During this week, I observed math in my
first grade classroom, but I also saw student math homework. I chose to bring in a sample of math homework
from Student A so that I could see how students complete work at home. The homework assignment was from the Everyday
Math book. The directions said "Cut
examples of numbers from scrap papers you find at home and glue them onto the back
of this page". Student A's homework
assignment that was brought back had pictures of numbers in a grocery
advertisement. Some of these numbers
were 2/$3, $6.99, and 1.98 per lb. The
student showed that she knew there were numbers in advertisements. The student did not have any other number
representations besides those from the grocery ad.
Student
A's artifact may reveal that she only thinks numbers are in terms of money in
advertisements or that she did not want to search for numbers elsewhere. Assuming the former, Student A does not know
that numbers can represent other things besides money. The artifact reveals that this student has a
gap in her understanding of where numbers can be found. One way that I could advance her thinking is
to show her samples of numbers in magazines, newspapers, and other papers that
I have at my home. This way she could
see that numbers are everywhere! Another
way that I could advance her thinking would be to ask her where else she sees
numbers on a day to day basis besides at the grocery store. Simply by asking her this question, she may
think of other places that she sees numbers.
My way of adding to the homework assignment would be for students to cut
examples of numbers from at least 3 different papers at home so that they are
seeing numbers in a variety of places.
A
question that I might ask Student A is what are the numbers used to tell
us? Another question that I may ask is
why do some numbers look different than others?
By this I mean why do some numbers say 6 and some say $6. This would get the student to think about
numbers in terms of money and numbers in terms of other concepts.
A
future math task that this student might find helpful is writing a list of
where she sees numbers while she is in public places and at home. This way she will see many places where
numbers are used and will not have to focus only on ones that she can cut out
from a magazine. The student could
complete this task on her walk home from school by noticing numbers around the
school community. This student will benefit
from constant exploration of numbers inside and outside of the classroom.
This is a very interesting example for its simplicity but also its depth. You've given a good analysis here and a number of good alternative ways to advance the students thinking. Might this case reveal that other students have similar [potential] misconceptions? The activity you suggest might be beneficial for all students: that is, to write down as many numbers as they notice (in the school, in the classroom, at home) and then to compare their lists and defend whether or not each case is an example of a number or not (e.g., can a "number" exist even when the numeral is not written out? That's a deep question.)
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