Category Archives: Classroom Theory

Three Good Things (I’m an overachiever)

At the moment (as in, this week) three things are going really well in my classes. I considered writing about one of them, but I’m an overachiever so I’m going to write about all three.

Also, my masters degree is going fine. Being an overachiever helps with that too.

Problem Solving with In-N-Out

On Friday, the kids started the In-N-Out problem (see link for Robert Kaplinsky’s take) and we finished it yesterday. I love this problem. This year, I hung up my group-sized (2ft by 2ft) whiteboards at the beginning of the year, put the kids into random groups (different groups on the two different days actually) and told them to get cracking.

They did great. They discussed with each other (as much as freshmen who aren’t used to collaborating on things could be expected to), they wrote their ideas, some of them labeled their work really well, and some of them looked around the room from time to time to get ideas or see if they were on the right track.

Today, since they finished the problem yesterday, I used it as an example in each class to move into discussing slope/rate of change and the y-intercept in an equation. When I brought it up, the kids told me they really enjoyed working on it and requested more problems like that.

So now I have to find more problems that are good for vertical non-permanent surfaces, and preferably are related to standards that I actually have to cover in Algebra 1.

This is an amazing problem to have. I am so excited right now. I told the kids that I had a great time watching them solve the problem, and it’s true. I had so much fun. I definitely want to do stuff like this more often, and would be very into the idea of moving toward a much more problem-based curriculum.


Yesterday I also had my formal evaluation, during one of these Algebra 1 classes. My administrator sat in my room and listened to the kids solve this problem, which is not exactly an EEI-structured lesson format but I don’t care. It’s so much fun. And it’s so great to do for an evaluation where the biggest thing they are judging me on is student engagement because I probably had nearly 100% engagement, nearly 100% of the time.

The administrator told me a funny story afterward, and is planning to put this quote in the write-up of the formal evaluation. Apparently the group he was sitting nearest had a student who just kept insisting “It’s 90 cents. It’s 90 cents.” Another student in the group kept asking him how he knew. (!!!) He just kept insisting that it was just right and couldn’t explain his answer, and she finally told him, “You know that when she [meaning me] comes over here, she’s going to ask us! You have to be able to explain it!”

Woo hoo!

I nearly jumped for joy in front of my administrator when he told me that. This is amazing – we’re seven weeks in and some of them already know that being able to explain it is more important than the right answer (as least, it is to me).

This is a great sign, and I’m so excited about what this means for the rest of the year.

KenKen Puzzles

Clearly my theme for this blog post is about explaining reasoning, because this point is also going to touch on that.

So I do a bellwork routine, where we do the same type of bellwork question every week. Mondays are visual patterns, Tuesdays are estimation questions, Wednesdays are Which one doesn’t belong, Thursdays are a writing assignment because our school is doing a writing initiative this year, and Fridays are KenKen puzzles.

Mondays and Fridays are my favorite. I’ll probably swap out the estimation and WODB days for other things as the year goes on, but I usually keep the patterns for the entire year. This year I think I’ll keep the KenKen puzzle all year, because it’s going REALLY well.

I do this bellwork routine in Algebra 1 and Geometry, and since I had a handful of the Geometry kids in my Algebra 1 class last year, the Geometry class has been trained very quickly and very well. They can do harder patterns and are ready for harder KenKen puzzles than the Algebra 1.

The Algebra 1 kids are definitely picking it up, and getting the hang of how to fill in cells, what’s helpful and what’s not helpful, and how to think about the clues. We moved up from 3×3 to 4×4 a couple of weeks ago, and I bet they’ll be ready for 5×5 after fall break. (6×6 will be longer because moving up to an even number is harder than moving up to an odd number.) Every week, I make them do as much as they can on their own, and then we go over the puzzle as a class. I ask the class “What do we know now?” after each step and write down pretty much whatever they tell me. I spend a lot of time paraphrasing and restating what kids tell me, because I want to focus on the logic of the puzzle.

So the KenKen puzzles are going well, but some really cool things happened on Friday.

First, Algebra 1 – I had kids raising their hands and participating in the KenKen discussion who have NEVER raised their hands in my class before. They can tell me what goes in a cell and how they know. At this point, pretty much all I have to say is “Ok, how do you know?” the entire time. They are really getting into it.

Now Geometry is a whole different ballgame. On Friday, we’d been doing proofs for about a week. They’ve done examples of proofs, they’ve used to explore proofs in a structured environment, they’ve written reasons for proofs that have all the statements written, and they’ve attempted writing their own proofs.

On Friday, we went over the KenKen puzzle on the board, solved the whole thing, and I stopped them. “You guys. Everyone. Did you hear what you just did?” They all stare at me. “Did you hear what just happened as you solved that KenKen puzzle?” Now they’re really staring at me like I’m a crazy person. They’re probably sitting there like, yeah, we solved the puzzle, just like we do every week. So I said, “You just did a proof.”

Now they’re 100% positive I’m crazy.

I said, “For every cell in that puzzle, you made a claim, and you justified it. You told me what should go in that cell, and you told me why. That’s a proof. You just did a proof to solve the puzzle.”

Blew their minds. It was amazing. It took a solid few minutes to calm them down again, but the sudden realization of the connection between proofs (which they currently hate) and something that they are generally enjoying was totally worth it.

Also, I enjoy blowing the minds of high school students. It’s a major part of the reason why I teach.


Week 14 Update

So I haven’t exactly been sticking to my resolution to blog every week. Since I hate it when other bloggers spend time apologizing for not keeping their self-imposed schedule, I’m not going to spend time on that. Down to business. Continue reading

Identity Crisis

I just realized something about myself as a teacher. I wonder if this is something that a lot of teachers experience during their third year of teaching, as it seems like kind of an appropriate time.

I’m having an identity crisis.

I spent many years of my life assuming that classrooms were supposed to look like they do on TV – neat, orderly rows of students sitting quietly with their hands folded, waiting for me to impart my precious wisdom to them. (I assume TV is where I got that idea. Or maybe my own elementary experience – I’m sure not everyone in my class was that kind of student, but I was. And I didn’t care if anyone else was.)

When I became a teacher, I did the reading and learned that the sitting-quietly-in-rows thing isn’t really the current trend. And I thought, “Oh, that’s cool! If kids aren’t the sitting-quietly-in-rows type of kid, we can still teach them! We are learning how to reach kids on their level, instead of forcing them to conform to ours! What a fascinating shift in education!”

I’ve spent two years trying to learn how to become one of those teachers who embraces collaborative work, who encourages conversation in the classroom, who teaches in a way that all students can learn from.

But I kind of suck at it.

I think I’m still fighting a battle between how I think I should be teaching and how I want to default to teaching. Direct-instruction, sitting-quietly-in-rows teaching is what I’m most comfortable with, because it’s the only way I was ever taught. I have never seen a good model of any other form of instruction. Mentally, I embrace the idea that the best teaching uses many different approaches – direct instruction, collaborative work, independent practice, flipping, problem-based, project-based, blah blah blah – but I’ve never seen many of these in practice. I have the time this year to do projects, and do cool, in-depth lessons, and all kinds of collaborative activities, but when they fall apart (because they always do), I don’t know what to do.

Take today, for example.

This week, my students are doing a lesson from the Shell Centre. They started with a formative assessment which they took on Friday. We began the lesson with direct instruction yesterday (no school Monday due to inservice) and the students spent today working on a card matching activity in groups. The short version of the lesson is that the students need to find the equation of the lines given two points or the slope and one point to figure out which lines are the same. They have just spent two weeks on slope in their Algebra 1 class. Apparently, all they’ve taken away from those two weeks was “something about x1 and y1 and x2 and y2” and “rise over run”. It took us at least 10 minutes in each class to decide that a line must have a constant slope yesterday during “my” part of the lesson. Today, they seemed to have forgotten all of that. If another person tells me that they don’t “know how to do it”, I might lose my mind.

(My biggest issue with that statement, frankly, is that assumption that there must be one right way to “do it”, and since I didn’t show them that one right way, they can’t “do it”. My other big issue with that statement is that I DID SHOW THEM. Yesterday. I did an example on the board. We talked about slope, how a constant slope means the line is straight, how to calculate it, how graphing isn’t always the most accurate way to determine something, how to calculate the slope, and how to find the equation of a line.)

Continuing with my parenthetical train of thought above, this is a normal thing at my school – this severe lack of retention. It feels like no matter what we do, our students will not remember any of what we have taught them all year. I’m honestly not sure if it has something to do with our school culture, if there’s lead in our water or something else messing up their brains, if it’s related to a drill-and-kill style of teaching rather than a focus on true comprehension, or if I’m really just a shitty teacher.

Actually, you know what, I’m not done with this spiral-of-doom train of thought. Maybe I am a shitty teacher. Algebra makes so much sense to me! Of course variables can be used to represent unknown quantities! Of course you can manipulate them like numbers! Of course you can write an equation using numbers and variables to show the relationship between these two things! WHY DON’T MY STUDENTS “GET” THIS?! Why can’t I seem to explain this to them in a way that makes sense? I can’t get them to focus, I can’t get them to stop talking, and I can’t seem to explain anything. I can’t teach.

Ok, I’m going to try to finish my main point.

I spent most of my time today trying to help students figure out a strategy to get them started on the activity (most groups had barely started by the end of class, some had still not started at all). I tried to ask them questions to lead them through the thought process they needed to follow (which, by the way, is the EXACT SAME thought process we used yesterday during the example problem). They didn’t know the answers. I tried to come up with better questions. They still didn’t know the answers. I gave them instructions to think/talk to their group about something specific. As soon as I walked away, they were back to doing who-knows-what and insisting that they didn’t know “how to do it”.

I don’t know how to deal with this. I don’t know how to get them from where they are to where they need to be. I really don’t know how to do all of this three times a day without getting really sick of the process and nearly-yelling (or actually yelling) at my last class. (And yes, I realize that telling them they should know how to do something does not magically make them know how.) They want worksheets with clearly-defined instructions, not open-ended tasks that actually teach them something they need to know, because that’s what they’re used to. They don’t want to have to think, and I don’t know how to get them to think.

I want to teach them to work together (without being assholes to each other the whole time) and I want to teach them how to reason through something and I want to teach them to explain their reasoning. I want to be that kind of teacher. But I don’t think I know how.

A Series of Observations on High-Fives

At Twitter Math Camp this summer, Glenn Waddell (@gwaddellnvhs) talked about a few things he does in his classroom to help create the culture of positivity that he wants to foster, and one of the things that resonated with me was giving each student a high-five as they walk into class. He said that at first, the students thought it was pretty weird, but after a few weeks, they were waiting for him to come to the door so they could get their high-fives, and would ask for an extra high-five if they had been absent the day before.

I thought I would try high-fives this year. I do already greet my students at the door, and I am a high-five kind of person, so I figured this could work for me. Here’s what I’ve noticed:

At first, most of the kids gave me weird looks as they high-fived me. One refused to do it altogether (in a joking, not defiant manner). I allowed them to make that choice – if they don’t want to high-five me, that’s fine.

After a few days or maybe the first week or two, everyone expected a high-five as they entered the room. I started to see them put their hands up in anticipation, instead of responding to my hand being up. (And that one kid started giving me very half-hearted high-fives.)

After a couple of weeks, some of the classes have lined up outside the door and waited for me to come greet them. This doesn’t happen often – I don’t usually have anything I need to do during the passing period.

One student (again jokingly) refused to give me a high-five because I “scared him” by not being at the door when he expected (I was in the bathroom). He informed me I was grounded. I asked him what I was grounded from and he said I was grounded from teaching that day. I told him that was ok because he was taking a quiz. He tried to change his mind and insist that I was grounded from giving quizzes, but I told him it was too late – he’d already chosen my punishment. (Freshmen are hilarious.)

Occasionally, someone will still get by without a high-five (usually because they weren’t paying attention) and I’ll make a pouty face. Someone else in the hallway (not one of my students) will usually come over and give me a high-five to make up for the one the first kid didn’t give. This is always funny.

Most of the time, the high-fives give me a chance to gauge the moods of each student in a split-second. (Glenn pointed this out too.) I can tell by the tone of their high-five, the way they return my verbal greeting, and their body language if something is “off” that day.

Most of the time, the high-five garners a smile from most of the students. The act of doing the high-five seems to elicit a smile, almost subconsciously.

Most of the time, the high-five has that effect on me, as well. I have to smile, which improves my mood (if it needs to be improved), and means that the first thing my students get from me each day is a smile, or at least an action with a very positive connotation. It’s good for me. And it’s good for my kids.

But are we learning?

A couple of days ago, one of my students asked me if I was going to stay up that night to see Mars. It was news to me that Mars was doing anything special, but I didn’t ask him to clarify. I just explained that no, I was not going to stay up late to see anything. I was going to get some sleep, because “I am a much nicer person when I’ve had a decent amount of sleep. Trust me, you want me to get some sleep.” Another student asked me if that’s why I’ve been so nice to them lately. Continue reading

Crazy-Busy, and One Good Thing

So have I mentioned I have a new job? I mean, like a second job. I didn’t change schools. I am still teaching at the same school, which lost its grant coordinator last year. We are receiving a grant for before- and after-school activities worth over a million dollars over 5 years, and this is the second year. The guy who was coordinating the grant last year is still in our district, but moved to another school. Anyway, I’m basically going to be in charge of overseeing our before- and after-school tutoring and enrichment programs. Our teachers have some cool ideas for things they want to do for enrichment, and many of them have stepped up to do tutoring a few hours a week, so I’ve got the schedule nicely filled out. It’s all coming together, but it’s been a lot of work. Continue reading

Link: What Students Really Need to Hear

Yesterday, a colleague of mine linked to this post on Facebook:

What Students Really Need to Hear by Chase Mielke at AffectiveLiving

If you haven’t already seen this, go read it. Right now. It’s ok – I’ll wait.

My first response: It’s like Chase Mielke works at my school!

This is exactly what has been causing me the most frustration lately – my students don’t persevere through hardship of any kind. I hear “I don’t get it”, “I can’t do this”, and “This is too hard” more times than I can even count every day, and I’m a math teacher. I can count pretty high. I was having a really hard time expressing in words why I’ve been so frustrated. I couldn’t explain why it drives me crazy to have to repeat instructions 56 times, or why I can’t stand hearing “I don’t get it.” Then I saw this post from Chase and I was floored. This is EXACTLY what’s going on in my classes.

This morning, my first period started asking me why I’ve been so frustrated lately. They’ve asked me this before, but as I mentioned earlier, I couldn’t really put it into words. I explained this to them, and said that another teacher passed along this post to me yesterday that explains it perfectly. I asked if I could read the post to them. I managed to make it to the last few paragraphs before I started to tear up, which I think is pretty good.

I’ve never seen them pay such close attention to anything I’ve ever said. Every eye in the room was on me, and every student’s body language said they were listening. I was interrupted in the middle of the post by an announcement over the intercom, and they asked me to finish reading before we left the room to respond to the announcement.

When I finished reading, the whole class applauded.

I don’t know if this will make any lasting difference in their attitudes about my class or their other classes, or high school in general. It will give me something to go back to with them:

Man up. Woman up. No more excuses. No more justifications. No blaming. No quitting. … Let’s do this.

We have 11 days of school left until final exams. Let’s do this.