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Commutativity is somewhat subtle property. I wouldn't expect a child to understand its implications right away and be able to act as the multiplication was not

• dalke 11y ago
  The essay suggests that covering the commutative property is possible at this age level. In any case, at this level that property means "with addition and multiplication of numbers, it doesn't matter which one goes first." The problem is that the test can't distinguish between two possibilities. Here's an account I once heard. An elementary grade state-level test for general science asked something like "of the following materials, which are used to make plates to test mineral hardness? a) wood, b) glass, c) porcelain, d) plastic". The answer in real life is b) and c), but only one answer was allowed. In one class, some students picked b) and others picked c). When the teachers complained, the state said that glass was too dangerous for an elementary school, so isn't part of the curriculum, so the student shouldn't know that. The problem is, a geologist had visited the class and showed different types of plates used in real life. The students, in essence, were penalized for knowing more than they were expected to know. I can make the similar case here. A good test shouldn't penalize a student for knowing too much.