Ancient Greek mathematicians had no notion of negative — or positive — numbers. Similarly, for most young children, numbers are not signed. Children learn to count with natural numbers. At some point, they learn about zero. Later, they encounter (regular) fractions, decimals, and percentages. Typically, a child’s formal introduction to the notion of sign comes after all this experience. Interestingly, we have found that many students in the elementary grades have some familiarity with negative numbers but have never heard of positive numbers. These children inhabit intermediate worlds that consist of regular numbers and negative numbers before they begin to (intermittently) inhabit worlds of positively and negatively signed numbers.

*Regular Numbers and Mathematical Worlds*

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I love this, and the attached abstract.

All the stuff on number in the CCSS is about “extending”.The negative numbers are no exception.

It has been abundantly clear to me that signed numbers are essentially different, and represent change and direction. Time for a radical rethink here.

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And fractions !!!!

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