Zero for Children

Date: 03/16/2002 at 16:07:55
From: Amy Buck
Subject: Importance of zero

I am in a college math course and our teacher gave this as one of our 
assignments. 

When you are teaching children to count (1-10), do you include zero?  
Why or why not? 

How do you explain to a child (K-2) what the value of zero is, and is 
zero just a place holder?

Date: 03/16/2002 at 23:23:14
From: Doctor Peterson
Subject: Re: Importance of zero

Hi, Amy.

First, I wouldn't include zero in first teaching a child to count, 
simply because we don't use it in counting. Counting means matching 
objects with natural numbers, starting with 1. When a child is first 
learning to count, the idea of counting nothing would be confusing.

However, I would mention zero frequently after this, using it as a 
word for "no objects," in order to introduce the concept. Soon, when 
we get into subtraction, we find that zero arises as the answer for 
some problems that make sense, yet have no answer if we don't consider 
zero to be a number. If I have five apples and give you five, how many 
do I have left? You can't say "you can't take five from five"; of 
course you can. But you have none left. What number should we say is 
the answer? We've been using the word "zero" for this; let's consider 
that a number, so we can answer the question.

I think that answers your second question, no matter whether I take it 
to mean "what is the meaning of zero?" (it means "no objects") or 
"what is the importance of zero?" (it is necessary in order to answer 
all meaningful subtraction problems).

This raises other interesting ideas. For one thing, negative numbers 
arise for just the same reason, though it can be harder to show why it 
makes sense to ask how to subtract a larger number from a smaller one. 
(I would use a thermometer, the one place in everyday life where 
negative numbers are essential, at least in my climate or where 
Celsius is used.) My seven-year-old has no problem with the idea of 
negative numbers, and can add them easily, though I doubt he could 
multiply them.

Another idea is the historical development of zero. As you suggest, it 
arose first as a mere place-holder, and only later was seen as a 
number in its own right. Children may be interested in hearing that 
there were people long ago who were just discovering these ideas, and 
had the same problems they have now! Here are a couple of pages on 
this topic:

   History of Zero and Place Value - Dr. Math archives
   http://mathforum.org/dr.math/problems/tristan02.17.99.html   

   A history of Zero - MacTutor History of Mathematics archive
   http://www-history.mcs.st-and.ac.uk/HistTopics/Zero.html   

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/