Compare these 2 sequences:
x 3 4 5 6 A 40.5 44.5 48.5 52.5 B 2.0 6.5 11.0 15.5
Will B ever catch up to A?
-after problem 48 from Park Math Book 1 (2011)
It’s obvious, says my student, that B will never catch A, because A starts off so far ahead. I am not convinced—what happens if the table keeps going? She comes back a short while later, with values calculated out to x=24. B is still behind A, which proves her point, she says.
If this exchange were between me and my young niece, I would be delighted. It would be charming. We would continue our debate, and we would be learning, and it would be fun. But since it is in fact between me and an Algebra II student, a young woman who will be a freshman in college next year, that same delight is there, but it is mixed with a discouraged, she-should-know-this, where-do-I-begin kind of feeling that I would not have if she were ten years younger. In short, my emotional response to this situation is far more strongly determined by my ideas about how things should be, than by what the student is actually putting in front of me.
So those ideas about how things should be are not helping. I think that’s why Shawn is so refreshing to read: he’s unwavering in reminding us that learning happens when it happens, not when the curriculum says it will. I have a choice, here, between delight in the learning now, or despair about the learning that hasn’t happened before. My niece proves that it’s possible to delight in a student holding this conviction, so delight in this situation is available. I’ll choose that. It’s not always easy to focus on that, not when it feels like everyone—me, my students, my school, my district, America’s public schools, the whole USA—is being judged by whether or not this eighteen-year-old is ten years more mathematically mature than my eight-year-old niece. But what choice do I have? This can be fun, or this can be miserable. I don’t see how misery will help her learn any more or any faster. What’s the Tom Robbins quote? “There are only two mantras, yum and yuck. Mine is yum.”