For those who are interested.
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For those who are interested.
If Scribd doesn’t work for you:
Except for Topology. That was all me…and the student presenter who taught for the first half of the class. But other than that, it was all me.
So here’s what I did today.
Got to work, had a free block first thing. Parent association was doing a breakfast thing for the faculty, so I went up and got myself a plate. Came back to my office and played the daily Set game from nytimes while I ate. Did a little work on my presentation for CMC South and in doing so went through my Evernote files. I found a rather well-populated tag for Coordinate Geo, which is my current unit so I opened it up and out fell my lesson plan for the day.
I start the class off with a warm-up (okay, this I wrote). Have a student put up a solution for each problem. Thumbs up/thumbs down for “do you agree/disagree” and we discuss the documentation of work.
Then I throw up this image:
The grid lines aren’t visible enough on the projector screen so I walk the kids through how to get to the dailydesmos page. [daily desmos, not just desmos] They stare blankly at it for a few moments before I tell them they need to reconstruct the graph on desmos before they can proceed. Students get themselves some parallel lines. I interject to show them that desmos will give you the coordinates for points of intersection and remind them that they need to make sure the side lengths are the same. Many “ahas” about how points with the same distance from the origin will have reversed coordinates (when lines are perpendicular).
Then we proceed to the Best Square video. We watch it twice because students didn’t realize what was going on the first time–totally expected. Much discussion ensues about whether Timon pronounces his name TEE-mon or TIH-mon. Consensus is that he has the best name. We discuss what information would be helpful in deciding who drew the best square. Coordinates, lengths and angles are all mentioned in both classes. I give them the coordinates and the angles. I ask the class if they really need the lengths after I’ve given them the coordinates and they agree that they don’t need them. Students start calculating distances. In my second time around, I assign each group one square to speed things along. Much better flow that way.
While the conversation about what made a square better than the rest didn’t really go anywhere deep, I was happy with the class. The combination of activities allowed students to apply some of the skills they’d been working on with distance formula and parallel and perpendicular lines, and it drove home the idea that coordinates are actually really handy things to think about and use to help them solve problems.
Since I just did all of this on the fly, I didn’t think to add in the Squareness activity! Maybe next year.
I’ve been thinking about assessments a lot in my Topology class this trimester. For the first few problem sets, I just copied the ones the previous teacher created…and they were a b**** to grade. They took me ages, and most of the questions we’d already gone over in class. Probably the worst part about grade these problem sets was that I didn’t care that much about the questions, and therefore I didn’t enjoy reading over students’ answers at all. I wasn’t learning enough about their thought process to keep me interested.
I came to my senses and revised the third problem set to just ask the questions that I thought were good ones–ones the students hadn’t already seen, that pushed them to think about new ideas, or about applying old ideas in new ways.
When it came time to do their last problem set, I realized I didn’t really have many good questions to ask students. The content of the chapters we’d gone over wasn’t as meaty as previous sections in the text. I didn’t want to ask the same numeric questions and just substitute different numbers into the problems. Not my style. So, I asked myself what I wanted the students to get out of the material.
And this was it:
I just finished grading their papers. And it was a breeze to read through them. I enjoyed myself. I enjoyed myself! I know: I can’t believe it myself.
You can’t hide in a problem like this; you can’t BS your way through; you can’t check your answer in the back of the book. And that’s what made it so enjoyable: I had hand-drawn diagrams that were beautiful, I had students describe spaces from a “Euclidean-eye view,” I had pictures of Pringles potato chips. My students explained their understanding of the material, in ways that were uniquely theirs.
change evolution I have gone through from the start of my career as a teacher up to now is with the use of student self-reflection. Giving time for it, and giving weight to it.
In “Teacher School” (as I like to refer to my certification program) we were told on many occasions about the value of reflection. I don’t really remember what people said, in what context they said it, or with what strategies they suggested using reflective tasks. Because I didn’t buy into the whole idea. Or rather, I agreed that it was good, but I didn’t see how to make it effective or useful to my teaching. After all, I needed to cover x amount of material in y amount of time (where x>y for all x and y). Who had the time? And, having students write about their work and their thinking meant that I then had to read it all. Who had the energy? I was resistant.
But I did it a bit. And sometimes it was really hard. When I asked students for feedback on my teaching, sometimes they wrote things that hurt. That made me confront weaknesses in my teaching that I didn’t want to acknowledge. But it was worth it. I got better. Both at teaching and in confronting my own challenges.
When people suggested that I ask students to comment on their own work and thinking, I was also resistant. I assumed that students would be dishonest, that they would see themselves through distorted lenses and only notice and comment on the good things, ignoring all the rest. But I was wrong. Students are sometimes incorrect in their self-assessments; sometimes they think things are fine when they aren’t, but more often they think things are going poorly when they are fine–or better than fine. The vast majority of the time, however, students know themselves really well–and they are willing to share to people who are willing to listen. They will tell you so much about themselves, with depth and complexity.
For the past four years I have written narrative comments for students three times a year. This is a major task, which requires me to know and speak to each of my students on an individual level. I comment on their work, their participation in class, their strengths and their challenges. I give each of them feedback on how they can grow as mathematical thinkers and as students in the classroom community. I have become more and more reliant on student reflections to help me with this task. Not because I want to get out of doing the work–but because the students’ reflections about what they need to work on are so insightful that without them, I would be groping in the dark, trying to make out the shapes of the objects around me. Student reflections are like flipping on the light switch.
So last year I tried out the mistake game, and it kinda bombed.
This year I am trying it out again…on the exact same material.
But wait, Bree–didn’t you say last year that these problems weren’t great for making good, rich, intentional mistakes? Why, yes; I did. Now, I’m not exactly sure *where* I said that, but I’m sure that I did.
Mistake Game, version 2.0 is already going better than last year. Same course, same unit, same material. What’s different? Well, mostly just the way I set things up and introduced the idea, but also the format to some extent. Last year I got the idea to do the mistake game on this packet of problems when most students had finished (or nearly finished) the work. This time around we’re doing presentations in several rounds as we go. The added bonus is that while students are waiting for other groups to finish writing up their solutions on the whiteboard, they have something to work on!
Several of my students wrote on their midterm self-reflections that the Mistake Game was one of the most helpful and/or most enjoyable aspects of the class. Now, that may be due in part to being one of the more recent things we’ve done in class, but I still count this as a success.
One more small share: Earlier in the year I used the red/yellow/green cups. For ONE day. ONE activity. And I still have kids in one of my classes who will draw a red or green cup on the whiteboard when they want to get my attention. I chastise them when they draw the red cup with green markers, and vice versa. But they have convinced me that this, too, was a good idea.
The cups are now living full-time in the classroom.
This is possibly my favorite meme on the interwebs these days. Nothing else expresses the sheer bewilderment, confounded-ness and exasperation that sometimes plagues our day-to-day life as teachers, working with people whose frontal lobes are not yet fully formed.
Take today, for instance.
The curtain rises on a math classroom, bustling energetically with fresh-faced junior and senior students. The happy children begin to work at their whiteboards, thinking industriously about intriguing topological problems involving the product of two surfaces.
The camera pulls in to our protagonist, crouched over her school-issued laptop. She clicks away for a moment, recording the attendance for the day–all present and on time.
Then, behind her, over-enthusiastic laughter abounds. The teacher arises, then turns around to see Student 1 holding up his shirt to partially expose his chest as Student 2 looks on, with Students 3 & 4 observing from the background.
Our teacher’s jaw drops to the floor.
T: I don’t even want to ask…
S1 (with an enthusiastic grin): S2 pinched my nipple!
I used to get super nervous at the start of every school year. Anxiety dreams leading up to the first day, the whole works…but it kind of stopped several years ago. I think the thing that made me the most nervous about starting the school year was not knowing what vision I had for the year, the unit, the first week, the first day…the first hour. Then as I learned more about myself and the kind of teacher I like to be–and keep striving to become, year after year–the nervousness subsided. I know that the lesson I do on the first day doesn’t need to be perfect–in fact it will most certainly not be perfect–and that I will still be able to have a successful day. I learned that bringing my whole self to class on day one and being warm and welcoming and starting the incredibly amazing task of building relationships with my students is the MOST IMPORTANT THING I can do.
But I have to admit something to all of you: I am super nervous about starting teaching this year.
This is actually the first time EVER in my career that I am starting up at the same school for the second year in a row (technically, I did return to a school once before, but I’d only taught there for half the previous year…so I wasn’t there at the start of the school year). I know some of you think that I’m a big-time-awesome teacher, like the rest of the MTBoS gang, but I’m really just a fraud. At least that is what I think when I take a peek at my much-submitted resumé.
But that’s not actually the reason I’m feeling nervous. Nor is it even the fact that I’m taking on the role of “Discipline Team Coordinator” (translation: department head). Nope. It’s the fact that I’m teaching a new course, our math elective, Topology.
Which is really strange to me. I mean, I’ve taught roughly 15 bajillion new courses over the past 7 years I’ve been a math teacher. Last year I was writing a new course, basically from scratch.
I have all of the notes and files from the previous Topology teacher, so it’s not like I’m having to do that again. But there’s just something about this Topology course that is freaking me out. I think the biggest thing is I don’t have a strong grasp on what I want students to get out of the course. I don’t know where exactly I’m taking them. This is scary.
However, reading back on my previous words, I can see that it’s going to be okay. I know what the students will do on the first day. I know what I will do on the first day: the MOST IMPORTANT THING. And if I haven’t figured out yet what we’re doing in week two, it’ll happen. I’ll probably be spending a bit more time on the weekends planning than most years, and I’ll likely be throwing more questions and pleas for help out on twitter. But in the end, I’ll get to the end of the course having survived and hopefully having had a really successful course.
But I’m still frikin’ nervous.
Bonus Post–My Favorite Anxiety Dream.
I had this dream when I was a student teacher, the night before my first observation:
I was standing in front of the classroom, doing my normal thing at the overhead. In the back of the classroom, there is a long line of probably about 10 different observers. They are dressed formally in black suits, holding clipboards or other writing surfaces. The door to the classroom opens and a student walks up to me with a late slip that I need to sign. I sign the slip. Then another student enters the door…with something that needed to be signed. Soon, there is a constant stream of students coming in, all with papers that need my signature on them. The black-suits in the back of the classroom scribble down on their notepads as I scrawl my name on slip after slip after slip…
Of course, my actual observation was nothing like my dream. I had the nicest, most down-to-earth woman ever as my observer. She was great.