Teachers Collaborating as a Professional Learning Network and Learning How to Implement Collaborative Problem Solving in the Primary Math’s Classroom

Abstract

Collaborative Problem Solving (CPS) is a pedagogy seldom used in math’s classrooms despite its relevance and ability to develop students’ 21st century learning skills. International reports from PISA have highlighted the necessity of both collaboration and problem solving as crucial 21st century skills and this particular study focusses on teachers learning about using CPS in maths. In this small case study, five Australian primary school teachers explore the introduction of this pedagogy into their maths classrooms whilst supporting each other in a professional learning network (PLN). The findings highlight the importance of the support and collaboration in a teacher team needed to assist with the development of this new pedagogy. They learned about teacher collaboration as their students too learned about student collaboration. Being a part of PLN helped them develop leadership as they were involved in common structured activities together, as they implemented CPS in their classrooms, and in the process, built trust. Other outcomes resulted, including development of collaborative leadership; a common vision; a collective vision developed alongside students, all leading to a deeper understanding of cooperative learning and collaborative problem solving.

1. Introduction

Students in Australia performed well in Collaborative Problem Solving (CPS) in the 2015 PISA online testing (Program for International Student Assessment [PISA], 2015), but there is little research about this pedagogy in maths classrooms in primary schools in Australia and internationally. CPS tasks in primary schools need to be carefully designed to match students’ developmental levels. The PISA testing in 2015 on Collaborative Problem Solving focused on students aged 15, so it is important to consider what is necessary in primary schools to develop these skills. Tasks that are too complex may lead to frustration or disengagement. Additionally, CPS approaches in primary schools often address social-emotional skills alongside academic goals. Explicitly teaching social-emotional skills and providing opportunities to practice them consistently throughout the day positively impacts both student learning and behaviour (Darling-Hammond et al., 2020). This is more likely to occur in the primary school setting, particularly due to the nature of primary school organisation in many countries, including Australia, where one teacher has a class for the entire day and teaches all subjects.

The latest OECD PISA 2022 Mathematics Framework highlights the importance of mathematical literacy being ‘an individual’s capacity to reason mathematically and to formulate, employ and interpret mathematics to solve problems in a variety of real-world contexts’ (OECD, 2018, p. 7). Solving problems and collaboration are key competencies needed today and developing twenty first century skills should be a key goal of maths education (Gravemeijer et al., 2017). Teachers need to be supported when introducing new pedagogies in their classroom, like CPS and teacher support in the form of a professional learning network has been shown to be effective and sustaining.

As argued by (Trust et al., 2016, p. 16),

If teachers are to continually develop their practice then they could benefit from broad, holistic, and flexible networks as they navigate shifting professional landscapes. The anytime, anywhere availability of expansive PLNs, and their capacity to respond to educators’ diverse interests and needs, appear to offer possibilities for supporting the professional growth of whole teachers.

This study focuses on a small group of primary school teachers working together in a school professional learning network, exploring how to implement CPS maths lessons in their classroom.

1.1. Defining the Terms

Teacher collaboration for teachers’ professional learning in the literature refers to a number of different terms/definitions and includes professional Learning Networks (PLNs), Professional Learning communities (PLCs) and Communities of Practice (CoPs). Teacher collaboration in professional learning communities or networks can help to ensure professional development is effective (Prenger et al., 2019) and a recent systematic review by Poortman et al. (2022, p. 96) has shown how ‘characteristics, such as active learning in collaboration, are, over a longer period of time, essential features of effective professional development’. Additionally, there are also no agreed definitions in the literature about what a PLC is but it has been referred to as “a group of people sharing and critically interrogating their practice in an ongoing, reflective, collaborative, inclusive, learning oriented, growth-promoting way; operating as a collective enterprise” (Stoll et al., 2006, p. 223).

Elements noted as important in these communities are leadership, being involved in structured or guided activities together and having trust in one another. It has been noted by Prenger et al. (2019, p. 442) that ‘All of the identified elements can be assumed to be connected to each other. A change in any of the elements invites changes in the other elements. This means that the various characteristics are intertwined and do not operate separately’. In a community of practice (CoP) teachers also share a passion for a particular topic and are interested in developing their knowledge independently on this topic together (Wenger et al., 2002). Communities of practices also have been shown to benefit both teachers and students as well as be a sustainable way of implementing Cooperative Learning (CL) into educational practices (Liebech-Lien, 2022, 2023). CL has synergies with CPS as highlighted below.

A Professional Learning Network (PLN), is the term chosen to be used in this study, is a kind of informal and more personalised professional learning community that describes a connected system of individuals and resources designed to foster continuous learning, first coined by Tobin (1998) and used by researchers since (Trust et al., 2016). A PLN often extends beyond one school with at times people using online platforms to connect with others. In this study the teacher team used digital tools, as well as more traditional ones for collaboration, as they connected with each other, shared resources as they engaged in professional development on CPS in their maths classrooms. Whilst engaging in the PLN about CPS in Maths the teachers learnt a great deal about how their students worked in CPS as they interrogated their own practices with each other, but also learnt alongside their students as they shared the journey in this inclusive approach.

1.2. CPS in the Maths Classroom

Problem solving, collaborative problem solving, computer and information literacy, and global citizenship are the four 21st century skills identified as being valued by many country systems (Care & Kim, 2018, p. 22). One of these four skills or competencies, CPS, the focus of this paper, has been defined by The PISA 2015 framework as ‘the capacity of an individual to effectively engage in a process whereby two or more agents attempt to solve a problem by sharing the understanding and effort required to come to a solution and pooling their knowledge, skills and efforts to reach that solution’ (Fiore et al., 2017, p. 2). Collaborative problem solving (CPS) is composed of two main elements: collaborative, involving sharing or social aspects alongside knowledge or cognitive aspects. Thus, the main difference between individual problem solving and collaborative problem solving is the social component. Cooperative learning skills are developed in CPS and this equity pedagogy helps create citizens committed to social justice with attitudes and dispositions which link, rather than compete with, others. Relationship building is therefore an important aspect of CL and CPS (Ferguson-Patrick, 2020) and social skill development is one way that students are likely to develop harmonious relationships.

Luckin et al. (2017) argued that effective CPS task design required positive interdependence, promotive interaction, individual accountability, interpersonal and group skills and group processing. These are the same key elements advocated by cooperative learning researchers (Gillies, 2007; Johnson & Johnson, 1994; Slavin, 1995) demonstrating the synergy between the two.

Social skills constitute the “collaborative” part of “collaborative problem solving”. They play an important role in collaborative problem solving but are also a feature of many other collaborative tasks. Cognitive skills constitute the “problem solving” part of “collaborative problem solving” (Hesse et al., 2015, p. 41).

It is only when a task requires collaboration that the social skills are fully utilised. As also argued by Liebech-Lien and Sjølie (2021, p. 224) there is a need to ‘accentuate the social pedagogy of learning through collaboration’.

The benefits of students working together in classrooms to solve mathematical problems has been well documented by many researchers as outlined by Webb et al. (2021, p. 1),

Explaining one’s own ideas and engaging with others’ ideas can promote learning in multiple ways. Developing and offering ideas to others, being challenged or questioned by others, and attending to others’ thinking all encourage students to rehearse information in their own minds, monitor their own thinking, reorganize and clarify material for themselves, recognize and rectify misconceptions and gaps in their understanding make connections between new information and previously learned information, reconcile conflicting viewpoints, and acquire new strategies and knowledge and develop new perspectives.

(Brown et al., 1992; Chi, 2000; Forman & Cazden, 1985; Roschelle, 1992; Whitebread et al., 2007; Wittrock, 1990)

Research has also shown that collaborative metacognition arises from combined individual and group processes when students are involved in CPS in maths (Smith & Mancy, 2018). Smith and Mancy (2018) furthermore assert that the ‘verbal interaction skills required for successful mathematical problem-solving in collaborative settings rarely develop alone’ (p. 29). When students are trained in how to use these cooperative and interpersonal skills in cooperative learning activities, ‘they demonstrated more cooperative behaviour, provided more help to each other, and used more inclusive language or language that invited others to participate than peers who had not been taught these skills’ (Gillies, 2023, p. 8).

CPS is a pedagogy that therefore develops students’ collaborative and problem-solving skills which are important skills more generally for the 21st century learner. Our students also require the ability to make decisions and take initiative, and these skills are also developed during CPS. CPS maths activities are usually open-ended tasks, requiring collaboration without teacher direct guidance, and as such require student agency. Agency is required by students in order for contributions to be made in CPS as they need to take initiative and contribute their ideas (Nieminen et al., 2022). Furthermore Webb et al. (2021) argues that when students contribute to mathematical ideas, by making suggestions as to where, or how to start to solve a problem, and contribute ideas to the solving of a problem, they are also required to react and build ‘upon, others’ ideas in ways that shaped the direction or nature of the work, such as suggesting extensions or alternatives’ (p. 13). Furthermore, when students are in classrooms where discussions are encouraged, such as in a CPS classroom, they see maths as creative and social as well as challenging (Boaler & Greeno, 2000).

However problem solving in maths can be challenging for some students (Heong, 2005) as well as their teachers. The number of barriers to the uptake of it in schools have included a lack confidence and relevant experience among educators, a lack of training and resources, a level of scepticism and concern, the prevalence of individually driven pupil assessments and competing curriculum priorities (Luckin et al., 2017). There are also many teachers who, despite the decades of research to advocate for its use in school, don’t use cooperative learning pedagogies, like CPS, in their classrooms (Baines et al., 2003; Ferguson-Patrick, 2016; Kutnick & Blatchford, 2014; Muijs & Reynolds, 2005). Cooperative learning implementation requires a lot of pedagogical support (Ferguson-Patrick, 2011) and Jolliffe argues, ‘CL requires a sustained and collaborative process in order to implement it effectively’ (Jolliffe, 2015, p. 79). Support is needed, especially in relation to teacher role during its implementation (Ferguson-Patrick, 2016; Gillies & Boyle, 2010; Johnson & Johnson, 2008; Kaendler et al., 2014). Teachers also need to have a good understanding of how to structure the key elements of CL effectively (Johnson et al., 2008) for it to be successful. As argued by Ruys et al. (2011) ‘Teachers should have insight in how to structure these key components in the classroom, in order to avoid the free-rider effect, conflicts in the group, etc.’ (p. 1091).

1.3. Professional Learning and Professional Learning Networks

Professional Learning (PL) for teachers is important as Australia’s Professional Standards for Teachers (Australian Institute for Teaching and School Leadership [AITSL], 2017) emphasise that teachers, whether newly graduated or in a proficient or leadership position, are expected to maintain an ongoing professional learning profile over their professional life. This should incorporate engaging with colleagues, community and parents/carers. Professional learning should support educators to consider the purpose of their actions in the school with a high quality professional learning culture being defined as having collective responsibility, for improvements in practice as well as ‘high levels of trust, interaction and inter-dependence’ (Australian Institute for Teaching and School Leadership (AITSL), 2022, p. 3). The term PL indicates an ongoing process of enhancing skills and competencies, and a network of teachers in a professional learning capacity has been said to be based on the understanding ‘that teacher attitudes, skills, and practices interact and influence each other. The dynamics of these interrelationships provide a basis for facilitating teacher development’ (Chen & Chang, 2006, p. 5).

PLNs are about people and resources working together to support ongoing learning. Some PLNs are groups of teachers who do not work as one teacher team in one school. However a broader definition is provided by Carpenter et al. (2022, p. 86), claiming a PLN to be ‘people who share information (e.g., teaching strategies, resources, ideas), provide feedback, advice, and emotional support, and encourage changes in teaching practices’ is the one that I will use in this paper. I would argue that by having one teacher team from one school, a team that already works well to support each other, develops trust, and this is paramount, especially if teachers are able to speak freely and be open with each other (Francisco et al., 2023). There is a growing body of research that acknowledges that trust is necessary for sustainable change (Kemmis et al., 2014; Wenger, 1998) as well as research that supports the idea of PLNs or PLCs contributing to the building of teacher skills, including leadership and trust (Prenger et al., 2019) thus allowing teachers to flourish (Owen, 2016).

1.4. Professional Learning in CPS in Mathematics

Professional learning in CPS is important for a number of reasons. It has been argued that when implementing challenging tasks, as in the case of those which are common in CPS, that teachers have a go themselves so that they can be prepared for student questioning and anticipate the prompts needed to help students’ progress (Bobis, 2023). Challenging tasks help increase student engagement (Sullivan et al., 2015, 2014) and student autonomy (Attard et al., 2016). It is a vital component of PL is that teachers are knowledgeable at problem solving instruction and are aware of the need for a constructivist approach. Teachers need to understand that a major element of guiding students to work collaboratively, ensuring autonomy is being able to decide when, where and how they should support the process (Chapman, 2015; Hourigan & Leavy, 2023; Lester, 2013).

Firstly, teachers need to be aware of what collaborative problem solving is (Luckin et al., 2017) and how the different activities relate to particular cooperative learning key elements (positive interdependence, promotive interaction, individual accountability, interpersonal and group skills and group processing) but also about different problem solving models, some of which are old but still relevant today (Polya, 1957). Fitzsimons and Ní Fhloinn (2023) more recent model argues it’s important for teachers to be aware of the components necessary in problem-solving, including the need to provide opportunities for students to discuss, conjecture, critique, build a solution, communicate reasoning and extend.

Teachers also need to be aware of how to develop their students’ problem-solving skills but also how to assess their students’ abilities in CPS. This includes cognitive abilities related to the task itself, their cooperative and interpersonal skills, their ability to resolve conflicts and disagreements and how to guide or mentor other team members (Zhuang et al., 2008). An awareness of the various social skills required in CPS, including participation, perspective taking and social regulation skills (Fiore et al., 2017; Hesse et al., 2015) are needed to be able to assess their students’ competence. There is little research about CPS in primary school settings, and this study examines this gap, exploring the ways that teacher collaborate about this pedagogy in a PLN to assist their confidence and experience in its implementation. This paper therefore examines the research question, ‘What is observed when teachers collaborate in a teacher team in a PLN when developing Collaborative Problem Solving in their classrooms?’.

2. Materials and Methods

2.1. Participants and Study Design

This case study examines a small teacher team of five teachers with classes of students’ aged 10–12 years. They taught in one local public/state primary school in NSW, Australia. They had a variety of different teaching experience ranging from 2–20 years. They signed up as teacher researchers on the project as they had an interest in the curriculum area of maths and were currently in the process of examining and learning about the new primary curriculum in maths to be mandated in the following year in NSW. They were very familiar with problem solving as one of the four maths proficiencies (Australian Curriculum Assessment and Reporting Authority (ACARA), 2023) being a key component of previous Australian maths curriculum documents. They had previously explored professional learning about maths problem solving but not CPS. They participated in two sessions of professional learning on CPS after school hours. The professional learning sessions ensured that the teachers were aware of the Pedagogical framing and Pedagogical interventions needed to successfully implement CPS in their maths classrooms. Pedagogical framing has been defined as ‘including the provision of resources, arrangements of space, daily routines to support cooperation, planning and assessment (documented through teachers’ reflections on classroom practice and wider information)’ and Pedagogical interventions as ‘face-to-face interactions (documented through observing classroom practice and listening to children’s reflections upon it)’ (Siraj-Blatchford et al., 2002, p. 23).

The five teachers were then asked to teach at least one CPS maths lesson a week in their classroom and subsequently reflect orally on these lessons, sending them weekly to the researcher. In total, between 8 and 10 reflections were received from each of the five teachers over a two-month period. Teachers met regularly as a part of their normal staff meetings and stage team meetings so informally shared resources, successes and challenges throughout the period of time (one term). They were also encouraged to participate in a private/closed Facebook group to share their stories and photos of their journey. Combining the professional learning workshop and inquiry into CPS, as well as the experimentation of this pedagogy in a supportive teacher team, the teachers’ learning and implementation of the pedagogy was developed (Liebech-Lien, 2020). During the PL sessions the teachers were taught about, and subsequently used a proactive action research process (Schmuck, 2006, p. 54). This involved the following steps: 1. List hope and concerns, 2. Try a new practice, 3. Collect data, 4. Check what the data means, 5. Reflect on alternate ways to behave, 6. Fine-tune practice and so on in a cyclic ongoing approach. They considered how they could move their class forward as they tried out this new pedagogy (see (Ferguson-Patrick & Liebech-Lien, 2024) for more detail about this approach). They reflected on the process, through the use of a researcher provided reflective observation proforma (including the prompts (1) why I chose this problem; (2) how the children worked: pairs or larger groups; (3) what I did to present the problem; (4) what the children did when they were solving the problem; (5) what the children learned; (6) what surprised me; (7) what I would do differently if I taught this problem again) based on the work of (Sakshaug & Wohlhuter, 2010). Using this reflection for at least one CPS maths lesson a week, they also considered how other teachers in the team were making sense of the pedagogy to understand the process of introducing CPS. This cycle of “knowledge sharing and creation as well as the development of new practices and the joint trial and refinement of these practices” (Poortman et al., 2022, p. 96) continued throughout the process of experimentation with the new pedagogy of CPS.

Teachers were interviewed about their shared experiences that were documented in the Facebook group, as well as through other methods of collaboration, during a focus group session with the whole teacher team at the culmination of the project. This session was recorded and transcribed. I used the cooperative learning strategy called the “meeting in the middle” structure (Kagan, 2021; Liebech-Lien, 2022) which can be described in three steps. First, all participants were given time to think individually about a question and to write down their answers. Second, all of the participants took turns in sharing their responses with the others. Third, the group tried to synthesise their answers. Questions asked of the teachers focussed on what they learnt about CPS in a PLN.

This paper focusses on this final focus group session data, with individual interviews and reflection data and results explored in other papers (Ferguson-Patrick, 2024; Ferguson-Patrick & Liebech-Lien, 2024).

2.2. Data Analysis

The researcher used reflective thematic analysis (Braun & Clarke, 2006) to determine what themes emerged from the focus group. As highlighted by Byrne (2022) ‘The reflexive approach to TA highlights the researcher’s active role in knowledge production (Braun & Clarke, 2006). Codes are understood to represent the researcher’s interpretations of patterns of meaning across the dataset’ (p. 1393). After using open coding, not having pre-set codes, but developing and modifying the codes to identify categories and decide on themes, five main themes emerged from the focus group data: Collaborative Leadership; Common vision; Collective vision with students; Trust; and this led to a Deeper understanding of CL and CPS.

3. Results

The following section will examine the five themes found from analysis of the focus groups transcript. These were Collaborative Leadership; Common vision; Collective vision with students; Trust; and this led to a Deeper understanding of CL and CPS. Vignettes from the focus groups are used to highlight these themes. The first of these is Collaborative Leadership. This theme emphasises shared decision-making, inclusive participation, and power sharing among all of the teachers in the study (Tschannen-Moran, 2001). Mutual respect and open communication are also aspects of collaborative leadership and this contrasts with traditional models of hierarchical leadership. Furthermore collaborative leadership fosters environments where teachers work together to analyse and improve teaching practices, leading to sustained improvements in student outcomes (Sharratt & Planche, 2016) a key focus of communities developed for professional learning (Timperley et al., 2008).

3.1. Collaborative Leadership

The following vignettes demonstrate how the leadership in the team changed as their project developed over time. One teacher, Joanne, started by leading the teacher team who all taught the same age group at the school. She was a teacher passionate about maths and naturally started to think about how she could incorporate the new learning from the PL sessions into their math’s programs. Once she started, however, other teachers took over the leadership role at times, also sharing their successes, or resources with others.

Vignette 1: Joanne

I think we left here [from the PL] like feeling really, like excited and enthused and energetic about it. I don’t think we like sort of sat and specifically planned how it was going to work…I think it sort of happened organically. In that Joanne really took leadership of it in planning some of those and finding activities and lessons to have a go at. And then I think as we got into it, that’s when we got more into a bit of a structure with it. So like I loved like when people would start to share things on the Facebook group or you know, or like back when you had one you’re like, oh, this was the best one ever, so automatically I was like, right, I’m going to try that. And then I think yeah, as our confidence grew things, like even from doing our reflections, it was like, someone’s like, Oh, I’ve made a template and I’ve, you know, done that. So it’s like, great, we’ll make a copy and use that. And then we just got into a nice little system with it…

This demonstrated aspects of distributed leadership and shared decision making.

And then in regard to planning how it might be implemented, we pretty much all just jumped in with two feet as well like it wasn’t like [teacher] said, we didn’t like sit there and go, well. Are you going to start this? Are you going to…we just did it. And [teacher] would create those templates, but we were all putting things in as well. Yeah. Which was fabulous.

Active participation is clearly identified by the comment we pretty much all just jumped in with two feet. There was also a demonstration of the teacher team sharing the power and a need of inclusive participation. She also mentioned,

Yeah, I think starting out, we used the same ideas and I just tried to find activities that I thought would be work well for CPS that would work in with whatever like math topic we were looking at that week. But to just kind of make it more relatable for the kids. And so I just put them in the weekly sides [shared google drive for the team’s math’s lessons] but then people would like find something and go, Oh, this would work really well for that. And so everyone was just putting stuff in and then as we branched as we like, went on and got more confidence, people would branch out and they’d be like, Oh, I found this thing here. I’m tried that and then you’d hear about someone trying something and like, oh, that sounds interesting.

Joanne further demonstrated that different teachers took on the leadership role, sharing their expertise and new ideas and also understanding the need for open communication.

…like when you said about using your windows for the whiteboards, I was like, oh my, that’s amazing. Like, what a good thing to do. And just like, you know, you’d pick up ideas of other people and then you’d be like, either oh, I want to go do that again with that idea…

The second theme, Common vision explored how teachers involved in an ongoing PL, using an action research approach, allowed them to explore a key pedagogy that developed their students 21st century skills as well as concurrently developing their own collaborative skills and ability to teach maths problem solving in this way.

3.2. Common Vision

The teacher team were already involved with trialing and implementing ideas from the new curriculum that year. They all mentioned how this new learning seemed to fit seamlessly with what they had already been doing, but at the same time invigorated them because of coming together and having the time to learn in the PL sessions. Practice and experimentation were important in the PLN. When the team of teachers implemented the same learnings and strategies based on this shared vision of introducing CPS into their classroom, they create a consistent learning experience for students. It also helped to build commitment to change and improvement among the teachers with this sense of collective purpose and responsibility for student success.

Vignette 2: Bianca

I think we walked away [from the PL] really optimistic and really positive and sort of going this will fit in to what we’re doing [already]. There was a lot of chat originally like early on about group size and what group sizes were and stuff and we all pretty much I think settled on three being a really good number.

The sharing of the common vision allowed them to create a consistent learning strategy for their students, particularly in relation to optimum group size for CPS groups.

Vignette 3: Liam

What I liked was, sometimes we did the same thing. We approached it in different ways and then we could talk about that. Obviously, we’re able to kind of share our successes and our failures. Yeah, but I agree with Joanne…back when we did leave [the PL sessions] there was a lot of enthusiasm. I think it was playing that Castle Game…we were buzzing when we left and I think we just went straight into it with our kids and it just grew from there. So excellent.

Liam demonstrated that despite their collective responsibility to the same goal, they were able to adapt and develop their own expertise in implementation. They mentioned the importance of the PL sessions allowing them to experiment, try out some of the activities first, highlighting the issues they encountered and why it was important to always have a go first, or talk to another.

Vignette 4: Kellie

And I think that’s why it’s so important, or why it was so beneficial [the PL]. When we actually had a play of them ourselves. You could really understand and then see how the kids were going to approach that.

It was nice, because we were…especially at the start usually doing like similar activities each week and…you’d like run into someone or you’d like pop next door, you know, like I’d go next door to [teacher] or I’d like see [teacher] in the staff room or something. I’d be like, oh, yeah, we tried this one out and this didn’t work and this group did this…And then you’d hear someone else doing it and you’d be like okay, and then that’s how I should [approach it]…you’d pick up ideas off other people…how can I tweak it you know, even if like something didn’t maybe go to plan as you had hoped…

The common vision maintained their focus and the shared purpose allowed them to experiment in ways they might not have thought of alone, as they embarked in this practitioner research study. They also mentioned that they will keep going with implementing CPS in their classrooms next year,

Vignette 5: Liam

I think I had great results from it. And yeah, just definitely going to keep it as part of our classrooms next year. I think we…when we started out this year…we talked a lot about building positive mindsets in maths and I know we’ve been building that up over a year and yeah, the CPS it was just that that push further and yeah, it’s something I’ll definitely do next year.

The third theme—a collective vision with students identifies how as teachers worked in collaboration as a teacher team, and reflected on their own journey of implementing CPS in their classrooms, students also joined the journey embarking on their own experiences of working in collaborative problem solving groups with their teammates.

3.3. Collective Vision with Students

The teachers were able to share and reflect on key aspects of CPS skills with their students. Collaborative problem solving (CPS) is an effective approach that can benefit students and seeing changes in students’ social and cognitive skills was firstly addressed by the teacher team.

Vignette 6: Bianca and Joanne

It’s really good for the kids to be reflective as well. Like I think that there’s lots of space for them to be reflective because I mean, every one of those things we would come together at the end we’d talk about how we did it…how somebody else did it. How that was different to how we did it or whatever. And they had that opportunity to reflect on what somebody else had done, but also on how they should have done it or how they could have done it or what they did. Well. Yeah, so yeah, you’re right. It was it’s really good for assessing.

Students were able to see when others found different ways to solve problems, and this helped them to see the power of communication and sharing in a reflection phase.

It’s also been good for the kids who will work out stuff quicker…who can process quicker than the other kids. And they have to learn to take a bit of a backseat and they have to learn how to nudge…How did you like nudge your teammates and get everyone on the same page without doing it for them or just being like, you know they know that you know, but you can’t tell them that you know, and you have to communicate and so they have to use all those skills. And these are the kids who will be like they’ll blurt out an answer in class or they’ll put their hand up and they’ll be the ones who want to share. And this is another way that you can just get them to work on that self-control, which is a really important social skill for them.

Another skill identified by the teachers was the importance of patience, stepping back and waiting and learning when to give and receive help.

I’m glad you said social because even that that’s something in my room that they’ve become more social doing maths as well, like we’re, I think, in previous years, like everybody and even when we were at work when I was at school, it was a very personal thing. It’s very get into your bubble and you don’t understand it or you hide it because someone will copy you or whatever. It’s all about the answer. But this has given that space to go…like to fail or to bring other people in…because I think we would always go with, these are the high achievers, these are the people that should be working together and we’re not doing that now. We’re spreading it out and the knowledge and the skills and everybody’s getting it because they’re not being ‘hogs’ and they’re not being ‘logs’. Yeah, it’s built the confidence of not only my lower [math’s ability] kids but my high [math’s ability] kids as well.

This vignette demonstrates how the two teachers were aware of their students’ development with CPS and their growing ability for both teachers and students to recognise that equal interactions are important in a CL classroom (Cohen & Lotan, 1995). Teachers began to recognise the need that they need to teach students to build responsibility for each other’s learning and also students had a maturing knowledge that they could not be ‘hogs’ or ‘logs’ in the classroom (Ferguson-Patrick, 2024; Kagan, 2021).

Vignette 7: Joanne

Yeah, everyone gets something out of it…Be it mathematically or socially. It’s been great for their self-reflection. Because we at the very start, we talked about like what is something that you bring to the table, what’s the strength you have, and what’s an area that you need to work on? And they were really honest, and I was really honest with them and I said, you know, look, I said ‘this is my strength.’ And I said, you know, ‘these are my weaknesses’. And I said, I’m telling you this as an adult, I said, you know, we’re all ‘a work in progress’, and I said you know acknowledging that you have something you want to improve on is like the first step. And then it was interesting seeing the kids that like really picked up on that and I had a couple who like just, like every like activity was like an opportunity for them to practice being better at the thing that they previously weren’t good at, which I really love to see. So, yeah, that’s nice.

As Joanne shared her strengths and weaknesses with her students, they felt more confident in being able to share their own.

And I remember when we first started it, some of the kids in the classroom…they weren’t really keen on having to work with people that they didn’t socialize with. And they you know, some people like I keep getting put in a group with this person…I’m like, it’s random, you know. And whereas by the end it just, it was a non-issue like there were no grunts no eyerolls whenever like the group generator would come up on the smartboard it would just be like, okay, yep, that’s a group or I’ll get scissors. Yeah. And like it was just, it just they just got into a routine with it. And so many of them said at the end that they said it was actually nice to work with people that they didn’t really know and I feel in some they are not all best friends or anything, but I feel like they’ve at least connected a little bit and have got to appreciate each other a little bit more.

Students also began to realise they could work with any of their peers, not just friends. They appreciated the skills and knowledge gained from all types of peers and this also meant therefore that less time was spent on management of students’ behaviour and on task behaviours.

The fourth theme, Trust developed as they embarked on this PLN journey as a collaborative group. Despite the teachers having different levels of expertise and years of teaching they learnt as a team to support and rely on each other, sometimes giving, and sometimes taking.

3.4. Trust

The qualities of respect and trust are important in a PLN whereby the teacher learning community are able to collaborate and share their professional growth with likeminded others (Tschannen-Moran, 2001). Developing understanding of CPS was easier to achieve in this teacher PLN with a shared sense of purpose. Teachers shared resources, successes and strengths and weaknesses in a safe shared space. This ‘widely shared vision or sense of purpose’ is important in a PLN (Harris & Jones, 2010, p. 179) and this also develops trust between the teachers as they realised they could rely on each other as others took turns to do their share.

Vignette 8: Joanne, Kellie, Bianca and Liam

[when] someone was first in the week to do an activity, we’d put in the group chat or something and be like I’ve cut out these cards if anyone wants to come and get them and just little things like that which just made things a lot easier and knowing what we’ve got ahead next year with the new curriculum. It’s nice knowing that we can like all depend on each other.

The establishment of reliance, and understanding that others were supporting, meant the teachers developed a comfortable working relationship; a safe space.

I think it definitely helped establish that it just felt really comfortable talking to people about things that went well or things that didn’t go well. And yeah, there was no fear of judgment. Oh, I can’t tell them this. Because yeah, I felt like a safe space between all of us.

That was the good thing. Like if you did have something that wheels fell off you would say, well, the wheels fell off. Like don’t do it this way when you do. Because I did it. And yeah, don’t put five in the group or whatever.

I think we do that a lot during stage meetings. We have a lot of brutally honest reflections on our own strengths and weaknesses. And we do, we’re quite honest about what works, what doesn’t work and it is a safe space, that trust and respect in the room.

[We’d] just blurt to each other or say, Well, this worked or that didn’t work or whatever or what do you…How would you do that? Or how did that work for you? Because the wheels fell off for me like…I think yeah, that was our biggest aspect that really made it work for us. Yeah. oh, and the shared sense of purpose, I suppose.

This vignette shows how the teachers had learnt to develop respect and trust among colleagues at the school as they critically inquired into CPS development as a team.

The fifth and final theme emerged as a result of the experience of working in a PLN, participating in the PL and in their ongoing sustained learning on how to implement CPS in their classroom.

3.5. Deeper Understanding of CL and CPS

They firstly needed to have an understanding of CL to be able to ensure CPS was successful.

Ellie stated: I feel like I also focused a lot on like the interpersonal and like group skills in my class, because especially sort of trying to model respecting relationships and how to communicate in a way that’s not just biting each other’s head off or snapping immediately.

Social skill development is a key element in developing cooperative learning and some teachers felt they needed to spend more time on developing these skills at the beginning of the project than others.

Joanne mentioned: We talked a lot about how individual accountability is important for the group to succeed, and how, depending on different activities, I would say to them, and maybe sometimes I would leave it until the end of the activity when we would reflect and say, you know, what worked really well in your group today. What didn’t work well, what would you do differently if you were to do it again with a new group of people?

Again individual accountability is another key element of both CL and CPS and some teachers really needed to ensure this skill was explicitly taught as well as the need to reflect on this skill in the reflection phase of the lesson.

Kellie built on this stating: Individual accountability…just because I think throughout this process, it made me realize how many kids just either try to go under the radar. They don’t…they don’t contribute. They’re very much…just so used to just going under the radar and just not contributing. But also then the other end of the spectrum of those kids who just want to overtake and do everything and not let others contribute.

Kellie realised how many of her students were not fully participating in activities and she also that others were monopolizing others and not allowing them to contribute.

Bianca stated: With promotive interaction where members are willing to support each other to complete the task. I always like with my ‘working at the windows’, I always just give them one marker for the whole group. And if they’re holding the marker, it’s not their ideas that they’re writing down. Somebody else has to be telling them. Yeah, and if the person that’s writing has a great idea, they give the marker off to somebody else. So they’re, they’re supporting each other to understand and they’re supporting each other to work out the problems as well.

Bianca shows a deep understanding of individual accountability can mean resource interdependence and ensuring they only have one resource (a marker) which forces them to take turns. She also supports the class in future lessons by providing reminders in the classroom for them to refer to in relation to group work skills.

Yeah, like I’ve printed posters and put them up for like rules. This is how we work in groups. Yeah, these are the questions we can ask each other. This is how we can what we can say if we like, or if we don’t like, what somebody’s saying.

Liam argued he’d learnt that: I feel like at the beginning of the year that definitely I think those group skills, interpersonal skills, that’d be very a big focus as it’s when you really need to build on these.

3.6. Discussion

Although this study focusses on one small teacher team in a case study approach and in one school and is not generalisable, it has provided insight into how teachers working in collaboration can support students working in collaboration to solve problems in mathematics. It is hoped that this study can support a naturalistic generalization where readers gain insight by reflecting on the description and findings of this study, resonating with their own experiences to inspire them to further inquire and practice in a PLN (Melrose, 2009).

The following five themes were explored above through small Vignettes and comments made by teachers during the focus group discussion which occurred at the Collaborative Leadership; Common vision; Collective vision with students; Trust; and this led to a Deeper understanding of CL and CPS. Vignettes from the focus groups are used to highlight these themes.

The first of these is Collaborative Leadership. Common elements of collaboration in schools have been identified as including open communication, mutual respect, shared goals, responsibility and decision making and active participation (Griffiths et al., 2021) and these are equally important in Collaborative Leadership. As identified in the shared vignette many of these aspects were identified. Harris and Jones argue that many researchers have found that ‘distributed leadership, shared decision-making and co-enquiry among teachers are strongly associated with better learner outcomes and improved organisational performance’ (Harris & Jones, 2017, p. 24). Improvement of learning outcomes is the key reason for a professional learning community (Timperley et al., 2008).

The second theme, Common Vision is essential for the success of a professional learning network. This shared vision serves several critical purposes including guiding decision making about teaching and learning and an unwavering focus on student learning. As the team were committed to changing their practices in maths to involve more CPS, the sense of collective purpose, participation and responsibility for student success in this area was apparent. Collective participation matters as ‘colleagues working together to master new knowledge can scaffold one another as they collectively make sense of new ideas and sort through emergent understandings’ (Evert & Stein, 2022, p. 2). This was showed by the teachers in this study. Sharing and joint problem solving occurred as a part of this common vision (Little, 1990). A common vision also includes the shared goal (in this project to include more CPS in their classroom), fostering a collaborative culture (Strahan, 2003) so to their expertise was being shared as they grew to understand the pedagogical practice.

The third theme of Collective vision with Students which describes the ways that as teachers embarked in a collaborative endeavour with their peers, they also were able to model collaborative behaviours and skills with their students. Thie own practices made an impact on their student practices. Teachers really began to notice the impact on student learning outcomes in terms of their reflective behaviours and social skills. Timperley et al. (2008) argue one of essential conditions of a teachers working in a professional learning network or group is the primary focus should be on examining how teaching practices affect student learning outcomes. Teachers began to see clear improvements in students’ affective outcomes. Research has shown the importance of interaction for learning in groups with achievement generally showing ‘that giving help and receiving help are positively related’ (Webb, 1982). The classroom became more harmonious as a result of students not being reluctant to work with different students as they learnt to accept who they were going to work with in each activity.

The fourth theme, Trust was developed as the teacher team began to see how the others understood the brief and began to share and collaborate in the development of the pedagogy as well as develop the benchmarks of improvement that were continuous (Harris & Jones, 2010). As argued by Francisco et al. (2023, p. 941) ‘Collegiality is an essential feature of a professional learning community (Wenger, 1998; Bryk & Schneider, 2003) and can be seen as ‘relational trust’ in action’. Trust is further described by Francisco et al. (2023, p. 942) in a number of ways,

Interpersonal trust involves responsiveness to different pedagogical approaches that instil a sense of belonging and understanding. Interactional trust creates safe, meaningful and honest communicative spaces. Intersubjective trust enables meaningful and relevant professional learning activities in context. Intellectual trust comes from professional knowledge. Pragmatic trust is about timely sustainable and strategic change (Edwards-Groves et al., 2016). Relational trust is formed in daily interactions, and these daily interactions determine trust more significantly than professional learning.

(Bryk & Schneider, 2002)

Trust in your colleagues enables teachers to take risks in learning about this new pedagogy with colleagues who share the same need (Lewicki & Bunker, 1996). As argued by Stoll et al. (2006) ‘Feelings of interdependence are central to such collaboration: a goal of better teaching practices would be considered unachievable without collaboration, linking collaborative activity and achievement of shared purpose’ (p. 227).

The Fifth and final theme: Deeper Understanding of CL and CPS demonstrates the understanding teachers developed of the essential elements required by students to work in a cooperative group, the same elements for CPS to work efficiently. These included positive interdependence, promotive interaction, individual accountability, interpersonal and group skills and group processing (Gillies, 2007; Johnson & Johnson, 1994; Slavin, 1995). By sharing and reflecting on their own and peers’ experiences, teachers developed a deeper understanding of these elements and their necessity for successful implementation.

4. Conclusions

CPS is complex and this paper only scratches the surface of this complexity examining teachers’ perceptions of their involvement in a PLN, and has highlighted some of their perceived outcomes of this process on their and their students’ learning. The question of ‘What is observed when teachers collaborate in a teacher team in a PLN when developing Collaborative Problem Solving in their classrooms?’ was explored finding five themes which described the features observed in the course of teachers collaborating when implementing Collaborative Problem Solving. The five themes demonstrated were Collaborative Leadership; Common vision; Collective vision with students; Trust; with all these leading to a Deeper understanding of both Cooperative Learning and Collaborative Problem Solving.

Being a part of PLN helped teachers develop leadership as they were involved in common structured activities together, as they implemented CPS in their classrooms, and in this process, built trust. It also invigorated them as teachers and as a well-functioning PLN allowed them to be reflective and willing to innovate (Stoll & Seashore, 2007). Teacher enthusiasm and passion were generated by shared work in planning, teaching, evaluation and reflection when learning about CPS.

As argued by Hunter et al. (2020) it is important for teachers to develop interpersonal and social skills in their students to shift towards more equitable classrooms and these are needed in a democratic society. As argued by Johnson and Johnson (2016) when ‘students give voice to and consider different opinions, ensure that every student has the right to express his or her views and be listened to with respect, stay open-minded, take other persons’ perspectives, and engage in decision-making with others’ (p. 163) they are more likely to develop ‘citizenship values, attitudes, and long-term behavioral patterns’ (p. 166).

It is also important for teachers to understand that when considering best practice in teaching maths in the 21st century, that maths, and the associated key skill of problem solving, should be seen as collaborative endeavours. Authentic and engaging maths teaching should include rich tasks and “the basis of any rich task is a need to pose and solve broadly-defined problems that are realistic, involve collaboration and comprise multiple levels of complexity” (Prescott et al., 2020, p. 23). It is also important, as argued by Liebech-Lien (2022), that any research ‘with a focus on collaboration [can be seen] as an investment in the future’ (p. 107). Teacher collaboration in a PLN is an effective way to support this student collaboration.