A Teaching and Learning Lab for Continual and Collaborative Growth

Diana Gomez with students at Germantown Friends School (Photo by Scott B. Foley)

I remember my first days at my school in NYC. I needed help with my classroom management and my principal suggested I spend some time in a colleague’s classroom. When I first got there, I couldn’t even find Abbie in the room, and I certainly couldn’t hear her. I was amazed at how she ran a class of 28 kids without ever raising her voice or disrupting her calm demeanor even one bit. She moved slowly around the room, taking her time in interactions with the children, listening to them, making direct eye contact, and speaking to them with an undeniable sense of authority. The kids knew what was expected of them without her using her teacher voice and doling out consequences.

It was a revelation to me. I couldn’t believe you could run a classroom like that. I had been teaching for a couple of years already, and the energy I was putting out each day to give instructions in a loud, teacherly voice was draining for me, and to be honest, it wasn’t that effective. Sitting down with Abbie after that to learn the cues she used to get her students’ attention, the routines and systems she used for building independence, and the ways she dealt with misbehavior gave me concrete tools to try out in my own classroom. I stood straighter, lowered my voice, and slowed down, trying out a slow turn of the head and an eyebrow raise.

In subsequent weeks, I had opportunities to watch Abbie and try out what she was doing in my own classroom until I had internalized these new ways of leading and communicating my expectations to the kids. Over time, these ways became my own.

The apprenticeship model of educator’s learning is powerful in the opportunity it offers teachers to learn from others who are further along the same path, in the same setting in which they’ll be trying out new skills and techniques. We’ve come a long way, and teaching is not the isolated, lonely job it used to be. And yet when the door closes and it’s you and the kids, it can be really hard to remember all those great ideas you wrote down at the workshop you went to. So how do we create the opportunity for teachers to experience this kind of apprenticeship? Mathematicians in Residence!

A Lab for Teaching and Learning

The belief behind Mathematicians in Residence (MIR) is that teachers do their best professional learning in the context of the classroom. Watching someone else model what you are trying to incorporate is powerful, and having that person teach alongside you so you can benefit from their wisdom is even moreso. Observing the skilled moves of a master teacher, documenting them and analyzing the interactions together allows us to bring greater understanding and skill to our own work. MIR is a summer camp for kids, and a collaborative professional development opportunity for teachers at the same time. During a week of intensive study, teachers will teach math units from the Contexts for Learning Mathematics (CFLM) curriculum with coaching from Cathy Fosnot, Mathematics Professor and lead author and developer of CFLM. Other colleagues will participate as observers, assistant teachers, and collaborators in a Lesson Study format. In the afternoons, the kids will have a traditional summer camp experience, while the teachers and Cathy will debrief the morning sessions and plan for the next day’s work.

Cathy Fosnot

There are actually three areas of knowledge that math teachers need to possess. First and foremost, they need to be able to engage students, helping them connect with the material, supporting and challenging their learning, and differentiating for individuals.

Second, they also need to be knowledgeable about the math content — which is no small feat. Most elementary teachers were taught to be generalists (“Jack of All Trades, Master of None”) and what they really need to be in practice is actually the opposite (“Master of All Trades.”) In mathematics, elementary teachers are required to have a depth of understanding that far exceeds what any of us learned in school. But those two skill areas are not enough.

Third, in order to excel at teaching math, you have to understand how children learn math, what we call the pedagogical content knowledge specific to teaching math and the developmental progressions one moves through as we grow toward true, deep understanding of the concepts. You have to know what it looks like when someone is on the way to learning something, so you can ask the right question or share a piece of information they can use to make a discovery. You have to know what came before and what the next step in development of that concept is in order to support and challenge children’s learning.

Teaching and Learning Together

So how would someone go about creating an environment where teachers could do all three of these things at once, providing a multidimensional experience of professional learning? In a classroom, for sure, with real students, with the materials we want to learn to use, and with expert guidance in the form of coaches and a real mathematician to provide guidance, modeling, discussion, in real time? That’s what we envision with our MIR teaching and learning lab. Think of it as a series of nesting dolls, where each one is learning from and teaching the next one, or a science lab, where we’re able to examine our practices, curriculum and interactions with students under a magnifying glass, with the expert whispering in our ears as we do so. In this lab, teachers get to watch other teachers teach, teachers who are doing the teaching get the benefit of having colleagues watch and give constructive feedback, and everyone gets to see how different teaching moves and techniques work in real time with real students. Unlike most professional learning that happens at workshops where no kids are present, the kids are there, doing the work.

There’s no gap between theory and practice, no time wasted trying to imagine how ideas are translated to the classroom. And everyone is learning together.

We intentionally set it up as a collaborative environment, taking advantage of the emphasis on group work in the Contexts for Learning Mathematics curriculum to help us build in experiences with collaborative groups for kids and teachers. We know that being able to collaborate with others is a skill that’s critical to every type of work and life, and yet it doesn’t always come naturally, it isn’t easy to teach or to do, and it’s messy. Interestingly what we often experience as teachers is that teaching can often be a solo venture, and while we have opportunities for shared and collaborative learning, the implementation, which is where the rubber really hits the road, is often left up to the individual. And so many great ideas go untried, or tried and abandoned, because the application to classroom practice is such a challenge. And so we hope that by creating a collaboration site where everyone is learning together, we’re helping the learning to be more fun and less isolating.

A Deep Understanding of Math

Another piece of the MIR model that is being developed in a unique way is the math content itself. There’s a big gap between what most American teachers need to be able to understand and do in their classrooms and what they were taught. Teaching 5th grade math is not as straightforward as it seems. Many teacher ed programs, which have needed time to catch up to national reforms, present very general approaches in hopes of preparing teachers for a wide range of teaching situations. That leaves a great deal of on-the-job learning for teachers when presented with curriculum materials. We aim to help our students develop deep mathematical understanding and robust attitudes about themselves as math learners, but we are often unprepared for that work. Elementary teachers often have less training in math content, while secondary teachers may not be familiar with the early (foundational/fundamental) stages of students’ mathematical development.

Working with a mathematician who can weave the mathematical understanding into the work with students is powerful. We can see firsthand what it looks like for a child to understand the associative property. Having Cathy Fosnot co-teach, support and point out what she sees so we can look through her eyes is an opportunity we teachers just don’t get all the time.

A Practice of Continual Improvement

And then there are the kids! We’ll be trying out units we will teach during the year, and in that way honing our own practice so we can be even more effective with our students. We can work out the kinks, get to know the units, and get to know the kids as well. Then we can tailor classroom learning to the individual. Seeing a child who understands something for the first time is a great experience. At MIR, the kids are mathematicians too, and they’re teaching us as they learn from and with us. We’re all in it together.

by Diana Gomez

Diana is a lower school math teacher at Germantown Friends School (GFS). Diana worked alongside Sharon Askew, a Lower school math coordinator, also at GFS, to design this program. Mathematics in Residence is generously funded by the Maguire Innovation Fund for Progressive Education and will launch in the summer of 2019.

Reflections on teaching + learning. Catalyst to inspire equality, integrity & community in ed. Send in your ideas! Curated by Germantown Friends School.

Love podcasts or audiobooks? Learn on the go with our new app.

Recommended from Medium

Writing in the Age of #Corona

Being a Mature Student

How to take care of teachers

Impact of Help Desk performance on Institutional Imperatives

Developing a “can-do” culture in your classroom

Public and Private Schools in a fog of war

7 Months Left, 10 Things To Do

How I Transferred from a Community College to My Dream School (And How You Can Too)

Get the Medium app

A button that says 'Download on the App Store', and if clicked it will lead you to the iOS App store
A button that says 'Get it on, Google Play', and if clicked it will lead you to the Google Play store
Irony of A

Irony of A

Reflections on teaching + learning. Catalyst to inspire equality, integrity & community in ed. Send in your ideas! Curated by Germantown Friends School.

More from Medium

Is Herbert Simon the 20th Century’s Galileo?

Google Translate add’s Konkani: What are the Limitations?

Competency vs Knowledge in Research and Development: Which One is More Important?

Notes on Engineering Health, February 2022