Five Analogies, Nine Students: Which Items to Keep, Repair, or Drop
Ms. Okafor runs a 40-minute verbal enrichment block for nine third and fourth graders. She gave a five-item analogy quiz and tallied how many of the nine chose each option. Item 1, WARM : HOT :: COOL : ___ (chilly, cold, winter, thermometer), drew eight choices of 'cold.' Item 2, PEDAL : BICYCLE :: ___ (rung : ladder, wheel : tire, driver : car, engine : fuel), drew three correct answers; five students chose 'wheel : tire.' Item 3, CHAPTER : BOOK :: ___ (note : song, page : paper, author : novel, shelf : library), drew six choosing 'note : song.' Item 4, PUPPY : DOG :: ___ (kitten : cat, cub : bear, calf : cow, foal : horse), drew nine choices of 'kitten : cat,' although the other three options describe the same relationship. Item 5, LIBRARIAN : BOOKS :: ___ (chef : kitchen, cashier : money, pilot : sky, gardener : plants), split four ways with no majority. Ms. Okafor wants to know which items to keep, which to repair, and what the error patterns reveal about how her students attack an analogy.
1. For each of the five items, state the bridge in one sentence, name the single best option, and flag any item where a second option also satisfies the bridge.
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Item 1. Bridge: the second word names a more extreme degree of the first. COOL sits below COLD on the same scale, and the direction must be preserved. cold is correct. 'chilly' is milder than cool, so it reverses the direction; 'winter' is a season; 'thermometer' is the instrument that measures the quality.
Item 2. Bridge: the first word is a part of the second that a person pushes or steps on to operate it. rung : ladder is correct. 'wheel : tire' keeps the topic but reverses the order - a tire is a part of a wheel - which is exactly the error five students made.
Item 3. Bridge: part to whole. note : song is correct. 'page : paper' is material, not part-whole; 'author : novel' is creator to created and also reversed; 'shelf : library' is a holder to the collection it belongs to.
Item 4. Defective. All four options fit 'young animal : adult of the same species,' so no option is uniquely correct.
Item 5. Bridge: a person whose job is to tend or manage the thing named. gardener : plants is best because it matches both the doer and the tended object. 'cashier : money' only handles money in a transaction; 'chef : kitchen' and 'pilot : sky' are person-to-workplace, a different bridge.
2. Item 4 was the only item everyone answered 'correctly,' yet it is the weakest item on the quiz. Explain that paradox and rewrite the options so exactly one fits.
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The paradox dissolves once we separate difficulty from quality. A high success rate usually means an item is easy; here it means the item is broken. Every option expresses the same relationship, so a student can reach the keyed answer by matching the topic ('baby animal, grown animal') and never has to check direction, part-whole structure, or anything else. The item therefore measures topic spotting and nothing more, and it would give the same result to a student who reasons carefully and to one who guesses from association. In test-construction terms it has three functioning distractors that are all correct, so it cannot discriminate.
Repair: keep the stem PUPPY : DOG and replace the options with one true match and three that break the bridge in different ways - kitten : cat (correct), kitten : milk (young to food), cat : kitten (adult to young, reversed), dog : wolf (domestic to wild relative). Now the only option that preserves both the species relationship and the direction is 'kitten : cat,' and a reversed-order or topic-only reasoner will be caught.
3. A colleague wants to know whether Item 2 or Item 5 is the better single measure of whether a student checks direction. Decide and justify with the specific failure each item produces.
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Item 2 is the better measure. Its most attractive wrong option, 'wheel : tire,' preserves the exact topic (bicycle parts) and breaks only the order, so a student who checks direction will reject it and a student who does not will be drawn to it. The error is diagnostic: choosing it tells you precisely which step was skipped.
Item 5 fails as a direction probe because its wrong options are not order errors at all. 'Chef : kitchen' is a perfectly ordered workplace relation; the reason it is wrong is that it does not match the bridge chosen for the stem (person who tends an object). A student can lose Item 5 while being scrupulous about direction - the problem is bridge selection and the best-answer convention, a different skill. Item 5 is still worth keeping, but as a discussion item about how to break a tie between two candidate bridges (here: prefer the option that matches both the doer and the object being tended), not as a direction check.