A large push in my district is to get our students to raise their level of input in the classroom. That is, get them speaking more academically, require more writing, and raise the importance of vocabulary. The primary focus is to give English Language Learners a comfortable environment to improve. I see it as a nice way to get rid of the bothersome "when are we going to use this?" problem. Any student who has ever stared at 5+5sin(theta) on a polar grid has surely wondered the same thing (as I did long ago). Neat picture, but what's the point?

Well I ask you, when am I going to use a stylistic analysis of the Canterbury Tales? the major players of the Tea Pot Dome scandal? the lattice structure of quenched iron?

It of course, depends on where you're headed. Most high school kids have no idea where they're headed.

But I imagine the teachers that face the dreaded question the least (I won't say never) probably teach Spanish, German, French, Latin, etc.

So, if you are honest with your students on Day 1 and say "You know what, for most of you, a lot of this will never be used again. But high school is about exploring your options so you can figure which subjects you really will use as an adult." They might appreciate that, or use it as an excuse to blow you off, I don't know. Then explain you're here to teach the language of math. One day, some of you could be fluent in it. For the rest of you, it never hurts to know how to make a sentence or two.

Why does this make sense to me? Well, I thought about what comprises language, in basic terms. Then I thought about what comprises math, in basic terms.

mathlanguage.png

Before you can hope to be fluent in a language, you have to spend a lot of time on the guts: tenses, verb placement, and spelling, etc. It takes a long time to climb that hill. I think in math we make the mistake that high school kids should be fully fluent by the time they leave. So we write word problems for "real world" situations no one ever encounters. If anything, when I left high school, I was more aware of how little I learned. It took three more years to really feel fluent. And really only fluent in the lower levels.

Let's examine how math progresses. For simplicity, I left out branch topics like statistics.

mathlevels.png

In Texas, to graduate high school at the recommended level, they must pass Algebra II. Better students will make it to Pre-Cal, and the elite will get to Calculus. The size of the elite is really dependent on factors outside a district's control like parent education level, involvement and economic situation. So depending on the school, you could have 20% of the graduating class get halfway up the ladder, or 5%. And the main goal of Calculus is to improve your Algebra and Geometry more than anything. So the idea that students will be fluent in math and using their skills every day is tough for me to see. Especially when there are plenty that leave at the lowest rung. To really model the world and dive into why things happen and how we can explain them requires a trip to the very top. Maybe 1 or 2% of that elite group of students will ever get that high. At best, we can hope that students can see a glimmer of the simple, perfect models we address in high school.

And that, is the equivalent of learning how to speak a couple phrases in Spanish. Is that so bad?

Posted
AuthorJonathan Claydon