Changing the Equation

Caroline Ebby, GR’97, and Janine Remillard are helping to lead a bold new fellowship to empower Algebra 1 teachers in the School District of Philadelphia—merging deep content knowledge, responsive pedagogy, and a shared passion for making math meaningful.

he career paths of Senior Lecturer Caroline Ebby and Professor Janine Remillard have overlapped and intersected many times over the years. Early on, both were math teachers (Ebby for middle schoolers and Remillard in an elementary school). In their classrooms, both found inspiration in an experimental curriculum from the 1970s, the Comprehensive School Mathematics Program, that “made big ideas in mathematics accessible to kids by using visual representations,” said Remillard. Both pursued PhDs in education and now research mathematics teaching and learning—Ebby with a focus on student thinking and Remillard with a focus on curriculum. And when Remillard first came to interview at Penn GSE more than 25 years ago, Ebby was the doctoral student on her hiring committee. They have collaborated on a number of teaching, research, and professional development projects ever since.

This year, their work converged once again when they partnered for the launch of a new Algebra 1 Fellowship for School District of Philadelphia (SDP) educators. This pioneering initiative, created in partnership with the SDP and the Neubauer Family Foundation and funded by all three organizations, aims to enhance Algebra 1 instruction, with a focus on research-driven teaching strategies that align with the district’s new curriculum, called Illustrative Mathematics. The fellowship is open to all SDP Algebra 1 teachers, with fellows earning continuing education credits and roughly $5,000 for their participation.

This past August, approximately 80 teachers came to Penn GSE for a four-day Summer Institute to kick off the fellowship, which also includes monthly peer collaborations, individualized coaching, and three follow-up professional development days during the school year.

“Our Algebra Fellowship is an example of partnership at its best—the district identifying a specific need, the Neubauer Family Foundation supporting our need through collaboration and resources, and Penn GSE co-creating a transformational, multifaceted learning model, in partnership with SDP, that gets to the root cause of the identified need,” said Michael Farrell, GRD’22, SDP’s Chief Learning Officer.

We spoke with Ebby and Remillard—together—about their piece of this innovative partnership.

How was this fellowship, and its Summer Institute, developed?

Janine Remillard: The district approached GSE, asking to collaborate on an effort to support Algebra 1 teachers. With generous funding from the Neubauer Family Foundation, we worked with district leaders to develop a multi-pronged approach that began with focused professional development through the Summer Institute. During the school year, fellows receive support through regular coaching visits and a monthly professional learning community meeting, led by one of the Institute instructors. For our part, we know that teaching is hard, and that in order to teach math—or to teach whatever you’re teaching—you need to understand the subject in a deeper way than the average person does. So we knew we needed to design something that would help teachers really understand the algebra that they’re teaching and they’re finding in their Illustrative Mathematics curriculum program.

Caroline Ebby: We also realized that this ask fit with what we knew from years of experience and research about teacher learning. Content knowledge is really important. But we know from research that just increasing teachers’ content knowledge is not enough to change what’s happening in classrooms for students. Teachers really need to be able to connect that content knowledge to student learning and to the curriculum materials and to their teaching practices. So that’s how we thought about the Institute. How can we bring those things together and really give teachers a space to engage in the content, make sure that they understand it, but also think about how to make it accessible to their students, and how to use their curriculum materials in a way that will enhance their students’ learning.

If we had gone to one of the days of the Institute on campus, what would we have seen?

CE: You would have seen teachers doing math together and talking about it and getting excited about it and asking questions and working together to make sense of things. We spent a lot of time on visual models, and so they were up at the whiteboards, drawing things out and seeing, for the first time, why some of the procedures that they teach actually work. What’s happening when you’re getting “x” by itself on one side of an equation, or why can you subtract the same thing from both sides of an equation?

JR: We focused on four features of high-quality algebra instruction, based on the research of Erica Litke, one of our collaborators from the University of Delaware. These features form the frameworks to help teachers realize, “I need to make sure that the procedures I teach my students have meaning.” And then we introduced five routines from Erica’s work, which are short, maybe 15-minute scaffolds that teachers can incorporate into Illustrative Mathematics that help them focus on one or more of these features.

How many of SDP’s algebra teachers are you able to work with?

CE: There were about 80 teachers who are in year one of the fellowship, thanks to the Neubauer Family Foundation and SDP, and they’ll continue with us throughout this school year. There are about 300 Algebra 1 teachers in the district, and the idea is that we’d bring in another 80 to 100 each year, so that we could reach almost everyone in three years. Instructional coaches who will be supporting the teachers also participated in the Institute.

And the Penn Learning Network (PLN) is your partner in this fellowship?

JR: Yes, Lara Paparo, GED’06, GRD’22, is leading this work with PLN, managing the professional development piece. She is working closely with us and the SDP team to coordinate the different components of the initiative. She is also using PLN’s extensive experience as a district partner to ensure that the PD is impactful and aligned.

I know the first year of the fellowship is still very much underway, but how do you think the inaugural Summer Institute went?

Janine Remillard, a woman in a dark shirt and white cardigan, presents, holding a clicker and papers in front of a projection screen showing algebraic equations.

CE: I didn’t know what to expect, because I have not done as much work with high school teachers, but the Institute exceeded my expectations in terms of how engaged the teachers were, how open to learning, how collaborative, how questioning and thoughtful they were about their work, and how excited they were about getting to work together with other math teachers and being treated as professionals.

JR: Every day felt really powerful! People were making connections left and right. We had the teachers in two different, smaller groups—I worked with PLN’s Bill Feeley and Caroline worked with Erica Litke. In each group, we went back and forth between doing the math and narrating our pedagogy and the decisions that we were making. . . . So, it wasn’t just, “Experience this as a learner,” because that doesn’t necessarily help you figure out how to manage complex content while teaching. It was both, “Experience it as a learner,” and then, “Let’s think about how you can facilitate these kinds of learning opportunities with your students.”

CE: In our room—and I’m sure in yours, too—we would often say, “OK, let’s put on your learner hat, and think about this as a learner.” And then we’d say, “Let’s put on your teacher hat now.”

Aside from wanting to be a good partner to SDP and support their efforts to improve math instruction, why did you want to help lead this work?

CE: I realized that the district and the Neubauer Family Foundation were making a long-term investment in teachers through this partnership. It wasn’t just one shot—let’s provide a Summer Institute—but there was thought and resources put into how to support teachers in their classroom practice over time. That’s when it became exciting to me, because that, to me, is when you can really make a difference. And so, once I saw that, I was all in. Because this partnership is investing in teachers, and that’s so important.

What did you learn from the Summer Institute?

JR: I deepened my understanding about a lot of things: aspects of algebra, different techniques that are taught in procedural ways. . . . I also saw that it was true that high school teachers—when treated as professionals, and when their ideas are respected—will engage in deep mathematical exploration and will participate as learners.

Caroline, your book, Becoming a Responsive Mathematics Teacher: Centering Student Thinking in K–8 Classrooms, based on your recent research-practice partnership in SDP elementary schools, just came out. Can you tell us a little bit about it?

The cover of the book "Becoming a Responsive Mathematics Teacher: Centering Student Thinking in K-8 Classrooms," listing the six authors and featuring inset photos of classroom instruction.

CE: We see the book as the culmination of that Responsive Math Teaching project and all of the work that our team did over five years in collaboration with teachers and leaders in Philadelphia around changing their practice. We developed and refined so many tools and examples that ended up being helpful for teachers who want to change their practice but aren’t sure where to start. This is our way of sharing what we learned with a broader audience so that more people can make use of the things that teachers told us they found useful. A big part of that project was building in sustainability through instructional leadership, so that we weren’t just coming in and doing some work with teachers, and then after five years, we leave and we’re done. . . . We really wanted to make it live on in a way that people could continue to use the model and the tools as a resource and, hopefully, continue to learn from them.

And Janine, what’s next for you?

JR: My research also focuses on responsive teaching. . . and right now, I’m working on a project with researchers from two other universities on how to mentor teachers in three very different teacher-education programs to support novices in developing pedagogical reasoning around responsive teaching in mathematics. That’s the headline, but a side note is that we think—and we have evidence showing—that this kind of work also helps mentors themselves develop their own responsive practices.

Back to Issue