In my measurement unit, we have worked on making estimations
about height in inches an feet during several lessons. This Tuesday, I asked my
students to act as architects and to design the buildings they would want to
create for our little-giant city. I then asked them to estimate how many inches
their buildings would be and watched intently as they began their first
designs.
One
student really took me aback when I witnessed her making her estimation. She
took her thumb and index finger and began counting how many of those measures
tall the building she had drawn would be. I asked her to do it again when I
witnessed it because I was extremely intrigued by her thinking. I had not
explicitly modeled that skill in particular, I had just given counting up as a
short example of how you could estimate.
On
her own thinking she said, “I take my fingers, and this is like, an one inches,
and then I make them go up like with the candies and then I get nine. So nine
inches.” I smiled so big right then, I could not help it.
“I love how you thought about that!”, I said, “Do you think
you could show everyone? I think that is a great way to estimate!”
I
had the student show how she made her estimation to the whole class. I was
excited when some students, who had already completed their assignment, went
back to ask for their math journals to try again. This student had really
inspired her classmates.
I
love to see this kind of thing happening. The “empty vessel” model of education
is, as we know, is so outdated, so “old hat”. The way that my student was
measuring was something of her own design, and it is a conclusion she came to
on her own. It not only benefitted her, but benefitted some of her classmates
as well.
I
was unsure, when I came to kindergarten, how much my students could learn from
one another, but I can say with confidence, that my students learn exponentially
from one another everyday. (Pictures soon!)
This was a great example of student thinking, and having students share their own methods with each other. Again, this example makes clear how a student's own method is just as mathematically viable as any...of course, now the trick is to advance this student's method with other approaches that other students might have come up with, as well as with other approaches that are more "conventional". Part of your role as a teacher is to construct these more formal sharing-out sessions that allow students to see as many different representations of measurement as possible.
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