Would You Attend This Sesion?

I’ve jumped through the yearly flaming-hoops-of-internet-peril that are the NCTM, and CMC websites to submit speaker proposals for two different talks. Luckily, tweeting has built up my editing-out-extraneous-characters muscles (but seriously, CMC-South: only 250 measly characters for a whole session description? I guess it’s 110 more than I should really need…)

NCTM:

Further Beyond Sudoku: Using Logic Puzzles to Develop Mathematical Reasoning

Logic puzzles are an engaging and accessible way to introduce students to deductive reasoning. Participants will break down the process of proof-writing, connect the rules of logic puzzles to axiomatic proof systems, make conjectures, write “because statements” & develop their ideas into simple proofs, modeling how to use these ideas with students.

As you might infer from the title, this one is a repeat/extension of the talk I gave two years ago in Philly.

CMC-North:

Telling Stories, Teaching Math

People love hearing stories. Harness elements of writing and the power of storytelling to engage students with mathematics. Who are the characters? What is the plot? How will the story end? Learn ways to design courses, units and individual lessons around the framework of narrative.

Gonna try again on this one–even though nobody seemed to care for it last year. I’ve tightened up the description. Perhaps this year the time will be right for this talk to make its debut. We’ll see.

CMC-South:

Telling Stories, Teaching Math

People love hearing stories. Harness elements of writing and the power of storytelling to engage students. Who are the characters? What is the plot? How will the story end? Learn to design courses, units and lessons around the framework of narrative.

That’s 250 characters on the nose!

I Had Nothing To Do

Monday was my first day back from Spring break. It’s always rough getting back into the swing of things after being away from school for a week–and due to Intersession the week before, I hadn’t seen my students for two full weeks.

Luckily, we had wrapped up our previous unit and we were starting fresh rather than trying to pick up from where we’d left off. Our unit on quadratics starts off with a boot-camp of sorts with a bunch of practice on algebraic skills such as simplifying, expanding and factoring. I told my students that some of them would love it, and some of them would HATE it, but that we were practicing and making sure we all had these skills down before we applied them to super-cool problems involving projectile motion, since everyone likes throwing things[1]. [One student immediately perked up and asked: "Do we get to throw stuff?"]

I start off by asking them the question:

What does “equal” mean?

We discuss various ideas about “the same,” “exactly the same,” “the same value,” etc. I ask them “How do they know that 2 + 3 = 5?” and then continue on to asking “Why does 2x + 3x = 5x?” We talk about how every value they substitute in for x will give them the same result on both sides of the equation. We describe what we would see in the graphs of both sides of the equation if we were to plot both on the same set of axes, or what we would see in the tables of both expressions.

Anyways, then I tell them that this “Investigation” is not a normal one. In fact, it is so different that I have renamed it “Algebra Skills Check” since they will not be investigating anything. They will be practicing their simplifying skills. And then I drop the big bomb on them…

Oh, yeah. And I’m not going to check your work for you.

I am giving them, literally pages upon pages of practice problems and not checking their work. Say what?!?

“Yep. You need to check your own work.” [Pause.] “How are you going to do that?”

At this point I hear the faint beeping of a car alarm off in the distance. This is the urban version of cricket chirping.

“What technology could you use to help you check?” I ask.

Light bulbs go off.

“We could graph them on our calculators!”

I smile and nod, and remind the little ones that have left their TI-84’s at home today about Desmos graphing calculator [2]. They get to work.

And then, for the next 50 minutes, I have nothing left to do.

 

 


[1] Not my favorite strategy for teaching, well, anything…but we’re planning on rewriting this class over the summer and I’m not going to change it all up this trimester. All you über-awesome people can just bite me. Okay?

[2] My students love Desmos. I had to coax some of them away from checking out the Desmos art. Repeatedly.

 

 

Collaboration Versus Autonomy

It’s been a long time since I’ve posted on this here blog…I feel like I’ve been reading that phrase a lot lately. What is it about the winter that makes us all burrow into our respective holes and hide for a few months? In my particular case, I think a lot of it had to do with being the only teacher at my school teaching a newly modified course. Our team has been re-writing the math 2 curriculum this year, and the first trimester was a great example of productive collaboration. It felt great. The second trimester, I was flying solo. And it wasn’t so great.

Not that I feel like I did a horrible job with the course. But, I didn’t do as well as I could have with the support of my team. I was less organized, less creative, and less on top of things in terms of assessing where my students were and what I should do next to help guide their learning. It was one big, trimester-long account for the Productive Struggle blog.

I did some awesome things that I’m really proud of. The transformations project was a blast, and the Mini-Feltron project went over really well. We did some fun explorations of collecting and analyzing data and looked at various ranked choice voting schemes.

But overall…the course was kind of blah. I did a lot of the same style of teaching. I didn’t branch out as much as I would have liked. I didn’t differentiate as much as I would like to. I didn’t give students a good balance of individual work time and group work time. I was doing the “one step ahead” thing way too often. It was hard to keep the big picture in mind.

It was just plain hard.

Collaboration is essential to my role as an educator. I am a far better teacher to my students when I work together with my colleagues to plan, to assess and to debrief. I really missed that last trimester.

And it’s not that I didn’t meet together with my fellow teachers. We did. My team rallied around me to do what they could to help me out. But I was the one forging the way, and it was up to me to say what I needed; which necessitated me knowing what I needed ahead of time–not always an easy task to accomplish.

I really wish I was teaching this class again this trimester, so that I could fix all of my mistakes. I am eager to teach it again next year in order to let my perfectionist brain relax a little. (though of course I will just make new mistakes…sigh)

This trimester I am teaching new [to me] courses, and I have a new team to work with. It is so nice to meet with them each week and discuss what we have been doing and what we have coming up in the near future. I really value this time.

But…

I’ve found that I also value my autonomy as a teacher. I enjoy finding new ideas and trying them out. Especially when they involve giving students a challenging task to do, or giving them an opportunity for more individual practice on a skill. These are things that I like bringing to the table. Sometimes they aren’t received as warmly as I might like. This is okay. At the beginning of the year, I requested that one of our team norms be “saying yes” when someone decides to try something out in their classroom. I’ve found that some of my colleagues are more comfortable with this than others–and honestly, my perceptions of their comfort levels may be inaccurate as they are almost certainly clouded by my own baggage.

When I was working by myself on the course last trimester, asking others about trying something new wasn’t something I did. I just went ahead and did whatever I wanted to try out. I’m still doing that to a certain extent, but I do try to share what I did–in real-time–with my team so that they can use the ideas if they want to. It’s an interesting balancing act, considering both the innovative things I want to try out and the needs of supporting my team and allowing them to support me. I think it’s difficult to strike the right note, and in the fall my team somehow managed to do this almost effortlessly. It’s taking a bit more effort from me to meld together with my new team. But it’s far less effort than the going-alone thing I was doing last trimester.

And for that, I am truly grateful.

Mini Feltron Project

I can’t remember who recently posted a link to Dan Meyer’s Mini Feltron post from ancient legend and lore, but THANK YOU, whomever you are. The reminder came at exactly the time I was thinking about ways to wrap up the data summary “unit” we almost didn’t have time for. [the pacing this trimester...it didn't go so well...]

But then, there it was. We had a four-day weekend ahead of us and I decided to just go for it. I threw together this description,

and students collected their data over President’s Day weekend.

When we got back the next week, every single student had done the assignment–including the student who had been absent the Friday before. Totally a-MAY-zing!

I showed them around infogr.am and let them loose to find some visual displays that were interesting and that told the story of their data clearly and in a compelling way. They delivered.

IMG_1638

Most students took screenshots of their infographics and printed them out. Many are displayed on the bulletin board outside our classroom. Some made posters; others published them to infogr.am and sent me the links.

IMG_1635One girl brought us a cake and used sprinkles to mark out the segments of her pie chart. And one girl asked me if “it would be okay” if she created a blog.

Umm. Let me think about that one for a second… Heck Yeah!

All The Things: Made 4 Math

Holy hypotenuse, Batman! It’s been a while since I posted anything.

made4math_small

So, in one fell swoop…here are some of the things I’ve created for my classes over the past few weeks.

  1. Strengths Inventory–The math strengths side of this document came to me via my former colleague and still current friend, Nicole. I made the group-work strengths side as an add-on. I gave this to students to do during the first week of school and I plan on revisiting it at least one more time this trimester.
  2. Transformations Project–Adapted from a project done at High Tech High. I saw a presentation at Asilomar that got me all inspired to do this with my kids.
  3. Trig Warm-Up Problems–I put these problems up around my classroom for students to practice on; I stuck post-its with the answers on the back, so they could check their work. Then I gave each student an index card and had them record how many they were able to solve correctly without help, and with help.

 

For some reason scribid is turning my two page document for the strengths inventory into four pages. Grrr. Here is an editable version in Word.

A Day In The Life

The fact that I took my Day-In-The-Life notes on Monday, and it is now Wednesday as I sit down to type them up, should tell you something about my schedule. [Update: and not posted till Thursday...more evidence supporting my theory.]

As for many teachers people, the alarm clock goes off far too early on Monday morning. I lie in bed for several minutes listening to NPR until my internal clock and my bladder tell me I’d better get up pronto. My morning routine is about as bare-bones as it gets. I make tea, clean out the cat’s litter box, brush my teeth, put in my contacts and get dressed. No breakfast until I get to work; Monday is a “bagel day” at my school.

I head out the door maybe a few minutes 7:00. Hopefully, not too much later, or I might miss my bus. I climb up over the hill and down to Haight & Masonic. Three buses pass through the intersection as I approach my stop and each sets my heart racing, but none are mine. Three minutes until the next MUNI. I made it.

I get a seat in the back of the bus. Today it’s not crowded at all. Where are all of the students? Then I remember: it’s Veteran’s day. Public schools are closed. I feel a moment of annoyance that I have to go to work, and some frustration that private schools don’t seem to feel that recognizing Veteran’s Day is important. I wonder if it will be mentioned at all throughout the day.

At the next stop a student from my school gets on and sits down next to me. She proceeds to chat with me for the duration of the ride. Part of me is happy to converse. Part of me wishes I could zone out and relax for just a few more minutes before putting on my teacher hat. I don’t teach, and actually have never taught, F, but we know each other fairly well from various connections, including our shared bus route. F also happens to be one of those students that everyone in the school knows.

The walk from the bus stop to school is glorious. It’s chilly outside, but the sun is shining and the grass and trees in the Presidio are green and sparkling with dew. Framed between two buildings is one of the orange towers of the Golden Gate Bridge. I am damn lucky to work here every day.

I let myself into my office and glance up at the clock. 7:50. I plug in my laptop and then change out of my sneakers and into one of the three pairs of shoes lined up against the bookcase behind my desk. I go back downstairs and grab a bagel, then come back and check my email. One of the other Math 2 teachers asked me about a review activity I did last week. I quickly grab my notes and type them up to send to her. By now it’s 8:08 and I need to head down to Morning Meeting. As I head out the door, I hear the gong. I’m late, so I turn around and head the other way so I can sneak in the back.

A teacher and a freshman student are giving a presentation on beekeeping. Both of them are dressed in their bee suits and they have brought an assortment of tools to show what beekeeping entails. It’s pretty awesome, but I wonder about the choice  to not talk about Veteran’s day.

We sit in meditation for a few minutes, something we do every day at Morning Meeting. Then students and faculty give announcements before we are dismissed to classes at 8:30—on time for once.

I don’t teach first block on Mondays, so I grab a cup of tea from the coffee station before I head upstairs. Once there, I finish reading a ThinkThankThunk post I’d opened earlier as I sip my tea.

By 8:40 the problem sets to be graded are calling me. I pull out the stack of papers from my bag. I took them home over the weekend but, as is my MO, I didn’t touch them. I have good intentions about doing work at home, but I never follow through unless it’s really crunch time.

I grade for a while, make some copies, get some more tea. As I’m heading back to my office with my copies, I notice a typo. Too late to fix it now. By 9:45 I’m done grading my stack of reassessments and late work. Class starts in 10 minutes. I don’t have time now to attack the problem sets, so instead I send an email to the parents of one of my advisees in response to a question they’d asked me. Then I write another to a group of students who owe me an assignment to remind them that they have to get it done before the end of the week.

At 9:55 I head to class. The room is freezing, so I give instructions to one of the students about how to turn on the heat. Then I head back to my office to put up my second NaNoWriMo sticker on my progress chart. I passed it in the hallway and remembered I’d gotten past the 20% mile-marker.

We have two visitors to class—one from @cheesemonkeysf’s school, though not her class. Having visitors is not unusual—this year our admissions staff has told us repeatedly that we have over 600 8th graders signed up for visits. I’ve actually been a little surprised at how few visitors I’ve had in my classes so far this year. I welcome them and give my little visitor spiel, then start class.

We work our way through the agenda.

0-Meditation

1-Check ToC

2-Practice Quiz

Grade or No Grade

3-Work on Review project

I gave the students an assignment to write the “Table of Contents” for their math binders yesterday, which they were supposed to finish for homework last night. Most have done it, and I hope it helps them to review the concepts for our final test at the end of the week. We do a short practice quiz, which I have them decide whether or not I should grade it. I did this for the first time last Friday, and the results were great. Most students asked me to grade their work. This time, I can tell from the looks on their faces and the length of time students are taking that the results will be different. Oh well. Sure enough, when I look over them, every student has asked for “no grade.” Well, that tells me what I need to review during tomorrow’s class.

The rest of class is spent on their review projects. I took a page out of SomeBloggerICan’tRemember’s notebook and assigned a very open-ended project for my kids. [I mean, seriously, this person really inspired me & I canNOT find the post in my Evernote] They were asked to create some type of review activity (those were, quite literally, the instructions. I kid you not). Most are doing games or some type of flashcard-style activity. I circulate around the room to see which groups need supplies or help. I grab a hole-punch, a glue stick and some index cards, but that’s about the extent of my involvement. The students are on a roll.

At 11:25 class is over and I remind students of our quiz tomorrow. They ask me to open another assignment on our online site so they can practice, so I quickly do that.

It’s lunchtime! We get fed here, which is one of my favorite perks. Today’s menu is mac ‘n cheese, which is kinda meh. I go to the salad bar so I don’t have to wait in line. I sit down with a table of teachers and have a very pleasant time. One of the norms of lunch at my school is that we don’t (usually) talk about work.

Monday is a clubs/lunch day, and I don’t sponsor any clubs this year. So, I have a nice long, relaxing lunch. At 12:15 I head up to my office again and print out the stories from my Wednesday writing group, then look at old versions of Math 3 tests so I can start to piece together one for my students.

I head to my next class at 12:37, which is not in the same classroom as my class this morning. All 16 of us are kind of crammed in to a small room. During class, two of my groups work outside in the hall on mini-whiteboards. The rest of the class does their Investigation inside. We’re starting a new Investigation today, so we go over the homework and then I pass out the new packet. I roam around the room and answer questions when students “page” me at assigned checkpoints throughout the packet.

At 2:00 class is over. I head back to my office, drop off my materials for class, pick up my stack of problem sets and make a U-turn back out the door to go to my Flex room. Each week every teacher monitors a “Flex” (most schools would call this period a study hall, but my school tends to develop its own language for EVERYTHING). Monday is my lucky day. Not that it’s a bad gig. The freshmen in my flex are pretty easy to deal with. They get to work pretty quickly and with minimal prodding, and they stay fairly quiet. I’m a pretty strong stickler for silence, so they know what the expectation is. I often get more work done during Flex than many of my free blocks.

I grade problem sets until I can’t focus any longer and then I play a few rounds of Dynomite. It’s the end of the day after all. I read an article on learning in the US and Japan that a colleague forwarded and that a few other teachers have responded to over email. Interesting, but not much is new.

At 2:55 I announce that it is “Free Flex,” which means that students have free time for the last half-hour of the block. I head out and go back to my office, plug in my laptop, which by this time hasn’t been charged since lunch. I print out the old versions of the Math 3 test that I’d glanced at earlier and organize them into piles based on the content of the problems.

A knocks on the door. He has come by to go over his “Recycle” (revisions) of a homework assignment. We go over the problems for about 20 minutes until school is over at 3:30. After A leaves, I run to the rest room, and then take the collection of tea mugs that has accumulated on my desk to the kitchen. I run off copies for tomorrow. By 3:40 I’m shutting down my laptop to leave for the day.

I see a colleague on my way out who’d asked me for a minute of my time earlier in the day. So I pop in to ask her what she wanted. We talk for a moment about homework assignments in Math 3. Thank goodness it was a quick question. I’m out the door, slipping on my sunglasses at 3:45, on my way down to the climbing gym.

I change into my gym clothes and hop on the elliptical machine. Students from school are rock climbing for their activity (required physical education credit) and several notice me and wave. I go for about 20 minutes until Avery arrives. Then we climb for a couple of hours. The gym is busy from people who’ve been off of work for the day, but we manage to get several good climbs in. I have almost finished all of the 5.9 climbs, so I start on some of the 5.10a’s—and I get a couple finished. They feel challenging, but doable. I think I’m officially up a level.

We drive home and heat up leftovers from last night’s mini-Thanksgiving feast. Foul-smelling smoke starts billowing from the microwave. One of us put in something melt-able and it has met its maker. Shit. We open all the windows, close all the doors, and “evacuate” to the bedroom. Avery sets up fans in the kitchen and living room and I move the cat’s litter box into the hallway. We hole up in the bedroom for the rest of the night with the cat, who is thrilled to be allowed up on the bed for a change. I work on my NaNoWriMo novel and crank out another 1,316 words—not too shabby for a school night. I’m behind by quite a bit, though I do have a bunch of old material banked in case I wind up needing to cheat in order to win, so I’m not too worried about it.

For those of you who were counting along at home, I taught two 80 minute classes, plus a 50 minute study hall and went to a grand total of 0 meetings. Tomorrow I’ll teach three classes, and have a 40 minute meeting during the first half of my one free block, leaving me with a grand total of 40 minutes of prep time and 40 minutes of lunch between the hours of 8:10 and 3:30. Also, for the next three days, school will end a half-hour earlier so that students can drop in for tutorial to ask questions and get help. Wednesday will be much the same as today, though I’ll meet with my advisory instead of Morning Meeting and attend a staff meeting after tutorial. I’ll take the shuttle and the BART over to Oakland when I get out at 5:00 to go to my weekly writer’s group; I won’t get back home until after 10:30. On Thursday I’ll teach two classes again, and have a meeting for the full 80 minutes of my second free block, followed by the last tutorial of the week—and of the trimester, since we’ll be done after this week. Friday will be another three-class day, but no meetings and no tutorial. And then we go on break for a week. Thank goodness.

Patterns Project

A few weeks ago, I assigned this project to my Math 2 students:

It’s a unit assessment on the various patterns we’ve studied in our first month or so at school. We’ve looked at linear, exponential and power patterns, as well as a few wonky “other” patterns. While looking at these patterns, we’ve figured out how to represent them in a variety of ways: in verbal, numerical, tabular and graphical forms, as well as in equations. There are two types of “equations” we discussed: NOW-NEXT equations (which are recursive formulae) and f(x) equations.

Well, I finished grading the projects, and they turned out nicely. Overall, I think my students need to work on explaining their thinking more, but I have another 6 weeks, and then they’ll have another trimester with me or another teacher to hammer that idea into them.

Here are some of the projects.

Some posters (click to enbiggen):

 

And some “training manuals”:

This student even dedicated her book to me. How cute is that?

[answer: super darn cute!]