In my district, and many others, Algebra II is a graduation requirement. Given that requirement, I find myself asking what life skills the class can give everyone, whether they continue to practice mathematics or not—and not just from math class in general, but specifically from Algebra II.
For example, an oft-quoted justification for requiring geometry is to teach students to “think logically”. In the 1930’s, Harold Fawcett taught a geometry class in which students learned, and practiced, thinking logically in non-mathematical contexts.
I wonder if a good candidate for a life skill that we hope transfers from Algebra II would be this one from Bowen Kerins, one of the authors of CME:
One thing a great context / question also gives you is the experience of figuring out what information is important and what sort of abstraction is most useful for extracting and using the right information thoughtfully. And that’s a skill a lot more adults will use than factoring …
If that’s to be our transferable skill, then we’ll need to practice it: have lots of non-mathematical examples where “extracting and using the right information thoughtfully” is required. And I have to admit: I’m so unconscious of when and how I am using this skill I’m not at all sure how to begin thinking of examples!
Work in Pencil 
>have lots of non-mathematical examples where “extracting and using the right information thoughtfully” is required.
The question in my mind is, is there any evidence that practicing the skill is extraction and selection in a mathematical context helps in any other context? If no, then we should just dump Algebra 2 and have a course on extraction/selection of information.
Good question. Mine is much narrower: given that we’re teaching Algebra II, what’s in it for everyone?
Until I hear otherwise, I’m going to assume that (like so many things) the mathematical skill of extraction isn’t transferable to other domains.
I think that everyone benefits from learning X, even if X is totally useless for them. The most important thing that anyone can leave school with is an accurate understanding of how to learn something new, I mean how to really learn something new, especially if it’s difficult, and especially if it’s supposed to be miserable.
Most kids have no use for the skill of modeling functions, and most kids have no need for the mathematical skill of extraction/selection of information. That stuff doesn’t transfer to new domains. But I’m more confident that an accurate picture of learning math will transfer to other domains, i.e. a person who thinks that math is learned a certain way will believe that other subjects are learned a certain way.
Of course, that’s a testable hypothesis. And I’m willing to bet that if we don’t make the connection between math and other subjects, the conception of learning won’t transfer. But this seems valuable and relatively available for all students in all of my classes.
> I’m going to assume that (like so many things) the mathematical skill of extraction isn’t transferable to other domains.
If your right, that could have some implications for Dan’s thesis.
So I guess I didn’t really mean “I think that everyone benefits from learning X, even if X is totally useless for them.”
I meant something more, like, “It’s easy to adopt any learning experience into an opportunity to learn about learning, regardless of the subject.”
Agreed. And people benefit from learning math, specifically, even if they don’t practice later, just as they do from learning music or poetry–it’s exposure to and inclusion in the human experience. But is there really no larger lesson to be taken from Algebra II, that is specific to Algebra II, other than how to do Algebra II? Maybe this is a stupid question, but if I found one, it would sure be easier to focus my year.