May 3, 2016

Reading and Repetition

Today I had my algebra support block (we run an alternating day block schedule so I see my algebra class every other day for 90 minutes, but half of my algebra class sees me every day for 90 minutes because they also have this support class) and my contained algebra class (they all see me every day for 90 minutes).

Sometimes during the support block we work out of the EDC's Transition to Algebra, which I love. They do a great job of starting with numeric examples and making the patterns very clear. However, they are filled with language. The page is chock full of information (I understand that they are consumable workbooks so they squished lots of information on the page to reduce cost). The problems and hints are conversational, not to mention the actual student conversations mixed in. Sounds great, right? Here's something you probably don't know about my classes - I have many students with substantial language based learning disabilities and a couple students new to learning English (I like the phrase emerging bilinguals except what if English is the student's third language like it is for one of mine?). So this much language is really challenging. However, especially this semester since I'm working with a co-teacher who was in English classes last year, I've taken on the responsibility of supporting their language acquisition while teaching the math.

Monday in support we began exponents in the TTA book. To start, we assigned parts and read out one of the student conversations. I was so pleased how many students wanted to read! It's a huge testament to how much they trust their classmates when students who struggle with reading are willing to read in front of the class. We read it, talked about it, read it again and then made a connection between the reading and their own work. As we discussed I took notes on the things my students said, but then they asked me where to write it down (no spare space on the page, remember?). But, everything we'd written down was in the conversation! So we pulled out the highlighters and kids read the conversation yet again to highlight the key observation we'd made. It's always surprising to me how challenging this is for them. I was always a strong reader and I just cannot imagine going through high school trying to learn content when it's a challenge to locate a key phrase that we've just discussed. Activities like these remind me to slow down, recognize the difficulty and continue pointing out (not to mention recognizing for myself) strategies as we read.

I don't remember who said it, but it's really stuck with me how in math, conciseness is valued. In an essay you read the main idea in the first paragraph, you read more detail and many repetitions of that main idea in the following paragraphs and a recap of the main idea and details in the conclusion. In math we make a definition as dense as possible and that's it. A problem set may contain many repetitions but the language is brief and requires many read throughs. Since hearing that I realized this is exactly what makes a math text book so hard to read and have focused on convincing students that math requires reading many times.

Today we worked on another page in the TTA book. It was all about powers of two. In one question students figured out that if the exponent decreases by one then the value would be divided by two. In the next question students needed to decide what half of 2^50 would look like. All around the room students wrote 2^25. But children! We just talked about that! And then I realized that 1) it's far from intuitive, that's why they included more questions in the book to solidify this idea and 2) the language changed. I went back and we made the connection that "double" and "multiply by two" are the same thing. So then we figured out that "halve" and "divide by two" are the same thing. Then we tried some simpler cases. Then a couple kids changed their hypothesis but most students were far from convinced. Then I wrote out what 2^50 and 2^49 look like. Then I had some more students explain. Then a student was stuck and I had him "phone a friend" and they were silly about it. One friend wasn't helpful. Another friend said "Call me!" The student put him on "speaker phone" to be able to talk and write at the same time. The friend got annoyed how many times he had to repeat himself and my co-teacher said "Now you know what we feel like!" But it was worth the time - first because it's important to play together, and second because hearing something that many times makes it stick! The next question asked students to find half of 2^100 and I was ready to have a debate on that solution but they all got that it was 2^99 on their own!

It's hard to be patient and say something a million times. I already get it. By the time I get to my contained class where everyone has a math disability in addition to other challenges, I've already spent the last 90 minutes explaining this thing. But students need to hear, see and say things many times for it to stick. I need to get them talking to each other as much as I can because I might pull my hair out if I have to repeat something over and over and over, but no matter how many times I've already explained something, hearing a kid explain it to their partner always results in me directing a genuine beaming smile towards the pair followed up with a hear felt "thank you! well done!" after the conversation ends. I love how I can hear myself in student conversations. Instead of telling an answer or even listing a series of steps, they've picked up the questioning and explaining. It's awesome. Sometimes the end of the year is hard, but the hardest part is giving up my wonderfully trained students who are willing to read to the class and take the time to make sure their partner could do the next problem on their own.

May 2, 2016

Community and Activism

My school has been focusing our professional development on culture and instruction. Last week we brainstormed in groups to come up with attributes of a strong community. Then we had the same conversation with our advisories a few days later. I have seniors in my advisory so I framed the question in two different ways - everyone was talking about what makes our school a strong community and how could it be stronger, but for seniors I also wanted to include: how can you join in creating a strong community wherever you go next year? Because it's easy to leave high school for a job and forget that you need to rebuild your community after friends scatter. Because it's easy to go to college and not join your ideal community. And, as ended up coming up in conversation, because there are lots of communities that need to be better and they can do something about it!

We started with some basic characteristics. A strong community is:
  • a group sharing a goal
  • members who help one another
  • members who grow together
  • like a family
  • members who are involved
Then we got sidetracked (as expected) on the negative aspects of our school community. All of their complaints were valid, but we do plenty of complaining, I really wanted this conversation to be more inspirational! But the complaining turned back toward big issues, important ones.

Play Together
The student recording our ideas on the board didn't want to phrase it like this, but I love this idea. A strong community has to have fun together. At the teacher brainstorm, one teacher suggested sharing a meal together. One student said that there should be events like a field day. Another suggested board games in addition to the physical games. When I asked what other strong communities students were involved in they referenced sports teams who hung out together outside of practice. I think strong communities have some insider aspects to them, the jokes that only make sense if you were there. Shared memories of group fun bring people closer. The dividing line between acquaintances and closer relationships is whether people hang out beyond the times when they had to be together anyway. It's hard to plan school wide fun, but it is a reminder that my favorite classes are always the ones who can play together while they work. Some classes develop that naturally, but I should try to manufacture some more opportunities for playfulness to arise in my classroom, especially early on when I want to accelerate relationship building and get students to trust each other (or at least be willing to be wrong in front of the class).

Play Fair
Our boys basketball team made it to the semi-finals this year. It was a big deal, and rightly so. However, one student pointed out our color guard and band place in competition almost every year and they don't get nearly the same level of pomp and circumstance. Another student followed up with noting that the level of support that the girls teams receive pales in comparison to the boys teams. Then a few students started sharing what they knew about women's soccer. Did you know that the USA won the world cup in 2015? I didn't. Did you know that the women get paid significantly less than the men? I had heard about that. But I was seriously impressed that my students knew the facts and could stage a debate. They discussed whether the pay should be proportional to revenue, whether the revenue is a reflection of advertising and who should be responsible. I pushed the conversation toward equity - if the country isn't as excited about women's soccer then we should be pushing media twice as much to create the excitement. Yes, this country is sexist. Let's do something about it! Then I gave them a pep talk about being the future and having power and fighting for themselves. I spent my April vacation traveling and listened to all the back episodes of The Get in the car/bus. This awesome podcast has me recognizing my privilege, the importance of voice and the need for change. You should totally check it out. And then empower your students whenever you can. I'm working on not shying away from difficult conversations or shutting down debate between students. They need to develop their ideas and identities and I can provide a space to do that. Goals.
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May 1, 2016

It's May!?!

Happy May Day!

This school year has been challenging. I think I've grown a lot as a person but as my life extends beyond being a classroom teacher, my teaching has been affected. With two months left in the year I want to take the push that Annie offered via #MTBoS30 to do some reflecting on my school year and what I need to do to achieve better balance going forward. I will try some prompts like these and then we'll see how it goes. You should join me in blogging this month about school, life, liberty, justice, ya know, whatever words seem to fit together...

Prompt 9 seems particularly appropriate today:
Make a list of the people in your life who genuinely support you, and who you can genuinely trust. (Then make time to hang out with them.)

I woke up this morning to a lovely post from Fawn; this community is absolutely filled with people who genuinely support me. I couldn't begin to list all of them, but I appreciate every one of you. Then best friend Ashli told me that she's applying to speak at the NCTM annual meeting. Last year I did a lot of speaking and it was hard to travel that much. This year I didn't do much speaking and it was hard to not see everyone. It is important to make time to hang out with my support group, so today I'm joining my friends in submitting a proposal to speak in San Antonio. It will be hard to find somewhere for Jordan to stay and then deal with the guilt of traveling without her. It will be hard to make sub plans and then accept that the students might not be given the same opportunities to explore as they would if I were teaching. It ... won't be hard to justify the expense. While my school occasionally finds funds to cover my registration fees, they definitely won't be able to cover travel and hotel (want to be my roommate?) but quality time with my tribe is worth it.

Thanks for all your support, this year especially. I can't wait to see you at TMC, a local tweet up, NCTM or on the interwebs!

April 22, 2016

T.I.M.E. Unconference

Teaching Innovatively Moves Education

A while back my co-worker Kelly saw a post on facebook for an unconference during our April break. Neither of us had plans for that day and so we decided to attend. Going in we had no idea what to expect, we hadn't hear anything more about it and were somewhat concerned we'd be the only ones there!

There was no traffic so we arrived early and wandered around campus while solving all of the world's problems. The event was at Olin College which has a unique feature - originally tuition was free, now (post recession decimating the endowment) students only pay half tuition. We wondered how that would work and decided that a "pay later" model for education is totally reasonable. Students could attend a school, get the education needed to find a job, and then pay tuition later. That tuition could be dependent on their salary or optional. It occurs to me now that this is exactly how public schooling works. The idea of opening a high school like this sounded radical on that early Saturday morning, and truthfully with the right branding we could run it as a radical new idea, only to follow up with "Hey! You just funded a public school! How about you keep doing that since it is a worthwhile cause all the time."

When we arrived at the meeting space there were only five other people there. But teachers, given the opportunity to talk about teaching, will jump right in no matter who is there. By the end of the last session in the afternoon we were up to about a dozen people. I was especially excited to talk to another teacher who teaches the language based disability program at her middle school since I have so many students with language based disabilities this year.

I was part of three round table discussions. The conversations in the first two flowed naturally as we shared ideas, asked questions, learned more and made connections. In the third session we had a more deliberate facilitator who made sure that everyone was given the opportunity to speak, including the pre-service teachers who had been quiet all day. Inspired by some NCTM tweets, I tried taking notes in a more free form manner. I don't know that it's fair to call these sketchnotes as there aren't any drawings/doodles (turns out I'm self conscious about my ability to rapidly create images! A new weakness I get to develop into a potential skill) but the web style of notes was interesting. I hadn't planned on doing this so I only had a pen with me. That evening, post-unconference, I went to a coffee shop with my markers and reviewed my notes. Adding color, highlights, additional notes (the brown) and taking the time to digest the flurry of information was a great way to spend the evening. Now that I blog I am more likely to look back at my notes but often I take notes more as a thing to do with my hands than because I expect to use them later. Taking the second pass to further process and connect ideas was time well spent.

I'm happy to further explain any of the ideas in these notes or discuss ideas inspired by them. For now, I leave you to the synthesized version of 4 hours of conversation:


April 10, 2016

Building Portfolios of Math Practices

This is a follow up post. I wrote about the original idea in August and how the first round went in November. The goal was to find an authentic way to assess the Standards of Mathematical Practice and the method was to have students build a portfolio of exemplars throughout the school year. They would submit their portfolio quarterly using this Student Form.

We just finished third quarter (so I'm writing this post while procrastinating grading!) and I had students complete this form for the third time. It was again a task for the last day of the quarter. Most of my students have figured things out by now and are good at this, it was just one task of many that class. Not everyone remembered all of my expectations though. A few of them only heard "find four examples of good work" and tuned out before I reminded them to give evidence of how they used a math practice in the exemplar they chose. Those students provided evidence such as "I did well on this." I went back to those students and had them read the quotes again and add more detail. Listening to my co-teacher (who has also worked in English classes) work with students to remind them to "use words from the prompt" - as I checked in with a student whose 'evidence' was to copy over the example I provided word for word - made me realize that this is a cross-curricular assignment. Our ELA data has shown that students need more practice explaining how evidence relates to their claim. They are good at making a claim and picking out the relevant piece of evidence, but communicating why the evidence supports their claim is a challenge. When I designed this portfolio task I didn't expect the writing to be a challenge, but now that I've done it a few times I think this is exactly the kind of challenge students need. Asking students to describe their evidence requires them to interpret the practice standards. Overall the results have been fantastic! Here are some of the examples and responses students wrote this quarter:

Make Sense of Problems and Persevere in Solving Them
Quad HW
Despite having difficulty completing the square and graphing I was able to factor.
Systems of Equations
For problem 1 on the back, at first for the x-value I got the wrong answer, but instead of just quitting like I was about to, I chose the other equation instead which I found to be much easier.

Reason Abstractly and Quantitatively
Complex Numbers 
I switched back and forth between thinking about i as a variable and sqrt(-1).

Model with MathematicsI used both the box method and long division.
I used the equation to make an easy to understand graph.

Use Appropriate Tools Strategically
Students listed a wide variety of tools including: Desmos, tables, graphs, multiple methods for solving quadratics, their conics dichotomous key... This list is much better than first quarter when tools were pretty much rulers and calculators!

Look for and Make use of Structure
Operations with complex numbers
I already knew how to solve these problems without imaginary numbers and could still solve with them. 

Look for and Express Regularity in Repeated Reasoning
The equations of circles, parabolas and hyperbolas are different. I discovered the pattern of the equation for each one. 
Powers of i
I figured out that the values simplify to the same four numbers in a pattern.