Math in New Orleans

Over our spring break last week, I traveled to New Orleans with two of my best friends from college.

I think at least once every day the whole trip I ended up saying, “well, you see, this is math.”

Because they love me, they were (or at least acted) interested instead of annoyed, and humored me in taking pictures and explaining things.

We found this beautiful Holocaust Memorial sculpture on the river walk along the Mississippi. The sculpture can be viewed from 9 different locations around its edge, which offer different perspectives on the Holocaust. I failed to take pictures of all 9 because I was too busy explaining the angles to Cat and Ali, but the 3 shown are the Star of David, a Menorah/rainbow, and a black background with colored squares to represent each of the groups that were persecuted and put to death during the Holocaust. You can look at the other views and their interpretations by the artist here. I loved that they had each of the viewing locations marked on the concrete ellipse around the sculpture, along with a sign that described how it worked.

 

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We always find the most economical way to get around when we travel and the NOLA RTA system was pretty awesome. (5 day unlimited ride pass for their whole public transport network, streetcars and buses, for $15!)

The only thing we struggled with was figuring out when the next bus/streetcar was coming. The app had schedules for each route that you could look up, but it only listed times for the major stops, not every single one. Math teacher me started finding weighted averages between the two major stops we were closest to in order to estimate how long we would have to wait. (This problem became less once we figured out there was a number on the sign for the stop you could text to find out when the next bus would arrive, but a few stops had broken or missing signs so I still felt helpful.)

 

We went to the National WWII Museum. As far as history goes, it’s not usually my favorite thing to learn more about in my free time (Cat and Ali really wanted to go), but this museum was really well put together. I loved that they gave you a dog tag card at the beginning and you could scan it at various points throughout the exhibits to learn more about a specific soldier. I was very excited that my soldier was one of the first graduates of the Tuskegee Airmen program and pioneered a lot of things for African American soldiers!

I did find these flight maps really interesting though. They had to measure all the wind speeds and angles and chart everything by hand. I spent a lot of time looking at these and figuring out how they would have been created.

 

I got to attend my first NBA game while we were there, the New Orleans Pelicans vs the Memphis Grizzlies! Cat and I went down to the gift shop after the first quarter and I discovered this mini exhibit about Kepler’s sphere stacking, complete with an example using basketballs! I was nerding out pretty hard over it, and when we got back to our seats, Cat just said to Ali, “Liz found math while we were gone.” Of course I did. It’s everywhere!

Later in the game, the ad banner by the court changed to this image that just read MATHLETES and I…kind of got excited. In fact, I think the exact exchange was:

Me: “GUYS THE BANNER SAYS MATHLETES!!!!!”

Friends: “What are you talking about.”

Me: “IT SAYS MATHLETES I’M TAKING A PICTURE!!!”

Further investigation has unveiled the Pelicans’ Mathlete’s program and I’m OBSESSED. You go, Pelicans!

 

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I was also very excited to see some more complex metrics on the stats board during the game. I read one of Dean Oliver’s books last year and really enjoyed it, and am generally fascinated with the process of major sports leagues gradually adopting the casual use of these analysis based metrics in their fans and coaching. The Four Factors aren’t super advanced, but to see them integrated into a mainstream enjoyment of a game was cool.

Finally, I loved being able to compare yourself in size to an NBA player at the game. Conclusion: Anthony Davis is a large human and I am a small one. Also, as my students said when I showed them these pictures yesterday, “Dude, a Point Guard is the smallest one and your hands are TINY!” Yup. Pretty much. I also loved that my students remarked that your arm span is supposed to be approximately your height, and we then had a discussion of how Anthony Davis’ arm span is EIGHT AND A HALF INCHES LONGER than his height.

 

Basically, math is everywhere. New Orleans was a great city, full of color and music and lots of cool things to do. And a lot of math. 🙂

EdCamp Iowa 2017

Attending EdCamps always fires me up and gets me excited about things again. I love the unique setup where teachers are directing the discussion, deciding what topics they want to be addressed, deciding which conversations they want to be a part of. I love how most of the sessions aren’t lectures, they’re discussions. Conversations. Multiple perspectives and not just one teacher who is “dispensing knowledge”.

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Love my DCSD coworkers!

Several Davenport Schools teachers hung out at Eldridge’s EdCamp this weekend and it was awesome. The things I’ve found myself thinking about the most since Saturday are the words of other teachers in the sessions I attended…

 

“No matter how good you are, everyone can get better.”

This came out of a session on teacher leadership structures. We were discussing the different models we all have at our schools and talking about how if you have the right teachers in the leadership roles, the structure doesn’t really matter. This comment kind of summed up everything.

For the teachers in official leadership roles, you can still get better. You can collaborate with other teachers in or out of the leadership structure, you can observe other teachers and seek out feedback.

For new teachers, the teacher leadership structure seems to work very well and they take advantage of the designated teachers in leadership roles to get insight on their teaching naturally. They want the knowledge others have to share.

For veteran teachers, some of whom react negatively to being asked to observe or get coaching from coworkers, it’s good to acknowledge that teaching should not be an isolated endeavor. We all have things to share with each other. We all have something we’re really good at and something we could work on, and it’s time to admit that. It’s time to admit that we’re better together.

 

“The most important thing about you as the teacher is not the grade you give them at the end.”

The session was about preventing teacher burnout, and how sometimes you have to let go of grading every single student project in great detail. The idea, though, came up again and again throughout the day.

What’s important about us as teachers? Why are we there?

We aren’t grading machines. We aren’t there to put a percentage value on our students.

We’re there to help them build a set of skills that will help them to successfully interact with their world. To show them strategies and expose them to information. Not to give a grade.

 

“Change is like moving a cemetery, you have to move one body at a time.”

We all laughed at this, but it’s incredibly true, especially in the transition many of us are making to standards based grading practices. We talked a lot throughout the day about pushback from parents and students. Parents who get upset about not having class rank, or valedictorian, or perfect 4.0 GPAs. How do we explain to them that we’re trying to reorient the entire system to be about understanding and learning instead of about points? How do we explain to them that we’re removing all of the goals and achievements that students have worked towards for literal decades and replacing them with descriptors of proficiency in content?

It’s tough to break traditions of 100 years.

How do we explain to students that assignments are practice, that they aren’t “getting credit” for them but are building towards understanding of the content that they can show on an assessment? How do we build the intrinsic motivation to get students to complete tasks and assignments if we aren’t giving points for them? How do we reorient their thinking to help them understand that they should do these things because they will help them get where they want to be at the end?

You have to move one body at a time.

Change one thing about your grading at a time.

Reorient their thinking one tiny piece at a time.

Maybe you’ll get a few students on board one year. Their parents the next year.

Half your students the year after.

We will get there eventually, and it’s tempting to rush because we know that it’s a better practice for learning and understanding. But if we move too fast towards something new and totally different…everyone gets left behind.

 

“Struggling students are everyone’s students”

Simple as that. Students who are struggling (with mental health issues, learning disabilities/IEPs/504 plans, attendance, outside of school things, motivation…) do not “belong” to the special ed department, or the counselor, or the BD teachers, an interventionist.

They. Belong. To. Us.

Every school should be working to educate every student. Not just the ones who want to learn. Not just the ones who stay in your classroom all day and never get pulled out for interventions or counseling sessions or supports. Every. Student. In your building.

If you can do something to help any student in your building learn…why aren’t you?

#5goodthings

It’s been…a week. I think it’s been a week for a lot of teachers across the country, but it was just, you know, one of those weeks at Mid City. A ton of our teachers sick, students restless, we’re in the bottom of the winter attendance pit, etc. Next week is going to be a rough one for some of our students and our staff as well, as it’s the birthday of our student who was killed this summer.

I need some positivity.

 

Katie Cotugno is a YA author whose works I have never read. (They’re on my infinite to-read list…) My friend Tedi however, who is a 6th grade Language Arts teacher on the other side of the state, is very into her. She often shares with me Cotugno’s comments on twitter, and participates in what has become one of my favorite twitter things – #5goodthings.

It’s pretty much what it sounds like – on Fridays or on whatever day you’re feeling down about things, post 5 good things in your life at the moment, to remind yourself of the ups when it feels like you’re drowning in the downs.

I’m making it my Friday opener for the students today, and so I thought I’d blog about mine to participate as well. Plus, like I said, I need it today.

 

  1. 2nd place at trivia 3 out of the last 4 weeks
  2. My Algebra 2 class and their penchant for calling each other “sweet dolphins” and their genuine love and care for each other
  3. A student coming in first thing this morning to show me pictures of another student’s newborn baby, born yesterday
  4. Snapchats, instagram posts, and tweets from 5 Seconds of Summer being back in the studio working on their third album
  5. Coworkers who will go out with you after school and just have an hour long vent session with no judgement

Seek Justice. Love Mercy.

A lot is going on in our world right now.

It kind of feels like what we have been debating recently is the relative worth of different types of human beings. If you’ve read my blog before, you know that perhaps my strongest belief is that we are all worth the same. I read the news and see things that are happening, and then I walk into my classroom and see my students.

 

I love my students. Some days, it feels as though the love that I have for them is causing me physical pain with how it wants to leap out of my chest and take over. It’s very hard to watch things happen that feel threatening to their abilities to be fully themselves. I walk into my classroom and want to wrap all of them up in a big hug and never let them leave – keep them in the safe space within our school walls that we have created together.

I can’t. I can’t keep them in this safe bubble that we’ve built. They have to go out into the world, and every day our staff of teachers and case managers and counselors try to build their resilience, their intelligence, their resourcefulness, their courage, and their sense of self so that they can leave our school and find success.

The news lately has been making me feel sort of hopeless. We can call our representatives, we can attend protests, share social media posts supporting the equality that we want, but then it feels like there’s nothing else we can do but watch it happen. Watch as decisions are made that will take away the freedoms and rights of certain types of humans.

“Courageous” by Casting Crowns came on the radio as I drove home from church on Sunday. The end of the song has a refrain that comes from Micah 6:8, phrased in the song as:

Seek Justice.

Love Mercy.

Walk Humbly with your God.

 

Those words struck me hard. I haven’t been able to get the song out of my head all week. No matter how hopeless a fight seems, we are called to seek justice. To love mercy. To walk humbly.

Teaching is its own form of this. Every day in our classrooms, we are fighting to create a future made up of compassionate, intelligent, resilient and resourceful humans. We are showing our students the importance of seeking justice, of standing up for what is right. Of loving every person you encounter, no matter their actions towards you. Of giving every life the same value.

To all the teachers who have been weary lately: you are heroes. You are fighting the good fight and striving to do what’s right, and what you are doing still matters. It’s important. You’re making a difference. Keep going.

Brain Melts and Typos – #MTBoSBlogsplosion Week 4

The theme for Blogsplosion this week is “We All Fall Down”. The times in your classroom where you make mistakes, accidentally teach a mathematical inconsistency, try to do a really cool activity and it’s a disaster…we all know those days.

One particular day immediately came to my mind when I read the theme. Algebra 2 was working on systems of linear equations earlier this year, and Ms. Kormann from next door was filming the class for my model teacher application. Of course filming leads to miniature disasters – why would something go well when you’re recording it?

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The day before, we had been working on an assignment and one of the students called me over, saying, “Miss Mastalio, the solution I got doesn’t work in the equations but I can’t figure out where I made a mistake.” I looked at her work for several minutes and also couldn’t find a mistake in her work. The whole class thought it was pretty funny that I couldn’t figure it out. When the bell was about to ring, I told her to just turn it in and I’d find the mistake later, and I would let her fix her solution then.

So we started this class with me coming in and saying, “Hey, so the mistake that we couldn’t find in [student]’s work yesterday? It turns out that 6+8 isn’t 13, guys. Just in case you didn’t know.” ARITHMETIC, MAN.

We all had a good laugh at our collective student/teacher brain meltdown, and I began the day’s activity.

 

We were completing a Question Stack (one of my favorite forms of practice) to  help them choose a solution method (graphing, substitution, or elimination) and get practice solving systems before their assessment. The nature of Question Stacks means that students don’t begin with the same problem, and they also have an answer bank of all the possible solutions to work from.

So I was circulating, answering questions and clarifying things, when one of my students hit a problem where she kept getting a solution that wasn’t in the answer bank. I came over, quickly glanced over her work, and couldn’t find the mistake. Because of the mistake I had made on the student’s work the day before, I checked all of my arithmetic with a calculator. A few other students noticed me doing this and laughed, then continued working.

When I still couldn’t find the mistake, the student suggested, “what if I tried to solve it with a different method and see what happens?” I agreed that sounded like a great idea, and began circulating again. Soon, another student hit that same system. She picked a different method than the original student was using, because they were sitting next to each other and she realized that there was some issue. So we now had all three possible solution methods going on this problem.

They kept getting the same solution. Other students in the class realized that something weird was happening in our corner – some of them were reaching that system in their work, and some of them decided to skip to it and try it. I called Ms. Kormann over from behind the camera to come check the work as well.

No one could find a mistake. We kept getting the same solution with every solution method. The whole class started a heated discussion of each solution method and the process behind it. Instead of getting mad and giving up, they started getting mad and analyzing their mathematics.

Meanwhile, I was panicking because I could not figure out where I had gone wrong. I grabbed the textbook I had pulled the problems from to double check their solution. In my classroom, I had students checking each other’s work, trying multiple solution methods, and discussing algebra. (To be fair, they were also yelling “WHY” a lot and declaring themselves failures, so that wasn’t good).

 

Anyone want to know what the mistake was?

Because it was awful.

I transposed the x and y in one of the equations from what the textbook problem said.

Just. Switched them.

Of course they weren’t getting the solution in the answer bank.

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That day was the best possible kind of disaster – the disaster where your students stay with you the whole time and persevere in their attempts to solve. Not all of my disasters go that way, believe me. This one was super memorable though. I was so proud of my students. We bonded over brain melts and those days where you just can’t even add.

They still tease me about it, and I’m totally okay with it.

Not My Words

It’s week 3 of the #MTBoSBlogsplosion 2017!!! I’m really loving this challenge to blog more, and discovering blogs of amazing math teachers through the summary posts.

The challenge for this week is “Read and Share“. Read some blog posts from other teachers, and share their words. I am so excited for this challenge, because it gives me the perfect opportunity to go back through some of my feedly tag folders and read posts I haven’t read in a long time. Click the first word of any quote to read the whole post.

 

These are about the WHY of teaching. The heart wrenching stuff, the hilarious stuff, the moments that keep me coming back every day even on the days I want to quit. I hope they help you remember those parts of the job.

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If you’re not reading One Good Thing, stop right here and head over there. These stories of finding the (at least) one good thing from every day of teaching are often hilarious, sometimes a struggle to find the thing, very real, and make me cry more often than I’d like to admit. I love this one from right before break:

Those are the real victories, my Teacher Loves. Those and so much more that you and only you know because your classroom is a safe place for kids to share their thoughts, their worries, their triumphs, and their fears.

 

 

I’m breaking the challenge rules a tiny bit because Love, Teach is not a math teacher, but I think pretty much everyone knows and loves her blog, and this post is one that I think about. Often. This paragraph felt like she reached straight into my own heart and pulled it out (I also wrote a post in response to Orlando that was very inspired by this one):

I care about all of this so deeply because of you. Teaching has fundamentally changed me, is changing me, and it has to, because I spend hours every week interacting directly with kids who represent a vast array of beliefs, values, and experiences. I love each of you so much that sometimes I think I’m in actual danger of my heart exploding out of my chest, and more than anything I just want all of you to live in a world where you feel safe and strong and valued, because feeling safe and strong and valued makes it easier to be brave and kind and inclusive. And in case you haven’t been paying attention, we need more of that.

 

Jonathan Claydon‘s posts often challenge me to think hard about curriculum and question design, but this one is more of the chills-all-the-way-down-your-spine types. Because you relate to it so hard. And this job is sometimes so hard, emotionally.

This is supposed to be a job? It’s just work?

But also, sometimes his posts just make me laugh. A lot. You all know how important it is to have fun in your classroom, right? Right?

43. Draw a kitty in a spaceship. Yes, you read that correctly. DRAW THE KITTY.

And here are 12 cats piloting spaceships, because I know what you want:

 

This one from Dan Meyer inspired me to do a bottle flipping project in my Sports Statistics class, which the students LOVED:

I didn’t think there was a useful K12 math objective in bottle flipping. My commenters served their usual function of setting me straight.

 

Tracy Zager has some lessons about how often we explain away our students’ interesting ideas because they don’t follow the formal mathematics we’re familiar with:

I drew the squiggly lines and asked who thought they were straight. A few hands went up. Abby raised her hand halfway, then put it down. She said, “I made up a new word for that kind of line. It’s vertiwiggly.”

 

I’m in love with Ben Orlin’s Math With Bad Drawings. I kind of want to wallpaper my classroom with them. Whenever a new one is posted, you never know if it’s going to be hysterical, inspirational, or hard hitting and challenging. Possibly all three. These are some favorites:

Graham’s Number can be defined by human symbols, but never fathomed by human minds. The notation can reach what the mind cannot grasp.

(my students have loved the concept of Graham’s Number when I’ve presented it to them in class)

But I can hate this view, this toxic meme, which I believe is latent in our stereotypes of mathematics: this belief that generating new mathematical ideas is man’s highest calling, while wallowing in old ideas is grunt-work fit only for mules, washouts, and the dim bulbs we call teachers.

I would love to quote the entirety of this post on why we learn math, but…just go read it:

Mathematicsis a safe playground with all the richness of reality.

 

And this post on sharing other people’s words would be incomplete without a nod to Sarah Carter. There are too many posts I could have chosen to include from her, but honestly one of my favorites is this one, where she shared incredibly detailed pictures from her classroom of all the posters. I always find myself looking in the background of people’s pictures from their classrooms, trying to see how they decorate and set things up. Sarah brought this gift to me so that, at least for one other teacher’s classroom, I get to see everything.

Whenever I read other blog posts where people share pictures of their classroom, I’m always left wanting more.  I want to see every single thing hung on the wall.  I guess you could call me nosy.  😉  So, I set out to write the blog post I would want to read.

Honestly, the Math is Secondary

If you had asked me in college, I would have said that the phrase “honestly, the math is secondary” would never come out of my mouth in reference to my classroom. In the last three and a half years of teaching…I’ve said that phrase. Out loud. More than once.

The theme for this week’s #MTBoSBlogsplosion is Soft Skills. Soft Skills are the interpersonal skills, the social behaviors, the habits of learning and communication that aren’t part of your curriculum but are, arguably, just as or more important for your students to learn. Of course the math is still important. I wouldn’t be teaching it if I didn’t think so. Francis Su’s closing remarks as president of the MAA are beautifully moving on the reasons why we should learn and teach mathematics.

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When I was searching for jobs during student teaching, I didn’t really know where I wanted to teach. High school? Junior high? Big school? Small School? I pretty much applied anywhere that had an open position in an area where I might want to live, and went to interviews. At the end of every interview, they ask you if you have any questions for them, and I made my question “Why should I want to work at your school over other schools?” because I thought it might help me make a decision. When I asked this at the interview for the alternative high school I now teach at, the principal started crying as she told me about the students there. About how they come to the school feeling like failures in so many facets of their lives. How they haven’t had many people believe in them. How they don’t know how to succeed because they’ve never done it. I knew in that moment that I’d found my school.

My students often don’t know how to act in social situations. They don’t have many role models in their lives. They’re often angry from experiencing failure after failure, from adults who should never say things like this telling them that they won’t amount to anything, that they can’t succeed.

My first goal with a new group of students every year is to know them. As people, not as math learners. I do surveys on the first day of school that ask their most important values, their favorite things, their previous experiences in math class. Based on their most important values selected from a list, I sort them into a Hogwarts house, which gives me an idea of how they might react to certain types of situations and of ways to push them to be better (Gryffindors thrive on competition, for example). These are students that very much do not want to open up. They don’t trust easily, so I have to find sneaky ways to learn more about them until they let me in. I make them list ten things they love, but give them the out that if they can’t fill the list with ten things, they have to finish the list with things that are the color orange. Many of them can only fill in three things before switching to pumpkins.

Every Friday for the whole school year, instead of a math question for their bell ringer, I post a hypothetical question on the board. “If you had a million dollars, how would you spend it on?”, or “If you were a ghost, what building would you haunt?”, “What would be your three wishes for a genie?”.

They write their answers on their opener sheets. They turn them in. They won’t share them in front of the class…until about December, when some of them start shouting their answers as soon as the bell rings. Every week, I read all of their answers, and I respond. Even if it’s just a smiley face. I start asking them questions in class – about their job, about their grandma who’s sick, about the TV show I know they love.

Slowly, they start to turn the questions back on me. They ask how my weekend was, if I got to see my nephew. They congratulate me when the Packers win. They want to know my answer to the Friday Question (I would haunt Madison Square Garden). As this happens…they do more math. They open up. They learn to trust. They get small successes and want more. They realize that when they ask questions (silly ones or math ones) they get answers.

No one is allowed to judge other people’s answers. They can ask questions to learn more, but they can’t call an answer dumb or boring or weird. They learn to treat themselves and others as people whose opinions matter. That how it has been for them does not have to be how it continues.

When you remember that you’re teaching people, the content becomes easier for them. When they know that they matter to you, they’re willing to ask questions until the Quadratic Formula makes sense.

My email signature contains a quote from Harry Potter: “Every human life is worth the same, and worth saving.” I don’t even begin to believe that I can ‘save’ them all. Not every student passes my class. Some of them leave with the same attitude they came in with. But ‘every human life is worth the same’? That I can show them. That, we can work on.

I have a student who came to us after dropping out for awhile. He barely scraped by in my class last year, rarely speaking, never turning in assignments on time. He sat in my room for a whole afternoon on finals day with me convincing him to keep trying assignments until he left at the end of the day saying “D-? Good enough.”

He won student of the month last month. He earned a B in my class this year. He told me a fifteen minute story about how he watched YouTube tutorials to learn how to fix his phone screen by himself to save money. He finished his assignments on time and then spent his spare time in class working on challenges I had posted. He tells me some of the funniest jokes and stories. He asks me for advice.

Do I think my Friday Questions caused this transformation? No. It was a lot of things, and most of them weren’t even involving me. But through the questions, I learned how much he loves drawing, how important family is to him, and how funny he is. From his intro survey this year, I learned that he’s a Ravenclaw, which helped me to seek out and push his curious and creative sides.

He graduates tomorrow.

Honestly, the math is secondary. (But he learned a lot of math, too.)