By Heidi Fessenden (Learning Specialist, Mozart Elementary School), Maggie Roth (Second grade teacher, Match Community Day Public Charter School), and Michelle Sirois (Learning Specialist, Perry Elementary School)
With Melissa Frascella (Math Dept Chair and eighth grade math teacher, Boston Collegiate Charter School), Meredith Hart (sixth grade teacher, Haley Pilot School), and Alia Verner (Math Director / Instructional Coach, TechBoston Academy)
TABLE OF CONTENTS
- Blog Post 1: By Teachers, For Teachers
- Blog Post 2: Changing the Culture of Math
- Blog Post 3: Changing Teachers’ Practices
“I figured out in 5 minutes there are 300 seconds, then I didn’t get any farther than that.”
“I was trying to come up with the rate of speed.”
I said 12 seconds per kid.”
“⅕ of 60 equals 20 seconds. Does that make sense? I don’t know!”
“Wait, wait. Didn’t we just figure out how long it takes to say a child’s name?”
The buzz in the room is palpable as teachers work in small groups to solve the High School Graduation Task, a problem about how long it takes to read out names at a graduation. These teachers, special and general educators in grades 2-8, come from a variety of schools in the Boston area, both traditional public and charter schools. Most of them have joined this class, hosted by and paid for by the Boston Teachers Union, with a colleague from their school so that they can plan together and observe each other back at school in between sessions. This is their first day doing math together.
The course they are taking is called Bridging Classrooms with Peer Learning Partners. It was designed and led by the six of us who all are Boston teachers and were 2017 Edvestors Zeroing in on Math Fellows. This course was the project we chose to work on throughout our year-long fellowship.
After reading research from Deborah Ball about the importance of pedagogical content knowledge for teachers, we knew we wanted to design a math course by teachers, for teachers. Heather Hill presented to the Math Fellows her research showing that when teachers do math together, the impact on student outcomes is greater than that of most other kinds of professional development. We knew then that we wanted teachers to collectively engage in mathematical tasks and routines and to reflect on those mathematical experiences with a “student hat” and a “teacher hat.” (See sidebar for examples of “Student Hat” and “Teacher Hat” reflection questions.)
As teachers reflected on their experiences as learners during the first session, the power of doing math together coupled with reflection was validated.
- “It was interesting, we were in such a hurry to solve that we missed some major elements – and that’s exactly what the kids do. But we had two people in the group that asked, ‘What questions are we supposed to answer?’”
- “What was cool is that everyone approached it a different way.”
- “We had such different strategies that I could not even listen to what she was saying, but then I was scribing for our poster. The act of writing it and having to convey her ideas with my hand forced me to understand it a little bit more.”
In these initial reflections, teachers saw connections between their own habits and those of their students, appreciated the value of sharing a variety of math strategies, and considered teaching structures that support mathematical understanding.
With a bit of trial and error, we crafted a simple structure that we used for most of the five sessions. Less is more, we learned. The structure was:
- Sharing: Each session began with sharing of teacher work and reflections since the last session.
- Math task or instructional routine: Teachers participated in an instructional routine or engaged in a math task as if they were students. We facilitated these the way we might lead them in our own classrooms.
- Reflection: Teachers reflected on the mathematical experience from the perspective of students (Student Hat), then thought about how they would use the task, routine, protocols, or class structures in their own work (Teacher Hat).
- Planning: Teachers worked with their learning partner to plan a lesson inspired by that evening’s experience.
- Intentions: Each session closed with teachers naming an intention of something they would try in their classrooms before the next session.
For providers of Professional Development, a common problem is decreasing attendance over the weeks of a class. One of the first signs that Bridging Classrooms was going well was that, of the 13 participants who came to Session 1, all returned for Session 2, and one brought a colleague. We did not lose any participants over the course of the five sessions.
The work we did during the five sessions together was inspiring. Though we were technically teaching and facilitating each session, we were learning and growing alongside the teachers in our course. Each of us did the math with the participants and had the same “a ha!” moments as we learned from each other. We never could have anticipated how much this course shifted not only our participants’ practice, but our own, too.
We’ll share more reflections about the course and how it changed teachers’ practices in a future blog post, but here’s a peek at some of their final reflections.
“I used to teach, teach, teach, teach math and never facilitate. Now I try not to say anything if I can.”
“I’m letting the kids lead more, taking a back seat, and seeing where their thoughts lead.”
“I cut back on a lot of scaffolding and stopped guiding the kids. I started to let them investigate and do more facilitating; [I] wait to see what they could come up with. It felt like before I was almost giving them the answer. Now I kind of sit back and even if we don’t get the answer that day, it’s to lead into the next day.”
“I used to be terrified of doing any kind of group work or partner work because I was nervous there would be one student doing all the work or they wouldn’t get along, but now as a class we’ve been able to develop skills like what kinds of positions can you play in a group and what kinds of questions can you ask each other. Now they use great mathematical terms and questions in a group and now they motivate each other.”
At an early session of our teacher-led math course, Bridging Classrooms, we began by asking, “Please share something you’re thinking about connected to math in your classroom.”
Here’s a sampling of what we heard:
- How do I make sure I’m not over-scaffolding?
- I am trying to get my students to work more independently in math class.
- I want my students to be more engaged and motivated to do math.
- I want students to think, “does that make sense?” when they solve problems, so they’re not just using procedures.
If you’re a math teacher, you’re probably nodding your head right now.
We have to do it all as math teachers: know content well, differentiate, motivate, play catch-up. It can be overwhelming. Often, we find that math PDs we attend don’t help. Instead of showing teachers how to implement new practices in the classroom, they focus on looking at data without discussing practice. Or, they focus on creating cognitively-demanding tasks without discussing how cognitive demand also comes through math discussions, routines, and approaching tasks in multiple ways. In creating this PD, hosted by the Boston Teachers Union, we were hoping that teachers would feel better supported and prepared for their classrooms. The teachers who took the class, special and general educators in grades 2-8, came from charter and public schools in the Boston area. Most took the class with a colleague from their school so that they could plan together and observe each other in between sessions.
Today we’ll share the effect Bridging Classrooms had on teachers. In our next post, we’ll explore why they think Bridging Classrooms altered their teaching.
What they got out of our class (how their classrooms changed):
During our final class we asked teachers to use the sentence stem “I used to _______, now I ______” to reflect on what they used to do to teach math and how that has changed. One teacher started with, “I used to rely on my comfortable bag of tricks and talk a lot.”
We could relate. It’s easy to get into a comfort zone and forget the myriad of strategies that push student thinking and engagement. As teachers reflected on what changed in their classrooms, a few themes emerged. Taken together, these themes could be summarized in one way: the culture of math changed in their classrooms. Below, we use the voices of participants to explain the many ways their math classes changed after this course.
Student-led, interactive lessons
Many of the teachers in the group spoke about making more space for student voices and group work. They found themselves talking less in order to increase student thinking.
- I used to teach, teach, teach, teach math and never facilitate.
- I used to be terrified of doing any kind of group work or partner work because I was nervous there would be one student doing all the work or they wouldn’t get along.
- Now I step back and let my students take the lead in their learning, let them struggle.
- Now I find that my students have been working with each other better than ever. They are using motivational language with their table groups and partners while also asking great mathematical questions to better understand their peers’ work.
Open-ended tasks (less focus on right answers)
Another common theme was that teachers began using more open-ended tasks in their classes, where the focus was on reasoning rather than on getting the right answer. Many of these were modeled on tasks we had done in our course, such as visual number talks, numberless word problems, noticing and wondering, and Three Act Tasks.
- Now my students have started having positive conversations about math. Students became comfortable sharing their thinking, regardless if they were right or wrong.
- Now I make a conscious effort to implement strategies that I learned from this class, particularly strategies in which there is no definitive right or wrong answers (i.e. “Give me a number that you think is too big to be the sum.”).
- Now I start every math class with a visual without a question and allow students to notice and wonder before giving them a question.
Increased support for students with special needs
Retha Reynolds, a fifth grade teacher of a substantially separate classroom for students with learning disabilities at the Sumner Elementary School in Roslindale, shared how she entirely changed the structure of her math lessons, turning the leadership of the class over to the students, primarily through using Three Act Tasks. (Read a summary of the structure of a Three Act Task, and see how Dan Meyer breaks one down.) Early in the course, Retha talked about her doubt about how to increase discourse among students with special needs. “They kept saying, ‘less teacher talk,’” she explained. “I didn’t know how to do that in a special ed class.”
After Bridging Classrooms, she explained, “when I plan I think about how am I going to get them talking about the math before we get to the math we’re going to do.” She does this using images or scenarios and asking students what they notice and wonder before giving them a math problem to solve. When district administrators visited her class on a walk-through, they “couldn’t believe it was a special education class” because of the level of dialogue and engagement with the math content. “I don’t know what I would have done without Three Act Tasks,” Retha reflected. Other teachers mentioned that they also felt better equipped to support students with special needs after taking our course, even if they didn’t entirely adopt a new structure like Retha did.
As we listened to teachers describe how their classrooms were changing, we wondered what it was about this relatively brief course that had such an impact. We asked them, and in our next blog post we’ll share some of what we found out.
What made teachers’ practice change?
We were curious to find out more about which parts of our teacher-led math course, Bridging Classrooms, had led to such deep changes in teachers’ practice. To find out more, we interviewed some of the course participants in pairs. A few themes emerged as to why this professional development had such an impact on their teaching.
Safety for Adults, Safety for Kids
A few teachers, particularly early-career teachers, spoke often about how safe they felt in this group. “I could take my shoes off there, literally and figuratively,” Shona Daye, a 4th grade teacher at the King School, said. The first day, she said, she was worried that she wouldn’t solve the math task correctly. “I was looking around, trying to see if I was using the ‘right’ strategy,” she recalled. She soon realized that getting the “right” answer or using the correct strategy was not the focus of the course. Instead, the focus was on the many different ways we can arrive at solutions and on the depth and variety of thinking in the group.
“…but after we shared out, you know, that fear just dissipated, and looking at different perspectives, I had all these epiphanies. And I wanted my students to feel the same way.”
Shona realized that if this safe environment to explore thinking made her feel safer, it would do the same for her students. “Allowing the children to explore and not give right answers, but just explore — That is phenomenal, that is huge, and totally engages everybody. Everybody was willing to take a risk. Nobody had a right or wrong answer. And that was exciting. That was really exciting.”
Experiencing Math as Learners
Shona and Emily Kmetz, a Tech Boston math teacher, both talked often about how important it was that they had struggled with the math problems that they then asked their students to solve. “My students loved hearing that I had trouble with the same problem they were solving,” Emily said. It also gave them insights into how it feels to take on a challenging problem and to have to try to understand someone else’s strategy, and a window into the different strategies their students might use.
Teachers had experiences of being stuck, of struggling to collaborate with a partner, of feeling frustrated because someone else solved the problem faster than they did — all of which helped them remember the challenges of being a math student.
In written reflections and interviews, many of the participants in the course mentioned that their curiosity was piqued by the idea of teacher-led PD. “These are teachers who are in the classroom every day, like me,” Retha Reynolds, a 5th grade teacher at the Sumner, said. “They know.”
When teachers had questions about the reality of implementing something in the classroom, or a challenge they face on a daily basis, the facilitators had ideas because they face the same challenges every day. This made the course more practical and useful than a class led by an “expert” who is not a teacher.
Expertise in supporting students with special needs to talk, struggle, and achieve more
Several teachers in the course work primarily with students with special needs. They expressed frustration with the number of professional development sessions they have attended that don’t speak to the specific needs of their students. Although this course was not billed as a course directed toward special educators, the facilitators were all teachers who often teach students with special needs. The focus on making math a more visual, creative, and discussion-oriented subject appealed to the special educators in the group. They enthusiastically tried out new instructional routines and protocols they learned in Bridging Classrooms, such as number talk images (see image, right).
Retha enthusiastically adopted Three Act Tasks as her pedagogy of choice after doing the Toothpick Task in class. (Read a summary of the structure of a Three Act Task here, and see how Dan Meyer breaks one down here.) After our course was over, she reflected on how well the visual and storytelling aspects of many of the tasks she did in our course worked for her students.
When she started to use Three Act Tasks and have her students notice and wonder, she noted that, “The kids [were] answering the questions and talking to each other about what they saw happening in the picture before I could even present what the problem was.”
For Retha, getting her students talking about a visual or a story was the key to both increasing conversation and engagement, but also her students’ ability to persevere and struggle.
“I felt like before I was kind of guiding them too much. I was doing too much for them…. Getting them to really talk about the math [first], that gets them to thinking about what it is they’re doing. I felt like I was able to just step back and let them struggle with it some.”
Logistics: Food, parking, etc.
We probably shouldn’t have been surprised by the fact that parking and food mattered. The teacher’s union building has a large, free parking lot, unlike many Boston locations, including the district’s central office building, where parking is a real problem.
Retha described being in workshops at the district office and knowing that she had to move her car every two hours. “If you’re worried about parking, you really can’t focus on the PD.”
We gave the teachers dinner each evening of our course, and that came up too in the reflections. Iris Coronel, a 5th grade teacher at the Sumner, said, “For some other professions, they are treated like professionals. We go [to PD and get] a bottle of water, we’ll be like, ‘Wow, they give you water!’”
The fact that we provided dinner and water was a real treat for teachers, and made them feel like professionals.
With these reflections, we are continuing to share our learning with partners and leaders in the math community. Recently, Heidi and Michelle presented these reflections and their learning to leaders in math education at NCSM conference in San Diego. In doing so, they asked participants – and we ask you – “What allows teachers and students to feel safe taking risks doing math in your setting?” and “How can you increase opportunities for teachers to feel safe and take risks as learners?”
Melissa Frascella (Math Dept Chair / Eighth grade math teacher, Boston Collegiate Charter School), Meredith Hart (Sixth grade teacher, Haley Pilot School), and Alia Verner (Math Director / Instructional Coach, TechBoston Academy) also contributed to this blog post.