Here’s what it’s like teaching kids who pretty much have no first language. That means the kids who speak no language other than English, but who missed out on enough language exposure as a little kid to speak even conversational English proficiently. All of my kids are English Language Learners for academic English, because most people just don’t use that kind of sophisticated vocabulary in daily life around here, but a few kids are simply Language Learners: they struggle with information presented through language.
We were trying to divide using partial quotients. We’ve been doing it for 3 days. It’s a one-on-one conversation.
Me: So we have 76 and we’re trying to divide by 5. We’re trying to think: how many groups of 5 can we make out of 76? Well, we can make 10 groups of 5. If we make 10 groups of 5, that’s 5 x 10. What’s 5 x 10? (I write it on the mini board.)
Me: Excellent! So we circle the 10, because that’s how many groups we made so far. Now we subtract our 50, because we used up 50 out of our 76. What’s 76 – 50?
Me: Awesome! So let’s think: how many groups of 5 can we make out of 26?
Me: OK. We can use 20 out of those 26. So how many groups would that be?
Me: Well, we aren’t making 20 groups. What’s the equation? How did you get 20?
Me: Good! We’ll start with 5. 5 times what?
Her: 5 times…20?
Me: 5 times 20?
Her: No, 5 times 4!
Me: Awesome! 5 times 4 is 20. That means if we make 4 groups with 5 in each group, we use up 20 tallies in all. So how many groups did we make?
Me: Listen to my question. We used 20 tallies, but how many groups was that?
Her: 20? 5?
Me: Let’s draw it. (I draw 4 groups with 5 tallies in each.) How many groups are there?
Her: 5? 20? 8?
Me: I see four groups. There are five tallies in each group. How many groups do you see?
Me: There are four groups. How many groups are there?
Me: What is a group?
Her: Um…..a circle?
This whole conversation took place one on one. At first, it seems like typical confusion, but the more you get into it, the more you realize that she doesn’t understand what you’re saying. When you write a computation problem on the board, she can do it. When you draw a picture, she can see the parts of the picture. But when you ask a specific question, she doesn’t know what you’re asking, so she just guesses random numbers. Even when you flat out tell her the answer, then ask the question, she doesn’t know. In the end, the whole thing is impossible because she thinks the word “group” is a synonym for “circle.”
This is the kind of kid who might tell you it was their grandma’s birthday party this weekend. You ask, “How old is your grandma?” and they say, “Saturday.” Turns out her grandma’s birthday was Saturday. But she didn’t really process or understand your question, so she just said something that was a little related. This is the kind of language difficulty that is really freaking hard to overcome and takes an enormous amount of instruction in the language itself, much less math.
On the plus side, I had 3 kids like this last year, one of whom would give this kid (and my other 2 low-low math girls) a run for her money in the Who Is More Mystified By Numbers contest, so I am getting pretty good at hiding the immense frustration I feel at this type of conversation. My kid last year used to sense that I was frustrated, feel stupid, and cry, which made me feel like a jerk. I am better at it now, so although this kid knows stuff is taking her longer than other kids, she doesn’t really get that I’m about to tear my hair out, so no demoralization = good thing. But seriously…teaching is hard.