Tuesday December 13, 2016
Substitute Teaching Vignettes #3
4th grade. Math.
Students are learning multiplication with "partial products". I know this concept as well but I use parentheses.
14 x 37 = (10 + 4) x (30 + 7)
I say "I'm not familiar with this way of doing it. I did things differently in 4th grade. Can someone show me how this is done?"
A well-spoken 4th grader raises his hand. With a serious expression, he walks to the board. I hand him the marker.
He writes the numbers in the boxes. He explains as he does it. He adds up the numbers. He hands the marker back to me and says: "Do you understand it now?"
I say "Thank you."
My favorite teaching technique. If they can explain it, they get it. (And, or so I believe, if another student explains it, that's better than a teacher just telling.) Plus, I got a quick lesson in Common Core mathematics.
One problem with the diagram method is that it's easy to get subtly wrong if you understand the process roughly but not the underlying concepts.
One student had this on his problem sheet:
10 x 4 = 40 7 x 30 = 210 210 + 40 = 250.All of the correct numbers. Multiply and then add. But he was multiplying and adding the wrong ones.
So easy to miss. Numbers is tricksy things.