Mathematical Mondays

So, You Want Me to Undermine My Colleagues, or What?

We had our first parent-teacher conference this past week. Overall, a great experience. I love the chance to talk one-on-one with students’ parents. They see what I’m all about, and I get new insight to the kids I teach.

The last encounter of the night was a little strange, though. It wasn’t a parent of one of my students. It was the parent of another teacher’s student, in the grade below the one I teach.

She was concerned about the teacher her child has (but I didn’t entirely get why). She was concerned about the new standards. (She’s not the only one, but guess what—I kinda like them.) She said she’d talked to the principal before school started, and then again that night. He’d pointed me out to her (I’m not sure why).

Bottom line, I have no idea what this mother wanted from me. Just hoping that I’ll have the same class assignment next year and will get her child? Just wanting to vent and have someone tell her they understand?

Did she want me to say, “You heard right. I’m awesome. Sorry my colleague sucks.”

On what planet would I ever do that?

On what planet would it ever be acceptable for anyone to do this?

That’s my gut reaction. On the other hand, I understand how frustrated parents can be when a teacher isn’t working for their student. There often isn’t much they can do about it, and I really know the kind of impact a bad (or good) math teacher in particular can have on a kid.

On the other other hand (the third one, right?), I’ve already been dealing with teacher reputations a ton this year. I’m the “new” teacher, so kids who didn’t want the other option (whether by past experience or by reputation) transferred to me just for that. The “other option” is not a bad teacher, nor a bad person. We plan our units together. As far as I know, we don’t teach that differently.

Try telling that to the people who figured even an unknown quantity had to be better.

Then again, I agree that sometimes certain personalities don’t gel in a great way, so one teacher might be more effective with certain types of kids than another.

But the end effect is that my classes are all bigger than the others in the grade.

*sigh*

Is there a solution to any of this? Probably not, other than to do what I plan on doing … continuing to do the best job I can in my classroom, and maintain my professionalism at all times.

I’m not going to cut down good, hard-working teachers. I hope no one else would do so to me, either.

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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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Undoing the Work of Other Teachers

It’s an inescapable fact of education that what we do as teachers today affects the work of other teachers later in a student’s life. That means we inherit strengths a good teacher built, which is great. It also means sometimes we have to fix mistakes other teachers made.

This fact came to mind last week as my classes worked on proportions. Some students referred to something called the “Fish Method.” Let’s use this proportion:

Start with the number in a fraction with x (in this case, 8). Draw a line from the 8 diagonally up to the 2 (multiply those numbers), curve down to the 3 (divide by that), then diagonally up to the x (your answer equals x). What you’ve drawn looks kind of like a fish.

To be clear, this isn’t a “mistake” I had to fix. Rather, it’s a case of students clinging to a method that only works in a limited number of cases. For instance, proportions like these had them flailing.

We had to discuss other methods that had broader scope. This isn’t a bad thing—I’m all for discussing multiple methods and their respective limitations. But whenever something like this comes up, I try to tread lightly. I don’t want to say that their other teacher was wrong, bad, or not as cool as I am.

There are other situations, though (not like this proportions situation), where that’s exactly what I’m thinking. It even happened to me as a student. When I was very young, I was told by a teacher (a student teacher, to be fair) that “it’s” always has an apostrophe, whether the contraction or the possessive. Yes, really. It took me a few years to (a) figure out she’d been wrong, and (b) correct my bad habit.

I’m sure it can go the other way, too. A teacher instills all kinds of wonderful things in a student, and another teacher down the line destroys all that work.

Is there a way to avoid it? Maybe not. There will always be human error, whether intentional or not. All I can do is try not to be one of those “bad” teachers, and try to repair damage where I find it.

Have you observed or been affected by cases of teachers working against each other? How did it impact you?

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Who Sets Your Potential and Decides When You’ve Met It?

Sometimes I get students who come into my class saying, “I love math! It’s my favorite subject, and I’m good at it.” It’s awesome when I do, but those students are definitely the minority. More often than not, students come in somewhat indifferent about math. Just something they have to get through, most of them with a mix of good and bad experiences under their belts.

Then there are those who come in with “I’m bad at math” oozing from every pore.

Some of them really do struggle, and for a variety of reasons. Learning disabilities, interruptions in their education, a string of teachers who made it impossible for them to learn one way or another … But several say they’re bad at math—loudly—but I don’t believe them. Their work on quizzes or answers to questions in class show they have plenty of potential.

Says who? Says me.

Maybe they’re holding themselves to an impossible standard of perfection, and anything less means being “bad” at it. Maybe it takes effort, and anything that isn’t easy must be something they’re “bad” at. Maybe they just don’t want the image of being good at math (or anything school-related). Maybe something else.

Whatever the reason, I can’t sit back and ignore the potential, just like I can’t ignore the potential of kids who do struggle.

Observations like this got me thinking about potential as a whole, though. Like I said, I’m the one who’s declaring an unmet potential in many of these cases. Unless I can get the student to buy in and agree that the potential is there, though, it’ll probably remain unmet. I can force some small increments at the beginning, pointing out their successes to build confidence, but I can’t force the level of self-belief it takes to achieve more.

I can see theoretical potential, but the student has to take control at some point to make it real.

Then I got to thinking about meeting potential. It’s kind of a stupid concept, isn’t it? Has anyone ever said, “You’ve met your potential—you’re done”?

Maybe some superstar athletes, who’ve reached the pinnacle of their sport, achieved its highest honors (multiple times), and retire while they’re on top. But even then, are they done? Or do they turn the level of potential they’ve reached to another target?

How do you meet your potential, when it should always be dancing ahead of you, just out of reach?

I may have mentioned before, but when I was in elementary school, everyone said I’d be a doctor. Not any particular reason other than that I was a brainy little thing, and becoming doctors is what smart people do. There are those who thought becoming a math teacher was a waste of my potential.

Was it? I’m the first to admit my academic pathway was not perfect, and there are things I’d like to have done differently. I missed opportunities. I made mistakes. But is the end result a waste? Maybe I just had a ways to go to narrow the gap to that initial potential.

After a few years of teaching, I went off to enter the world of deaf education. It added more challenges, maybe pushed me closer to that initial potential everyone saw in 10-year-old me. In the midst of that, I began writing novels, activating a part of myself that had been quietly lurking in the corners. Definitely a stretch.

I signed with an agent, and now I’m to be published. All while I’m still a math teacher.

Is this enough to equal my original “going to be a doctor” potential?

That’s the wrong question.

My potential is what it is. What I do with it can’t be quantified and compared to earlier expectations. It’s not something for me to reach, but rather something to keep me moving forward.

People in my life help me see my potential, and in the end, I’m the only one who can decide whether I’m moving toward or away from it.

So that’s what I’ll try to do with my students … help them see their potential, point them in the right direction, show them that its current position is something that can be achieved. All the while, making sure they know that by the time they get to that mark, their potential will have moved forward even more.

And that the only way to not “meet” their potential is if they refuse to move at all.

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Learning the Hard Way

Sometimes it doesn’t matter how many times you tell someone that a surface is hot. They’re just going to have to touch it.

In my first math lesson with my new classes this week, I noticed a trend in my first couple of classes. As they worked on their homework near the end of class, several of them got to a particular problem and didn’t know what to do. It had three different variables and they were supposed to evaluate it.

Without exception, those who asked had neglected to read the instructions, where it gave a value for each variable.

I figured I’d save myself a little trouble and warn my remaining class periods. A part of the lesson had the exact same type of problem, so when we got to that, I mentioned the issue. I told them that other students got to those problems in the homework and didn’t know what to do because they didn’t read the directions.

Later, we get to homework time. I walk around the room, helping students when they get stuck.

Invariably, more than one raises their hand. “I don’t know what to do here.”

I point to a line in their textbook. “Did you see this?”

“No, I—oh! You totally warned us and I did it anyway!”

They felt like idiots. I assured them they weren’t the only one to do it, and made a little joke about how they’d never forget to read directions again, right?

I already know there’s only so much they can absorb at one time, and which parts stick depends on their own priorities.

Live and learn, kiddos.

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Tales of a Tutor

The past couple of weeks, I’ve been helping a friend’s daughters with a college math course they’re taking over the summer. I’m geeky enough that this is fun, and getting paid is a nice bonus.

While doing so, certain things have struck me more than they might while working with my own students. So I figure, why not share?

Even math teachers don’t remember all the math, all the time. Conic sections … I’ve never actually taught them as a whole topic. I’m fine with circles and parabolas, because those come up regularly on their own. Ellipses and hyperbolas, however, not so much. I remember some general things about them, but not how to find the coordinates of the foci, or how to rewrite an equation to the proper form. Fortunately, all it takes is twenty seconds glancing at the right material in the book.

Math teachers don’t always agree. When tutoring, I almost always come up against something where the way the teacher showed them is bonkers (in my opinion). I try to determine if there’s any good reason to do it that way. If there is, I go along with it. If there isn’t, I try to determine whether the teacher will know or care if the students do it a different way. If not, I’ll show the kids my way, explain how it relates to the teacher’s way, and tell them they can choose whichever they like better.

Math teachers don’t always act rationally. Often these college courses don’t allow the use of calculators. I understand the idea—with some calculators these days, you could solve every problem on the test without engaging more than a couple of your own neurons. But it’s kind of ridiculous when the long division to reduce a fraction takes longer than applying the math concept that’s actually being tested.

And the thing is, I’m sure I’m guilty of all of the above in my own math classes. Somewhere out there a math tutor is saying, “Miss Lewis said that? Is she nuts?”

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