Mathematical Mondays

If You Need Help, THEN TAKE IT!

I started something new last week. After I finish the lesson portion of class and it’s time to start on the homework, I have the kids move around. Those who feel like they’ve totally got it, ready to rock head to the back and work quietly. Those who are still feeling a little (or a lot) fuzzy come to the front, and I work with that smaller group on a few select problems from the homework.

The first day I did it was interesting. My A1 class had several takers who were like, “Dude, yes, help!” Most other classes, I had to twist some arms to get anyone to join in.

Second time around, though, more people joined in. I think some kids were like, “Uh, yeah, that actually looks helpful. Might be a good idea.”

It’s nice, because in those smaller groups, the struggling kids are more likely to ask questions, stop me when they don’t understand. I’m liking it. I think I’ll stick with it.

Still, some kids who I know really ought to join in are heading to the back and working with their friends instead. That’d be fine if their friends were helping them understand, but based on the daily quiz results and homework scores, it’s more likely their friends are breezing through the assignment and distracting them with random chatter instead.

It makes me mad at the struggling kids for not prioritizing. It makes me mad at their friends for not recognizing how much harder they’re making it.

I mean, I get it. Social pressure and all … not wanting to “look stupid.” I wish they’d notice that several popular kids are joining the extra-help group. Then again, an outward self-confidence often coincides with teen popularity. (Comes with its own problems, often under the surface, but that’s another post.)

I’ve only been through it two times with each class so far. I could force it, telling specific kids they have to come to the front. I’d rather not. For now, I give a strongly worded suggestion that if they didn’t get the homework done, struggled on the daily quiz, or got a bad grade last quarter, they really ought to join us.

Hopefully the more we do it, the less stigmatized kids will feel.

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One Term Down, Three to Go

First quarter ended last Friday at my school. Naturally, the past two weeks have been filled with kids desperate to get their F to a passing grade … or their A-minus to an A. And in order to keep on top of the late work, make-up work, and occasional piece of extra credit, I set aside the quizzes that won’t count until second quarter.

This means now I have large stacks of quizzes to grade. I knew this would happen. I was aware of the consequences for my decision.

Still … it kinda sucks.

It’s okay, though. I think at least a few kids figured out that desperately trying to raise their grade at the last minute is a lot more work than just keeping up through the term. As we start the new term, I’ll try to get the message through to a few more.

Now that I’ve got my feet under me, I’m also hoping to keep things a little more organized from here.

Here’s hoping.

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Parental Priorities

This one’s not exactly about math. It’s kind of about math, but more education in general.

I’m not one to judge right and wrong ways of parenting. A lot of things have to depend on the individual child’s needs, the family’s background and values, etc. But I have some observations about different types of parents.

There are parents who apologize profusely for their kids missing school for legitimate reasons, like medical issues. Then there are those who check their kids out of class to go get smoothies.

It’s not like either extreme is always great or always terrible. Sometimes the kids who miss for doctor’s appointments aren’t great about getting caught up on what they miss, and sometimes the smoothie-getting kids are.

Still, I wonder what message the smoothie-run parents are trying to send. That they’re a cool parent? That sometimes you have to give yourself a mental-health break? (I can agree with that on occasion.)

What message are the kids getting? Like I said, those kids are often okay with making up what they miss. They’re usually kids who clearly believe school is important, at least to some degree. But what about other students, who know why their classmate misses a class or two in the middle of the day? What does it say to them about where their priorities belong?

I don’t know. I do know that with math in particular, if you miss a component or two and don’t catch it up, you risk being very lost on concepts that follow. If you don’t solidify basic equation solving, for instance, you’ll have a very hard time with most other topics in algebra.

Most parents do the best they can, especially considering the bull-headedness of some teenagers. Some teens already understand the importance of their education, even the parts that don’t immediately seem relevant. Others take a while to figure that out.

I just hope parents aren’t delaying that understanding.

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Catching Your Glitches

We all make mistakes. Ideally, we learn from the mistake and don’t make it again. Realistically, there’s a certain type of mistake that we make over and over again. I’ll refer to that as a glitch.

Some glitches we’re aware of. I have plenty of students who see “three squared” and automatically think the answer’s six. But they know they have that tendency, so they catch themselves and say nine before I say anything.

Other glitches sneak around, leaving us oblivious until someone else points them out. Sometimes they turn into the first kind after they’ve been pointed out. But sometimes they stay rooted, refusing to be corrected.

Students who continue to combine unlike terms no matter how often it’s marked wrong. Or who say X plus X is X-squared.

It’s not just in math, I’m sure. We fail to shift from second to third gear properly with our manual transmission. We mix up “lay” and “lie” or “affect” and “effect.”

With the math, at least, I suspect part of why the glitches keep happening is because the student doesn’t understand the foundation of why it’s a mistake. Attempting to memorize arbitrary rules without understanding their basis is rarely effective.

Unfortunately, students are often so used to thinking of math as a matter of memorizing arbitrary rules, they don’t shift into looking for meaning. At least, not easily. All I can do is try to open their eyes to the hows and whys behind the what-to-dos.

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The Power of "I Think I Can"

I have several students who struggle with math. That’s okay. Perfectly normal. My job is to work with them and help them improve anyway.

By the time they get to me, these struggling students have often come to the conclusion that they can’t do math, period. So a big part of my job is to undo that damage.

Not. Easy.

I’m not a magician, so it doesn’t always work. But if I can find one thing they’re successful with, reinforce it, and find another … sometimes that sets off a chain reaction. They think maybe they can do a few things in math. They’re a little more willing to try, a little more patient with their own mistakes.

They stop saying, “I can’t.” Instead, they ask questions.

And that can build momentum that’ll take them far, long after they leave my class.

Other times, the barrier remains. They’ve given up. They refuse to believe. (So I try a little harder, try other ways. Jury’s out on whether it works in a lot of cases.)

How often in our own lives do we let “I can’t” become self-fulfilling? Not that saying, “I can,” instantly makes all possible … but it certainly doesn’t hurt as a first step.

What helps you get past that, to begin to believe it might be possible?

And when the larger obstacles come, what helps you keep going?

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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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