Happy Pi Day!
Before we begin, you really must watch this video if you haven’t seen it already (and, actually, you should watch it again if you have – it’s that awesome):
Now down to business. There are some kids who just love everything you ask them to do. Some of them love it because they love, love, love math in all its forms. Some of them love it because they love you so very much. (This is true in 3rd grade, at least – it’s less true after that, sadly.) But some kids have a lot of trouble digging in. The things you say, the activities you plan, the enthusiasm you bring – none of it grabs them and compels them to make a niche in the mathematics you’re studying, to make math their own.
The third grader whose conversations with me are the topic of this post is one of those hard-to-grab students. She LOVES to draw, to make up characters, and to create cartoon stories. She HATES math. Or so she told me today. Here’s conversation number one (clearly not verbatim – I don’t have that great a memory. But it’s close enough.):
Note: I’m calling her Olive, but that isn’t her name.
OLIVE: Can I draw my ballerinas instead of doing math today?
ME: I think not. We have lots of things to do!
OLIVE: What are we doing?
ME: We’re going to learn about division! (Exclamation points indicate me communicating enthusiasm!)
OLIVE: I don’t want to do division. I don’t like division. I hate math.
ME: What about math do you dislike?
OLIVE: I don’t know. I just don’t like it.
ME: It’ll help me to understand what you’re thinking and what we can do about it if you can give me some specifics. Do you think math is boring? Do you think it’s too hard? Do you not like certain parts of math? What do you think?
OLIVE: Math is too hard. It’s too hard because I don’t know the basics.
ME: (Taken aback a little by response. Not what I expected to hear.) Can you explain what you mean by that? What basics do you feel like you don’t know?
OLIVE: I can do some things, but I don’t know the basics.
ME: Ok. Here’s a basic – do you know how to add?
OLIVE: I can add two-digit numbers.
ME: Great! You sure can! I’ve seen you do it! How do you add two-digit numbers?
OLIVE: Well, you put one number here (gesturing) and the other number here (gesturing below the first number) and you line up the digits and you add them.
ME: Awesome! Can you add three-digit numbers?
OLIVE: Yes, I can. You do the same thing. But I can’t add one-digit numbers.
ME: (Pause.) No?
OLIVE: Adding one-digit numbers is harder.
ME: Huh. Why don’t you show me how you’ll add two-digit numbers. (Grabbing paper and pencil.) Ok – what’s 99 plus 99?
OLIVE: (Writes numbers stacked digit-wise.) 9 plus 9 is 18, put the 8 here, carry the 1. 1 plus 9 plus 9 is 19. So it’s 198.
ME: Super! Ok, so what’s 999 plus 999.
OLIVE: (Adds.) It’s 1998.
ME: Alrighty. 9999 plus 9999?
OLIVE: That’s easy, I’ve already done that. Just stick another 9 on the inside. Ooo, that’s an interesting pattern.
ME: Yeah, it is. Olive, look – (pointing to the nines in the ones column) – you just did one-digit addition here.
OLIVE: (Pause.) I know. But it’s harder when it’s just one digit.
ME: What about it is harder?
OLIVE: There’s less there. There’s just one digit. (Doing some gesturing indicating lining numbers up.)
ME: (Really trying to understand what’s going on.) Because there’s nothing to line up? Because there’s more riding on that little addition, because it’s the whole answer?
OLIVE: No, kinda, no. It’s just harder.
ME: Ok. Well, what’s 4 plus 4?
And the conversation continues in this way for several more minutes, until class begins.
Now for conversation number two:
Olive is sitting on the rug with another girl. Second girl is working on division sheet. Olive is doodling.
ME: Hey ladies. What’s going on?
OLIVE: Can I draw my ballerinas instead of doing the sheet?
ME: That’s a great ballerina. But how about you try this problem?
OLIVE: No, I don’t want to! I don’t like this. I don’t like math.
ME: I remember you said earlier that you didn’t like math because it was too hard, because you thought you didn’t know the basics. Well, this kind of division is one of the basics. It’s a good thing to learn if you want to know more basics.
OLIVE: No, that isn’t why I don’t like math. I don’t know why I don’t like math. I just don’t like it.
ME: Well, what are some things that you like that math doesn’t have?
ME: What are some things that you like to do that you don’t do in math?
OLIVE: I like things involving pictures.
ME: I have an idea – why don’t you make a picture for this division problem? (Not really expecting her to go for this.)
OLIVE: (Pause.) That’s a really good idea! 8 divided by 2…
Starts drawing an 8 spliced into two pieces, top circle and bottom circle. 8 has arms and legs. It is being menaced by a 2 – fanged, with a giant sword.
ME: I really like the teeth on the 2. But what goes in the eight-halves?
ME: Well, what is each eight-half? What goes in each circle?
OLIVE: Ummmm. 4?
ME: I think so! What can you do with that?
OLIVE: They’re boogie-ing!
Draws a little dancing 4 in each half of an eight. Moves onto next problem – 14 divided by 7.
OLIVE: How many pieces should I break the 14 into?
ME: Well, what’s it being divided by?
OLIVE: 7? That’s going to be hard to draw.
ME: And what’s boogie-ing?
OLIVE: No! That’s too hard! Can you tell me, pleeeeeeeease?
ME: Olive! It’s your artwork! I can’t make part of it for you!
OLIVE: Ok, ok! (Really intensely focused expression crosses face.) 2, 4, 6, 8, 10, 12, 14. The twos are boogie-ing.
Olive and I spend the next 45 minutes doing seven very basic division problems this way.
Pros: She dug in. She was so very into her artwork that we worked almost a half-hour beyond math class on this. This is one of the only times this year that she’s chosen to do math over other things.
Cons: We didn’t do much dividing. We did a lot of personifying numbers and the act of division, which is important for her understanding of division. But we didn’t get much hands-on experience with numbers and division.
She loves to draw, and I like that we found a way for her to incorporate drawing into math. But I’m not sure we did enough math. She wants to learn math – in her own words, she recognizes that her skills are weak, and she wants them to be stronger. But she isn’t compelled to work on those skills. This doodling division was great for today, but I need better ways to get her invested in doing mathematics – for the long haul.