For the first time in several years, I am teaching our college
developmental arithmetic class, so I decided to try some activities to help
students understand the metric system.
After making a few measurements of books and desks together with the class,
I assigned students to measure their own heights in centimeters using a
meter stick. One student wrote 124 cm and three others wrote 126.5 cm.
When I wrote the heights measured by the class on the blackboard and
compared them, I demonstrated how short 124 cm (~4'1") was for a college
student (no, we don't have any midgets in the class), explaining that the
measurement must have been wrong. Next, I demonstrated that 126.5 cm
(~4'2") was also too short, expressing surprise that we had three students
that size. Immediately one girl turned to another accusingly, "I copied
from you and you were wrong." Then a third girl joined in, "Yeah, I copied
from you too; it's your fault we had the wrong answer." I explained that
since all three girls were different heights, they would never have the
correct answers if they copied each other; they would need to measure
themselves to find the correct answers.
The following day, I explained and demonstrated to them how to find the
length of their paces by walking forward, then stop in mid-stride to
measure the distance from the front of one toe to the front of the other.
When they began to measure in centimeters, using a meter stick, I found
some were placing the stick from toe to toe as instructed, but were getting
the wrong readings. Instead of placing one end of the stick at the end of
a toe, they were randomly placing the stick, and randomly reading any
number that happened to land near a toe. Thus they could have read almost
any number from 1 to 100 cm! I showed them they needed to measure with the
zero end of the stick placed at one toe, and read the number beside the
second toe.
Next, I asked them to find the area of their shoes by tracing the bottom on
a sheet of centimeter grid paper and counting the centimeters squares
enclosed by the outline. One student said she did not have to trace the
shoe, she could find the area of the shoe by just drawing a rectangle on
the paper and count the squares. (She chose an apparently random size for
her rectangle). She seemed surprised when I told her she could not find
the area of her shoe that way.
Asked to find the perimeter of the shoe by stretching string around the
outline of the shoe and then measuring the length of string needed, one
student inquired whether she could just count the squares along the outside
of the outline. I explained that counting the squares would not give as
accurate a measurement as the string. I supposed I should have let her try
it both ways and compare the measurements.
There is hope. Many students were using their meter sticks on the test to
estimate answers, and the test scores were higher than with my previous
traditional arithmetic classes where students memorized symbols and
procedures without activities.
Shay Cardell
Central Arizona College
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