I’ve been writing a few pieces on and off, trying to get focused, and suddenly I thought of Darryl Yong. I’d forgotten his name, but I just googled “professor teaches high school math”.

Darryl Yong, a math professor at Harvey Mudd, decided to teach high school math for a year. He didn’t teach calculus, he taught algebra and geometry, and he taught at a low income school worried about test scores and gangs.

You should read his entire excellent paper. He outlined four key lessons:

Lesson 1: Schools Are Complex Systems Involving People, Culture, and Policies

Lesson 2. Student Self-Concept Is the Best Explanatory Variable for Student Success

Lesson 3. Teaching Is a Far Less Respected Profession Than It Should Be

Lesson 4. It’s Not the Written Curriculum That Matters, It’s the Assessed Curriculum

Yong is writing for math professors, but his essay ought to be required reading by reformers and politicians all. I came into the game knowing 1 and 4 already. (Lesson 4, in particular, is something that no test prep instructor ever needs spelled out.) I’ve never felt disrespected as a teacher, so I can’t speak to lesson 3. His description of typical professional development is very similar to my experiences at my previous school. However, my first school and particularly my current school do a good job with PD. It’s not so much that I find it all useful, as it’s not a waste of time and it’s blissfully short of jargon. We are also given lots of department time. However, I don’t see why pointless PD has anything to do with respect or lack thereof. The administration gets mandates, it all rolls downhill.

But the first four or five times I read of his experiences, I growled when I got to Lesson 2. Self Concept, blah blah blah:

That’s the purview of happy talkers like Carol Dweck, I snarled mentally every time I read it previously.

So why, tonight, did I reread it? Couldn’t tell you, but for some reason I saw something I’d missed the first times I’d read Lesson 2. Yong gives an example of the need for “scaffolding” using factoring quadratics. It’s perfect. He gives a list of quadratics and points out that math professors (and many textbooks) think of all quadratics as roughly equivalent: easy to do, functionally indistinguishable. But to struggling algebra students, they are tremendously different activities. Hardest to factor are a>1 and b=0. (And then, after you beat that into their heads, they are suddenly stumped by c=0 cases—which they thought were easy before. Sigh.) He then goes on to describe a student who was stumped by solving simple equations but could do the same task if it was finding the x and y intercepts of a linear equation in standard form.

And I sat up and thought Hey.

I can’t even begin to tell you how many times I’ve expounded on this to my colleagues. I write about it, too, of how I redefined an algebra curriculum so that I could keep my weakest kids engaged and passing. In The Driftwood and the Vortex, I delineated the careful sequencing needed to keep struggling students engaged:

*I learned how long I could run an upfront discussion before their attention waned, carefully timing the moment when I moved them onto practice problems—which had to be carefully managed, too. Struggling students need to build momentum on a string of problems before they get to their first hesitation point. Hit that hesitation point too early and they “shut down”. They look away and find a more rewarding activity: talk to their neighbor, take a nap, turn up the volume on their iPod, sketch, tiptoe out of the room when I’m not looking, send objects airborne in pursuit of a target. Finding worksheets that started with problems simple enough to get them working and then built to more challenging work that wasn’t too hard took up a big chunk of my day. I’d spend hours looking through practice sets to be sure they didn’t leap to tough problems too soon, and often just wrote a dozen or more identical problems on the board, simply varying the numbers. Even with all that effort, some concepts were still too hard for some students, and I couldn’t always reach each one before he got pulled into a disruptive vortex. And so, from managing the math back to managing the students.*

I’ve also seen amazing things happen when I just let kids listen to poetry and think about it, rather than insist they read, understand, and analyze it as standards would dictate.

In the TEACH! documentary, Lindsay Chinn achieved improvement by teaching less, and giving her students a sense of success.

But read Dweck or others on “self-concept”, and they mean something quite different: If students believe that intelligence is malleable, their story goes, teachers can convince them to work harder.

Yong is not really talking about self-concept as it’s understood in the education policy world. And yet—he is. Which means that I, too, think that student self-concept is important, even though I’ve been sneering at the idea for the past two or three years. I just go about it, like Yong did, like Lindsay Chinn did, in an entirely different way than the one pushed by experts. I give my students the experience of success, of taking on a task *they find difficult* and then triumphing over it.

But you don’t achieve this by lying to students about intelligence, which is not terribly malleable.

The way to give students an improved self-concept in math is to make the math easier.

Not easy. Not, as it is usually dismissed by politicians and reformers, by “dummying it down”. But by setting reasonable goals for the students you have.

Do you teach the math or teach the students? I’ve asked this before. It’s a fundamental question for teachers working with populations that so obsess education reformers. Yet reformers spew trite platitudes about “higher expectations”, as if teachers can eliminate struggles simply by superior pedagogy and refusal to tolerate failure.

I wish Yong had taken this issue on directly, rather than hinting at the problem but wrapping it in a popular buzzword that hid his message. Plenty of people read his work and think “ah, that’s the key! Get the kids to believe they can succeed at math!” when in fact, I think the message is closer to “give the kids mathematics tasks they can handle” which isn’t at all the same thing. I don’t ever let my kids think they are math rock stars. Many of them don’t, in fact, have the ability to learn the math necessary for advanced understanding of chemistry or engineering. But that doesn’t mean they shouldn’t be challenged, shouldn’t begin to understand the confidence necessary to dive in and give it their best shot.

But no one really dares advocate making math easier, particularly in the era of Common Core. Instead, we get platitudes like this paean to an old-school music teacher, advocating drill, failure, and, god save us, “grit”.

Both Yong and I are guilty of what education reformers everywhere decry as “the soft bigotry of low expectations”. It’s rhetorically convenient to ignore the fact that teachers lower expectations *because* they want to give their students the experience of struggling with intellectually challenging material.

Reading Yong again led me to realize that I need to start talking more about “self-concept”—not to dismiss it, but to redefine it. I care about my students’ self-concept. That’s exactly why I lower expectations, creating a rigorous yet achievable curriculum that dangles a reachable carrot in front of my students. In doing so, I get them to try.

This piece was originally written in 2013.

“I learned how long I could run an upfront discussion before their attention waned, carefully timing the moment when I moved them onto practice problems—which had to be carefully managed, too. Struggling students need to build momentum on a string of problems before they get to their first hesitation point. Hit that hesitation point too early and they “shut down”.

This. A valuable lesson I still struggle with both professionally and privately. When i feel like my audience is unengaged right out of the gate, I always seem to think I can talk them into engagement. The back of my brain is always telling the front to shut up, but I think the front keeps talking because I am not as good with the engagement part.

Thanks for sharing this Michelle.

Mike DwyerQuote Link

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“When i feel like my audience is unengaged right out of the gate, I always seem to think I can talk them into engagement.”

Arghh. Welcome to my world.

But here’s the good news: I’ve found that success creates a positive feedback loop. The more success you give them, the more willing they are to launch off into the unknown. That is, starting with manageable math over time will give you a math class where students will honestly and authentically grapple with interesting, open-ended questions and tough problems.

Michele KerrQuote Link

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Good advice. I will need to figure out how I can apply that to my world, especially at work.

Mike DwyerQuote Link

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The back of my brain is always telling the front to shut up, but I think the front keeps talkingBrother Dwyer is strumming my pain with his fingers and singing my life with his words.

Mike SchillingQuote Link

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This was always my issue with HS math, that the material leapt away from me right as I was beginning to wrap my head around it. I constantly felt I was behind and that the teacher was not allowed to slow things down so I could catch up. And asking for help outside of class was always an exercise in the teacher being disappointed in me (my perception, as a teenager).

One of the big differences when I took algebra in college (the other being that the instructor taught multiple approaches to every solution) was that before the instructor moved on to another topic, he spent a day just fielding questions and reviewing everything. He also encouraged the class to participate in answering questions, so before he’d dive in, he’d open things up for class discussion. More often than not, he didn’t need to answer anything, one of us would explain things as we understood it, or if it was clear more time was needed, arrangements were made between students to work on it outside of class.

Oscar GordonQuote Link

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Honestly, a lot of the feel-good movies and stuff about “inspiring teacher turns around class” do a disservice, I think, to teaching. It has set up this image of the “superstar” teaching, suggesting they are preternaturally gifted at it…..and so the rest of us who teach might as well give up, let those folks be videoed for MOOCs, and we can slave as low-wage graders. (Yes, I had someone present this idea in a seminar aimed at college professors).

The “superstar” teacher idea also totally ignores how much hard work goes into teaching “right.” It’s like the singer who walks out on stage and gives a perfect performance – you don’t see the 80 hours of rehearsal she went through, and the years and years of training. There’s this prevalent myth in our culture that “talent” is this magical thing some people get, and that means they can do things well effortlessly, and it ain’t so. I can say that as someone who earned good grades in school and is generally recognized as “smart” – it’s a lot of hard work.

(And so, I guess we’ve got #3 right there. And I do feel disrespected some, these days. *Generally* not from students – though there was one nightmare class several years ago – but frequently from certain bureaucratic offices on campus. In fact, friends had to figuratively talk me in off a ledge yesterday when I learned one of these offices set something up, without consulting or even telling me about it, that was counter to how I had always done it and had planned to set it up for my classes this fall…)

And I have seen a lot of people who don’t spend a lot of time in the classroom (or who haven’t spent any time in our particular classrooms, with our particular issues) presuming to preach to me about “how I should do it” and I admit it makes me VERY prickly.

As for “self-concept,” IDK if this is related to that concept but: I teach an intro-level specialized stats class. I REGULARLY get students coming in telling me they struggled with algebra or calc. Or that they’re “afraid” of math. I tell them three things:

a. The basic stats we do tends to be very applied, so if it was the more abstract nature of the other classes you found challenging, stats is different. (I have taken calc twice in my life and tried twice more to teach it to myself from books, and I still feel I only have a rudimentary understanding. But I am good at stats)

b. Do the homework. Keep up with the homework. Pay attention when I go over the homework after I hand it back. If you got something wrong and are still confused, come in to see me. Earlier is better. We don’t have a lab so my office hours, I consider meeting individually to give help as “lab” time for me. And also: the homework for me is a way of judging how well I am teaching. If most of the class gets an 8, 9, or 10 out of ten, I can assume I did OK. If most people are earning 5/10 or below, that means I need to go back and explain the concept differently, or spend more time with it.

c. If you are confused, either speak up in class (I can guarantee someone else is too) or come see me, I will help you. Do it sooner rather than later.

I have had a large proportion of my self-identifying math-phobes earn Bs or better – and my class is not an easy class. The people who earn Ds or Fs? Are the ones who think they know it all already, who skip the homework, who zone out during the working of example problems. (And yes, I know: the new thing in stats is to go straight to the software but I tend to think if students know the “how” and “why” of the numbers in simpler examples, they seem more prone to choose the correct test off a drop-down menu).

fillyjonkQuote Link

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I was in high school when Stand and Deliver came out.

We gave our AP Chem teacher some guff about getting us to the finish line where we’d all get 5’s and used that movie as an example of how it was possible and he told us “Jeez, watch it again. He had those kids for 4 years plus summers. I have you guys for 180 days.”

JaybirdQuote Link

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Thanks for sharing. It makes me wish I had some math teachers who took your approach. I never had great aptitude for the subject beyond basic algebra. This was compounded by a series of unfortunate turns in my education. When I was in Catholic middle school we had two tracks. The fast track and the slow track. I was too advanced for the slow track but needed more help than was available in the fast track. In that class an ancient nun (who I learned had taught my father) just wrote things on the board and if you got it you got it and if you didn’t you didn’t.

Next came high school where the county implemented a combined algebra and geometry program that was supposed to be regular math for your first 3 years. Except halfway through my sophomore year they decided the program was a failure and crash course turned IAG2 back to geometry. By the time I was a junior I was so lost that to this day I have no idea how I passed those classes and managed the SATs.

InMDQuote Link

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Oh, god, integrated math. They say it’s the norm in Europe, but American math teachers are pretty universal in their despite for mixing it all up.I’m sorry you suffered through it. And I’m sorry for all the people who have a tough time in math. But remember, I’m the one lowering standards, which is a Bad Thing.

, many students have a terrible time with stats because they have to explain what the answer means.

Michele KerrQuote Link

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