The conference is here.

The question of what’s at the rapidly beating heart of your classroom is a tough one. Let me rephrase that: for me, it’s tough, because it is totally evolving. Also whatever is at the heart of your classroom is your hidden curriculum — something that isn’t content, but just as important (if not more so) for kids to take away. So it’s pretty hard to get a handle on. It’s values.

Beginnings

In my first three years, I would have said the heart of my teaching revolved around three words:

clear

consistent

fair

Yes. Those three words drove me. The thing about having a core philosophy is that: everything revolves around it.  Every assignment. Every interaction. Every expectation. And although there are hard decisions that have to be made, when I struggled through them, I found I eventually turned back to my core beliefs, and I saw the light. Do I let that kid, that sweet sweet kid, take a re-test? Do I really need to create a super involved rubric with benchmarks, or can I just outline the project? If everyone in the class bombs an assessment, what do I do? [1] When holding core beliefs, every choice has to be intentional. Because these are what you value, and you need to enact those values. If you can only “say” your values, but you can’t “see” your values… then you’ve failed. [2] [3]

This philosophy has helped me out a lot with classroom management. It has helped me gain the respect of at least a good number of students. But I have started to see that philosophy as a baseline, now, of what I am doing. I believe in more.

Current Status

In the past year, the heart of my classroom has expanded to include more than clear, consistent, and fair. Thanks to the philosophical reorientation that Standards Based Grading has given me, it now includes metacognition and proactivity. [4]

I want my kids to be aware of what they know and what they don’t know. I want them to aware of the process of learning, and strategies to help them along the way. And I want them to be able to act on that knowledge. This is my hidden curriculum.

In Calculus, I used Standards Based Grading, which is all about kids getting a handle on their own learning. It forces them to understand what they know, and what they don’t know, and really articulate it! [5]

Dismantling the course into individual skills allowed me to have a specific breakdown of what the student knows and what the student doesn’t know. A student might have mastered how to apply the product rule, but struggle with explaining in words where the formal definition of the derivative comes from.  With SBG, I know this. In a school newspaper article written about my calculus class, one student was quoted: “The fact that the material is broken down into very specific skills as opposed to chapters or sections means you can focus on what you don’t know and figure out what you need to improve.”  More than me knowing where my students’ strengths and weaknesses are, my students themselves can recognize them.

I talk about metacognition, but that’s only half the battle. Who cares? Kids knowing about their learning habits, that’s great. But it doesn’t help them unless they believe they can grow from it. This is something I’ve been thinking a lot about since reading Carol Dweck and her notions of growth mindset. If a student — especially my students who tend to come to class never really appreciating math — thinks they suck at math, that they aren’t a “math person,” they’ve already stabbed themselves in the eye, shot themselves in the foot, whatever. There is blood everywhere, and it sucks. My kids come in with a fixed mindset. To get them engaged, to act on the “metacognitive” work, to see that doing well in math isn’t a matter of being “born with it,” I need them to see themselves as people who can change through hard work. Because really, if they don’t believe that, they won’t be doing hard work. They’ll simply continue to try to get by in math.

The thing is, we’re human beings. We suck. It’s hard to alter our own perceptions of ourselves. It’s also hard to say “we suck” and then decide to move on from there to say “let’s do things to suck less”!

This year I’ve been trying to do some good work in getting kids to be proactive, and to build their confidence. It involves a lot of individual communication with students. It involves me showing them that I care. It involves me avoiding ever comparing a student to another. It involves me demonstrating passion which occasionally translates into passion in them. It involves me talking explicitly about how math is a process, a journey, and how anyone can do it. It involves me not falling into the trap of thinking of certain kids as “smart.”

Standards Based Grading has helped me get kids to be proactive. My favorite example of this is a student reflection I’ve blogged about before:

1. I like the way that even though I was falling rapidly into a hole, and it felt almost impossible to get out, once you talked to me I became proactive and tried my best to do better. I like to continue meeting with you. I also like to continue to participate in class and asking questions. I think asking questions in class was the biggest way for me to better understand the topics.

2. I wish I would have started from the first day of school in this attack math mentality. I was acting very passive and like ‘oh I don’t get it now, but I will later,’ which honestly was the worst thing I could have done. I also wasn’t used to the class setting and the grading system. But once you emailed me and I met with you and I know that this is a class that I have to be in it 100%, and that your method is one that helps us actually learn, it was just beneficial. I needed that scare and wake up class because I was in serious denial. I became more on top of things. However, I had to dig myself out of a huge hole that I put myself in, but eventually the rhythm has become one that I used to. And I’m almost in a weird way glad that I learned the hard way because now I truly understand Math.

[1] Of course I don’t mean “clear, consistent, and fair” to mean everyone gets the same treatment. Context matters, and what’s fair is not always “treat everyone the same way.”

[2] See Sizer and Sizer’s The Students are Watching (my review here)

[3] A grand experiment would be to have someone watch a video of your class, and try to suss out your values, and where they are expressed through your actions and words.

[4] SBG also has helped me remember the point of teaching: student learning. And now I have a razor sharp focus on that goal.

[5] In Algebra II, I deal with metacognition also, but not as well. I do this by talking to my kids explicitly about categorizing what they know and what they don’t know.

I tried to make homework more meaningful, by creating a full feedback loop. If a student got something wrong, they were asked to re-do the work and correct it. Otherwise they would have practiced the skill incorrectly, or illuminated the concept poorly, and never fixed it. (The “ill-leave-it-to-learn-before-the-test” syndrome.) I did this using binder checks (and redux), which had the added benefit of keeping (most) students organized.

So as I wrote before, I had a dickens of a time getting the courage (courage, as they say in French… not that different) to share my teaching video with others. But I did it, and here are my general thoughts based on my feedback — thoughts reinforced by what y’all commented:

(1) To do video analysis, there needs to be some sort of safe space for teachers to share. This was terrifying for me, because I felt like I was going to be exposed as a fraud — someone who can’t teach. And more importantly, I was afraid that people who lose any respect they had for me. I think teachers who are participating in video analysis need to have someone help them deal with the emotional aspects of this. The thing that helped me, personally, was realizing that I would be a pretty sucky teacher if I never learned to grow. So I had to change my outlook about sharing the video: from a vulnerable place where we feel we’re exposing ourselves to a cruel world, to an exciting but challenging opportunity to really improve my practice through the help of friends. It’s like with our kids… we don’t want them to see our class as an unsafe space to make mistakes and grow from them… we want them to see our class as a place to learn and grow and be excited about what they do.

(2) I sent out the 50 minute video and asked my friends to look at it without any directions. Basically because I hadn’t learned how people actually analyze videos. I got a diverse set of responses — each focusing on different things.

EXCERPT ONE

–Wow, great way to respond to a kid asking a question that was just asked. I’ve never thought of having kid 1 respond for me and will be stealing that for next year.

–Thank you for using the word ‘exemplar’

–I wonder what other students would have done if you had written what [STU] had originally said at 9:15; 10x vs 10^x.

–You use the phrasing “will you..” when intro-ing the problems on the board. Sounds like kids have the option not to.

–I like your use of ‘crazy’. A lot of your side-comments to the students are super-similar to mine and it’s just nice to hear that I am not the only teacher that talks like that.

–I like how at 14:20 you have her point to things on the page instead of doing it for her.

EXCERPT TWO

EXCERPT THREE

EXCERPT FOUR

There were a lot of things that I didn’t notice, or acknowledge, about my own teaching that came through in these. Especially the things the reviewer liked. I also really appreciated when I was given a suggestion for an alternative thing I could have done (e.g. “I keep thinking here that if the kids were writing their explanations instead of explaining to you, and you writing, it would help them develop their communication skill and help the rest of the class see what they are thinking”).

(3) Of the various ways I got feedback, I think the third one (+, delta, ?/notes) made the most sense for me. I would love for it to also have had approx times on the video (like in the second one) so I could go to the video and look at that particular point of the video without having to do a lot of skipping around.

(4) I don’t know if sharing 50 minutes (a whole class) was worth everyone’s time. I wonder if picking a 10-15 minute clip and having the reviewers focus on three things (e.g. my questioning, my body movements, the students engagement) would have worked better. It’s hard to know exactly what to do with all the feedback I got, because it’s not targeted. It would make sense to have some particular things I want to work on, and get feedback just on those. Also, making explicit what I need to work on makes the notion of getting negative feedback less nervousmaking, because I already have admitted to everyone “I suck at these.”

(5) I wonder about doing this in person vs. doing this virtually. One thing about doing this virtually is that people can do it on their own time, and it might feel safer for everyone. At the same time, there isn’t any discussion about the clip. If there were three reviewers and the presenter together, it could generate some fantastic discussions.

Thanks for those who helped me with the video analysis! I appreciate the time you took and the comments you gave me!

UPDATE: One reviewer writes about her process.

I’ve taken away a lot of valuable ideas from the Klingon summer program. I wanted to distill them into a really strong set of reflections, but I’ve found I haven’t been able do that because I am still trying to play and tease them and turn them into some sort of coherent philosophy which I can envision being enacted in my classrooms. So as opposed to most of the blog posts I tend to write, I’m going to go a bit theoretical, and ask for your help to come up with concrete ways to show these things happen.

The first thing I’ve been struggling with, and I now see as one of my biggest weaknesses as a teacher, is the lack of attention I’ve given to bridging the gap between “the taught curriculum” and “the learned curriculum.” What’s strange is that I thought I had been giving that a lot of attention — and was one of my strengths. Here’s the idea:

We all have a plan of what we want to cover in a year, in a class, or in a small bit of a class. That’s our “intended curriculum.” Then we go about and teach stuff. That’s our “taught curriculum.” Then there’s actually what our kids learn. That’s our “learned curriculum.” It has been kinda obvious to me since my first year teaching that there is always going to be a gap between the taught curriculum and the learned curriculum. These commonplace catchphrases are things I’ve heard over and over in the blogosphere…

Just because you teach it, it doesn’t mean they learn it.

Teaching is not the same as student learning.

So the goal of teaching is to minimize the gap between the taught curriculum and the learned curriculum. And I thought I was doing that. I see myself as being cognizant of the mistakes that students tend to have in thinking, I work on developing their understanding rather than having them rely on algorithmic/procedural learning, I teach my classes at the pace of my students — and alter how far we get with the material based on how much time I see them needing.

However, I have come to realize that I have been missing a gigantorific thing, because I’ve had some sort of blinders on. Especially egregious because this has been the central idea and nexus of the math teacher blogosphere for over a year now. I’m embarrassed to say: I don’t have any idea if I’m being successful at reducing the gap between the taught curriculum and the learned curriculum.

In other words, if asked how I assess student understanding in the classroom before tests, I wouldn’t have a good answer. Yes, I do that whole I look at their faces thing (which tells a lot) (but some of them are good at playing the game with their faces too) and I do the whole check yo’self before you wreck yo’self thing (questions which have students solve a problem after we have gone over a concept and done one together as a class) and I do the whole let me ask you a question thing and I very occasionally do the whole “put your head down and raise the number of fingers” where 1 finger is ‘totes got it’ and 5 fingers are ‘what just happened?’ …

But when it comes down to it, if my department head came to my class three-fourths of the way through, and froze the kids (okay… okay… no… she can’t do that… only I wield that power with my magic unicorn wand!) and asked me “what is the level of understanding of each kid in the class for the material you covered yesterday?” and “what is the level of understanding of each kid in the class for the material you covered today?” I wouldn’t be able to answer her with much confidence.

I don’t have strong systems to formatively assess my kids understanding.

Yes, there you have it. I said it.

Now I need to find ways to do this. I am currently thinking of giving short quizzes at the start of every class and exit slips at the end of every class. I would like to pilot out clickers at my school. And I would like to come up with more intentional questioning which can get to the heart of whether a student understands a topic or not (meaning: I have these questions prepared before class and I can whip out when I’m ready to check their understanding).

But more than anything, I’d love to hear ways you come up with ways to formatively assess kids understanding during a class or even outside of classtime. Big, small, thoughts on how to form questions that get deep to the heart of the subject matter, ways to figure out what every kid or what most kids know?