Algebra 2
For the record, I got an A in Algebra 2. In 1984/85.
My first year teaching, back in another millennium, I made a mother of one of my students as happy as I had ever made a parent. I was teaching my favorite class to teach, American Studies, a combination of American History and American Lit. Man, I miss those days: integrating with myself–a really great teaching partnership!--and having kids 100 minutes per day, and therefore getting to know fewer kids, better, in a year.
One day, we were meandering through a side conversation when kids started debating what the hardest class to teach was. AP Physics? Calculus? Maybe computer science? The mad dash through AP US History that some of their friends were going through? They went to me and sought an opinion. What’s the hardest thing to teach, they asked me?
None of the above, I said.
“The hardest thing to teach is first grade,” I told them.
They scoffed, but I believed and stuck to it. “In first grade, for some of them, they’re learning to go to school. I mean, they’ve done half-day kindergarten (remember, this is in another millennium, when full-day kindergarten was not yet the norm), and that’s one thing, but for most, first grade is the first time they’ve been told to sit down for six hours and do real academic work. And then you have to teach them how to read. Like, this shape represents a sound, and when you put them together, they form a word, and that word represents some tangible thing out in the world? How the heck do you even do that?”
Toughest teaching gig. First grade.
A few days later, at parent night, the aforementioned mom came up to thank me. It turns out she was a first grade teacher! “Because of what you said,” she told me, “my son demonstrated respect for me for the first time.”
Happy to help out my primary-grade colleagues!
But–with apologies to that long-ago first-grade teacher mom–I am having a change of heart. I think I have found something tougher to teach than first grade. In any event, I now have an unimpeachable champion in my mind of the toughest teaching gig in a high school.
It’s Algebra 2. (Or is it Algebra II? I’ll go with the Arabic number. It’s easier to type.)
I’ll type it again, to see how it feels: The hardest class to teach in any school is Algebra 2. Period.
For starters, Algebra 2 teachers face a very interesting clientele. For some students, it’s the last math class they will ever take. Those are the kids who are going on to postsecondary education but are not huge fans of math. They are, as one of my Algebra 2 teachers put it, “at the end of a long bus ride. They didn’t choose the bus. They didn’t enjoy the ride. But here they are, at the end of the trip.” As a result, they are not happy campers, and can be quite surly about the content.
Those kids sit alongside some math-loving juniors and even sophomores. They’ve breezed through Algebra 1 and Geometry and feel like they’re pretty hot stuff. Then…Algebra 2 hits them, and their world–their self-image, even–changes.
So many things happen in that class that even really skilled math teachers struggle to make kids engage.
For example, consider the kids who hate math but need this last class for college. They do not have any kind tangible reason to learn Algebra 2 skills. As a guy in a non-math profession, there are times that I use Algebra 1 skills in my daily life. I have an amount, x, that I can spend on Christmas presents this year. I want to spend a little more on my children and wife than on extended family. What is the ideal amount I can spend on immediate family (f) that leaves enough for decent gifts for extended family (e)? What equation will help me determine this? There are times I use what I learned in Geometry. What is the best shape for a rug that will maximize the coverage of my living room but still let us see some of the beautiful hardwood floors? But I have never–not once–tangibly used anything I learned in Algebra 2, Calculus, or whatever they called the class in between back when Reagan was president (I think it was Trig, but time may have made my recollection inaccurate).
Note the emphasis on “tangibly” above. We’ll get back to that in a bit. But in the tangible realm, I am with Kathleen Turner in Peggy Sue Got Married as far as the relevance of Algebra 2.
To investigate this, let’s take a look at my state’s description for Algebra 2:
In Semester 1 Modern Algebra 2, students explore sequences, functions, inverses, transformations, polynomials, rational functions, rational exponents, and exponential functions. In Semester 2 this content is further developed through mathematical modeling and includes four or more of periodic functions (trigonometry), finance, introduction to data, data science, matrices and vectors, and advanced modeling.
Maybe a little of that Semester 2 stuff has proven important for me to understand (finance and data), but that’s different from me needing to do it. I know how finance works well enough to make big decisions for my retirement fund and smaller decisions like how to buy my car. Critically, however, I don’t have to do the math myself. I can plug information into an on-line tool and see what numbers come back to me for my mortgage or retirement savings. So while it is important for me to understand, it is not necessary for me to know how to calculate. I suspect I didn’t have to be in Algebra 2 to use that on-line tool, but I think I’m better off for understanding the basics of what is happening to my money mathematically.
When our teenaged math haters are faced with this dilemma, they usually don’t come to the same conclusion I do. Instead, they often view their presence in Algebra 2 as nothing more than a flaming hoop to jump through on the way to college. They lack even a glimmer of a hope that they’ll need any of this unless they are going into a math-heavy profession.
Meanwhile, many of those hot-to-trot math lovers in the class are going through their first math struggles. In fact, they are going through their first academic struggles. My older son, who is really gifted at math, found Algebra 2 was the first time he couldn’t do a math problem in his head–and, since this was the only math strategy he had ever needed, his self-esteem and his grade plummeted. This frustrated him (and his teachers).
I am not a math expert, but I strongly suspect that some of this frustration stems from the shift not just from tangible to intangible concepts, but also from procedural to conceptual thinking. That semester one on my state’s Algebra 2 syllabus is filled mostly with conceptual ideas. The work I see kids doing in Algebra 2 happens more between their ears than on a paper. It’s a new world, and for a good student, that can be scary.
As a result, from the start of the year until November, our Algebra 2 students take the biggest hit in an engagement survey out of all of the math classes we offer. Part of this measure is based on whether they find the subject to be relevant, interesting, and/or cool. Algebra 2 kids start the year finding the class to be irrelevant, boring, and stupid, and their negative feelings towards the subject actually increase as the year goes on. It’s heartbreaking.
A couple of my Algebra 2 teachers do better on this measure than their colleagues. Their students may not like math more in November than they do in September, but they at least avoid a nosedive. They hold steady. This measure is sustained mostly in the questions related to relevance, questions like “I am confident the subject matter of this class is going to be important to me someday” and “I can think of ways the material I am taught applies to things I do every day.” While most students’ scores on questions like these go way downhill during Algebra 2, a couple of teachers’ numbers manage to stay put. This made me curious: what do they do to make their students find Algebra 2 relevant-ish? I asked them. What do they do to persuade their students that the material matters?
Their answers were identical: they don’t.
“I tell them straight up that they may never use this in their lives,” one told me. “But I do tell them that they need to learn how to fight through hard things.”
My brain is still working with this. Teachers who are struggling to make the math relevant see their students’ belief in the relevance and importance of the math crash. But teachers who say “nope, you won’t be needing this, but let’s work to learn it anyway” wind up with their kids maintaining their (admittedly already low) scores on relevance.
I honestly don’t understand what this means, and I’ve been noodling on it for a long time. I’d love your opinions.
Another thing has popped up that I’m mulling over: Cutting-edge techniques (like those espoused in Peter Liljedahl’s Building Thinking Classrooms) are less popular with Algebra 2 students than with their younger friends in Algebra 1.
I have a teacher, Ms. Q, who absolutely slays it using BTC techniques (most notably having the kids work in teams of 3 on vertical surfaces) with struggling Algebra 1 students. They come to her having failed at math their whole lives. Their experience with math is sitting at their desk unable to do things that kids all around them can seemingly do with ease. When they arrive in Ms. Q’s classroom, they discover that everything is different, and this is an immensely freeing experience. As a result, her students’ engagement scores go way up. They like math way more in November than they did in September.
This same teacher uses the exact same techniques in Algebra 2…and they don’t work as well. The engagement scores for those kids go down a ton. Why?
I think it’s because those students are better students: what Adeyemi Stembridge would call “school-proof.” School, to them, is a place that they go, sit still, listen to a teacher, and take notes. They then study the notes and pass a test. Maybe they learn, maybe they don’t, but their GPAs are high. When Ms. Q busts obliterates that old paradigm of how school works, it is an anxiety-producing event for the typically-successful student who takes Algebra 2. Why can’t you just give us notes like everyone else has? they ask.
To her credit, Ms. Q doesn’t capitulate. She has modified Liljedahl a bit, having kids sit in groups at their tables working together rather than standing at vertical surfaces. I can live with this adaptation: Liljedahl’s book wasn’t carried down from Mount Sinai by Moses. We can tweak it if it feels like we need to. More importantly, the students at their desks were doing exactly the kind of conceptual thinking that Liljedahl values most. The day I watched Ms. Q’s experiment, students were examining what happens in several different kinds of exponential functions, looking at how the various twists and kinks in the parabola got there. Conversation was deep, and engagement was unquestionable. I feel like Ms. Q’s engagement numbers in March might turn back in the right direction because of her adaptations.
Yes, some of the kids might wonder why they have to learn this stuff–as they wonder why they have to learn mitosis, the Haitian Revolution, or the poetry of Walt Whitman. But if they get their minds deep into it, if they develop their brains to think logically just a bit more, doesn’t that mean they’ve gotten what we want them to get out of Algebra 2? Isn’t a set of thoughtful kids working every part of their brain on a puzzle going to develop into better thinkers and better adults?
Hey–I’m just a poet. I haven’t spent my life trying to sell the utility of parabolas to teenagers. I don’t know whether we should junk Algebra 2 in favor of math more likely to come up in kids’ daily lives.
But I do know that Algebra 2 is the most difficult teaching assignment in any high school. Tougher than AP Anything. Tougher than remedial anything.
It may even be tougher than first grade.
As a result, for me, it has become the most interesting laboratory for what makes for successful teaching, and I will keep heading back there to see teachers try new things, fail a little, succeed some, and try to make deep, thoughtful, but intangible thinking a skill that kids value.
What are your experiences with Algebra 2, as a student or as a teacher? What have you seen there that works or doesn’t? How do we make something that won’t be used in life…relevant?