brian

PD with Dan, modeling with mathematics

With the help of the NYCDOE, this past Wednesday was the third of three workshops that I’ve attended with Dan Meyer this school year. I’ve written about the first two, so why not cap off the trilogy? Read more here and here. In an effort to solidify my experience and have something to reflect upon at a later date, here’s a recap of the session.

The focus was on mathematical modeling. This is one of my weaknesses, so when I walked in and looked at the agenda, I was pretty happy. Teach me Dan! Things opened up with us sharing what we thought it meant for students to model with mathematics. The answers varied, but after feeling us out, Dan emphasized the difference between model the noun and model the verb. I had to catch myself here too as I hadn’t played close enough attention to this subtly. He used Desmos to collect our responses and our comfort level with mathematical modeling.

We then dove into the Penny Pyramid 3-Act. Dan worked his magic, as usual. During the debrief, he pulled from the CCSS and presented five actions that are necessary for students to be part of modeling experiences:

Identify variables
Formulate models
Perform operations
Interpret results
Validate conclusions

We talked about how the Penny Pyramid, while probably not ideal, works to get students to do all of these things. Our questions helped us to identify variables. Interestingly, Dan highlighted the vocabulary that we chose to represent the variables. This is important because, indirectly, he demanded precision and consistency from all of us when it came to describing key parts of the experience. Our tabular, algebraic, and physical representations of the pennies were the models, which we used to calculate the number of pennies in the pyramid. We spent time as a group discussing the meaning of our calculations and parts of our models – even those that weren’t correct. For example, one group landed on 22,140 pennies, which didn’t take into account that each stack was 13 pennies. Also: what does the 612 mean? The weakest part of our models was the validation. It’s not like we could actually count all the pennies. That said, we would compare outcomes of different models. There was also a newspaper article on the pyramid which helped with the actual count of pennies. Validation runs on a spectrum.

The afternoon was spent creating and improving some modeling tasks. We started with 25 billion apps and then went into a few graphing stories. We spent time thinking about how to structure modeling activities using these tasks. A great conversation occurred while exploring Distance from Camera. Someone brought up whether the graph should be piecewise linear or rounded periodic (like the solution). It was a great discussion, worthy of its own post. Dan remained vulnerable and eloquently showed us this ferris wheel Geogebra applet from the awesome John Golden. (Check out his full collection of Geogebra resources.)

We brainstormed how technology can help make our modeling dreams come true. The list was plentiful. Staying away from “textbook traps” topped the list. These include giving up numbers, tools, and other key information far too early in the modeling process. It’s also ironic that, because of technology, Dan was behind a desk for extended periods of time while we worked (he was typing our insights and using Desmos). Without technology, this teacher move is frowned upon.

The culminating task had us dig into several different versions of Barbie Bungee. Having never actually done this modeling activity, I learned not only about how to do, but also what not to do. Truth be told, if I would have looked at the activities before the workshop that day, I wouldn’t have suggested any changes. I would have been excited to implement them as is. But after purposefully rethinking modeling with mathematics with Dan for five hours, I felt very different.

Takeaways:

The Penny Pyramid task would serve as a great introduction to summation notation.
Dan: “When there’s a great classroom experience, I ask myself: how could I have ruined this?“
Not every aspect of modeling needs to every lesson. The goal is to feed students a healthy diet of modeling verbs.
Focus on broad questions. These will lead to more specific, granular questions. Avoid the reverse.
Seeing every teacher move I make as an investment into the lesson. Which moves are worth their investment? Which aren’t? This reflects the gravity that every decision we make. I need to be more deliberate.
Depending on what info we give kids, the level of modeling that they do could be very different. Don’t do the modeling for them! Give them procedural stuff.
It’s not if to give a handout, but when. This outcome was directly tied to Dan’s first session back in December, which helped things come full circle.
Once again, I was impressed with how Dan managed the audience. There were so many slick teaching moves (see notes).
I loved catching up with Sahar during lunch. We talked about her experiences visiting students homes with her school. She also gave me a tip about taking photos while students are working during the first couple of days of school to showcase how mathematical discussions should happen amongst students.
This wonderful periodic modeling Desmos activity.
If I ever do Barbie Bungee, I need to use Dan’s intro video.
Be mindful when moving between the real and math worlds. Don’t get lost on your travels.

Dan’s Google Doc for the session.

Day in the Life: May 24, 2017 (Post #11)

I’ve decided to chronicle this school year through my blog. It’s part of Tina Cardone’s Day in the Life book project. This is the eleventh post in the series.

5:45am | I wake up. Boy, I’m tired. After staying up late to watch game 4 in Eastern Conference Finals between my hometown Cavs and the Celtics, I certainly feel it. The early sunrise this morning helps pick up my mood.

I take an hour to eat, sip some coffee, draft this post, and shower. I’m on my way.

7:05am | I make it to school after a wet, soggy ride in. I make it up to my room and change into the clothes I keep in my closet for rainy days like today.

One of the Spanish teachers comes in to say hello and we chat. He’s no stranger, as we have periodically had some in-depth conversations about a variety of things this year. Today we talk at length about how our school years have gone and how they’re shaping up. We both have had disappointing moments and growing pains, but remain hopeful in the future. He’s a great guy. Our random talks have been a welcome respite his year.

I also spend a few minutes for an interview with a senior whose working on a project related to discrimination, racism, and stereotypes. Sharing my thoughts on camera with a student is a breath of fresh air. I don’t know her well, but I’m so happy that she’s dedicating time to researching these social issues. Our school needs it.

7:40am | Just like that, a half an hour passes. I throw on some music and begin mapping out the day for my students. Because the state tests are around the corner, we’re basically in Regents prep mode. At this time every year, I become a machine.

9:00am | First period comes to an end. The class is basically all seniors and today is prom. So yeah to say that they struggled to maintain focus is an understatement. I usually go to prom, but I’m sitting this one out. This is largely due to my lack of connection with the senior class…which is a consequence of this being my first year at my school. Next year.

I make it back to my room and remember that I need to run off a bunch of copies for my after-school Regents prep session after school today. I do that and come back to finish off plans for period 4 and 5.

10:35am | Fourth period begins. The focus is on solving a system of equations graphically. Specifically, we are using the graphing calculator to approximate the solutions to a given system of equations. I also give back their mock Regents that they took the previous Saturday. The results of which were promising. The lesson is ok, but nothing to call home about. The kids see a rational function for the first time and sort of freak out upon graphing it. Oops. We manage, but my poor pacing this year has caused all sorts of hiccups like this. I also manage to screw up one of the systems because the logarithm that I included in one of the functions doesn’t display properly on the graphing calculator because of a logarithm. This reminds me of Patrick Honner’s talk at MT^2 a few years back.

11:25am | Fifth period gets going. I head across the hall to the customary standing ovation. These kids are a blast. (Did I mention that I’ve started clapping for them when they walk out of the room?) The lesson is the exact same as period 4, but I make sure to develop the rational function a little better and skip the erroneous system.

12:15pm | I go heat up my lunch in the teacher’s lounge and run back to my room to scarf it down. I have some minor prep to do for period 8. While on my computer, I get a notice from UPS that my You Can Solve the Cube class set of Rubric’s Cubes arrived today. Excited, I pick them up from the main office. I recently learned how to solve a Rubric’s cube myself, so sharing this joy with my period 7 students (there’s no state test) is going to be great.

1:00pm | Speaking of period 7, they walk in. Because most are seniors, it’s a smaller group today (prom). I forewarn them that path to solving a Rubric’s Cube can get very frustrating. They nod, passively. I hand out the cubes and show them the first step in solving the cube. They practice this step over and over before the end of the period. They’re excited, I’m excited. It’s awesome.

1:50pm | My period 8 is officially starting “Regents Prep” today in class. A colleague made these fancy booklets containing all the Regents questions from like 2013 or something. We use those to review finding and using regression equations.

2:35pm | After school Regents prep starts for my algebra 2 students. I really like how I chose to set it up this year. Based on each student’s overall performance this year, I assigned them X amount of tutoring hours that they must get in before the Regents exam on June 16. They have a sheet to track all the hours that I stamp after every session they attend. It seems pretty efficient and holds every kid accountable.

4:35pm | The students staying for tutoring/Regents prep head home. I sit at my desk, reply to a few emails, and wait for the students completing their mock Regents to finish. At 5:05pm, I head home.

8:30pm | I’m still grading the mock Regents that the kids took, so I dedicate an hour to knocking out a good chunk of that.

9:50pm | Off to bed.

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?

While bogged down by the Regents and essentially turning myself into a test-prep machine during the last week or two, I’m pumped about getting the Rubric’s Cubes for the kids. It’s different, fascinating, and fun. In fact, that may just keep me afloat until the last full day of instruction on June 13.

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?

Hmm. Why am I drawing a blank? Too many highs and lows to describe? I’ll rain check this one. TBD.

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.

This month, I had a powerful moment this with a colleague about a t-shirt that she wore to school. To make a long story short, we connected on her decision to wear the shirt and, unfortunately, the disciplinary action that took place as a result. The entire situation was off-putting, but through it I learned so much about myself and my school about we address race and representation with colleagues and our students.

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?

While not one of my classroom-specific goals, this school year was to make a whole-hearted attempt at National Board component 2. All year, I’ve had this thing in the back of my mind, but it wasn’t until February when I began to seriously think about the specifics of what I was going to do. After losing about two weeks worth of sleep, I managed to submit it this month. The focus was my mini-unit on complex numbers. I’m pretty sire that it won’t be the best that NBCT will read, but I was super proud of all the thought that I put into it. I learned a lot, too. Next year: components 3 and 4.

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

On an unrelated-to-teaching note, this month I’ve decided that I will be taking piano lessons during the summer. It’s always been something that I’ve wanted to do since I was young, a “lifelong goal” of sorts. I’m thrilled!

Day in the Life: April 24, 2017 (Post #10)

I’ve decided to chronicle this school year through my blog. It’s part of Tina Cardone’s Day in the Life book project. This is the tenth post in the series.

5:30am | Rise and shine. It’s later than I would have liked, but I didn’t sleep well last night. I throw lunch together, a simple salad. Waffles for breakfast. No time to read.

6:30am | I’m out the door. The ride to school is brisk. The sun is out earlier these days and it reminds me that the end of the school year is close.

6:45am | I lock up the bike and walk into school. I make it up to my room and spend 15 minutes drilling holes in the large, 4-ft-by-4-ft whitebaords that recently picked up from Home Depot. I have these super magnets that I’ll be using to hold up the boards on the lockers in my room. It’s cheezy, but I’m so proud of this solution.

7:35am | I walk my large whiteboards down to my first period classroom. It’s painless, but pretty annoying. They’re awkward to hold for long periods of time, like down the hallway. We’ll be using the whiteboards for some VNPS and VRG action today on factoring.

I make it back to my desk and finish up plans for first period. I print out a few articles for a student who walks in. At 8:10am, I make my way down to first period.

9:00am | First period comes to an end. For what it’s worth, I consider it a win. I’ve learned so much from that class. More below. Whew.

I walk all of my crap back down to my room an decide that I need coffee. I head out to the bodega at the corner. As always, black, no sugar.

9:15am | I’m back at my desk and sit to map out a couple of other lessons for the day. Specifically, I put together the group speed dating activity for period 5. It’s a review of factoring and the conic form of a parabola.

10:05am | I run down the hallway to use the bathroom and I see one of my 7th period students wondering about. I ask her what’s up and she says tat she doesn’t want to go to lunch because her friends aren’t here today. I invite her to hang out with me in my room since it’s empty. We talk. She tells me that she’s looking for a job. I share my experiences working at Chick-fil-a. Good memories of good sandwiches ensue. She cuts up my problems for speed dating.

10:40am | Period 4 begins. Today we’re writing the conic form of the equation of a parabola. On Friday they used Desmos to explore how a parabola is the set of points equidistant from a line and a fixed point. I overview the two common forms, first vertex and then manipulating that to get standard form. I whip out the small whiteboards and pair up the kids. I post graphs of parabolas and have them practice writing the vertex and standard forms for it. They hold up their boards and we discuss. I’m always amazed at the high levels of assessment that whitebaording permits. The lesson is a keeper.

11:30am | I head across the hall for period 5, also algebra 2. This group is one day ahead of period 4. The group speed dating is going to sum up our quadratics unit. I quickly realize that the problems I included in the activity will need three days to be completely reviewed by every group. That said, I would consider the period is a success.

12:15pm | Lunch. There isn’t much planning I need to do for the remaining two periods that I teach so I manage to actually enjoy my feast, if a bare-bones salad and two oranges qualify as such.

One side note. On Monday, Wednesday, and Friday there is an “Assimilation” elective that takes place in my room when I eat lunch. It basically th college advisor sharing all kinds of useful knowledge with the kids. I always stay in the room during lunch for his class. I find him to be incredibly cultured and knowledgeable on so many things. Today’s topic was real estate. It didn’t disappoint.

1:45pm | My period 7 class ends. More VNPS and VRG action. They eat it up. Pure and utter engagement for 30 minutes, easy.

My period 8 walk in. I love these kids. They’re my only ninth grade class and they keep me in touch with the younger side of high school. We’re shifting parabolas today. The lesson is rushed — we’ll need to take a closer look tomorrow.

2:35pm | On Monday, my school holds district-mandated PD for us. I head down to room 229, where the PD will take place. The focus today is curriculum maps. It’s the first of a series of four workshops on the matter. The idea is that as we close the school year, we adapt and improve the maps we currently have for next year.

The session was better than expected. I really like the teacher who ran it…and his approach was untraditional. Instead a dry, boring approach to curriculum maps, he encouraged us to look to and learn from our colleagues to help us envision the ideal student. We talked. He emphasized hard skills and soft skills as something we should gear towards. This, he argued, would help us build a curriculum map for the whole student that plays off what our colleagues believe in.

4:00pm | The faculty meeting finishes and I leave school in a haste to make it to Math for America for a interest group meeting. I’m helping plan the first-ever MfA summer conference and tonight the planning committee is getting together.

4:21pm | I get on the 6 train, doubtful that I’ll make the 5:30pm start time for the meeting.

5:05pm | Shockingly, I arrive at MfA. I grab some pizza and catch up with a few of the committee members. Our goals tonight include improving the conference website, putting together a loose schedule of the sessions with the proposals we’ve received, and create a Google form for registration which starts tomorrow. I agree to help tackle the website with Carl Oliver.

6:35pm | Carl and I give the site a face lift. A part of the website is a blog. I write a brief post on the origins of the conference. Sometimes I still can’t believe this conference is actually happening…and that I’m helping to make it happen!

7:35pm | We wrap up a very productive meeting. Everyone heads out.

8:40pm | I arrive home after a long, yet productive, day. I wide down for a while before heading to bed at 9:30pm.

Though I’ve really enjoyed teaching them, I know I’ve put my ninth grade class on the back burner of my teaching responsibilities this year. I’ve basically been teaching from a textbook with them. I’ve been improvising where I can with Desmos and other tools and strategies, but the engagement and rigor for that class is not even close where it should be. I’ve dedicated almost all of my energy to my Algebra 2 classes. I sort of regret it. One side note: they LOVE VNPS and VRG. It’s crazy.

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?

I’ve had a couple visitors in my classroom this month, all of which from the Superintendent’s office. One was the superintendent himself, and another was in relation to the Big Apple Award that I was nominated for.

The observed lesson wasn’t ideal by any stretch. But maybe it’s fitting because that happens so often anyhow. (Thank you to 16th school trip of the season and random students from Denmark.) Nonetheless, the entire experience has been uplifting. Thank you to Mike for the humbling nomination that led to all this. Throughout everything, I couldn’t help but think of all the educators and leaders that have inspired me, like my former principal.

Regardless of the outcome, I hope that the passion, dedication, and thoughtfulness that I have for my students and school community was felt. I hope that the immense respect that I have for learning and the teaching profession also this came through.

All of I can think of in response to this prompt is my first period class. Our relationship this year has been a roller coaster, but for the last couple of weeks I think we’ve really connected. I realized this month that for a good part of the year I didn’t enjoy teaching them. I wouldn’t say I was merely going through the process, but I definitely wasn’t all in. I would rarely smile. I wouldn’t listen to them.

I was too frustrated with what I thought was their lack of motivation and ability. But that was just me teaching above them. I was focusing on curriculum and standards. I was ignoring who they were. I wasn’t teaching to their strengths.

Things still aren’t perfect now. But they’re far better than they were earlier this year.

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?

Although I didn’t explicitly state them in my goals for the year, I’ve discovered a place for VNPS and VRG in classroom this past month. My recent experiences have changed my classroom forever. It’s ironic that no matter how hard you try, sometimes you simply can’t plan for the best things that happen to you. They just do. Mostly out of necessity. It was sort of like that with VNPS and VRG.

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

My National Board submission is kicking my butt. Thanks Michael for all of your help with complex numbers.

On my journey and the mathematicians beyond white dudes initiative

At the end of last school year, I did a lot of soul-searching. In the midst of finalizing where I was going to teach beginning this year, I found myself reevaluating many of the core values that I held as a teacher. A huge dilemma for me was reflecting how I address identity and representation in my classroom. Race and ethnicity were of specific interest. Thanks to Claude M. Steele, so was stereotype threat. I thought about al this frequently, but it wasn’t something that I gave focused attention to over the previous ten years of my career.

I thought about all of this regularly over the previous ten years of my career, but I never gave it focused attention.

Inspired, over the last several months I’ve begun to evolve. I decided that I wanted my teaching to better serve the underserved population of students that I encounter every day. Located in the poorest congressional district in America, 90 percent of the students at my school are of color. My previous school was of a similar demographic. It was time to deliberately integrate these statistics into my practice.

Over this time, I’ve learned a lot. I’ve realized that as a white male, I have inherit privileges in our society. Privileges that almost all of my students know nothing about. Although my ignorance prevented me from openly accepting this earlier in my teaching career, I now see that I must do my best to understand my whitenes in order to best serve my students and school community. It’s not enough to simply ignore race and try to teach above it, like I’ve done in the past. I cannot assume that my lessons and the mathematics I teach need not address the racism that my students face every day.

I’ve read works by Jose Vilson, Monique Morris, Claude Steele, Robert Moses, and Stuart Buck. After sparking conversations colleagues, I’ve absorbed a great deal from those who are addressing race and equity far better than I. I’ve attended workshops where I’ve publicly confronted my own biases. I’ve made myself vulnerable by opening dialogue with my students about their take on things. I’m learning directly from them.

This brings me to the Mathematicians Beyond White Dudes initiative that I started this year with my students.

C7tREjRX0AAH7mV

I got the idea from Annie Perkins. Back at TMC16, I attended her workshop where she shared her approach of profiling outstanding mathematicians that weren’t male and weren’t white. I was immediately hooked. I knew that I had to bring this to my kids. Read more about Annie’s outstanding work.

I’m not going to go into the worthiness of this project, because Annie has done that so eloquently already. Instead, I’ll just share how I’ve implemented it.

So far this year I’ve featured a different mathematician for each unit. (Next year I hope to do it more often.) I pull from the list of mathematicians from Annie’s post and piece together a one paragraph biography that highlights each mathematician’s life, achievements, and contributions to the mathematics community. I formally present each mathematician at the start of each unit. The conversation doesn’t usually last longer than 5 minutes. I print and copy the bio of the mathematician on the cover of the unit packet that students receive. I also post the bio of each mathematician in the classroom. Link to the doc containing the posters.

My students have really enjoyed it. They look forward to the big reveal of the next mathematician. Rounds of applause for the mathematicians are not unusual. Other teachers have even seen the posters in my classroom and commented about how they like the idea.

Now I’m not going to sit here and say that all of a sudden I’m doing an excellent job at addressing representation in my classroom, because I’m not. Gosh no. I’m still struggling and haven’t done anything to address the curriculum I teach. I’m just trying harder to be more aware of my own ignorance on the matter and teaching towards it. This is just one small way that I feel I’m accomplishing that. There’s still a long, long way to go.

Becoming an anti-racist teacher is my goal, I think. My students enter my classroom each day with the hopes of becoming better students of mathematics, better people. This is their parents’ hope too. I owe it to them to ensure that my instruction addresses and embraces who they are, really. We all do.