Today, I ask Billy to set up a two column table in his notebook, labeling one column “Addition (+)” and the other “Multiplication (x)”. I want to return to the idea of math as a language, to teach him that “times” is just another “word” we use in mathematics to describe a special type of addition problem.
I write the expression 2 x 3 in the multiplication column, and ask him if he knows what it means.
“Two times three.” he responds.
“What does two times three equal?”
“Six!” he proclaims smugly. Time to shut him down.
“Why?”
“Uhhh,” he fumbles, “I just remember it from school.”
I write 2 + 2 + 2 in the adjacent column, and ask him if he knows what it means.
“Two plus two plus two.”
“And what does two plus two plus two equal?”
“Six.”
“Why?”
“Because.” he shows me two raised fingers, raises two more, and then another two, and then counts them out loud: “One, two, three, four, five, six—six!”
“Good. How many twos are you adding together?”
“Three.”
I point him back to the original 2 x 3 expression, and explain to him that 2 x 3 is the same as 2 + 2 + 2. I explain that, in math, we often need to add the same number over and over and over again, and so we created this new word called “times” to make things easier. Saying “two times three” is much easier, and much more concise, than saying “add three twos together”. We use it so much, in fact, that it’s easier to remember that 2 x 3 = 6, rather than have to calculate 2 + 2 + 2 each time.
To drive home this point, I ask him to write the problem “2 x 10 = ” in addition form, and to solve for the answer. He scribbles a long and unwieldy vertical addition problem in his notebook, and after a long and laborious series of calculations, arrives at 22—one two too many. I correct him, to his dismay, and then ask him if he wants to do another one.
His eyes bulge outwards in silent rage as he shakes his head vigorously no. I make him do another one anyway. 2 x 15. He bites down on his pencil in frustration.
With some additional prodding, he finally arrives at an answer, correct this time around. I ask him how he feels.
“I hate math.” he answers quietly, careful to avoid making any eye contact.
“I’m sorry it had to happen this way, but don’t worry, you’ll never have to do that again.” I explain that I have a special present for him that will ensure that something like this will never, ever, happen again.
“A calculator?” he asks.
“No. Even better.” I smirk. Rummaging through my bag, I pull out the holy grail of multiplication—the times table.
It was a hard lesson, but hey—nothing good ever comes easy.
No comments:
Post a Comment