Mistakes on the Key

I rarely assign students homework out of the textbook. Instead, I write up worksheets for each week and assign those instead. Reasons are myriad.*

It is policy in my department to give the key with the assignment.** With a textbook, that just means assigning odds, or evens, depending on your publisher. Because I write my own worksheets, though, I write my own keys. That’s good for a lot of reasons, most of which have to do with the fact that I’m actually doing the homework.***

The problem, of course, is that I’m human, doing a ton of other things, and don’t have an editor. Textbooks occasionally make mistakes, but most of the time, they’re caught before publication. I write three to four worksheet keys a week, often at 5:30pm while making dinner, and no one’s checking my work. I make mistakes.

In the past, that’s really frustrated some students. How are they supposed to know if they did it correctly if the answer key is unreliable? And I get that frustration. I only see them three days a week, so the key is their main source of teaching and support on their work-from-home days.

This year, I’m taking a new approach. Instead of beating myself up about something that is going to happen anyways, I told every student on the first day of school that there were mistakes on the keys. The first person in each class to find a mistake, email me about it with the correct answer, and justify their answer gets bonus points on the homework.

Will this radically change their grades? No. Most of them get 100s on the homework anyways – I grade for completion – and it counts for a very small part of their average.

But it has changed their approach to homework. I hear from a lot more students on their home days, which is good. Because of the competition, a few are doing their homework earlier than they would have, which is also good. Also, it’s a little too early to say for sure, but I’m seeing a growth in confidence. Students who would normally ask, “Did I do this wrong?” are now emailing me to say, “There’s a mistake on the key, and here’s how I know.” That’s a total change in perspective for them, and I love it. I don’t want them to just believe my answers; I want them to think through things and find the right ones on their own.

Also, I can now communicate mistakes to the class quickly. Every class has a Google Drive folder, divided by week, and I have a “Week n Key Errata” file in each folder. When a student emails me with a mistake, I copy/paste the relevant part of the email into the file, and the entire class can check to see if what they think was a mistake actually was one instead of waiting for the next class day to ask. That also means I don’t have 5 kids emailing me about the same mistake. I didn’t implement this plan until a few days in, and it was definitely needed.

That also means that I have a record of the mistakes, so if I want perfect keys next year, I can go back and fix them. It’s like I’m crowd-sourcing my editing. Although I like this plan, so I probably won’t go fix them. Actually, from time to time, I make intentional mistakes, and not just ones induced from doing math while I’m tired.

Also…it’s made a difference in my attitude. I felt bad and beat myself up for mistakes on the keys, because I was making it harder for the students to learn. Now it’s an intentional part of the class, and I don’t have to feel bad because it’s a learning opportunity. So while I still cringe a little bit when a student emails me with a mistake, it’s a lot less, and growing smaller.

* I like writing worksheets more because it lets me pull problems from a variety of sources – the textbook, other teachers, old AP problems – and have it in one neat package that’s easy to grade. The students like it because they say that the way I phrase problems on the worksheet is like how I phrase problems on the test, which is different from the textbook’s phrasing. Also, even a 20-page worksheet (Don’t judge! It’s for the entire week! And the really long ones only have something like two problems per page!) weighs significantly less than the textbook, and everyone in my school is concerned about backpack weight. I’m under 30 and have arthritis. This isn’t cool, man.

Of course, then I have to write the worksheet and the key, which takes a lot longer than just pulling problems from the book. So there’s that. But I can reuse them with minor tweaks every year, so it’s not like I have to rewrite everything every year. Although I’ve yet to successfully save and reuse the bulk of my keys. Goal for this year.

**The logic of this has to do with the fact that our school is weird. We’re halfway between private school and homeschooling, and parents are considered the co-teachers. The younger grades give the key to the parents, who then checks the work and helps reteach the student. That makes sense, because the parent is the co-teacher. But I teach Calculus and Precal, and very few parents can help their kids with my homework. I just give it to the students, explain how they should use it, and let them take responsibility for their own education.

***I know exactly what I’m assigning, in terms of difficulty and time; I’m able to say, “Oh, yes, that problem” when they ask me about the homework in class; etc. It also let’s me adjust how much support I’m going to give them. Do I just give them the answer, or show each and every step? Do I write notes on why I did each step, or just do the work and let them figure out why? It depends on the topic and the class, but it lets me support them more or less, depending on my goals for them.


Competitive Grades

This year, I get to teach two students Calculus II (basically, AP Calc BC, plus whatever fun things I want to cover once we finish the curriculum.) Two really fun students who are best friends makes for an entertaining class.

Today, they started talking about their grades. It’s the second day of school, so it’s not like they have a lot of grades. But they took a pre-assesment in science, and they were talking about how one of them tied for best in the class with CG, and how JL won’t ever talk about her grades even though they know they’re really good, and how one of them is table partners with CT and managed to beat her on some question.

I spent a lot of junior high hearing remarks along the lines of, “Hey, what did you get?” and “Wow, I beat her!” and “Aww, I’ll never beat her!” I got really tired of being the measuring stick for other people’s self esteem, and I got really tired of people gloating when I didn’t do so well. I stopped discussing my grades with people. It didn’t matter if it was the PSAT or a spelling test, I stopped telling people what I scored in 8th grade.

I told that to these two today, and I briefly told them why. (More briefly than the previous paragraph.) They thought a minute and then said, “We’re really competitive.” And they’re right.

It’s not just those two, though. As soon as I hand out a test in any class, someone will say, “Hey, so-and-so, what’d you get?” Once they hear, they respond. If they scored higher, it’s, “I got a xx!” If they scored lower it’s a, “Oh…ok.” Some of them will go ahead and share their grade; some of them won’t.

Everytime, I say, “It’s not a competition.” “Yes, it is,” they tell me. “No – you’re only competing with yourself. It doesn’t matter what someone else made.” They don’t believe me.

I know that in some schools, it is a competition. It certainly was in my high school – the top ten percent and, even more, the top ten was a really competitive fight. They posted class ranks every semester starting junior year; intense speculation about who would rise and who would fall swirled through the lunchroom on those days. “Hey, what’s your rank?” was the most common question for days. College admissions were tied to being in the top ten percent; glory was tied to being in the top ten. At graduation, the top ten students were called up on stage and honored specially. Families of those students got special seats. The students got plaques. I have no idea who #11 was, but that had to be rough to watch, knowing that they missed out because of that one map quiz on Africa that they failed back in freshmen geography.

But at our school, we don’t rank students. If a college really, really needs to know, the registrar will compile a list and tell the college a rank, but no one else knows. I don’t know. The students definitely don’t know. We don’t even say who the valedictorian is.

So why the competition? Why are other people’s grades the measuring stick for their self-esteem? Why is satisfaction in knowing that you did your absolute best not enough?

I especially hate it when it’s a really strong student asking a struggling student what they got so that they can gloat. Sometimes I want to tell them, “Who cares if you got a 93 and he got an 87? He’s been making Cs all semester; an 87 is huge for him! As for your 93, you really should have made a 98. You can do better! Why are you gloating when you didn’t do your best?” I don’t, of course – privacy laws on grades and all. So what should I say instead?

Why does this happen? And more importantly, how can I change their minds?

Math Club!

I have the best students. No, no, I know you like yours. And I’m sure they’re great and all. Sweet, thoughtful, etc. But mine are just plain awesome. A few weeks ago, a student emailed me this:

I’ve been thinking that maybe in order to help get kids for their standardized testing and maybe TAPPS events we could form a sort of club where we could e-mail out tests or work on new methods of solving problems or things like that? I have a few kids who are interested and their parents are willing to help out, so I was wondering if you could help us make it official with the school and help lead it? As a group we could all go to TAPPS together and take tests there as a team, and also meet maybe once a month. Potentially, I think we could even start tutoring as a group which would be really cool!

My most recent email from her concluded thusly:

I will, and thank you for helping me see this through!

Again, thank you so much!

To clarify, this student

  1. wants to start a math club,
  2. has recruited other students,
  3. has a plan for what this should look like,
  4. wants to tutor, and
  5. is thanking me for helping her.

How can I not love this child?

So, we’ve been emailing about specifics for the last few weeks, and I got a budget from the administration. I put together a handout for meet-the-teacher night, and I may ask my student to make a poster.

Current plans:

  1. Join Mu Alpha Theta. (It seems like the thing to do…)
  2. Go through Crossing the River With Dogs, more or less. (Discuss a different strategy every month, and give problems to play with at home?)
  3. Compete in the AMC 10/12.
  4. Do other competitions (TAPPS, Rocket City Math League, etc.)

Questions for the world:

  1. Why join Mu Alpha Theta? I plan on it, but I’m not totally sure what the benefit is, other than putting it on a college application.
  2. What do you do in your math clubs?
  3. What math competitions do you compete in? This is high school, so no MathCounts.

Most of what I’m currently planning on is inspired by Kate Nowak’s post here. My choice of book to go with is definitely inspired by her.

Between this, Quiz Bowl, and the Spanish club, my school gets three new academic clubs before. Last year we had zero. Now we have three. Yay for non-athletic extracurriculars!

One more day until I meet my students. 🙂

Classroom Rules and a Productive In-Service

In-service began today. (Bye-bye, vacation! The long days of reading, sewing, organization, and mid-morning snacks will be missed…)

We talked about Wong’s The First Days of School today. Back to the basics – partly because we have a ton of new teachers, and partly because we probably all needed the refresher. So, classroom rules and procedures.

I haven’t really had rules in the past. I certainly haven’t had a poster with the rules on them. I’ve never had a class discussion creating rules for our classroom. Those are all things that you’re “supposed” to do, but they just have never felt right for who I am as a teacher and for how my classroom works with my group of kids. I try to treat them like adults until they prove I can’t, and laying down rules felt like I was disrespecting their maturity. Still, clear expectations are probably important, so this felt worthwhile.

We were told to sit with our grade level, so that we could have discussions about what rules and procedures were appropriate for the age of students we have. (Sidenote: we started doing the Fundamental Five last year, which includes small group purposeful talk, and my dean really has made an effort to include small group discussions in in-service. I appreciate this – listening all day is boring, and the fact that she practices what she preaches demonstrates integrity. If she’s willing to do something in her teaching time, I’m willing to try it for her.)

We were told that, as a grade level, we should come up with ten rules. My fellow junior/senior teachers and I panicked – ten rules? We weren’t sure we could come up with five! There are school rules, of course, but those already exist. What else needs to be said?

At this age, we decided that we value principles more than rules. There aren’t going to be a lot of classroom rules next year in college, so our goal is to teach them to govern themselves.  So we talked principles, and how to spell it out for them. It was a good conversation, and at the end, I jotted down my expectations for my students this year. (Yay, productive in-service!)

1.) Be respectful.

2.) Be responsible.

3.) Be edifying.

That’s really it. Most of my students already buy into these principles. Respect could probably cover all of that – being responsible is showing respect for yourself, and being edifying is showing respect for others. On the other hand, owning their actions and choosing edifying words are things my students struggle with sometimes, so making my expectations more explicit in those areas seems worthwhile to me. I’ll make a point of discussing this with them on the first day, but I’m still not doing a poster. It just feels too childish for these kids.

We were also reminded that rules need consequences, but you don’t want to shame a student. My standard consequence is to keep a student after class and discuss their behavior. (“Was what you did respectful?” or “What you said wasn’t edifying.”) If that doesn’t work, I’ll email the parents. I’m terrible about consistency, though, because I don’t have a way to quietly tell a student to stay, and I hate calling them out in front of everyone. (Yes, there are times everyone needs to see the problem dealt with, but it’s pretty rare for my kids to act out that badly.)

So, my plan this year: keep a pad of sticky notes that are already filled out with “See me after class.” I’ll keep this on my desk. If I need a student to stay, they get a sticky note, and I don’t have to worry about the entire class overhearing me tell a student that I need to see them. It’s between them and me. We’ll see if that helps.

We talked about procedures, too – how to start class, end class, quiet the class, handle the flow of paperwork.

I pass out papers while they’re working. (Does anyone not? What do you do?) I used to walk around and pick up papers, but last April I started telling them to turn their papers in on my desk. I even got them to put their papers in alphabetical order by last name. That gets them moving and means I touch papers fewer times. I like this one.

Absent students’ paperwork is my bane. My goal is to post all handouts in Google Drive this year, so I think I’m not going to hold onto extra copies and just send students to Google Drive. That’ll help keep me accountable, and it’ll mean fewer papers to hold onto.

Also, my warmups are for a grade. That means that a student who is late or tardy needs to make it up. Which means I have to go write it down and put it in the makeup box for them to do in study hall. This. is. a. pain. This year, I think I’m going to take a picture for any absent students and immediately send copies to the printer of the photo. It’ll be black and white, but it’ll also get done.

So. I left in-service today with some concrete ways to fix problems in my classroom. That’s a pretty productive in-service.

Also, 48 hours until I meet students. 🙂

One Good Thing: A Student Corrected Me

This happened on Monday.

Monday was my brother’s birthday. He turned 22. When I got to school in the wee hours of the morning, I drew a birthday cake on the board next to the date and labelled it 11000.

Wrong Birthday

As you can see, I typically make the date a puzzle or a problem to solve. Sometimes it’s math the students know, sometimes it’s not. Sometimes they ask about it, sometimes they don’t. 11000 isn’t anything that I’ve taught in class, but I thought they might ask about it.

No one in Calculus asks, or in first period precal. But in third period, Advanced Precal, they notice the birthday cake.

Student: “Who turned eleven hundred today?”

Me: “It’s not eleven hundred, it’s twenty-two.”

Students: “Huh?”

I just smile and keep walking around, letting them work on their warmup. If they were interested, they’d think about it and keep asking after the warmup. If not, they’d let it go. I wasn’t going to force it.

Eventually, a student raises her hand. This student is very tentative and doesn’t always believe in herself, but she’s almost always right. She’s also extremely sweet. “Are you sure it’s twenty-two? It’s not twenty-four?” she asks.

I look back at the board. “Oops. Yes. Thanks. It should be…”

“10110, I think,” my student finishes for me.

Right birthday

So, while I’m not thrilled that I can’t add 8 and 16 correctly, I was thrilled that a student figured out that it was binary, figured out I’d made a mistake, and had enough confidence in herself that she would point out my error.

Oh, and my younger brother is a computer scientist. Thus, binary.