## Monday, October 11, 2010

### The middle of the road

I've proposed several times in this blog that we consider math to be a language of counting, measurement, shapes and calculation; a language with precise definitions and specialized terms.

I'd like to adjust my definition to include the concept of comparison. Math provides us with the means to compare and evaluate the world around us.

While there are subtleties which require us to use a wide range of comparison terms, the simplest comparisons could be narrowed down to two choices.

• This object is the same as that one.
• This object is not the same.

A much more satisfactory comparison can be made using three terms. In essence, we are still using the single comparison as well, but we are leaving that comparison unspoken.

• This object is the same as that one
• This object is better than that one (therefore it is not the same)
• This object is not as nice as that one (thus it too is not the same)

Kindergarten Excel Math starts off not with numbers, but with comparison words that a 5-year-old person could use. The table below contains a variety of these sets of words used by English-speaking people of all ages. I invite you to think of more terms:

Minus

Equals

Plus
less than
equal to
greater than
lower
same height
higher
below
same height
above
shorter
same height
taller
shorter
same length
longer
narrower
same width
wider
under
middle
over
bottom
middle
top
left
middle
right
thinner
same thickness
thicker
inside
on the line
outside
off
midway
on
before
during
after
fewer
same
more
fewest
same
most
least
same
most
different
similar
identical
front
middle
back
forward
not moving
backward
in front of
aligned with
behind
younger
same age
older

This concludes my list of comparison terms. But before I leave, here's a gift for those who insist on numbers in every math blog. Your assignment? Describe the relative positions of these three numbers using at least 3 sets of comparative terms from the table above: