Will You Ever Use Math After High School?

[Maureen Downey of the Atlanta Journal-Constitution (who writes a smart, thoughtful blog everyone in education should read) referenced a 2009 piece by math teacher Ken Sprague, Sr. in her recent post on whether all students need Algebra II. I've seen it referenced more than once as being great; it's about time to challenge that.]

One of the most memorable lines I’ve heard in education reform came from a speech by Bill Cosby. He said that in schools, one of the most important questions we have to answer is, “Why we gotta know this?”

Every teacher knows if you don’t nail that one, it’ll be a long time before you get your legitimacy back – if ever.

Ken Sprague, Sr., a math teacher in the Atlanta area, wants to answer his kids honestly when they ask how they’ll use the material he’s teaching.

He wants to tell them that they won’t:

I teach high school math. My teaching career began as a social commitment after building a successful business.

I can’t remember one time during my business career that I used what I now teach to average high school students.

Imaginary numbers, conic sections, and rational functions aren’t the stuff of financial statements, contract negotiations, cash-flow and marketing.

We need informed, thoughtful criticism in education reform. We need people on our own side to tell us where we fall short and we need folks on the opposite side to point out where we’re wrong.

What we don’t need is ignorant cynicism – that low-hanging fruit of criticism that simplifies and jettisons as it finds that sweet-spot at the intersection of nay-saying and hindsight.

Sprague’s criticism isn’t really about math curricula the utility of specific concepts. It’s about social justice. Still, he starts by citing some math concepts that just don’t matter to his kids.

So, this history major is about to take math teacher Ken Sprague, Sr. back to school.

Imaginary Numbers

Some of Sprague’s students might just have an interest in engineering down the line. I’ve found it’s a common answer to, “So, what do you want to study in college?” among high school students who like math or science.

Sprague could always shoot them an example of how imaginary numbers help electrical engineers represent the two dimensions of AC voltage.

Or Sprague could be more general/conceptual about it in a way that would appeal to all his students rather than just the aspiring EE majors. Perhaps together they could think — critical thinking, they call it? — of a more everyday situation in which our system of describing/quantifying just doesn’t express every aspect we need it to express. Give it some time; you’ll likely think of a few instances in which we need such combinations.

Rational Functions

Well, here are 125 lesson plans that look at ‘real life’ examples of rational functions. I haven’t looked at them all, so caveat emptor, but the price is right.

Sprague, though, used to run a business. You know, that area in which you don’t use any of these academic concepts? It’s all bean counting over there — until you start scaling.

Let’s say we run a salon. A decent one; not something Tabatha Coffey is going to rip apart. We’re starting to get a lot more clients, so we need more shampoo – and several suppliers are courting us.

One supplier offers us shampoo at $60 a case. That’s it; $60 x the number of cases we need.

Another supplier will sell us the first 5 cases at $65 each; each additional case after 5 will be $50 each.

Once we’ve identified how many cases we’ll need, we want to choose the supplier with the cheapest cost-per-case for our situation. We can do it the clunky way – multiply it out, add up both scenarios and go for the more appealing number – or we can use a simple rational function.

By the time that situation comes up, a student might not remember how to set it up or execute it – there’s no arguing that point. But is it useful to train a kid’s mind to handle a problem like that? Whether he’s running a business or shopping for his family at Costco, you bet.

Conic Sections

Cut a cucumber. Really.

How a plane intersects a cone (or similar shape) comes up in cooking all the time. Maybe you’re trying to decide how something should cook – do you want greater surface area to contact the pan on high heat for a shorter cook time, or do you want less surface area and lower heat to prevent burning?

That depends on whether you cut your cucumber (the cone) so the intersecting plane (the knife) gives you circles or ellipses, doesn’t it?

What about how food is presented, as a chef on the Food Network – let’s say one being judged on Chopped – might consider central to his dish? Does his decision about how to cut and cook a particular ingredient have an effect on how his dish is received or whether he finishes it in time? One could even throw in how the golden ratio might apply to plating.

Why We Gotta Know This

Anyone – teachers, parents, community members – involved in education needs to grasp these concepts and be able to relate them to their students. Why? Because we don’t know where they’re headed in life.

I’ve always felt that education is about preparing someone to pursue whatever they’d like to pursue in adulthood. It doesn’t mean every kid necessarily gets to study every topic that interests him, but he should be equipped with the skills he’ll need to pursue what his school or community might not have been able to offer.

And that’s why we gotta know this, Mr. Sprague. We gotta know it because we don’t have a clue what the students we’re charged with teaching will do after high school. We can give them what Sprague calls “practical math” – or we can give every kid a rich body of mathematical experience he can access or ignore. We need to be mindful of what will prepare kids for success in adulthood, but deciding on a narrow, mundane list of tools we can be bothered to give our students deprives them of the opportunities and possibilities we’re supposed to foster.

The funny thing is that I call that rich body of mathematical expertise “practical math,” too. I suppose “practical” just depends on who your teacher is and whether they’re able to make concepts relevant to the student sitting in front of them. Some folks seem to be better at that than others.