After our Video
Conference sessions, I would like to plant some seeds for thought. Think
about concept based teaching. How would you explain to a student the
difference between 4 divided by 2 and 4 divided by 1/2. How could you
demonstrate the difference through drawings or representations? You have seen
that we can often teach a concept itself with pictures that spark questions or address
a concept creatively.
As I work with older
students who have been taught in a purely procedure driven manner, I find that
they are as confused as many adults about the meaning behind this
concept. Even students who perform very well computationally may
experience difficulty estimating and applying these concepts if they do not
understand them. Why is 3.5 divided by 0.125 a whole number answer?
How could we estimate a solution for 30.069 divided by 9? How does a
student know whether or not his answer is reasonable or not? When the
student reaches algebra, he should know. Before she gets there, we should model
the thinking and the language of estimation.
I find that the
language of fraction division is among the most important we create. We must
strive to help students reason why ½ divided by ¼ is 2. In division with
fractions, we can ask how many pieces the size of “__” we can make if we start
with a specific quantity…but sometimes it is not how many, but how much of.
How much of ¾ can we
make from the quantity 3/8? Consider, ¾ divided by 3/8 is 2, but 3/8 divided by
¾ is ½. Can you explain with simple, comprehensible language why that is
so? The language lies in the “how many of” vs “how much of” and we need
to help students see the meaning behind the math if they are to reason
mathematically.
The videos and conference sessions where you show multiplication and division of fractions in such a concrete, accessible way was enlightening. I can't wait to try this with students!
ReplyDeleteI devised my lesson for this class based on a need I saw with my students, not understanding even and odd numbers. I used manipulatives to have them divide a number of marbles evenly between themselves and a friend. The numbers that had one left over were odd numbers and the ones we could divide evenly were even numbers. The lesson paved the way to discussing that we divided our numbers by 2 or we gave half of out amount to our friend. Using your examples I used the time to just incorporate and use the math words that they would hear and use later.
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