I see we are continuing the “but why do i gotta learn this if i’m never going to use it?” drivel and once again the quadratic formula is the punching bag.

For reference here’s a post on BlueSky.

Listen folks, if you have a crystal ball like that, go ahead and laser focus on zero-waste education. Put those blinders on and never deviate from your clairvoyant messages.

But don’t be surprised when you’re in the hottest part of the room (the corner, of course, because it’s 90 degrees — math joke!) and have nowhere to go because you’ve painted yourself there.

Math education for a lot of folks is a kind of torture. I get it. And the response to anything about math tends to be hostile and fearful. “I don’t want it near me. I hate it. It was a waste of time.” Otherwise well-meaning parents will quip “I’ve never needed this and look at how successful I am.” as a form of justifying ignorance. Grade school teachers who themselves are fearful of the subject, impart that educational hierarchy onto students, where “math is for the smart kids”. And as kids get older, they tend to get pushed into STEM or not-STEM because for whatever reason we feel that dichotomy must exist. These are sentiments that permeate through almost all strata of society and have knock-on effects in business, government, etc.

There are also a ton of tropes: “Why did I have to learn the quadratic formula? Why didn’t I learn about mortgages or taxes or credit cards or or or …”. The anti-Calculus movememnt also is a favorite thing for folks to latch on to if the anti-quadratic formula sentiment weren’t enough.

Yes, we could have always learned something different. Maybe Combinatorics would be better received as a high school topic. Or we could spend a bunch of time on graph theory. [I mention these two because I’ve introduced these topics to second graders with success.] But this is all a type of heap fallacy. You can pull one problem out of the curriculum and it wouldn’t change anything. But this doesn’t extend ad infinitum because each change is not massless.

All of this hostility toward mathematics and math education is understandable even if it is narrow in thought.

Math is the only subject you can’t quit. And gym. You can’t quit gym either. Even if you choose to go to college and choose the least technical of majors, there’s often still an Algebra requirement. On the other hand, the Chemical Engineering major doesn’t have to take 12 years of art or music. They don’t have to endure through 4 years of high school Shakespeare. They’ll take their Algebras, Geometry, AP Calc, some programming, etc.

Because of this nature of not being able to quit math, it leaves people with an anti-curiousity — meaning, they would prefer to simply have not known about it. I’m ok with knowing about the Great Gatsby and Huck Finn and Fahrenheit 451 and that there are other authors out there. I’m ok with knowing about the Bard and what a sonnet is. And I think most people feel the same way about these other subjects even if they don’t actively rely on them for income. And that’s what this is about, because for a good many folks, the majority of life is about earning an income. But math … man, some of us just want to forget it. That’s the consequence of mandatory coursework.

But the story is deeper than just that the subject matter is forced. Math has to marinate. Kids don’t get that chance. Math also builds on itself. Algebra II requires Algebra I which requires a whole host of other topics taught in elementary school. Continuation requires consecutive mastery of topics. Just passing isn’t enough as the knowledge gaps catch up and we go from Swiss cheese knowledge to full-blown onion ring knowledge.

I maintain that working with an unforgiving symbolic system like in Mathematics isn’t for every kid at every point in their development. It’s complicated. And forcing students to sit through coursework where they are, effectively, illiterate does no one any favors.

I haven’t done the formal research, but I can tell you from my own many years of experience of having taught night classes to adults aged 30 years or older, their reaction is “Why was this so hard when I was 16?”. The answer is, “You were 16!”.

For many of us, the abstractions that are taught in grade school / high school, I believe are out of order. As we get older and have to venture out into the working world, we are forced into abstract systems having to navigate bureaucracies (latest spotlight on healthcare), legal systems, corporate hierarchies, cultural structures, etc. And while these may not seem math adjacent, we learn intuitively about placeholders and templates and frameworks, which is a big chunk of what Algebra is, mechanically speaking. So when those 30-year olds come to my classroom, Algebra is a breeze.

The chicken vs the egg here is that can learning Algebra help you think about one of many ways on how to process the adult world, or if after flailing in the adult world, do you get to better process Algebra? Of course, it’s not so simply and diametrically posed. But that’s the general gist.

I am misleading you a little bit. Algebra is a breeze for those 30-year olds, no doubt. But it’s not just that they have absorbed abstraction into their soul. It’s because they saw Algebra in high school. They saw and were exposed to these topics as kids. Math marinated. If they were confronted with Algebra in their 30s with never having been exposed to it in their teens, it’s doubtful it would be so breezy.

Because, and this is the AcTuAlLy part, the truly first time we are exposed to something, we have almost no anticipatory process. We rely on intuition and reflex to process new things. We have no intuition for x^2 + 3x + 7 = 0 if we are seeing it for the first time. We have to enter a state of “cognitifve compliance” to put it harshly or more cheery, we have to keep an open mind. Then when the lesson is finished, it needs to be revisited many times until we can start anticipating the next steps. This is not easy with Mathematics. It is much easier with music, art, Shakespeare, etc. because we grow up in an environment immersed in that language. We listen to music while we’re still in the womb. We scribble and color and play on paper very early on. Shakespeare is still tough because we usually have to get used to the language, but we quickly adapt to it since we are fluent in English [yes, I know what I am assuming here].

Now, before the pitchforks come … no one is saying music is easy. It takes years and years of intense training to master the instrument(s) and the theory and the style and the genre and the history. The same goes with art. We can recognize the cheap AI knock offs even if we couldn’t draw to that level ourselves. But the professional artist has spent thousands of hours learning anatomy and shape and color and value and styles. None of this is easy. But all of this is quittable.

The negative side effect of having the choice to quit is that as we get older, time becomes more expensive. That pivot into data science or game design or astronomy or in a professional capacity usually does require learning the fundamentals of Algebra, Calculus, Linear Algebra, and a bunch of other math. It’s not a three month intensive bootcamp that gets you slinging code. It’s still a few years of study and people just don’t have this time. You don’t see too many people pivoting into genetics from a non-technical background.

So, I get it. The quadratic formula sucks. But I challenge you that maybe, just maybe, you retained something from Algebra and if you decided to pick it up again, you might surprise yourself with how breezily you can consume the subject topic.