowboat'; two choose 'wheel : car' and insist that both pairs are 'a part and the whole it belongs to,' so either answer should be accepted. On the previous practice set, five of the six also missed item 12 (ORCHESTRA : MUSICIAN), where the most popular wrong answer was 'library : book' and the keyed answer was 'team : player.' Nobody spent more than 35 seconds on either item. The tutor has 20 minutes left and cannot decide whether to run more items or stop and teach a checking routine. She also wants an explanation of the PEDAL item that does not amount to 'just trust me.'
1. Adjudicate item 7. Which response is correct, and what exactly makes 'wheel : car' wrong even though it is also a part-and-whole pair?
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State the stem's relation precisely enough that only one option survives.
Step 1 - name the relation. A pedal is (a) a part of a bicycle and (b) the part a person pushes directly to make the bicycle move.
Step 2 - test every option against both halves.
- oar : rowboat - a part of the boat, and the part a person pulls to make it move. Passes both.
- wheel : car - a part of a car, but not the input the driver works; it is driven by the axle. Fails (b).
- handle : door - a part of a door, but a handle is not what drives the door's motion in the sense of propulsion. Fails (b).
- engine : airplane - produces motion, but no person works it directly. Fails (b).
'Part and whole' is true of almost every option, which is exactly why it cannot be the rule: a description that eliminates nothing has no discriminating power. The specific relation is hand-worked input part : the vehicle it moves. The two dissenters stopped at the first true description. The correct move is to keep adding qualifiers until exactly one option fits.
2. Write a 15-second checking routine the tutor can teach, and show it working on ORCHESTRA : MUSICIAN with the trap answer 'library : book.'
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Three moves, each a sentence said silently:
- Say the relation in one sentence. 'An orchestra is a group made up of musicians.' Vague labels such as 'a group of things' are banned, because they cannot fail.
- Add the qualifier the stem forces. An orchestra is a collection of people, each of whom performs, and the whole is defined by the shared activity. 'Library : book' now fails - books do not perform, and a library is not a collection of participants.
- Run the sentence in reverse. 'A musician is one member of an orchestra' still reads true. Reverse the option: 'a book is one member of a library' is shaky, while 'a player is one member of a team' is exact, including the person requirement.
Budget roughly 5 seconds per move. The routine works because it forces the student to commit to words that can be shown false, instead of to a feeling of fit that cannot.
3. With 20 minutes left, should the tutor run more practice items or teach the routine? Argue from the evidence in the session.
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Teach the routine first, then spend most of the clock testing it - roughly 8 minutes teaching and 12 minutes on items used purely as a check.
The evidence says the problem is not exposure. The students are fast (under 35 seconds on both items against a 90-second budget), so time pressure is not the cause. And they had already met the ORCHESTRA type in an earlier set and still missed it 5 out of 6. More items of the same kind will reproduce the same first-fit behaviour and strengthen the error.
Two independent items showing the same failure mode - stopping at a relation that eliminates nothing - is enough to justify changing the method rather than adding volume.
The check is not optional. A routine the tutor believes in but the students cannot execute at speed is worthless, so six to eight fresh items at 60 seconds each tells her whether the qualifier step survives under time.