The Mathematical Agency Improvement Community (MAIC), facilitated by the High Tech High GSE’s Center for Research on Equity and Innovation (CREI), has woven public lesson study into its approach to improvement.
Alec Patton interviewed MAIC Director Daisy Sharrock, and Improvement Coaches Katerina Milvidskaia, and Curtis Taylor to explain how MAIC got started, and how the practice of “lesson study” fits into the program, and what one actually looks like.
Where does this story begin?
Originally, I taught math and chemistry at High Tech High. However, six years ago I was hired by CREI to work on their college access grant, which was the start of our work on trying to get more students applying to, and getting accepted by four-year colleges. We were fairly new to Continuous Improvement at that time. I had read some of the original papers by Anthony Bryk about the work in Chicago, and when he became the head of the Carnegie foundation, there was a big push to bring some of these Continuous Improvement methodologies over to education. The sentiment seemed to be “This seems to work really well in healthcare—education is another really complex system full of humans—maybe some of these methods could create some benefit for students.”
Around the same time, I read Jo Boaler’s Mathematical Mindsets, which is a book that highlights some of the issues around the way that we think about mathematics education, and right then, Jobs for the Future (JFF) put out a Request for Proposals for new improvement networks, and it seemed like an amazing opportunity to use continuous improvement to dig into this new way of thinking about mathematics in education.
And they funded us! Which was great. So, we reached out to neighboring districts and ended up with a number of interested teachers from Southern California, and MAIC got going.
MAIC has possibly my all-time favorite mission statement. Where did that come from?
In our very first “community of practice” convening event with the other JFF grantees, we attended a communications workshop. The facilitator asked “What’s the one-sentence thing that you’re trying to do?” And Stacey Caillier, the Director of CREI, said, “Well, we’re trying to abolish the phrase ‘I’m not a math person.’” And it resonated, so we kept it.
That sentence gave us our goal: we wanted students to feel like they were math people. That they had mathematical agency. It turned out that we had a number of math teachers who were giving their kids survey questions about sense of belonging, growth mindset, and relevance. And there were a few classrooms that were reporting “a hundred percent of the students felt like they belonged in that classroom,” which is really rare for a math classroom. And when we talked to those teachers, they were all iterating on a related set of practices. One of those teachers told us he had been really inspired by Katerina, who was teaching math at Vista Unified in north San Diego county.
I had also read Jo Boaler’s book and my district was contracting with her to provide professional development for the middle school teachers over the years. So, we had a lot of close work with her and like Daisy mentioned, she helped to reimagine what mathematics instruction should look like. And so, I began thinking about how in my class, I wanted students to recognize the importance of each other’s mathematical ideas. And I wanted their voice to be the center of instruction that was happening. And so, I started implementing different strategies around group work and presentations and belonging, to build this culture of discussing mathematical ideas that came from students. And then at that same time, I had made a connection with Daisy and MAIC, and it felt like two worlds were colliding with the same goal in mind.
That was our starting point: we felt like we had some practices we could share and some goals around supporting students’ mathematical identities and sense of belonging to the mathematical community. And we started from there.
What were those practices that you started with?
We were focusing on routines or structures in the classrooms to allow it to be more student centered: How to launch a lesson, how to allow kids to explore the mathematics, and then having the kids actually participate in their own student discourse, so they engage with each other in the mathematics. Things such as number talks, agency warmups, participation quizzes, accountability quizzes, status interventions with students, as well as thinking about inside or outside questions as you’re working with students to understand their thinking. All of those practices were valuable in helping to create a classroom that felt more of a mathematical learning environment where the students’ voice was valued and heard and, and they were starting to feel more sense of “belongingness” in the classroom.
What differentiates a classroom like this from a traditional math class?
A lot of traditional math classrooms follow the, the, “I do, You do We do” model of teaching, which is how most of us learned: like, our teacher taught us the procedures of how to do a problem, we did it on our own, and then she, or he would have us come back and we’d discuss if our answers were correct. And that was pretty much how math was.
What we’re doing is a “You do, Y’all do, We do” model. So, it starts with “You do,” where I will pose an open-ended problem and allow students to have individual think time, where they can structure out or create ideas around the problem and to use what they’ve learned from their own background in trying to make sense of this problem.
Next, we move to “Y’all do,” where the students are put into partnerships or groups to share their initial thinking. And now they have to talk through and be skeptical of each other, but also try to come to a consensus.
Then we move from “Y’all do” to “We do,” where we now all come together, and groups share their ideas with the class.
“You do, Y’all do, We do” allows the students to have ownership of their learning and to see that they have a lot of brilliant ideas and are very creative in their mathematical thinking.
It also allows them to see that mathematics is a subject that needs to be talked about and a subject where collaboration is key, and for students to see the beauty of coming up with their own ideas and making sense of their own learning. I think that that’s what makes it really different. And the teacher is moving from being in front of the classroom to being immersed as a facilitator within the classroom. A lot of the time I try to stay in the back of the classroom to allow the students to have that time to talk and share their ideas with one another.
Got it. So, you got your network together, working to abolish the phrase “I’m not a math person,” you got a shared approach to teaching that you could all experiment on. How did the “lesson study” start?
It emerged from the first year. We had these practices that supported productive group work, so we were sharing them in workshops and teachers were saying, “This is great, but I’d like to see it in action with students.” And then we were like “Well, we’re embedded in a K–12 organization here at High Tech High – so let’s do that!”
We had some brave volunteers from within the network who were willing to try out the practices in their classrooms with students while other teachers in the network observed. Then we would debrief about how well the practices worked and how we might improve them.
From those first observations, we realized how important it was to see instruction in action and in particular, to see how instruction impacted student learning. Around the same time, I went to a workshop at the Carnegie Improvement Summit, and saw a presentation on lesson study by Catherine Lewis, at Mills College and Nora Houseman from the San Francisco Unified School District. As they described their process I realized that I wanted to see it in action. About a month later, Stacey Caillier and I went up to San Francisco and saw one of their elementary school public lesson studies, and it was the most powerful experience I’ve had in education.
What did you see up there? What were they doing?
It was in a third-grade classroom. We came in and briefly met the students, and then we sat down with the team of teachers who had crafted the lesson together. They explained their theory of action and what they hoped to see, what student strategies they thought would show up in the class that day, what questions they might ask to help students make connections between those strategies and deepen their own understanding of the concepts they were focusing on. The superintendent and principal both attended the lesson study event as well. But the best part was when the parents showed up to watch the lesson. So, it was all these little third graders and their parents who were super proud.
Before the lesson started, the lead teacher, Karen, told us all “There may be times when I’m just going to speak Spanish to the students, or the ones that are more comfortable sharing in Spanish are going to share out in Spanish, and then we might have another student translate for you, but we might not. So, just a heads up!” And then the students came in to wild applause like superstars. During the lesson, it was amazing to watch them think about the mathematics, and then share and discuss the solutions that they came up with.
After the lesson the parent association hosted a lunch. It was delicious. And it was just this incredible atmosphere of celebrating student thinking from the whole community. It was just magical.
How did you bring Lesson Study to MAIC?
When we got back to San Diego, I reached out to a number of high school and middle school teachers to try this out, and Sarah Strong, who teaches math at the original High Tech High, volunteered to go first. We composed a team to co-design with her, and they designed a lesson, and we hosted our first public lesson study.
From there, the team regrouped, and we did a middle school public lesson. Then we convened a team of elementary teachers from across the schools and hosted a third-grade public lesson. We did three iterations of a public lesson ourselves, in order to learn from the process. That also meant we had a cadre of teachers across the K–12 spectrum who had all been through the lesson study inquiry process and could support lesson study in their schools.
Can you talk me through what “make it public” looks like?
Normally the lessons happen in the Forum, which is a big open space, like an auditorium but with no stage, so everyone is on the floor together. That allows for researchers, other educators, administrators, school leaders and parents, to watch the lesson together. Usually the teacher is wearing a lapel microphone, and I’ve seen examples where they all have mics at the tables or folks with a mic and a boom who go around to different groups as they’re discussing. It’s a little like when a surgeon is performing a surgery at a teaching hospital, and there’s a bunch of people behind glass watching.
We also have two “commentators” at these events: a “content commentator” who gives us feedback on the mathematics, and an “equity commentator” who gives feedback on our equity goals, as well as the social dynamics between students that are taking place within the lesson.
Like a sportscaster, narrating as the lesson is happening?
That would be awesome, but distracting. So, the commenting happens after the lesson, in a couple different stages: first, there’s commentary that happens publicly right after the lesson, and later the design team debriefs with the commentators privately.
So, to the extent that this can feel like a normal lesson in this highly artificial environment, a normal lesson then takes place? Like, it takes the amount of time you would expect it to, no one’s like pausing and freezing in the middle of it. Is that right?
Yeah, that’s pretty much how it is. This year I taught a public lesson myself, and it feels like a real lesson, you’re just much more nervous! But it’s a wonderful experience, ‘cause after you get past the nerves and settle into doing what you usually do in your classroom with the kids, being mindful of listening, everyone else flies away. This could just be for me, I don’t know about others, but when I got into the zone it just felt normal and then at the end it was like “Oh, everybody’s still here!”
In terms of logistics, the lesson wraps up with a big celebration and applause for the students. There’s usually an exit card, and the students’ work is collected because the team is going to look at that next.
One thing that’s really important is that the lesson belongs to the team, so if it goes totally off the rails, it’s the whole team, it’s not just that person who’s teaching the lesson: it’s collective ownership.
The debrief starts with the person who taught the lesson. They share how they experienced the lesson and what they felt went well and what they would change. And then the team members weigh in with the reflections they want to share publicly. And then we usually hear from the expert content commentator and the expert equity commentator. Sometimes the commentators have been involved in the planning process, and sometimes they just show up for the lesson study event. Their role is to provide an outside perspective on the team’s content understanding goal and the equity goal. To wrap up, there’s usually questions and comments from the audience and the parents.
The other thing that’s been incredibly powerful about lesson study has just been for teachers to be able to watch each other teach, and normalize the practice of teaching. When I was a teacher, there were plenty of times when I would reflect at the end of the lesson and feel like, “Oh my gosh, that went terribly! Thank goodness nobody was in here to watch that debacle!” But that’s actually just the reality of teaching. We all experience those moments, so how do we normalize that so we can move onto the next step ask our colleagues, “Oh, what would you have done in that instance?”
And having parents there is so powerful too. In Japan, where lesson study is widely practiced it’s the norm for parents to be there. As a society, it reflects their values because there’s a communal sense in raising kids. In the US we tend to be individualistic in our views, but lesson study flips that dynamic. When you plan a lesson as a team there is a sense that these are OUR kids, and we want to have a community around them to support them in their thinking.
That’s so awesome. Connect for me how “lesson study” as a structure has informed your approach to continuous improvement.
Within Continuous Improvement, you’re conducting “inquiry cycles” of different durations. Normally you’re trying out a small tweak, and then you collect some data to see how it’s going and whether what you’ve done is an improvement or not. Then you make some decisions based on what that data tells you. And that’s where we started in MAIC: “Hey, test these practices in your classroom, collect some data, see if it’s working for your students, and then maybe iterate and then share your iterations back with the rest of the network.”
Lesson study starts with that model, but just makes it more open and collaborative. So, for example, one of the first things that teachers do when they’re planning a lesson for a lesson study is to select focus students and conduct empathy interviews with them – which is a big part of all Continuous Improvement work, and you do it to get a sense of questions like “How does this student experience my class?” “What are the student’s math experiences like at home?” “What resources can we draw from?” “What connections we can make?”
From that information, you’re think about the student’s mathematical thinking, and as a team you can decide what the next level of understanding is that the team wants this student to reach, and how best to craft a lesson to get at that. And then, because this is going to be public, one of the teachers on the team can watch that student during the lesson, and see whether the lesson study team’s instructional planning works for that student or not. So, at its core, a lesson study cycle has the shape of a classic Continuous Improvement inquiry cycle, but it has these added elements of collaboration – extra minds in thinking through the process, observing, and then debriefing. To me it feels like a richer, more fleshed-out version of Continuous Improvement.
Yeah, normally when a teacher is doing an inquiry cycle the “laboratory” is the classroom and the teacher’s going “I want to get this outcome, so I’m going to do this thing, and I’m going to figure out what data I can collect as a proxy for this outcome.” And you’re talking to other people about your findings, but you’re doing most of the observation and testing as an individual, with your own class. And so, a lesson study is really the same thing, just with lots more people in that classroom, observing and sharing ideas.
That’s the way I view it, yes.
That makes so much sense, thank you!
1You can find more information about these practices on the MAIC website: https://www.mathagency.org