Will be giving a talk next month–need to know: How did your math courses/major prepare you for teaching? NB: Math specific, not Ed courses.—

Breedeen Murray (@btwnthenumbers) February 14, 2014

You see, I was asked to be the high school teacher-speaker at an MSRI workshop.

The 2014 CIME workshop will focus on the role played by mathematics departments in preparing future teachers. As part of this focus, the workshop will consider two broad questions: What mathematics should teachers know, and how should they come to know this mathematics?

Harvey Mudd professor, creator of morning problem sets at PCMI, and all-around awesome person, Darryl, asked me to think about the following questions,

“Do you have any thoughts on the connection between the mathematical preparation that you had in college and the mathematical skills and knowledge that you need now as a teacher? In what ways were you prepared well, and in what ways not? What could we do better?”

and I was intrigued enough by these questions to say “yes” and commit to giving a little presentation.

I’ve been thinking over the past couple of weeks about the “lessons” I learned in my college math classes and how they impacted me in my work as a math teacher. So far I’ve come up with this list of things I learned:

- I don’t hate math.
- Math is supposed to make sense–even when math doesn’t make sense,
*it makes sense*. - Seemingly different ideas in math are connected, often strongly & deeply.

Which I will flesh out more fully when I write my talky-thing, of course.

So what I need from you is your answer(s) to the question:

**How did your math courses/major prepare you for teaching?**

Comment here, send me a DM (or a regularM) on twitter, email me using the comment form below, hire a sky-writer, send off a carrier pigeon, whatever. Just get me the goods (pretty please).

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Dan’s question reminded me of this moment when I was at Palm Springs in November. I was at a workshop—the first workshop in fact—in which the presenter came from the Phillips Exeter Academy. If you don’t already know, Exeter is a private boarding school. Small class sizes, privileged population…perhaps you’ve heard of it? The presenter introduced himself and his school at the beginning of the talk, so I assumed we were all on board. He spoke about how the classes worked at Exeter—the Harkness table mythos—and how the curriculum developed over students’ time at the school. At some point during the talk, the presenter showed us a blog from a teacher in a typical public school situation who was using the Exeter problem sets in his classroom: *Harkness for Thirty*. Shortly after this very part of the talk, a woman seated at one of the back tables asked our presenter about his classroom setting. He told her the information I outlined above. Said he had classes of about 14 students. She immediately replied

“We can’t talk”

and followed it up with

“You’ve just lost all credibility.”

I remember writing down on my paper “Wow!” I couldn’t believe the rudeness. More importantly I couldn’t believe that her attitude towards his classroom situation—which was very unfamiliar to her own—meant that she shut out all possible benefit of the ideas being discussed because her idea of a classroom didn’t match up to the classroom situation at Exeter.

Every classroom situation is different. At the same school, even moving from one section of the same course to another section of that course—taught by the same teacher, no less—can require different approaches. Obviously, not everything we hear about in a conference, even in an individual workshop, will work for us without adaptation—whether it’s to better suit our student body, to better suit our teaching style, or to reduce cost, or de-technify something, we make changes to things we learn about all the time. I can’t remember the last time I took something someone handed me, and handed them to students unchanged. So of course we are not going to find the perfect match for our needs at a workshop at a conference, no matter how well we select our speakers. It just doesn’t exist. We have to take what we can use, discard or postpone the rest, and make new ideas work together with our old ones in the environment we have.

But to dismiss everything a teacher says because they teach at a different type of school that you?—Wow.

Avery had a great answer for Dan’s question. Avery talked about how he sees the professional role of teachers as one where their job at a conference is to find the parts that work for them, with their students. I liked Avery’s response. And this is something I think about, as I too teach at a private school. Students who attend my classes are mostly there because their parents can pay the 37,000 dollars a year it costs to go there. My classes this trimester are 10, 10 and 13 students. Last trimester I had a “large” class of 18…teaching Topology to juniors and seniors. I know that I have it good.

Just because it was on my mind, I decided to track the types of comments regarding “my school” versus “your school” that I heard at Asilomar last weekend. I was surprised—and happy—that I didn’t hear that many. Both of these came out of the first workshop I attended:

8:14 am: “teaching at a demographic such as mine…75% free and reduced lunch…”

8:44 am: “for those of us teaching at school’s where students are mostly far below basic…”

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For those who are interested.

If Scribd doesn’t work for you:

Telling Stories Teaching Math CMC South 2013

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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.

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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.

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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.

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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.

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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.

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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!

…#childplease

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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.

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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.

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So, I know I was supposed to fall head-over-heels for the whole un-conference ed camp ju-ju, but I must confess that I came away from the experience feeling a little meh.

However, for full context, I should probably make crystal clear the fact that I’ve been feeling this way more and more about pretty much every conference I’ve been to over the past several years. When I first started out teaching–lo, so many years ago–I loved going to conferences. I found them exciting and energizing and inspiring and awesomely wonderful. But lately, I think the whole thing is just getting a little old–a tiny bit stale. I still enjoy attending conferences, but the big draw for me now is reconnecting with former colleagues and going to tweet-ups. Oh, and giving the occasional talk myself–that is certainly exciting…in a “I want to puke all over my fancy teacher shoes” kind of way.

I joked with Avery on the drive down that I had low expectations, so I wouldn’t be disappointed if things weren’t great, but I think I lied. I guess I had a deep-down secret wish that the edcamp model would knock my socks off for being so cutting-edge and grass-roots and innovative and I don’t know what else… and I didn’t find my experience to be all that different from an ** un-**un-conference (a.k.a. a normal conference).

From my exhaustive one-day experience I’ve concluded that edcamp is basically a good forum for talking with other teachers about interesting ideas that you want to ** start** exploring. If you want to talk about something you’ve been thinking about for a while, you will very possibly be the most experienced/opinionated/knowledgeable person in the room about that topic. I don’t know if there are some topics that might be more “edcamp friendly” than others…but the conversations I participated in seemed more like we were developing a list of online resources than hashing out a big idea. In some conversations I feel that was intentional, in others it seemed more like the underlying culture of people wanting to share “here’s something I did in my classroom” bubbling to the forefront. Not that sharing isn’t a great and meaningful activity, but sometimes it can come across as sounding overly dogmatic. “I did it this way, and so should you.” And, y’know, sometimes your cool idea just doesn’t do it for me.

Also, another layer to the edcamp being so tech-focused and virtually everyone being on twitter was that in every session I went to between 80 and 90% of the attendees were on some sort of device. And while I know that tweeps were likely just tweeting out the conversation, or were scoping for a different conversation that better suited their needs, I found it irritating. I think that the format of edcamp is actually one that doesn’t work for simultaneous tweet streams. Since the purpose of the sessions is to join into a conversation with other educators, your presence in the room should ideally be an active one. If you are listening to a speaker give her speech and are tweeting out the best bits, that is very different from trying to do the same *and* also participate in a conversation with the other people in the room. In this context it doesn’t work so well…

Upshot: I certainly don’t feel like I wasted my time by going to edcamp, and I’m glad I got to see what the fuss was all about. Though I do feel that with maybe a bit more structure I could get more out of the experience. Maybe have the session board online for the week leading up to the un-conference, and then people would have a bit more time to think about things before discussing them. That could also lead to developing those lists of resources ahead of time, and then you could do something with them the day-of in order to deepen the discussion.

So, would I go to another edcamp? Maybe. But probably the reason I would go is because there were other people going that I wanted to connect or re-connect with and/or it was taking place closer to home.

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