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Mathematics Education: Number sense and early counting · Counting Principles

The principles children must grasp to count meaningfully, how researchers test them, and how teachers can support each one.

Mathematics Education · 24 questions

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1. Counting five blocks, a child touches one block twice and announces six. Which counting principle is broken?

  1. One-to-one correspondence
  2. Stable order
  3. Cardinality
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Answer: One-to-one correspondence

One-to-one correspondence requires exactly one number word for each object; tagging a block twice inflates the count.

2. A child always counts "one, two, four, five," in exactly that sequence every time. Which principle is already in place?

  1. Order irrelevance
  2. Stable order
  3. Cardinality
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Answer: Stable order

Stable order means using the same list in the same order every time; a consistent but nonstandard list still shows it.

3. After correctly counting seven toys, a child asked "How many are there?" starts counting all over again. What is missing?

  1. The stable order principle
  2. One-to-one correspondence
  3. The cardinal principle
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Answer: The cardinal principle

The cardinal principle is knowing that the last number word said tells how many are in the whole set.

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