Analysis of the data focused on identifying the consensus features of effective PD participants determined were influential in their learning, and on the perceived outcomes supported by these features. The primary finding was that teachers found two of the five consensus features especially important for their learning: (1) teachers found ways to collaborate regardless of their initial organization and (2) when they did collaborate, they focused on improving their understanding of the curriculum content and richer pedagogical practices. A secondary finding was the similarity of outcomes observed across all PLCs. Even though the goals adopted by each PLC varied, the outcomes participants reported were similar.

Collaboration

Of all the features of the PD program provided, one that rose to the top of the value list for teachers was collaboration—within and across PLCs. This was true even though not all PLCs began the project prioritizing collaborations among teachers. The analysis of both the survey responses and the interviews suggested that collaboration was the key feature that influenced and supported the participants’ learning. Each excerpt coded as collaboration was sub-coded as either “within PLC” or “across project” to differentiate between collaboration that was a scheduled monthly occurrence and that which occurred beyond individual PLCs, either through project-wide meetings or was initiated by participants.

Responses to Q5 and Q9 of the survey captured the influence the project had on the participants in this study. Code application for the two survey questions is presented in Fig. 1. Of the 14 survey excerpts coded as collaboration, 4 were coded as collaboration within PLCs and 11 were sub-coded as collaboration across PLCs.Footnote 1

Fig. 1

Frequency of code application in phase 1

Eighty-nine percent of participants reported a moderate to large influence, highlighting collaboration within and across PLCs as most influential or a key highlight. Jill (PLC 1), for example, stated that the project had a large influence on her own professional learning and identified connecting with others as the most influential component of the project for her. Through connecting with others, she was introduced to ideas to experiment with from educational researchers:

We learned about using rich tasks to drive instruction from William and [the PI] suggested a Jo Boaler book for our group to read and try. Following that our group continued to learn about Thinking Classrooms and spiralling [the] curriculum, mostly being influenced by the group from Field’s and William and Wayne’s energy and excitement about their work.

In terms of the highlight for the project for her, she again pointed to collaborating with others, both within her own school and across the project:

Learning together. Feeling supported for our learning by the principal and the project researchers. (empowering!!) Collegial discussions - with my PLC and from around the province. Having discussions with my principal about how to best support student learning in mathematics. (I felt heard!!) Summer Institute where I feel valued for the work I do and where my learning is supported.

Maya (PLC 10) identified similar influences as Jill, not only for herself but the mathematics department at her school. When asked to identify the most influential components of the project, she stated “The project was extremely influential for myself and my department. There was a huge culture shift in my department on teaching practices and how students learn best” and the highlight of the project for her was connecting with others from across the project “I enjoyed all of the learning but more importantly the connections that I made with other educators throughout Ontario.”

Overall, the fact that a high percentage of participants reported a moderate to large influence of the project on their learning suggests that collaboration—reported as a key feature of their experience—was genuinely important to them.

Collaboration and a focus on content and pedagogy were the only two features of effective PD that every participant referred to during their interviews, and they referred to these more often than the other features (Fig. 2). The interview data had 74 excerpts coded as collaboration, 45/74 sub-coded as collaboration within individual PLCs, and 29/74 sub-coded as collaboration across the project.

Fig. 2

Frequency of code application in phase 2

Participants discussed how collaborating with colleagues at their own school influenced their learning and practice. For example, PLC 7 engaged the co-planning and observation of mathematics lessons followed by a debrief to refine the lessons further. Participants shared how this collaboration was supported by the different perspectives and expertise of the PLC members. Sharing ideas and challenging one another pushed their learning, introduced new ideas in different ways, and encouraged them to enhance their lesson ideas. William described:

One of the big things for me was that getting in a PLC makes a big difference…having time to sit down with staff and share ideas and go and try different things. It just made it very clear to me that teacher efficacy, teacher collaboration is super important if we’re going to achieve what we’re trying to achieve in a school. (William, PLC 7, phase 2 interview)

Participants also collaborated across PLCs, including sharing ways they were experimenting with pedagogical approaches. One new approach included spiralling through the curriculum, an approach consisting of revisiting mathematical concepts several times throughout the course. Drew, from PLC 1, explained how interacting with other school districts influenced her in terms of this idea:

I think that when it came to…the networking across boards… you were able to take some keen educators from our board to connect them with keen educators somewhere else ramped up the professional learning. Right? Like so we could read about spiralling. We could read about different ways to assess students but to actually see that or talk to somebody that that’s their focus was very valuable. (Drew, PLC 1, phase 2 interview)

Similarly, Chrissy shared:

We’re going to spiral [the curriculum] too, which is another thing I met [through] the [project] there were people that were already spiralling…I didn’t believe it, I couldn’t get my head around it, that you can actually do this. But now that I’ve seen them do it successfully I’m seeing what their plans are [and] revising what their plans are to work with (Chrissy, PLC 4, phase 2 interview)

The project also provided different examples of what teaching and learning in Grade 9 mathematics classrooms could look like. Teachers described how this sharing broadened their perspective of what is possible and at times helped them feel they were on the right track. Elena, from PLC 10, described this during her phase 2 interview:

I really enjoyed being able to get that perspective, like I really enjoyed meeting people from other schools and thought about wow everybody should, we all should know what’s going on out in all of Ontario so we do have a better perspective. Where we are at compared to them and where we should be at or what we should be, you know, aiming to be at. So, although, I mean in some ways it was confirmation that we were doing good things too. (Elena, PLC 10, phase 2 interview)

As one of the five features of effective PD, opportunities to collaborate across the PLCs was an intentional design component of the project. As the interview data show, teachers took advantage of this feature to establish professional relationships among their peers in other PLCs and created opportunities to work together beyond the scope of the project. For example, members of PLC 7 visited and worked with Jill and her colleagues in PLC 1. Chrissy from PLC 4 made sure to participate in other PD opportunities provided by the PI and the OAME. Wayne shared how the cross-collaborative design of the project led to individuals making connections across the project and arranging visits at others’ schools.

I seemed to be connected with new people along the way…and that led to all kinds of exchanges with other teachers and other schools. It also led to some dates where we went to [other] school boards… and then of course we had [PLCs] coming to our school as well. (Wayne, PLC 7, phase 2 interview)

Every participant in this study mentioned they still maintained connections with other project participants through social media, email, or in person.

Collaboration does not occur in a vacuum. Teachers collaborate about something. Participants in this study consistently commented about the value of collaborating around the content of the curriculum and pedagogical strategies to implement it effectively.

Focus on Content and Pedagogy

Participants did not use collaborations to chat about general issues of teaching—they mostly focused on content and pedagogy including specific collective practices which are considered the outcomes from the project. These practices included the use of richer tasks, integrating the BTC model, spiralling through the curriculum concepts, and orchestrating more math-related class discussions. Collaborations were not just pleasant social occasions but were significant work times.

When considering Q5 and Q9 of the survey the second most cited influence or highlight of the project was a focus on content and pedagogy. A total of 67% of the participants mentioned a focus on content and pedagogy when asked to describe influential components of the project or a component that was a highlight for them. Specifically, they mentioned how learning about different ideas related to pedagogy was influential and challenged their thinking. Elena (PLC 10) shared that the most influential component of the project for her was sharing ideas with others across the project and having time to interact with these new practices herself:

The components of the project that were most influential were the opportunities to share innovative ideas that teachers felt were making a difference in student learning. The workshops/sessions that most stuck with me were those that involved orchestrating group work in a way that lowered the floor and raised the ceiling for all learners - including learning about the work of Margaret Smith and Mary Kay Stein and Peter Liljedahl. It is most meaningful for me to get new information from the original source where nothing is lost in translation.

Elena identified several highlights of the project for her, including:

[1] watching teachers putting their ideas into practice in presentations and workshops and experiencing the student perspective to get a better understanding of why some strategies work better than others [2] being able to present our own ideas to colleagues from around the province and get feedback on our work [3] meeting and sharing with teachers in informal settings, ex. over lunch.

In these quotes from Elena, she identifies a focus on content and pedagogy as well as time to share ideas and collaborate with others. Elena was not the only participant to mention both features when identifying influential components and highlights of the project. In fact, 56% of the participants who identified a focus on content and pedagogy as influential also identified collaboration as an important component of the project, suggesting that when teachers were collaborating they were engaged in more than just social chatting.

Collaboration frequently co-occurred with a focus on content and pedagogy. Of the 59 times collaboration was co-coded with a second code, 73% of these excerpts were co-coded as focus on content and pedagogy. Similarly, when an excerpt was coded as a focus on content and pedagogy ~ 80% of these excerpts were co-coded as collaboration (Fig. 3).

Fig. 3

Frequency of code co-occurrence

When asked to describe some of the collaborative work their PLC engaged in, Drew explained that PLC 1 used the project time to explore different pedagogical strategies using the 5 Practices as a framework and this led to a more collaborative and open sharing among the PLC members.

We focused a lot on the consolidation of what we were trying to get out of [the lesson]. There was a lot of videotaping the [5] practices, debriefing after. There was a lot of co-planning and co-teaching together so the door, like all the doors were wide open. (Drew, PLC 1, phase 2 interview)

Jill described how interacting with resources shared by the research team supported the PLC to focus on specific content areas such as algebraic thinking:

I think kids can no matter where they’re understanding level is they can think deeply and they can think algebraically…That was part of the stuff that Chris showed us when. When the Jo Boaler [and Cathy Humphreys’] book, when we jumped into the border problem and Jo pointed out [students] have to be able to describe the algebraic operations before they [use those strategies]… I think that made it a lot clearer, so that I was listening more for what the kids were saying before we were forcing algebraic operations before we were forcing that model. So, I think those things have changed, and since that was kind of our goal talking about algebra wow 10 years later, win! (Jill, PLC 1, phase 2 interview)

PLC 4 analyzed student work and discuss student thinking during their monthly meetings. Chrissy explained that “sometimes we brought work from our students. [We] brought images, brought video of what we had seen in a classroom” (Chrissy, PLC 4, phase 2 interview). The PLC would then observe and discuss these videos and images and strategize different pedagogical responses to support and enhance student learning. This focus on content and pedagogy and its co-occurrence with collaboration appears to have led to the adoption of new practices and sustained changes in teachers’ practice.

Outcomes—Perceived Changes in Teaching

Findings show that teachers in each PLC reported similar outcomes in terms of changes to their practice 5 years after completion of the project. Every participant reported adopting at least one of the sustained changes to teachers’ practice that emerged from the project.

The survey asked participants how the project continued to influence both their practice (Q6) and their approach to their own professional learning (Q11) 5 years after completion of the project. In total, 89% of the participants agreed that the project was still influencing their practice and 78% of the participants agreed that the project continued to influence their approach to professional learning. Present in the survey responses was evidence of the sustained changes to teachers’ practice that emerged from the project. These changes included incorporating the 5 Practices as a framework for planning and leading classroom discussion around the use of rich tasks, the BTC model as a way to engage students in rich mathematical tasks through the use of vertical non-permanent surfaces (VNPS) and visibly random groupings (VRG), and the spiralling approach to teaching the mathematics curriculum in order to revisit concepts multiple times throughout a course.

For example, William (PLC 7) shared that “yes” the project was still influencing his practice, sharing “I still use some of the pedagogy that we tested in the lesson studies…VNPS, VRG, spiralling to name a few” and that the project had changed how he approached his own professional learning, stating that it was “more collaborative-and more learning of pedagogy close to the classroom.” Chrissy (PLC 4) shared how new practices learned about through the project (e.g., building thinking classrooms, spiralling) were still being incorporated into their mathematics classrooms, that the project increased collaboration across their mathematics department, and they sought out more opportunities to engage in professional learning:

We are still using the whiteboards (both individual and on the wall) and have continued to value non-permanent and low-risk methods of communication for students. We have also had a greater buy-in for collaborative projects since the project finished…Because we got so much from the project and our participation in the annual general conference, we have continued to participate in online conferences, webinars, podcasts, and professional reading both as individuals and in small groups.

All interviewees referenced at least one new practice and described how it changed their teaching. Chrissy pointed out during her zoom interview that her room looked different now, gesturing behind her, she said “look at what our classroom looks like, there’s [whiteboards] on every wall yeah, and so this is the first time that we have actually defronted our classrooms” (Chrissy, PLC 4, phase 2 interview). Defronting is one of the features of the BTC model. Charlotte, the special education teacher in PLC 10, noticed that overall mathematics is being taught differently in her school.

[The project] kind of changed the whole way that we approach teaching math. Right? So now, when students are coming to the resource room to get support from me. I’m seeing them come with algebra tiles some of them bring whiteboards with them to try their project or their questions before they write them on the paper So, I see the influence of that the project and that way of approaching math still now. (Charlotte, PLC 10, phase 2 interview)

Outcomes—Perceived Changes in School Culture

The survey asked questions related to individuals’ experiences and did not provide the opportunity for teachers to talk about perceived changes in their school culture directly. This finding draws exclusively from the interview data.

Looking beyond specific outcomes, participants from three of the four PLCs mentioned ways the project influenced their school culture. Teachers reported having more opportunities to share ideas and work together led to a more communal and committee-based approach to teaching practices. William from PLC 7 reported that participation in the project helped shift his school’s conception of mathematics learning. “We changed the culture of our school to be all about thinking and problem solving. And not all this detail of like can [students] do all these different math things?” This shift in the department’s conception of mathematics learning moved the department beyond disseminating procedural math skills, which William refers to as “all these different math things” toward fostering deep conceptual understanding and encouraging students to engage in critical thinking and exploration.

Maya described that her school’s involvement in the project resulted in a “culture shift…it opened most peoples’ eyes” (Maya, PLC 10, phase 2 interview). Maya described how the mathematics department became more collaborative overall and teachers were willing to experiment with new ideas and practices. This willingness came about when they saw the increased engagement in students because of new practices, “I think that [students] were just a little happier to go to math class, like they weren’t, ‘this is my least favorite subject’. Now, it was like ‘what are we going to do today?’” (Maya, PLC 10, phase 2 interview). Lisa and Chrissy both mentioned how the project led to a more collaborative way of working in their department and this influenced how the administration hired new staff to join their schools. Lisa shared how the administration now asks potential new hires specific questions about collaboration and willingness to engage in professional learning when interviewing for new positions.

My [vice principal], she’s like “we’ve got your back”, she said, “the questions we asked, we were really impressed with this teacher, with their willingness to try new things, and you know, maybe they…haven’t done spiralling before, but we made sure that we were picking somebody who was really open to learning and open to sharing and connecting with colleagues.” (Lisa, PLC 7, phase 2 interview)

Similarly, Chrissy explained:

[The project] has changed so many different things because it changed the way we even hire in the math department, because if you are not willing to be collaborative, you’re not allowed to be in the department. So, this siloed behavior that we used to have where nobody would even enter someone else’s classroom, let alone actually ask about “I don’t know how to do this, can you help me?” is completely gone…And our administration doesn’t hire without asking us what we recommend as well. (Chrissy, PLC 4, phase 2 interview)

These findings suggest that time to collaborate around issues related to content and pedagogy rose to the top of the list of features that teachers gravitated to when engaging in the PD initiative designed using the key features of effective PD. These features supported significant and sustained changes in teachers, schools, and professional practices.