Trying to find math inside everything else

Day in the Life: First Day

The day I signed up for in the DITL project was the 5th, but this month that was Labor Day. So I figured I’d write up both.

Monday, September 5th (Labor Day)

I woke up at 930. Not exactly a getting-ready-for-the-school-year time, but not, like, noon, so it’s fine. I roll up and get started on some chores – laundry and dishes. While the laundry goes I work on the blog post I wrote about teaching Integration first. Thinking through the post helped me solidify how I wanted to start the year in Calculus, so that was productive.

Laundry, however, took much longer than it should’ve because one person decided to split a single washer load into all three dryers and hog them for an hour. That gave me some time to start working on captioning the photos from my August trip. All the chores were done and we were ready to go around 1215. We grabbed some lunch and headed to the apartment of a friend of my boyfriend. There we played some video games (including the hilarious Ultimate Chicken Horse, a game where you lay traps that everyone has to race past and over to get to the finish, and the creepy Push Me Pull You). Then we played some board games (Coup Rebellion, Tokaido, and Alhambra). Around 730 we went for dinner at a nearby Japanese restaurant. Then the BF and I went home to get some rest for the big day tomorrow.

Tuesday, September 6th (First Day Teachers Report)

I had my alarm set for 7, but I woke up at 630 because I couldn’t sleep anymore. Anxious? Trepidation? Excitement? Who knows.

After getting frustrated with Facebook a bit because of the aforementioned subtitling, I got ready and caught a ride with my BF so I could get there by 8. There were bagels and fruit and tons of people excited to see each other. It made me miss my old LAD coworkers, as we’re all scattered to the winds after fleeing our previous school. I settled into a table in the library and found two more teachers new to the school. Of course, I’ve been here for 15 days over the summer working as the programmer, so I know some people fairly well, but there’s still so many new faces. And this school is over twice as big as my old one! So it’s a little overwhelming.

Around 830 my principal (who is also new to the school) does an introduction and talks a little bit about the instructional focus for the year. Then she introduced some key people like the APs, as well as the new teacher (there are 7 of us out of the 71 teachers on staff). After that the programming team and the guidance counselors were dismissed while the rest of the staff stayed for other procedures, announcements, and PD.

My coworker Luke, who was the programmer last year and has been working with me on it all summer, and I went down to our office and started to work on the final touches of the schedule  (as when I had left on Friday evening all the students had schedules).

Or so we thought.

I was working on mapping course codes (tying one class to another) and Luke was replying to some emails. But then we got more emails. And more. We had to send out a list of students without full programs to the guidance office so they could tell us what classes to give them. We had a teacher who didn’t have a schedule (because she is retiring in a month) in need of one. We had sudden changes in who was teaching certain classes that needed to be accommodated.

Around 1015, the meeting upstairs was on break, and so we started to get a lot of teachers popping into the programming office to make their requests in person. Often they were the results of typos, or information we didn’t know before (such as, say, Chemistry needing to be in a certain room for labs), or new students arriving that had to change classes around.

Around 11 I went and delivered the newest, most up to date teacher schedules I had to the meeting, as they were going to do a run-through of a school day to make sure no one was teaching the wrong amount or in two places at once (or two classes in the same place at once). Of course, lots of confusion and issues arose from that. I sent out a staff email to collect all of those issues and began hammering them out.

At 12 the school’s food services provided food for all the staff and faculty members in the cafeteria. Luke and I headed down and got some – it was pretty good for school food (though I felt the same way last year, too). I sat at a table with some people I hadn’t met yet and we chatted a little bit. But by 1230 it was back to programming.

By this time I finally got back to work on those mappings I had barely started in the morning. I finished those around 2 and did some final checks on the student schedules, but found out that a lot of changes made that day have caused overcrowding issues that we’d have to resolve. On top of that, the AP of Special Education came in to request the schedules of all of her students, so she could check they had the right services. I got those printed out and waited for her changes, as those would have a big effect.

Around 3 I noticed a big problem with the schedules of about 30 9th graders, so I had to really work on how to solve that problem, considering everything was so tight and locked up for most of the school’s schedule by now. During that time we were getting changes from the AP of SPED, throwing even more disorder into the process and I watched those “Students Partially Schedules” counter tick up higher and higher. Around 430 the AP who’s been in charge of programming came in and we ordered some sushi as a snack. By 530 we finally finished those SPED changes, and now had to make everything work again.

By 715 we were starting to hit a roadblock. 1120 students were fully scheduled, but 12 remained and we were just running out of spaces in the classes they needed. Luke and I took a short dinner break to Trader Joe’s, and I informed my trivia team that I would not be making it to trivia tonight.

Armed with a burrito and an egg salad, we set back into figuring out these final few students. We also worked on closing gaps that students may have had in there schedules. We tried a lot of different changes and were unsuccessful with many of them, but finally, at 945, every student was scheduled! We did some saving and tidying up and left the school at 10.

I walked to the subway (the bus is faster/shorter but I’d been sitting all day and needed the walk) and got home around 1115. Notice how I didn’t do anything with setting up my classroom or planning my courses! Luckily we have one more day before students arrive – I hope I can get some work in them.

1) Teachers make a lot of decisions throughout the day. Sometimes we make so many it feels overwhelming. When you think about today, what is a decision/teacher move you made that you are proud of? What is one you are worried wasn’t ideal?

There were some choices I made about the PE schedule that made most of the PE department angry. Part of it is because what I thought they wanted was not what they actually wanted. It should be mostly a solvable problem, though. I hope.

2) Every person’s life is full of highs and lows. Share with us some of what that is like for a teacher. What are you looking forward to? What has been a challenge for you lately?

Since I’m starting at a new school, I’m looking forward to a fresh start in a new environment. And in a new building, like, literally new, built 7 years ago. My old school was built 150 years ago and felt like it. The challenge has come with not feeling like I’m prepared to teach because I’ve spent so much time with programming.

3) We are reminded constantly of how relational teaching is. As teachers we work to build relationships with our coworkers and students. Describe a relational moment you had with someone recently.

Working with my coworker and AP over the summer I’ve been initiated into many of the in-jokes of the office and of the school, which has helped me feel more belonging for the school.

4) Teachers are always working on improving, and often have specific goals for things to work on throughout a year. What is a goal you have for the year?

My major goal is to be more kind – and to have students see that. I’ve always care about my students and how they are doing, but I’m not always sure they pick up on that.

5) What else happened this month that you would like to share?

Well, I traveled in August, which was nice. The 40 hours of plane rides and 10 hours of train rides were the only times I did prep work!

Integration First

Last year I went to a PD at Math for America that was about approaching calculus from a geometric point of view. The presenter mentioned during it that, historically, the idea of the integral was developed first, followed by the derivative, and then the limit. Yet in many calculus courses, they are taught in the exact reverse order. I decided that, should I teach calc again in the fall, I’d do integration first.

Well, school is rapidly approaching, and so I’ve been thinking about it again. I did so searching and found this intense forum discussion (oh, old Internet), which pointed me in the direction of the Apostol’s Calculus 1 textbook, which starts off with integrals. The post also had a bunch of arguments about why I shouldn’t do it. One of the notable arguments was that in order to fully teach integration (including u-substitution and integration by parts), you need differentiation. But I actually view that as a benefit, not a downside, because it forces a more spiraled approach. I can start with integrals, then go to differentiation, and then tie them together.

In general, I feel like area is a much more approachable subject than slope. My years of teaching Algebra I to 9th graders certainly seems to support that claim. But I also think it’s easier to understand the linearity of integration than the linearity of slope. “If you add together two functions, the area under the new function is the sum of the areas under the old functions” seems much more evidently true than “If you add together two functions, the slope of the tangent line for each point of the new function is equal to the sum of the slopes of the tangent lines at the same points on the old functions.”

Of course, Jonathan has already worked to restructure his calculus course, and I plan on taking a number of cues from his more spiraled sequence – but still with integrals first.

Here’s what I’m thinking:

Q1 (Intro to Integrals) – (Sam’s Abstract Functions, Area Under Stepwise Functions/Definite Integrals, Properties of Integrals, Riemann Sums, Area Under a Curve, Power Rule for Integrals, Trig Integrals, some applications)

Q2 (Intro to Derivatives) – (Average vs Instantaneous RoC, Tangent/Secant Lines, Power Rule, Trig Derivatives, some applications)

Q3 (Fundamental Theorem) – FTC, Chain Rule/u-substitution, Product Rule/Quotient Rule/Integration by Parts, Curve Sketching/Shape of a Graph)

Q4 (More Applications) – Related Rates, Optimization, Volume, etc

How does that sound?

Twitter Math Camp ’16

I’m currently on the road back from TMC16 in Minneapolis. (Ed: See, that’s when I started this post….) This long drive back is giving us all a lot of time to process and reflect on the experience. (I guess Rachel was right about that!)

I think I approached TMC differently this year. Lots of people have spoken about the rejuvenative properties of TMC, and I think I really needed them. I mean, everyone always feels tired when the summer finally rolls around, and rest and energy makes that better, but this time I needed something more than that. And TMC provided.

It started with Descon. You can read more about that in Rachel’s post here. But when I was struggling to choose a morning session, I settled on Tessellation Nation. Both those experiences gave me a deep joy of forming questions, exploring ideas, having successes, failures, and breakthroughs. It was like doing a hard reboot on my mind.

Some things I played with in the morning session:

20160717_104610_HDR

Here I was trying to picture creating some sort of "inversion" tile that would connect the lizards of different chirality.

Here I was trying to picture creating some sort of “inversion” tile that would connect the lizards of different chirality.

With that in mind, my afternoons provided me with guidance about the upcoming school year. Really, I can sort them in what, how, and why.

What: I went to Jonathan’s session about hacking up the curriculum. His main idea was that the curriculum should not be focused around the nouns, but rather the verbs. That is, instead of having, say, a linear unit where you solve, graph, model, and then a quadratic unit where you do the same, have a solve unit where you do both types.

The approach sorta lends itself to the kind of spiraling that I was inspired by Mary Bourassa and Alex Overwijk to try, but was afraid to. So this is a step in the right direction.

How: I’ve heard about Talking Points for a while, but never had any experience with them, so I had to go to Elizabeth’s session. It was really nice to walk through the activities and see how the points can spark cognitive dissonance in their sequencing. I also enjoyed Elizabeth’s “deleted scenes” method of instructions, which reminded me of the dialogues in the Algebra Project.

Julie‘s session on giving feedback was helpful. I’ve worked on giving feedback without grades, but it can get a little overwhelming, so it was nice to get some strategies for streamlining the process. I think the most important one for me to remember as I start the year is to make space for the comments built right in to the assignment. That’ll make the whole process easier. Also, I need to remember that EVERYTHING should get a comment, not just things that are wrong. That way comments don’t become a proxy for grades.

Joe‘s session on teaching moves for implementing games was just what I needed. I can come up with some great games, but sometimes when it comes time to play them in class, it looks more like “Okay, here’s a game, go play it.” The most important one IMO was to have the students notice/wonder about the board/materials before the game is introduced. It’s a tenet of game design that a game is well-designed if players can (mostly) figure out how to play without looking at the instruction booklet. So the noticing and wondering works well with that.

Tracy’s keynote was amazing in so many ways, but she did hit on something I’ve been working on with my math coach and is now, I’m glad to see, becoming more of the thing in the MTBoS – never skip the close. Gotta work on that more.

Why: Social Justice, of course. Jose’s keynote obviously hit on those notes – as he said, students need to trust you before they can learn from you.

I went to Andrew’s session, which wound up just being a small conversation with him, me, Sadie, and Sharon. That’s where I decided my #1TMCThing – to decorate my classroom with more explicit social justice signifiers (like a rainbow flag, or a BLM poster).

Then at Annie’s session, she talked about her Mathematicians: Not Just White Dudes project where she tried to present mathematicians that identify the same as her students – even when they got super precise on her (“Is there a gay female Dominican mathematician?”) I definitely want to bring that into my class – although I would like it if, since I’ll be teaching calculus, I could get a good variety who contributed to calculus (or I guess just used it.) There as a group we also decided to start using the hashtag #sjmath (after I determined it wasn’t be used for anything else) to share social justice math resources, which Julie pulled a lot together here.


I started writing this on the ride home from TMC, but I ended it now, and I think that was actually a good thing. TMC is so early in the summer (for me) that I don’t go into vacation-mode until after. Now that I’m actually ramping up for school again, it was good to reflect and remember what I actually want to bring into my class. So my procrastination actually paid off! (For once!)

To conclude, here’s the camp song in MP3 form.

Since Kate asked us to post more unsexy things, I thought I would throw up this review book I made for geometry, which basically covers all the things students should “know” (not necessarily be able to do, or deeper understandings) for the course, especially for the NY Regents (Common Core). The students can fill in the blanks and are then left with a nice study guide. So far my students seem to like it! (Although one student said they wouldn’t do it if they didn’t get a grade for it – so frustrating!

Great Geometry Book (doc)

Great Geometry Book (pdf)

When I think back on my first five years of teaching, I can identify big initiatives that I took and tried each year.

  • My first year – well, it was my first year, everything was new. But I was implementing stnadards-based grading as sorta my big thing.
  • My second year, I was very focused on interdisciplinary work, creating cross-curricular lessons with my colleagues, and implementing all this new 3-Act and other stuff I had just started to find on the internet.
  • My third year, I structured my class around math labs and introduce the interactive notebook after I learned about it at TMC12.
  • My fourth year, I overhauled my grading system.
  • My fifth year, I introduced the Standards of Practice portfolios as a way to grade on those standards and, thus, have them be valued in my class. To go along with that, I had a new way to give feedback, instead of writing grades on assignments.

And this year? My big initiative? I don’t have one. It’s felt weird. Every year these big things I was trying and perfecting felt like steps I was taking towards becoming a better teacher. And if I didn’t have one this year, was I stagnating?

No. (I say it confidently now, but it took a lot of reminding myself.) First of all, my big initiative this year was teaching Calculus and Geometry for the first time. I had taught Algebra I for the whole first 5 years of my career, and the bulk of my student teaching as well. Despite the switch to the Common Core curriculum, I was still very familiar with the ins and outs of the material, and that let me focus on other things. But teaching a new course is a lot! And two, twice as much!

But, even with that…I still tried new things, tuned things, had small initiatives. And these things matter! So I’m writing a list of new things I’ve done, to remind myself. And also to keep looking forward, for new initiatives – as Black Widow says, “There is no mastery, only constant improvement.”

  • I greet my students at the door every day with a high five.
  • With the other hand, I have them pick a card so they can find their seat with their visibly random grouping.
  • I put up new boards on my walls to have even more surfaces for the students, and designed lessons around using them, facilitating group collaboration more than usual.
  • Instead of saying “Ladies and Gentlemen” to address the class, I now say “Mathematicians” (or “Computer Scientists”), to keep a gender neutral term.
  • I swapped out the Name spot on my assignments for one that says Mathematician.
  • I had up a “Good Questions” bulletin board, after going to Rachel’s session on better questioning (couldn’t find a link for this one) for a while during the year.
  • And I’ve continued the initiatives from the last two years, which were raw in idea but are now becoming fully realized structures, as I find better and more sustainable ways to do them.

I bet you’ve done a lot this year, too. More than you realize.

During the slow Parent-Teacher Conferences tonight, some of my colleagues and I got into a discussion on privilege. We shared some things about our experiences, and I figured I could write up what I talked about for my #MTBoS30 post tonight.

I used to think racism didn’t exist anymore, that affirmative action was reverse racism, and other such things. On top of that, when I’d hear about things that certain groups faced, I would just counter with my own. My family was stolidly working class (though not as poor as when my oldest brother was growing up), my “summer camp” growing up was sitting in the public school cafeteria playing Connect Four, I’m queer and have faced my share of discrimination from that. Certainly not privileged, right?

When I went to Bard for grad school, one of the classes we took was called Identity, Culture, and the Classroom, taught by Michael Sadowski. There were a lot of interesting readings and deep sharing of stories in that class, but the single most powerful moment was when we did an activity about Peggy McIntosh’s Unpacking the Invisible Knapsack.

Michael had us all go outside and stand in a line on the grass. As he read he had us look straight ahead and, if the sentence was true for us, take one step forward. As he went down the list, there were a lot of items I did not step forward for because of the aforementioned class and LGBT spheres. At first, I felt like this supported my feelings, as I watched much of the class pull far ahead of me.

When Michael had finished, he told us to look around. At this point, I was about halfway across the grass. Ahead of me all the way of the front were all of the other White students. To my side, about level with me, was my friend Jack, who is Asian.  And then I looked behind me and, back at the start, were all the Black and Hispanic students in the class.

In that moment, the idea of intersectionality suddenly became clear. Sure, I may have not been privileged in some domains, but I was privileged in others, and this was a physical representation of that fact. It felt like my eyes were opened and I saw the world as it really is, and I haven’t closed them since.

Talking to my colleagues, it seems they had similar experiences, so I know mine isn’t unique or particularly noteworthy. My one colleague was fascinated that I grew up in Queens (the most diverse area on the planet), went to the schools that I did (middle, high, and college), and it still took until I was 23 for this idea to get through to me.

Formatting

For previous portfolios in my class, students have asked me how I want them to format their work. Should they write their reflections all on one sheet, or on each assignment? If on one sheet, should get organize by the assignment it refers to, or by the standard? I had said it didn’t matter to me, they could do what they like – and this may have contributed to how hard it was to grade them all.

This time I demanded they write the reflections on the assignments themselves (or, at least, on a slip attached to that assignment), and it was so much easier to grade – I didn’t have to flip back and forth between the reflections and the assignment to see if what they wrote was accurate (often it isn’t – they’ll say they did a thing they didn’t actually do). And the few students who didn’t follow directions took so much long to grade. Maybe I shouldn’t have graded them at all – just returned them and had them redo it.

So I think I’m going to be stricter about formatting from now on. There are things that are important to have students have a say on in class – but I don’t think this is one of them.