Sorting the Word Cards
In a word-study center, Ms. Grant gives four students eight cards: puppy, kitten, eagle, oak, rose, tulip, maple, pine. The task is to make two groups of four cards and to write a rule for each group that another person could check. Sam pushes puppy, kitten, eagle, and rose together and says, 'These are things I like best.' Jo puts oak, maple, pine, and tulip together and says, 'These are plants.' Ms. Grant asks, 'Could a new student use Sam's rule without asking Sam?' The class notices that rose fits Jo's group better and that eagle does not fit it at all. Ms. Grant does not move the cards. She adds a ninth card, sparrow, and asks where it belongs and why. Two students say sparrow belongs with the plants because sparrows live in trees. Jo says she wants to keep the plant group together, but she is not sure about tulip, because a tulip is small and a tree is tall.
1. What is wrong with Sam's rule, and which two cards should move?
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The problem with Sam's rule: 'things I like best' describes Sam, not the cards. No other student can check it, and it could change tomorrow. A sorting rule has to name something the items share, so anyone can test a card against it.
Cards that should move:
- rose belongs with the plants. It has the same kind of feature as oak, maple, pine, and tulip.
- eagle belongs with the animals, next to puppy and kitten.
After the move, the animals are puppy, kitten, eagle (and later sparrow) and the plants are oak, maple, rose, tulip, pine.
The lesson: the test of a rule is not 'do I agree with it?' but 'could a stranger apply it to a card I have never shown them?'
2. Where should sparrow go, and why is 'it lives in trees' a weak reason?
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Sparrow belongs with the animals (puppy, kitten, eagle), because it is a bird - a kind of animal.
Why 'it lives in trees' fails:
- The rule for the plant group is about what a thing is, not where it is. Location does not make a bird a plant.
- The reason proves too much. If 'lives in trees' put something in the plant group, then a squirrel would go there too, and so would a treehouse.
- An oak is in the plant group because it is a plant that grows, not because of where it stands.
A fair exception: a class could choose a location rule, but then it must be stated out loud and applied to every card the same way. A rule is judged by whether it is used consistently, not by whether one card happens to fit.
3. The groups are now 4 animals and 5 plants. Is unequal size a problem, and what rule should the class follow?
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It is a problem for the game, not for the categories. With nine cards the class cannot make two groups of four, because one card is left over. That is a fact about the cards, not a flaw in the plants rule.
The class has two honest choices:
- Keep the meaning rule (animals vs. plants) and accept groups of 4 and 5.
- Keep the game's 4-and-4 shape and find a narrower rule, such as 'trees' (oak, maple, pine) versus 'everything else.' That works, but the trees group is now built to fit the shape rather than to describe the cards.
What the class should not do is move a card into the wrong group just to make the numbers even. Size is a rule of the game; 'is it a plant or an animal?' is a rule about the words. When they conflict, name which one you are following.