Graduation

My first freshman graduated today. We grew up together, me a first year teacher when they were freshman, and now as they graduate I feel I have experienced some kind of rite of passage as well. I wrote little blurbs for a few for when they come up to the stage, after saying their name, but before they actually take their diploma in hand. Here is one I wrote for one of my dearests:

"WR. In the hallway, in the classroom and on the basketball court, your smile and intelligence have lit up our community. Your quiet and fierce determination to do things your own way has helped you achieve success today: may it continue to do so. May your life bring your joy and deep satisfaction. You deserve it. Congratulations, WR."

As a staff, we wished them success, joy, satisfaction. We admired them, acknowledged their accomplishments. Some of us sang a song to them, which got everybody clapping and energized. It was a simple, sweet graduation ceremony. I felt (I thought strangely) a little numb.

Then I went to the staff after party down the street, where we were going to be celebrating and relaxing together, and also toasting the staff that are leaving this year to have babies, pursue PhDs, move to Miami and get married, become lawyers. We spent over an hour singing the praises of the people who are leaving us. We sang, cried, told stories, expressed gratitude, cited evidence of the amazingness of each person and all the ways they would leave us with holes in their absence but also with the teachings and memories to inspire us and continue to help us grow.

After about the 5th person (we had 8) I realized that we could do this for every single one of us. There wasn't one person I could think of that we would have to fake it for. We genuinely love, admire, appreciate and learn from each other. It was at this point that I started crying, really feeling the grief and upsurge of energy that perhaps needs to come on graduation days, on days when we say goodbye.

I realized that we had done the same sort of thing (albeit with a little less specificity or at least at less length) for our graduates that morning. This specific expression of love and appreciation, admiration and encouragement, is amazing. It was amazing to hear, to say, to feel indirectly, knowing that I would get it directly if I decided to leave too.

I thought it was deeply nurturing for our community, even as we say goodbye to so many, to reinforce and make explicit our deep wells of gratitude. Statistics aside, I believe today that what we're doing matters, that we're being human together in amazing ways, and that we can do amazing things, that I can do amazing things as a part of our community.

May we all know our own worth, which is extraordinary, downright priceless. May we weep with abandon when we say goodbye and welcome the relief and hope that comes of endings and new beginnings.

kids thinking

We had meetings all day yesterday. I got discouraged. Thinking about the past year has left me a bit deflated. I have grown more confident in my own thinking about teaching mathematics, but remain discouraged about my ability to teach it well.

In the math department meeting yesterday, I heard my colleagues describing how our students simply don't think when we give them mathematics to do. Even when they have all the necessary skills, they don't engage their minds. We were in agreement that this is not because they can't do it. We all believe they absolutely can. I believe that it's one of the things their brains are designed to do naturally. My new idea is that somehow they are not deeply thinking in math class because they haven't found it useful to do so.

I know that I have a tendency to go too hard on myself and my colleagues in moments like this. I asked myself, "Do I want a revolutionary miracle in every class?" If I do, I am probably setting myself up for failure. Is getting kids to use their naturally pattern-seeking powerful minds such a huge demand? What is the part that gets kids really deeply involved, not just taking a class for the sake of passing this adolescent rite of passage?

How do I get kids to value the power of their own thinking?

I remember this day a few weeks ago when I was at a loss of how to teach finding the slope of a line in a way that demanded this from them. Of course I could just show them, and they could do it, no problem. Maybe even some of them would think about what they were doing while they were doing it and notice some patterns and sense in the whole thing. Maybe even they would all be so successful that if I gave them a quiz they would all ace it and I could pat myself on the back feeling very successful because my kids were successful.

I talked with Ben about it and he reminded me: "But it wouldn't be math."

Right. So I'm trying to teach math.

This last year I feel like in many ways I've been doing math for the first time. Truly discovering, playing, exploring and sense-making about actual phenomena. Maybe I just need a little more practice to teach this way well.

I'm looking forward to next year. I will be better at classroom management, at cultivating positive open relationships with kids, at organizing and structuring transparent systems and routines in my classroom, and at unit planning. So I'm excited that having those ducks more in a row might mean that I have more time to think about inviting my kids to really think, figuring out what they are thinking and celebrating and honoring and valuing that so that they do it more.

Yeah.

Ben Peled Saves the Day

My math teacher friend Ben Peled sent me this yesterday and it made me gape, smile and feel a bit better.

"Often at this time of year, surveying all the kids (may not) have learned, I feel overwhelmed by the gap between the teacher I am and the teacher I'd like to be. That's why it's always good to be reminded that, however often I screw up in the classroom, there's someone out there effing it up much, much worse."

For all of you who have been having a challenging week, doubting the value of your practice, feeling discouraged, or frankly just need a little eye-popping.

May you be reassured and rejuvenated for these final days.

Jascha on Sims

My brilliant friend Jascha Hoffman sent me an awesome interview he recently did with John Sims, who creates and curates mathematical art, and who has a year long series of exhibits at the Bowery Poetry Club.

Sims is articulate about the intersection, even union, of math and art. At last. I'm interested to learn and see more!

2 Additions to my Conceptual Understanding

I just graphed these inequalities for the first time. I was filling out the end of year survey for Math for America and the last section asked us to identify the common misunderstandings that might arise and how we would address these misunderstandings.
I've been thinking a lot this week about how to teach for conceptual understanding, how to get kids to use skills as their inherent pattern seeking mechanism activates. How to create curricula that gets them generalizing useful and true patterns (rather than, for example, that every function is linear), and how to offer accessible depth in mathematical thinking.
So I was excited to play with these inequalities, partly because they were new to me, partly because they demand conceptual understanding and resist procedural memory. Rather than go on, I leave you to play with them yourself if you're not already familiar. I'm going to use them with my 10th graders next week!

Then I discovered that jd2718 came up with this activity back in March, and there's a nice discussion of them in the comments on that post. Check it out! Thank you jd2718 for being so creative, brilliant, infectious!

Also, I did some catch up last night on Ben's blog and was really inspired by his discussion of revising how we teach and present negative numbers. He writes beautifully and at length about this, and I seriously encourage you to take 10 minutes and read his post. He's been reading some awesome primary texts and the history they tell has convinced him that we should teach negatives a bit differently. First, we can we ask the question (perhaps often) do negative numbers even exist? Then let's introduce negative numbers first as solutions to things, like 5-7. Let arithmetic necessitate these new creatures. Once we're comfy, we can start using those things as objects with which to do arithmetic, as solutions to equations, etc. Last we can use them as coefficients (and exponents?!). I love this!