One of the students I interviewed recognized the array, but
could not think of the name. When I asked her to create her own, she drew five
rows of five. She told me the array had
ten parts to it, thought for a second, and began to correct herself. She had to
count each x she drew to realize there were actually 25 x’s in her array. The
student then said, “I think I said ten because five times two is ten. This is
actually five times five and it equals twenty five.”
This student work shows me the student does not have a
strong understanding of what an array is or what a multiplication fact actually
means. Instead of recognizing there were
five rows of five, she had to count each x in order to come to her answer. Her intial guess of ten shows me she knows
her math facts, but not quite be able to visualize what happens when to factors
are multiplied.
The next step I would take in helping her strengthen her
understanding of multiplication would be to give her an open ended problem that
challenged her to see how multiplication is simply repeated addition. I believe she would also benefit from
creating more arrays, maybe with manipulatives, to see that x number of rows by
y number of columns is equal to a greater number and is just addition over and
over again.
What might this open-ended problem look like? And are there other students in the class who you think have similar misunderstandings or more complete understandings of the array at this time? How might you give them the opportunity to talk to each other?
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