## Tuesday, June 9, 2009

### M7n1 a - Meaning of 0

M7N1. Students will understand the meaning of positive and negative rational numbers and use them in computation.
a. Find the absolute value of a number and understand it as the distance from zero on a number line.

I usually don't get many comments on my blog entry (and I would be happy to hear from more of you), but on May 30, PJGould said that he had come across a child who started his counting with zero. Of course, he noted, that made his counting always off by one. After all, zero is not a counting (natural) number. But what does zero mean?

In elementary (K-5) curriculum, there are 3 meanings of zero - perhaps it is more accurate to say 3 ways zero is used. First, zero indicates the cardinality of an empty set - that is, zero means 'nothing.' This is probably the most commonly used meaning of zero in elementary school. Another place zero is used is as a place holder in a written numbers, such as 3042. Of course, this is a slight extension of the first meaning in that there is no unit of one-hundred in this written number. So, it is still pretty close to the first meaning.

The third usage of zero in elementary schools is the starting point of a number line. In some textbooks, a number line actually starts with zero as shown below.

In other textbooks, the tick mark for zero is not at the end of a number line, implying that there may be something to the left of zero as well.

As students study positive and negative number, one of the important understanding students have to make is the meaning of zero as a referent point, or the origin, on the number line. As long as students are stuck with the idea that zero means 'nothing,' some will have difficulty making sense of numbers that is 'less than nothing.' Rather, students must look at zero as a referent point on a number line, and those number to the right of zero are positive and those on the left are negative. The distance from zero, whether on the right or left is the absolute value of the number.

For those of us who already understand positive and negative numbers, this way of looking at zero is not a major issue. However, we should be aware that this meaning of zero isn't something students are familiar with. In most elementary curriculum, very little explicit discussion takes place about the role of zero on a number line. Thus, when we introduce positive and negative numbers, we do have to keep this shift in understanding of zero in our mind.