The Graph Factory

I want my students to see graphing as a subtle, meaningful craft. But when I mess up and assign too many graphs for homework, they just sprint through them, cranking them out like cheap factory products. It goes something like this…

Me: How’s that graphing going?

Student: No time, man! I’ve got sixty logarithms that need to ship to customers tonight, and the assembly line’s been down for hours. I’m cranking out asymptotes by hand over here – I’ve got no time for your funny business!

Me: But why? What’s the point of these graphs?

Student: Hey, not my place to ask questions. I just hit my graph quotas, and try to make it home for dinner with the wife and kids.

Me: But you’re making mistakes. Sine curves don’t have sharp corners.

Student: So slap a warning label on ‘em, for all I care! You think I’ve got time to sand down those edges? I’m just connecting dots here, bing-bang-boom. If you want overtime work, then give me overtime pay, capisce?

Me: But… what are you even graphing?

Student: What do you think, wise guy? Graphs, that’s what!

Me: Yes, but where do they come from?

Student: Well, hell if I know! Equations! Functions! Who cares? Go away, you’re slowing me down!

MORAL: High school math students shouldn’t feel like hurried assembly line workers. They should feel like master craftsmen. We should direct their time and energy into a few thoughtful graphs, and then we should demand that they inspect their work, play with the moving parts, discover what secrets the graph has to share.

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13 thoughts on “The Graph Factory

  1. My high school physics teacher called it “the so-what factor.” Okay, you’ve got a graph (or an answer to an equation or a number on a calculator or whatever)… So what?

    • I like that. It always surprises me that kids are willing to work on something when they have no idea what the “so-what” answer is… although I guess the explanation is that they’re not really all that willing.

      • “I like that. It always surprises me that kids are willing to work on something when they have no idea what the “so-what” answer is… although I guess the explanation is that they’re not really all that willing.”

        Well, students are also used to being told what to do, even if they don’t understand why.

        On the other hand, it will prepare them for dealing with management should they find themselves working in a large organisation. Managers *love* having graphs in their hands at meetings. They’re not so good at asking “So what?”, in my experience. Work for the sake of work, and meetings for the sake of meetings, I guess.

        Sorry. It’s been a long week, and I’m owly.

        • Ouch.

          I used to read a lot of Dilbert as a kid. Maybe one of the reasons I never had the slightest interest in engineering… or regular jobs, for that matter.

  2. Ben
    Terrific post. I cannot help but feel that you can replace nearly every reference to graphing and replace it with, oh, say the word factoring or the phrase solving absolute value equations, or balancing chemical equations, or conjugating verbs, or….

    Your last sentence in the moral is KEY. We as teachers have to be more careful to ask out students to do thoughtful work. We need to figure out how to balance a number of repetitions that help our students become more automatic in executing certain skills, but there needs to be some thoughtful payoff in the end. I’ll be sharing this one with my colleagues.

    • I hadn’t thought about it as applying so broadly, but I think your right – this is the same mindset students take to any kind of rote skill development. Such roteness is sometimes necessary, of course, but they’ve got to know the payoff, or else they won’t properly learn the skill.

      Another analogy: If you’re teaching someone how to pitch in baseball, you should probably explain about home plate. Otherwise you’ll get a pitcher who makes roughly the right arm motions, but whose pitches wind up all over the place.

      • Nice example. I am reminded of a pitcher with control problems. A great baseball writer, when writing about him, remarked that to that pitcher the strike zone was just a rumor.

      • I agree — it can apply to any kind of rote skill development! I hadn’t thought about that, either.

        Today, I showed some 6th graders a box-and-whiskers plot with some sample data (hello, diagram with no meaning for an 11-year-old). I asked them to create a question that may have generated the data.

        STUDENTS: But there’s nothing but numbers!
        ME: Well, what do you notice?
        STUDENT #1: Numbers! isn’t this just a graph?
        STUDENT #2: Was the question about… favorite numbers?

        It was painstaking to elicit anything else from there. Eventually, a student commented on the range and spread of the data, and wondered if it maybe matched the number of pets 6th graders have, since the data clustered around the numbers 1 & 2 and ranged from 0 to 6.

        The students were so much happier when they were just churning out graphs to match fabricated data. Sign them up for internships in the graph factory.

        • Thinking is hard, isn’t it? Following directions at least lets you turn off your brain.

          I had some 12th-grade Stats students last year for whom that would’ve been a good, challenging activity. I like the idea of “here’s the data, now guess what these numbers come from.”

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