Thursday, May 24, 2012

Thinking about Zero

Just think, without the numeral 0 there would be no place value system, 10 would be 1, and we wouldn't have a clue how to show a million. Traditionally, in our base 10 place value system of numeration, 0 has been called a "place holder" which is pretty meaningless when you stop to think about it. In the number 307, the zero means there are no tens in just the same way that the 3 means we have three hundreds and the 7 signifies seven ones. To call it a "place holder" reduces the real meaning of zero to a valueless grapheme that in no way contributes to young children's understanding of our place value system. Zero, or nought,  means nothing, none of, the starting place, neither positive nor negative,

Whether we should teach children to start counting at 1 or 0 has been a point of discussion among academics for some time and has recently been complicated by the addition of subitizing, the instant  identification of numerousness without counting. It has recently seemed to me that we need to start at 0; here's why. All children know what it's like to have no ice-cream or no M&Ms or no Hotwheels so why not begin counting with this idea that all children are familiar with. We still need to teach number naming, the sequence of the number names similar to learning the alphabet, and we can still teach subitizing skills. If we start with zero, however, the introduction of fractions and negative numbers later will make so much more sense.

If children see 0 as the point of reference they will better be able to see how fractions fit between 0 and 1. Fractions are initially taught as being parts of wholes, which on a number line, for example, is the space between 0 and 1. All the models used to teach fractions rely on students being able to take one apart into its fractional parts.

It's a similar issue with developing the idea of negative numbers. Without 0 as a reference point many children develop the misconception that anything less than one, such as a fraction, is a negative number.

It's as if 0 is a state of equilibrium, a fulcrum, an origin, a place at which all life begins.


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