The Makings of Mathematical Mistakes

In my years of teaching math, I’ve amused myself by taking note of the types of mistakes students make. (Yeah, okay. I’m easily amused.) You can pretty much figure out the type of mistake by watching my reaction.

The “Fell Through the Cracks” Mistake

This usually happens in complex, multi-step problems. The student does all the hard stuff right but overlooks something. More often than not, it’s losing a negative or mistyping something in the calculator.

R.C.’s Reaction: I just point wordlessly at the paper or calculator and wait while the student looks, ponders, then says, “Oh! Oops.”

The “You Know Better” Mistake

Another “careless” variety of mistake. Can I tell you how many times I’ve asked what four-squared is only to hear, “Eight. No—wait! Sorry. Sixteen.”

R.C.’s Reaction: Students often catch those without any help from me. When they don’t, they get my ‘Did you seriously just say that?’ look. If that’s not enough, they get a verbal, “Really?”

The “You’re Still Learning” Mistake

This happens when students are mostly getting a new concept but aren’t quite there yet. OR … when they have to apply something they learned previously that hasn’t quite solidified.

R.C.’s Reaction: Usually I ask them to explain their thinking first, then ask some follow-up questions until they see the wrong turn. Sometimes a neighboring student will try to tease the other about the mistake, at which point I remind them that they made the exact same mistake two minutes ago when I was helping them.

The “Someone in Your Past Failed Both of Us” Mistake

I teach high school math, which naturally relies on concepts learned over several years before arriving in my class. Sometimes we’re working on some complicated algebraic thing and I realize some/all of the students have a problem with an underlying principle. (Fractions, anyone? Or measurement conversions?)

R.C.’s Reaction: What can I do? Go off to the side of our work and make up a simplified example (i.e., non-algebraic addition of fractions), quickly refresh the kids’ memories on that, and parallel it to the problem at hand.

The “Back the Truck Up” Mistake

These mistakes on the part of the student tell me that I screwed something up as the teacher. Didn’t explain clearly, allowed for a massive misconception to take root, etc. Sometimes I even did something just plain wrong.

R.C.’s Reaction: Confess to the class that I made a boo-boo, very clearly indicate where we went wrong, and emphasize the proper way to move forward.

Some people might say it’s a teacher’s job to eliminate mistakes and a student’s job to avoid them. I don’t agree with that. Mistakes are great! They’re how we learn. (Well, so they’re great as long as we learn from them.) And one thing to keep in mind is that I have extremely small classes, and I’ve taught most of my students for more than one year, some for up to five straight. My reactions to the “Fell Through the Cracks” and “You Know Better” varieties are done in an environment where the students and I are able to laugh off mistakes without embarrassment. (And where I’ll accept “It’s calculus on a Monday morning,” as an excuse for the careless mistakes as long as they keep trying.)

I know some people who were always terrified to volunteer information in class, certain they’d make a mistake. I was one of them. Now, I’m okay with making mistakes in the classroom. Still working on being okay with it in the rest of my life.

What We Learned During MindyMania 2012

This week I’ve been discussing the weekend I spent with my critique partner, Mindy McGinnis. I’ve covered the wildlife and the writing, so today I’ll just sum up a few things we learned.

Thing We Learned #1: Mindy and I really are twins separated at birth.

(And Mom was in labor for about three weeks.) We already suspected. Our birthdays are very close, down to the year. Our opinions and tastes are often the same. We complete each other’s sentences. And now we know that we use the same shampoo.

Thing We Learned #2: Fast food employees can take the “twins” idea too far.

To the girl at Wendy’s who thought Mindy was me after I’d already ordered—really? Okay, we were both wearing glasses and both tend toward the chalk-white end of “pale.” But there’s a seven- or eight-inch difference in height. My hair is mega-short; hers is long. Beyond that, the differences are what make things interesting. Mindy was ready and raring to go for the school presentations. I was freaking out about having to introduce her each time for about thirty seconds.

Thing We Learned #3: Handprint petroglyphs are the best.

I mentioned earlier in the week that we visited Petroglyph National Monument. It was very cool hiking around one of the canyons, and right on the edge of the city. All the petroglyphs were fascinating, and we had a lot of fun wondering about the meanings of different symbols, but I particularly liked this set we saw right at the end of the canyon. Strange thing, too—a few hikers had been ahead of us, and the hike is an out-and-back, not really a loop, but we never saw them coming back. Maybe the hands were warning us … ?

“Turn back! Alien abductions beyond this point!”

Thing We Learned #4: Going out of your way can really pay off.

I don’t know if any of you watch the series Breaking Bad. I don’t, but Mindy does. There’s a particular restaurant that figures prominently in one season, apparently, and we went to check out the actual restaurant that provided the front for the show. Bonus: The lot next door is where we saw the emu I posted about Monday. Double Bonus: The food was awesome.

If not for the glare, you might see the ostrich out the window.

We learned several other things, but I’ll save those for another time. 🙂

"The Writer’s Voice" Contest Entry: Stitching Snow

For my regular readers, this is my entry for a contest I’ve entered. (See details here.) Feel free to peruse or ignore as you’d like. 🙂

Query:

Seventeen-year-old Essie knows how to stitch up robotic drones so the men in the mining settlement remember she’s worth keeping around. She knows how to use her fists to make sure they keep their hands off her. What she doesn’t know is how to deal with a boy who’s depending on her to get his crashed shuttle off the ground and out of orbit.

He’s polite, chivalrous, even a little charming, and he gives Essie the kind of attention she’s never had … until he discovers her secret. She’s the missing princess of his people’s greatest enemy. One betrayal later, he’s taking her home whether she likes it or not, to exchange for prisoners of war. What he doesn’t know is she had damn good reasons for running away. His ‘leverage’ means her death.

STITCHING SNOW is 68,000 words of Snow White in space, if Snow were a cage-fighting tech-head with daddy issues.

First 250 Words:

It took seventeen seconds to decide Jarom Thacker’s reputation as the sharpest fighter on Thanda had been a minor exaggeration. At twice my size—and age—he was still quick, forcing me to move or risk getting pinned against the cage. Like everyone else who came through Mining Settlement Forty-Two, though, he aimed for my gut or back. Never the most obvious target.

Wouldn’t want to botch the pretty girl’s face, right? Idiot.

I blocked him on the left, but missed his swing on the right slamming into my ribs. Pain flared through my side. I let it fire me on and slipped Thacker’s grip when he tried to grab me.

Unlike him, I had no qualms about uglifying him further—not with the way he looked at me, the shudder it sent across my skin. The heel of my palm slammed into his nose with a satisfying crunch despite the cushioning of my shock-fiber handwraps. He ignored the blood and lunged blindly; I dodged with a knee to his groin. When he doubled over, I kicked his legs from under him. He went down and I followed, pinning him. He tried to raise himself up. Before he could throw me off, I grabbed a fistful of his hair and knocked his head against the floor.

“Three … two … one … fight goes to Forty-Two’s own Essie.”

Telling Teens Reading Doesn’t Suck … Using Vomit

As mentioned previously (twice now), critique partner extraordinaire Mindy McGinnis joined me in the southwest for the weekend, including a set of presentations to my school.

The first two presentations were to younger students (grades 1-3 for the first, then 4-8 for the second). We broke the kids into three groups and had one come up with a character, one a setting, and one a “problem,” plus each group had to offer one random word. Then Mindy had to pull all that together and make up a story on the spot.

Ninjas are very popular this year. And Mindy managed to turn our school’s founder into a zombie ship captain on Mars.

The other presentation was a little more formal for the high school kids. Mindy talked about the idea of lots of stories having the same basic plot at their root, but weaving in specifics that make it interesting and new. She’d give several examples of a particular Big Idea, then offer a specific premise for the kids to guess.

For example, under “Boy and girl fall in love but can’t be together because ______,” she gave, “Pretty blonde with a perfect life falls for a Hispanic gang member from the wrong side of town.” Several of my female students jumped right in with the answer: Perfect Chemistry by Simone Elkeles.

I think many of the kids came away with the point Mindy wanted to make. The “sameness” of many stories is a good thing, because if you find one you really like, you can find others you’re likely to enjoy as well. (And librarians can help you with that!)

As writers, though, we need to remember the second part of that formula—bringing a fresh, new take to the same old story. Too often, we find ourselves just writing the same story with only superficial differences, and that’s just boring.

Oh, and the vomit? Yes, Mindy totally has a story that makes vomit relevant to reading. But you’ll have to hear her tell it sometime.

MindyMania 2012: The Wild Aftermath

Okay, this is supposed to be a Mathematical Monday, but hey—I worked the word “math” into the title.

As I mentioned on Friday, Mindy McGinnis (critique partner extraordinaire) came to visit for the weekend. The three presentations at my school Friday were awesome. More on that Wednesday. Today, I’ll talk about wildlife.

After school, we saw a camel. Well, sort of. We went to Camel Rock.

See? Totally looks like a camel, right?

On Saturday, we went out to Petroglyphs National Monument. I’ll share some pictures of the actual petroglyphs on Friday, but I said this was about wildlife. Here’s a bug we saw as we were hiking.

Can anyone tell me what kind of bug it is? It was a quick little thing, so I’m pretty impressed with the picture I managed.

Later on, during the hike back, we saw this lizard. Not at all uncommon for me—I see them all the time outside my apartment complex—but not an everyday thing for Mindy. Unlike the mystery bug, this guy was happy to stand and pose for us as long as we didn’t step any closer. Hooray for camera zoom!

After Petroglyphs, we went to a very particular Twisters restaurant. That’s a burger/burrito chain around here. No big deal, except this specific location was featured prominently in a season of the TV series Breaking Bad, which Mindy is a fan of. We weren’t expecting more wildlife, but in the lot next door, we saw an emu.

Yes, an emu.

Seriously.

Sunday didn’t involve any wildlife, except for the angry passengers from Mindy’s cancelled flight. Don’t worry. She (hopefully) made it safely away this morning and will either be on her way home or there by the time you read this.

More to come the rest of this week.

People on the Internet are Scary! (No, They’re Not)

You know how they say to be careful with people you meet on the internet? How they might not be who they say they are? Maybe they’re scary and strange?

Apparently I’m allowed to throw that advice out the window under the right circumstances.

The illustrious Mindy McGinnis safely arrived in the dusty, dirty, just-plain-BROWN southwest today. (Seriously. Mega-winds kicking up the dirt creating a cloud of brown over the city.) We’ve known each other (on the internet) for about two and a half years. We’ve been critique partners (on the internet) for about a year and a half. Today we met in person for the first time.

People knew this was happening. No one thought it was weird or scary.

Maybe it’s because of how ubiquitous the internet is now, how big social media has become, or maybe it’s just that Mindy and I have known each other in online arenas that are public enough to validate our identities. Or something.

At any rate …

Today she’s the guest author at my school’s second biannual Author Illustrator Competition. Not only is this her first visit anywhere in the west that isn’t Las Vegas, it’s also her first foray into Deaf-World.

Should be fun.

I’ll be sure to report back.