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.