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.


  

Zero, Nought, or Nothing

Noughts and crosses is a popular game usually played with a pencil and paper especially during a long and boring lecture by two overly competitive students. I still call it this even though it is inexplicably called tic tac toe in the US (If you Google the origin of the name you'll find it has to do with the sound Roman pencil's made when they hot the ground - still inexplicable).

The word 'nought' is the British equivalent of zero and has given rise to some interesting phenomena such as the 'early noughties', the first ten years of the current millenium as in '04 and '08. Shakespeare loved 'nought', of course, as in " That it yields nought but shame and bitterness" from Henry V.

Today,  the concept of zero is something we must focus on developong with young children as they learn to count and understand the intricacies of our base ten system. The idea of the concept of zero was first introduced as an "empty set" through the disastrous New Math of the 1960s. Math educators are still frequently erroneously tarred with the same brush when any mathematical ideas are suggested that differ from traditional mathematics; but that's another story.    

When we teach children how to number name from 0 - 100 we must start with zero so that they recognize it as a number with a place on the number line. Later when children start to develop their sense of cardinality, the ability to recognize and name a quantity, they can start with 0 before they have any objects to count. The importance of developing this idea only really becomes apparent when they encounter the base ten system.

Traditionally, children have been taught to think of 0 as a "place hloder'. The problem with this idea is that it doesn't help in the development of the child's conceptual understanding of place value. For example, in the number 306, the zero stands for no tens. The idea of the "place holder" simply means that it keeps the 3 and 6 apart which does nothing to develop an understanding of what each digit in a number means. It's another  example of the useless metaphors that are sprinkled throughout traditional math.  

The Value of a Place

I can remember being told, as a student in primary school, to put a comma every three numbers when writing large numbers. I was told it would separate the hundreds, thousands, millions etc. I remember dutifully doing this with absolutely no sense of why or feeling any nearer to being able to read very large numbers.

Today, we still use the commas when writing large numbers but
unlike the instruction of the last century, we now teach why we put a comma every three numbers. It certainly does separate things but, more importantly, it shows the repetition of the ones, tens and hundreds every three numbers. First we have ones, tens and hundreds of ones, then we have ones, tens and hundreds of thousands and then we have ones, tens, and  hundreds of millions, and so on. If we learn this repetition of the place value referents it makes reading and understanding large numbers much easier.

It also helps students develop a far more realistic idea of what zero, or nought, is.  I remember learning 0 as a "place holder", a bit like a pot holder, perhaps. What did that really mean? The 0 holds a place when there is no number there, perhaps. What nonsense!  The 0 means there are none of that particular referent in this number as in 23,405, where the 0 means there are 0 tens. In this number, 305, 877  the 0 means there are no ten-thousands; there are 3 hundred-thousands and 5 thousands but 0 ten-thousands.

'Nought', by the way is the British word for zero and became quite popular during the first decade  of the current  century with years like '03 and '06 which was referred to as the 'noughties'.