dinosaur math teachers

What Your Math Teacher Probably Didn’t Tell You

First off, this isn’t about the ubiquitous question every math teacher faces: “When are we ever gonna use this?” (The answer: You may not use an individual skill from class. Then again, you might. Few of us end up doing exactly what we thought we would as kids. More importantly, while learning the skills, you’re developing the problem-solving, critical-thinking part of your brain, and THAT you will always need.)

With that out of the way, here’s what it is about. Sometimes math teachers or textbooks make us do things in an overly demanding way, or using arbitrary rules. It’s not always the times students think. There are good reasons for doing things the long way before learning shortcuts.

Here’s one example where I think we get away from the spirit of mathematics. “Put your answer in the form of a fraction unless there are decimals in the original problem.” Um, okay. Why?

What if I have a problem involving money, using only whole numbers initially, but the answer isn’t a whole number? It only makes sense to give that answer in a decimal. That’s an obvious case, but what about regular bare-numbers equations? What’s so wrong with saying 0.5 instead of 1/2? They’re equivalent.

So I’ve gone for a rule that’s a little tougher. It means I have to watch for multiple correct answers when I grade work, and it means students actually have to think a little extra. I want the exact answer, not approximations, except when (a) the instructions say to round to a specific place value or (b) the context dictates an approximation is the only way it makes sense.

The reason? That’s how answers get used in the real world. You use the form of the number that makes the most sense for the situation.

Kids need to know how to think, how to reason, how to work something out. When they get used to memorizing arbitrary rules (“Do it this way because that’s how the teacher said to do it”), they don’t delve in for deeper understanding.

That’s what I think, anyway. Are there other rules your math teachers made you follow that didn’t seem necessary to you?

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Teachers Making Do, Like It or Not

We’re a few weeks into the school year, and I admit, I’m not entirely teaching as I’d like to.

I’m not teaching badly (I don’t think), but I’m doing things pretty traditionally. The circumstances added up.

I didn’t find out exactly what I was teaching until just before school started.

We don’t have textbooks yet (supposed to finally arrive this week).

My classes average 38 students each.

More importantly, due to the way our math lab classes for struggling students work, the other 9th grade teacher and I need to stay in lock-step with each other. The same sections covered on the same day, the same homework assignments given.

I’m still free to teach the material any way I want to. But there’s no time for that kind of planning. Not with all the grading that has to be done. And not with counselors still letting students transfer from one teacher to the other.

In the end, though, I feel like I’m making excuses. I could spend every hour outside of school developing my own curriculum (or at least modifying the one I’ve been given). But what about writer-me? What about having free time to keep my sanity intact?

Selfishness or self-preservation? Maybe a little of both.

Despite these reservations, I think I’m off to a good start this year. A few things need tweaks and adjustments. The kids are learning, regardless of how I feel about the style of instruction.

I’ll see what I can do moving forward, and if nothing else, make sure I’m ready to tackle next year more thoroughly.

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The Make-or-Break Teachers

I’m getting ready to start a new school year. As always, there’s a thought that lingers over all my preparations.

I hope I don’t screw up any of the kids too much.

To be fair, I’m pretty sure I haven’t screwed up any kids yet. There have been a few I wish I could’ve done more for, but I think my track record’s pretty solid. There’s a little extra anxiety this year since I’m starting at a new school—or rather, my old school after several years away.

It’s an interesting situation, because it’s the school I went to as a teenager, along with being where I launched my teaching career. My family and I are rooted in this area, so a lot of the neighbors know I’m returning to teach there. Several of them are hoping to transfer their child into my class if at all possible.

No pressure, ha-ha.

Seriously, though, one thing I’ve heard from parents in the last several weeks (and indeed the past several years) is how important they feel it is that their child gets the right math teacher. A good math teacher can take a student from hating math to at least tolerating it, if not better. A bad math teacher can bring a skilled student’s progress to a grinding halt. Often that damage is never recovered.

Is it the same in other disciplines? Probably, to a degree, anyway. But it seems like the near-irreparability is more severe in math. I had English classes that I hated, but they couldn’t kill my love for reading and writing (obviously). Then again, if I’d been a struggling reader in elementary school, and a bad teacher only reinforced and exacerbated my struggles, that could’ve set me back for the rest of my life.

Once past the learning-to-read stage, moving on to reading-to-learn, it seems the make-or-break power of teachers lessens somewhat. (I hope so, considering teens I’ve known with English teachers of … questionable quality.) Math works a little differently, always with a new skill, a new principle to learn.

That makes my job potentially dangerous.

Maybe a different approach is in order. Maybe if I keep the focus on helping kids develop their ability to think, to reason, to problem-solve—and I don’t mean “A Train leaves Station A at 6:45 am” kind of problems, I mean real “Here’s a situation and we need a solution” problems—maybe that means I won’t have to worry so much about breaking anyone.

Because you know what? There’s something else underlying this whole line of thought. To have the power to break, I have to keep a monopoly on the power to build.

The students need to be allowed to build themselves. Maybe they’ll suffer minor breakages along the way, too, but maybe that’s what I’m really there for …

… to provide the super-glue when they need to mend their own breaks.

Have you had experiences with teachers (math or otherwise) who had that make-or-break position in your life? What made the good ones good, and the bad ones terrors?

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Hating Math

Last week I discussed my deep and abiding love for calculus. I understand not everyone feels this way, and in fact, some people don’t even have the slightest hint of positive feelings toward any kind of math at all. If you’re one of those, this post is for you.

I’m not going to tell you it’s wrong to feel that way, or that you have to change your mind. (I will ask that you try to refrain from saying, “Ugh, I hate math!” around children who are still forming their own opinions. Can’t tell you how many times I’ve had a student who tells me, “My mom/dad hates math and thinks it’s stupid and doesn’t think there’s any point to learning it.” Thanks for sabotaging my work, Mom/Dad.)

The people I know who hate math usually fall into a couple different categories. Some hate it because they really struggle with it no matter how hard they try. Sometimes a learning disability is involved. Sometimes nothing’s been diagnosed, but it’s clear their mind just isn’t wired for numbers.

I recently had a student like that. Brilliant artist and some strong writing skills, but math just Would. Not. Click. Bless her, though, she kept trying and was incredibly patient, no matter how many times she had to erase and rework a problem. And the thing is, she did make progress. Not at the same pace as her peers, but she improved, because she didn’t give up. She admitted she didn’t like it at all, but she hung in there.

I think most of the math-haters I know, however, fall into the second category: those who had at least one really bad math teacher, usually at a critical juncture in their math education. This often happens either at fractions in elementary school, or a little later somewhere around pre-algebra/algebra, when things start to get more abstract.

What’s the key to teachers not facilitating the mathematical downfall of their students? I think a big part is recognizing that many students are likely to hit a wall a those junctures, so the teacher needs to be extremely flexible. One way of explaining a tough concept isn’t likely to work for everyone. If a kid isn’t getting it, you have to look for another bridge to get them across.

Even bigger key—don’t make the kid feel stupid for not getting it right away. Kids are good enough at doing that on their own. They don’t need our help.

Many times, I’ve had adults watch me teach or listen to me discuss a lesson and say, “If I’d had a teacher like you, I probably would’ve liked math.”

Best compliment I can receive, but I don’t really mind the hating math. My goal with the haters in my class is for them to hate math a little less. Even if they still hate math, I try to make sure they like the class. Because if they do, their minds stay a little more open, and even if they don’t want to admit it, they learn.

Are you a math-hater? If so, which category do you fall into? Or is there another reason I haven’t accounted for here?

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But … I WAS Teaching!

Funny thing happened the other day. Less “funny-ha-ha” and more “funny-huh?”

My school has this thing where a collection of administrators and specialists rotate around, observing different classrooms each week. Some look at how we’re using ASL, curriculum, or technology while others just look at the general classroom experience.

A few weeks ago, I had one such observation. I had a great little activity for my class. We briefly reviewed what we knew about three different types of functions, and I explained the activity. They’d be making predictions about a list of equations, checking those predictions, and then forming some generalizations. I circulated as they worked, dialoguing with them about what they were noticing. It all went really well.

I didn’t think about it again until I got an email from the observer a while later. She apologized for not getting any notes to me sooner, but she’d had a hard time writing up anything because she “really had not observed a ‘lesson’ so to speak.” She wanted to schedule another observation when I was teaching a new concept.

Excuse me, what?

I had taught a new concept. I’d taught my class how to recognize linear, quadratic, and exponential functions by their equations and without graphing them. The students were actively engaged in learning the whole time, doing something, rather than sitting there in a lecture-coma as I told them everything from the board.

Clearly, though, she wants to see something that looks more like a traditional “lesson.” So she’s coming back this week to observe a lesson in my physics class.

Le sigh. I don’t mind being observed again. I do mind the fact that I’m trying to follow nationally recognized “best practices” is being discounted as “not a lesson.” If it wasn’t a lesson, what did she think it was—busy work? That, I definitely mind.

Is it just me? If you were back in math class, would you rather take notes on a lecture or work on an activity that helped you figure out a concept for yourself?

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Math Rant: College Professors

The subject of this particular rant is a few years behind me, but the effects linger. And now, the horrors are being inflicted on my former students, and it’s enough to make me want to inflict something of my own—a forceful *headdesk* on the perpetrators.

Through my undergrad and graduate schooling, I encountered a number of college mathematics professors. Here are two facts:

#1 Many of them are absolutely brilliant mathematicians.

#2 Hardly any of them can teach to save their lives.

I even had a few classmates who were likely to join their ranks in the future. Kids who could do multi-variable calculus without breaking a sweat and thought abstract algebra was a great weekend activity. Kids who could not teach it.

Make no mistake. Doing math and teaching math are two entirely different skill sets. Thing is, the teaching skill requires the doing skill, and then some. (Do I get tetchy with the old “Those who can, do; those who can’t, teach” line? Don’t get me started.)

A former student came by to visit the school the other day and we chatted about how her first semester at a new college is going. Because she has issues with test-taking, she didn’t do so hot on her placement exam, which landed her in a math class that’s dirt-simple for her. She understands the material, but then the teacher goes and confuses her by insisting she use his methods, which she didn’t understand. She tried to ask a question to clarify, and he cut her off.

Okay, this particular girl is very assertive and kind of blunt, so maybe she could have handled the exchange better. I don’t know—I wasn’t there. Then there’s the fact that he tried to hold her interpreter back after class to talk to the interpreter about the student needing an attitude adjustment. (Grr… don’t get me started on that, either. That’s a rant for another time.)

Bottom line, this student didn’t expect the same kind of bend-over-backwards-to-help teaching she got in high school. She just wanted to understand.

If there’s one thing I remember about several of my college math classes, it was the clear undercurrent: If you don’t understand the magic I’m performing on this blackboard, it’s your own fault, because you must be too stupid to grasp it. No one ever said it in words, but you felt it.

Thankfully, they’re not all like that. I found a handful who didn’t just want to get their teaching hours out of the way so they could get back to their “real” work. The kind you could ask a question, and they didn’t just repeat their last two statements. They elaborated on the in-between step, or what justified some conclusion.

If you find college math professors like that, add them to your Christmas card list for life. They’re rare, but they’re also golden.

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