Monday, October 24, 2011

The Albert Hall....How Many Holes Fill It?

Many years ago The Beatles assumed we all knew how many holes it takes to fill the Albert Hall. To be absolutely sure we'd need to know both the size of the Albert Hall as well as the size of the holes they were filling it with. We'd also need to know whether the holes were pressed together with no gaps or overlaps.

More recently, an article on the MSNBC website described the extent of Ted Turner's ranch as "just shy of three Rhode Islands". Since most of us have no idea how big Rhode Island is, beyond the fact that it is quite small as States go, we can only assume Mr. Turner's ranch is rather large.

The Beatles' "holes" and Turner's "Rhode Islands" are examples of referent units, things we use to give us a sense of the size of something.  As useful referents these two example are not terribly useful but there are literally millions of referents that are. In fact, mathematics in the elementary school, as well as our lives in general, would be pretty bleak and meaningless if we were not familiar with a good number of these referents. Just about every noun you can think can be a referent. A referent can be an orange, a house, a universe, a plant, a person, a feeling, a hope or a penny.

There are also things made up specifically to act as referents. A "byte", for example, is a referent as is a foot, a pound, a dollar, a gallon or a  degree Fahrenheit. There are also referents that are culturally defined such as a gram, liter,  or centimeter. How wide is the span between your thumb and little finger in inches? How far in centimeters?

This ability, or inability, to think in terms of referents is what we can call quantitative literacy and is a key component of the elementary school math curriculum where we need to try to avoid the use of "naked numbers" or numbers without referents. The use of a referent changes a numeral, a grapheme, into a number and gives it magnitude. For young children this is an important part in learning how to use mathematics in everyday life as well as learning the joys and wonders of mathematics.

I once asked a group of kindergartners what was the biggest number they could think of.  After most had strung together a bunch of jumbled, familiar number names one little girl responded "One Universe".  

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