Supporting Young Children’s Exploration of Mathematical Concepts: Co-teachers’ Involvement in Joint Play

ABSTRACT

There has been a major international focus on the education and care of toddlers. To date, empirical studies on adults’ interactions in play with toddlers have focussed on the proximity of teachers, teachers’ affective responses, and joint attention between adults and children in play. However, less attention has been given to the role of two teachers working together in supporting children’s exploration of concepts in joint play. This paper takes a cultural-historical perspective and draws upon the concepts of play and subjective positioning to investigate how co-teaching promotes toddlers’ joint play and exploration of mathematical concepts. Visual data of a group of toddlers playing with two teachers is analysed to explore how the teachers applied co-teaching pedagogy to support children’s exploration of mathematical concept. The study argues that co-teaching provides potential to support collective play as two teachers can work collaboratively to address the toddlers’ challenges and needs and support their exploration of the rules and mathematical concepts in play. Co-teaching by paired teachers enables toddlers’ joint play to become more complex, helping the children to explore mathematical concepts and, in turn, further enhancing their play.

Keywords:

• co-teaching
• exploration of mathematical concepts
• joint play
• toddlers
• pedagogical positioning

1. Introduction

Play supports children’s conceptual learning and development (Fleer, 2011; Li, 2022; Vygotsky, 1966). There is a shared understanding among scholars that some characteristics of play, such as imagination, creativity, interactions with peers and adults, and communicating and negotiating the play rules can contribute to children’s mathematical thinking and problem-solving (Ginsburg, 2006; Li and Disney, 2021; Marcus et al., 2016; Trawick-Smith et al., 2016). In this paper we emphasise that play is not chronologically determined but a cultural process that highlights the social interactions between toddlers and their surrounding adults and peers (Fleer, 2013). To support toddlers’ mathematical learning, teachers need to be responsive to young children’s demands and interests in play. Previous studies have shown that teachers’ guidance in play supports children’s mathematical concept learning (Anthony and Walshaw, 2009; Sarama and Clements, 2009). Mathematical thinking begins in early childhood, and as such, it is suggested that early childhood teachers should respond to young children’s demonstrations of mathematical thinking (Franzen, 2021). In her study of working with toddler groups (1 to 3-year-old children) to support children’s mathematics concept learning, Bjorklund (2012) proposes that the interactive process of learning such concepts requires the teachers’ awareness of the toddlers’ intentions when using mathematical language in play. Tirosh et al. (2020) further explain that teachers need to make sense of toddlers’ mathematical development while providing suitable playful mathematical learning experiences. They also suggest that there is a need to explore how teachers can actively participate with groups of toddlers in play to support children’s engagement with mathematics. Thus, an important question to address for early mathematics education is how to support toddlers’ exploration of mathematical concepts in ways that mediate mathematical meaning and thinking (Bjorklund and Plamer, 2022; van Oers, 2010).

A large body of research on play emphasises adults’ active role and regards adults’ joint play with children as a significant pedagogical support for children’s learning (Fleer, 2015, 2018; Hakkarainen and Bredikyte, 2019; Li et al., 2021; Pursi and Lipponen, 2018). However, considerably less attention has been paid to adults’ positioning in play, that is, how adults pedagogically position themselves as play partners to support toddlers’ exploration of mathematical concepts. Through video analysis, Fleer (2015) has shown that most teachers position themselves outside of children’s play by staying in close proximity but not engaging closely in the play itself. Instead, teachers play ‘in parallel’ with children’s intentions and provide suggestions or support children’s group play. Fleer (2015) has advocated for an understanding of how adults can take an active role and be ‘inside’ children’s play to support their learning. In seeking to help address this gap, this paper focuses on how pairs of teachers can co-position and teach together as play partners inside children’s play in order to support children’s exploration of mathematical concepts and to increase the possibilities of children’s active engagement in play.

2. Co-Teaching as a Strategy in Education

Empirical evidence has shown the effectiveness of co-teaching to promote students’ learning in the classroom (Hsieh and Teo, 2023; Pareto and Willermark, 2022; Pratt, 2014). Co-teaching is a widely used collaborative approach that draws upon two teachers’ combined expertise to meet the demands of students and benefit their learning in the classroom (Pratt, 2014; Rabin, 2020). Further, reference to co-teaching highlights the importance of team-teaching, in which each teacher contributes to the learning in ways that cannot be achieved by one teacher alone (Schwarz and Gorgatt, 2018). Co-teaching has been investigated in different disciplinary areas such as English as a foreign language/secondary language teaching (Hsieh and Teo, 2021; Tasdemir and Yildirim, 2017) and bilingual classrooms (Schwarz and Gorgatt, 2018). Studies have also suggested that co-teaching benefits inclusion and students’ special learning needs (Friend, 2015; Morfidi and Samaras, 2015) and in peer mentoring for pre-service teachers (Drescher and Chang, 2022; Rabin, 2020). Numerous studies have concentrated on a co-teaching approach and explored the strategies that co-teachers use to improve collaborative teaching relationships. These strategies include secondary school co-teachers effectively resolving challenges in collaboration (Pratt, 2014), computer-supported collaborative teaching in virtual classrooms (Pareto and Willermark, 2022; Watfa and Audi, 2017), and collaboration in teacher education programmes (Nevin et al., 2009). For instance, Pratt (2014) described partnership building in collaborative teaching through secondary school teachers’ exploration of strategies in coping with classroom challenges. Pratt highlights that effective co-teaching partnerships find ways to strengthen relationships with each other through open communication and by learning about each other as teachers use their individual strengths and expertise to break down barriers to co-teaching. There is, however, limited research on co-teaching in early childhood education, despite recognition of their possible educational benefits.

Hsieh and Teo’s (2021) study examined early childhood teachers’ perspectives on collaboration with English language teachers in Taiwan. They suggest that collaborative teaching needs to be promoted by recognising and embracing each teacher’s active involvement rather than following a ‘one teaches, one assists’ approach. Hsieh and Teo’s work also highlights that collaboration is affected by organisational, interpersonal, and personal factors. However, how these factors affect collaboration and their impact on the contribution to young children’s learning has not yet been resolved. Through video observations and interviews, Schwarz and Gorgott (2018) demonstrated that, in bilingual preschool classrooms, co-teachers cope with challenges in negotiating their roles and teaching strategies by relationship building while co-teachers acknowledge their cultural and professional backgrounds. Sanders-Smith and Davila (2021) have focused on co-teaching relationships in trilingual preschool classroom in Hong Kong while considering how to promote the children’s interests. However, there is limited research and even less evidence towards co-teaching practices in toddlers’ mathematics education. This study charts new ground by looking at co-teaching as a driver to support toddlers’ mathematical exploration processes in play and capturing the process of co-teaching positioning in relation to the toddlers’ demonstrated intentions. This paper draws upon Vygotsky’s (1966) cultural-historical concept of play and imagination to investigate how two teachers can co-position themselves to support toddlers’ mathematical conceptual thinking and learning in play.

3. Cultural-Historical Play and Teachers’ Positioning

A conceptual term such as play in early childhood education has many dimensions and covers many forms of activities, which makes it hard to define. Instead of reviewing and discussing traditional perspectives and views of play, this study draws upon Vygotsky’s concept of play (1966) that was later developed by other scholars such as Fleer (2011, conceptual play) and Kravtsov and Kravtsova (2010, subject positioning in play). The key characteristic of Vygotsky’s (1966) play is the creation of imaginary situations: through their imagination, children can change the meaning of objects and actions, enabling them to engage with the ‘greater word of meaning and adventure’ through their imagination (Meng et al., 2022, p. 2). Imagination as a psychological function creates a source for child development. Lillard et al. (2013) suggests that there is a need to show evidence of the impact of imaginative play on cognitive development and conceptual thinking. Fleer’s (2011, p. 236) conceptual play elaborates on the dialectical relationship between imagination and cognition and argues that imagination becomes a ‘bridge between play, as the leading activity and learning as a leading activity’ (p. 236). Building this bridge requires a teaching methodology that supports it.

Kravtsov and Kravtsova (2010) found that teachers can take different pedagogical positions while interacting with children in play: above the child, where the teacher guides the child, below the child, where the child takes the initiative, and equal with the child, where teachers and children are equally positioned. The primordial we position suggests that the child needs more support from the teachers, while independent suggests the child is more capable of solving the problem or engaging in play activities by themselves. Fleer (2015) has offered different categories of the pedagogical positioning of the teacher, including being in parallel with the child as narrator of the play, being proximally close while supporting the play, or engaging in sustained collective play with groups of children (e.g., providing the suggestion to what kind of play should happen) but suggests that generally teachers are not acting inside the children’s imaginary play (taking play roles). Her research proposed a need for more exploration of teachers’ pedagogical practice inside of children’s imaginary play. In the Disney and Li’s (2022) study of the intervention of Fleer’s (2018) Conceptual PlayWorld in Mathematics, teachers’ pedagogical positioning was elaborated through taking different character roles inside the children’s imaginative play. Their research shows that the teachers’ dynamic pedagogical positions shape the way children and teachers explore mathematical problems through their imaginations. However, their research does not explain the co-teachers’ relational strategies in the collective imaginary situation. What is new in this study is how the pedagogical positions that teachers take can create conditions for toddlers’ active exploration of mathematical concepts in joint play.

4. Visual Narrative Methodology

This paper draws on a cultural-historical theoretical framework to investigate toddler’s engagement in play, and concept learning and the pedagogical interactions with their six teachers within their play over a seven-month period as part of a larger project. To capture young children’s lived experience, including their verbal and non-verbal behaviours and their voices in their everyday activities, a visual narrative methodology was applied (Ridgway et al., 2020). Hedegaard’s (2008) wholeness approach was used to interpret toddlers’ play and their engagement with peers and teachers, and this took into consideration the children’s perspectives, including their body language, gestures, choices, initiatives and movements, and their teachers’ pedagogical choices, positioning, and teaching agendas in play.

Research Participants

This project involved six teachers from two classrooms and 29 children under three years old attending a long day-care centre in Melbourne, Australia. The teachers included three with qualifications at a diploma level who had completed an 18-month, full-time early childhood education course, and three with Certificate III qualifications, who had completed a six-month, full-time course. This paper focuses on one group of six children who were 2–3 years old (mean 2.6 years old) and two teachers with diploma qualifications (Deb, the room leader, and Sally, a qualified teacher).

Ethics approval was granted by the researchers’ university and the Department of Education and Training in Australia and written informed consent (including use of the recorded images in research journals/books) was obtained from the participants. Children’s consent was sought from their guardians for the use of data collected in the field of education and research. Pseudonyms were applied to protect the privacy of the participants. In addition, the children’s approval was sought during each visit. Filming did not go ahead if any child did not feel comfortable with the video filming. Personal information such as facial expressions was deidentified.

Data Collection Procedure

The larger study included data from video observations, focus group discussions among the teachers, a researcher and two research assistants, and video-prompted reflective interviews with six teachers, as shown in Table 1. With this process, the study aimed to understand the teachers’ beliefs about their pedagogical practices and the children’s perspectives, and to capture the children’s interactions with their teachers and peers in the class. To specifically respond to the research question of how teachers co-positioned themselves to support toddlers’ mathematics concept learning in play, this paper focused on one hour of video observation for an in-depth data analysis and teacher Deb’s interview.

Table 1: Details of the data collection methods

Research methods	Research participants	Hours of data (81 in total)
Video observation	Teachers and children; Two classrooms, each room with two cameras, nine two-hour visits	72
Focus group discussion	Four teachers (two classroom educational leaders)	5
Video interview	Six teachers (individual, 25–45 minutes)	4

Video observations were collected to document the dynamic movements and interactions between the teachers and children using two video cameras. Nine weekly visits of two hours each were organised to observe toddlers’ and teachers’ daily experiences, the transition moments, emotions, body movements, gestures, and facial expressions. The first camera followed the teachers and the second camera focused on the children.

Selected video clips of observations were presented to the teachers as a prompt in a reflective interview to elicit their views on the relationship between play and learning. The videos showed moments of teachers’ co-teaching practices, which illustrated their relational pedagogy in teaching. The video-prompted interview also aimed to make a fair representation and interpretation of teachers’ pedagogical practice. Each interview lasted one hour and was video recorded. One-day focus group discussions (each lasting five hours) were conducted to discuss the quality of play and learning.

This paper focuses on a one-hour long video clip to explain the dynamics of interactions between two teachers and a small group of six toddlers. The co-teaching observed in this clip was analysed in depth and is indicative of this approach generally.

Data Analysis

The data were analysed by drawing upon Hedegaard’s (2008) wholeness approach, which suggests three levels of video interpretation: common sense interpretation, situated practice interpretation, and thematic interpretation. All three levels of interpretation are dialectally interrelated, and the analytical process is carried out progressively in a spiral way (Li, 2014). The raw data were categorised into different clips by considering the transition moments, imagination in play, and the activities in the class.

Common sense interpretation comprised the first spiral of analysis and was used to capture multiple perspectives of the interactions in play and learning, including toddlers’ initiatives and teachers’ demands and intentions, without considering the theoretical concepts. The next spiral of data analysis involved situated practice interpretation, which required the researchers to revise the video clips and identify interactive patterns within one single activity setting, such as the two teachers’ collaborative actions, the teaching agenda, their responses to the toddlers’ initiatives, and the demands toddlers made of their teachers. The conceptual relations were applied to identify the key conceptual patterns, such as teachers co-positioning themselves in responding to toddlers’ demands. The third spiral of data analysis, thematic interpretation, aimed to theorise the findings to answer the research question of how teachers co-position themselves in supporting toddlers’ mathematics conceptual learning in play. It required the use of theoretical concepts to analyse meaningful teaching patterns and themes in relation to the research aims. Concepts of play and subject positioning were used to identify co-teaching pedagogical patterns and dynamic interactions within joint play activity settings. Next, new conceptual relationships were developed to answer the research question. The following vignettes explained in the findings section, representing the whole data set in relation to co-teaching in children’s play, was selected to elucidate the findings.

5. Findings

The vignettes were taken from video of the morning outside play time as part of the play-based learning program. Children and teachers went outside after morning tea, and two teachers and a group of toddlers engaged in a game of ‘What’s the time, Mr Wolf ?’ The children had read this story book with the teachers and had played this common game several times before. Vignette 1 was selected to exemplify how toddlers and teachers played together and how the two teachers collaborated to support the children’s understanding of the game while also teaching them mathematical concepts such as the time, counting, and spatial relations.

Vignette 1: Children Initiate the Play

One child, Ben, calls out, ‘Dinner time!’ A second child, Amy, also yells out, ‘Dinner time!’, while jumping up and down. The teacher, Deb, understands that they want to play ‘What’s the time, Mr Wolf’. Teacher Deb asks the children to wait in line as Amy (Child 2) calls the time. Meanwhile, more children run over to the teacher and show that they are ready to play this game. The children and teacher Deb together ask, ‘What’s the time, Mr Wolf ?’ Amy then answers, ‘7 o’clock.’ Together, teacher Deb and the other children started walking towards Amy while counting their steps: ‘One, two, … ’. They have only completed the second step when Amy calls out ‘Dinner time!’ and runs towards them. Teacher Deb say, ‘Wait until we are closer, Amy.’ Amy does not listen and continues running towards them. Teacher Deb then says, ‘Okay, I will come and help you.’ She walks over to Amy and says softly, ‘I’ll help you, Amy, we’ll do it together’. The other children follow teacher Deb, who then asks another teacher, Sally, to come and join the game.

In this vignette, a small group of toddlers initiated a rule-based game. Amy’s actions implied that she took the role of Mr. Wolf. Teacher Deb understood that Amy had initiated the game, ‘What’s the time Mr. Wolf’, which the children had observed both when older children had played it in their shared large yard and had played themselves with the teachers a few days earlier. Therefore, teacher Deb herself joined the game with the group of toddlers. Soon, she realised that wolf Amy needed help when she did not wait until the others were closer before saying, ‘Dinner time’. Vygotsky (1966) argues that ‘the imaginary situation will always contain rules (p. 7).’ Here, Amy imagined that she was Mr. Wolf. The game was regulated by certain rules, including Mr Wolf calling a clock time and waiting until others got closer before calling ‘Dinner time.’ The children in the line who are responding need to ask the question, ‘What’s the time Mr. Wolf’, then take the correct number of steps indicated by the response, counting them aloud as they go. Several mathematical rules emerged in this interactive game, including how to tell the time, counting, and spatial relations, which were all quite new to the toddlers. Teacher Deb did not stop their play but acknowledged the toddlers’ initiative and interest in the game while recognising Amy’s challenges, that is, that she needed extra support to understand the rules and tell the time. Meanwhile, Deb realised that the children in the line also needed support to count their steps and understand the rules, and so she asked for help from her colleague Sally.

Vignette 2: Two Teachers Join the Game

Once Sally had joined in, teacher Deb asked the other children to go back and line up with her. All the children went back to the line with Sally, who explained to them what they needed to do: ‘Let’s come and stand here, we need to wait and listen to how many steps … ’ Teacher Sally was standing back from the line and got the group of five children ready. Meanwhile, teacher Deb and wolf Amy were standing a few metres away from the children with their backs facing them. Teacher Deb held Amy’s hand, saying, ‘We’re going to do this together. Ready? I’ll show you’ (see Figure 1).

Figure 1. Teacher Sally models counting steps

Then teacher Sally asked, ‘What do we ask now ?’, and the children replied softly, ‘What’s the time, Mr Wolf ?’ Teacher Sally and the children waited for the answer. Teacher Deb asked wolf Amy, ‘What is the time?’, while holding Amy’s hand. Amy replied, ‘7 o’clock.’ Teacher Deb repeated what Amy had said, ‘7 o’clock.’ Teacher Sally took the first step and took one child’s (Cam’s) hand on the way and waited for the other children to take their steps. Teacher Sally also counted, ‘One, two, …’. The children imitated Sally’s counting with soft voices while they followed Sally towards wolf Amy (see Figure 1). Sally led the children pacing behind Amy and teacher Deb, taking big steps, kicking her leg out in front, and saying the numbers loudly and clearly in correspondence with her steps, ‘One … two … three…four … five … six … seven’. The children followed Sally’s counting and steps. For instance, child Judy walked normally beside Sally, slightly kicking out her legs on some steps. While she did not step in synchrony with Sally, she counted with her.

In this vignette, two teachers, Sally and Deb, joined the game, taking it as a learning opportunity for the children and supporting their rule-based play. This demonstrates that both teachers affectively valued the children’s interests and motives in their game while supporting their play to increase its richness. As noted by teacher Deb when asked about the collaboration with other teachers, ‘it is very beneficial, the more we, teachers are all in tune … it will definitely increase children’s learning … as we are in the same boat.’ Sally was with the group of toddlers lining up. When the children understood how to ask the question, Sally positioned herself as a co-player, appearing to be equal with the children, and together they called out, ‘What’s the time, Mr Wolf ?’ and listened for the answer. Later, at the start of counting the steps, Sally took an ‘above’ position to support the children’s counting. The vignette draws attention to how important it is to intentionally teach a mathematical concept in relation to counting from the ‘above’ and ‘equal’ positions in this interactive game. This provides the opportunity for children to make conscious mathematical links while they walked the correct number of steps. Counting the walking steps also affords them the opportunity to see and feel, and encourages them to make sense of a mathematical concept. While toddlers learn play skills in the form of rules, the support of the teachers in the game also enables them to explore mathematical concepts, in this case the one-to-one correspondence counting principle (Reikeras, 2020).

Vignette 3: Teacher Deb Holds Amy’s Hand

As the children and teacher Sally began to pace towards her (Sally demonstrating each step to the children), Amy watched and tried to run. Teacher Deb leaned over to Amy, saying, ‘Not yet, not yet (shaking her head), they need to step seven times.’ Amy and teacher Deb turned so their backs faced the children pacing behind them and waited for the rest of the steps to be taken. Once Sally finished counting, all the children gathered in a group around her. She looked at the children and said, ‘Okay, now what to ask?’ Child Judy softly replies, ‘What’s the time, Mr Wolf ?’ With a dramatic voice, teacher Sally then suggested, ‘Mr. Wolf is sleeping. Let’s say it loudly!’ The children laughed and together yelled out, ‘What’s the time, Mr Wolf ?’ Amy turned around and looked at the children. Teacher Deb held Amy’s hand (see Figure 2), and leaned into Amy, prompting her to ‘Pick another number’. Amy pauses for three seconds and says, ‘Ummmmm’. Then Amy held one finger up to the group and said, ‘Seven o’clock’. Teacher Deb confirmed what Amy said and yelled, ‘Seven o’clock.’ Amy tugged on teacher Deb’s hand, trying to pull away and yelled ‘Dinner time!’ Teacher Deb stopped Amy from running away and said, ‘Not dinner time yet, wait until they are closer.’

Figure 2. Teacher Deb holding Amy’s hand and explaining the time

While teacher Deb stopped Amy from running away, the other children took the seven steps. Although teacher Sally did not hold their hands, this time the children took the initiative in counting their steps, ‘One … two … three …four … five … six … seven.’ When they completed the counting, Sally prompted the children again, ‘What do you ask?’, and the children responded, ‘What’s the time, Mr Wolf ?’ Teacher Deb prompted Amy, ‘What time?’, and Amy looked back at the children, paused, and then yelled, ‘Dinner time!’ Teacher Deb let go of Amy’s hand and dramatically said, ‘Oh, dinner time!’ and followed Amy. The group of children ran back towards the line screaming as Amy and teacher Deb chased them. After this round of the game, the children requested to continue playing this game a few more times, stopping for their lunch time.

This third vignette shows teacher Deb taking the ‘above’ position to support wolf Amy’s understanding of the play rules. This intentional teaching allowed some mathematical concepts, such as spatial relations and telling the time, to emerge. Teacher Deb helped wolf Amy understand spatial concepts such as ‘close’ and ‘far’ by explaining ‘not dinner time yet, wait until they are closer’. Spatial language was used here to direct her attention to spatial information. Adults talking about the spatial world using spatial language with children through their everyday play interactions enhances children’s spatial thinking (Pruden et al., 2011). Positioning herself as ‘above’ provided the opportunity for Deb to explain the play rules and the spatial world. Again, teacher Sally continued to prompt the children’s lead by asking them, ‘Okay, now what to ask?’ Children showed their competence in taking the lead in play. When child Judy’s voice was soft, teacher Sally was playful and used a dramatic voice to explain that the wolf was sleeping and that they needed to speak loudly. Her playfulness reflects her dynamic subjective positioning and the invitational play actions in her intentional teaching.

6. Discussion

Drawing upon cultural-historical concepts of play and subject positioning in play through an in-depth analysis of this child-initiated play episode, we show the pedagogical approach of co-teaching in play being utilised for toddlers’ exploration of mathematical concepts in joint play. By investigating co-teachers jointly playing with a small group of toddlers in an early childhood classroom, this study indicates co-teaching with dynamic pedagogical positions might advance toddlers’ mathematical concept exploration and take their play to a more complex level.

This paper extends previous research in toddlers’ play that emphasised teachers’ physically close to children to support children’s play (Singer et al., 2014) and affectively positioning oneself with young children in play (Quinones et al., 2021). Co-teaching relationships in joint play with toddlers create conditions that support children to develop both conscious awareness of rules in play as well as of emerging mathematical concepts. In the example of Vignette 1, the group of toddlers demonstrated the challenges of playing the game ‘What’s the time, Mr Wolf ?’ while the teacher, Deb, played the wolf. Teacher Sally was invited to join the game, thus supporting teacher Deb in playing with the group. The play actions between the teachers and children from Vignette 1 to Vignette 3 illustrate the toddlers were supported to make their sense of meaning of complex play rules as they imitated teachers’ words and actions within the joint play. In other words, the joint play created a zone of proximal development (ZPD) and the co-teachers’ collaborative actions provided meaningful assistance to the toddlers. This interaction echoes Vygotsky’s (1998, p. 201) argument that imitation does not mean simply copying, but that ‘the child can enter into imitation through intellectual actions more or less far beyond what he [she] is capable of in independent mental and purposeful actions or intellectual operations.’ In this study, through imitation, a group of toddlers was able to move from ‘not being able to play’ to ‘being able to play’ with the support and instruction of their co-teachers. This also echoes teacher Deb’s comments in the interview that when teachers are in the same boat, it increases children’s learning opportunities. The children’s play was continued and extended, and their awareness of the rules in play was enhanced. Learning the rules in play also required the toddlers to explore and make sense of mathematical concepts such as numbers, spatial relations, and time. In this situation, one teacher alone could not have made this possible, as shown in Vignette 1 when teacher Deb followed the children’s initiation and intentions in playing the ‘Mr. Wolf’ game. Until teacher Sally was invited to join the game, the toddlers’ play could not effectively continue. The co-teachers’ collaborative actions and thoughts were critical to supporting the children’s play in this instance.

Second, as the co-teachers dynamically changed their pedagogical positions, it afforded the toddlers a wider experience of a game with rules and allowed them to explore mathematical concepts. Mathematical language was introduced, regulated by the co-teachers and represented by the toddlers through imitation. Teacher Deb positioned herself above, which allowed her to support Amy as Mr. Wolf when calling out the time. In Vignettes 1 and 3, it was evident that Amy did not have a clear understanding of the play rules as she would rush to say ‘dinner time’ too early. Teacher Deb understood Amy’s intentions and her motivation to joyfully chase her peers after exclaiming ‘Dinner time!’ By capturing this teachable moment and holding her hand, teacher Deb introduced the mathematical concept of spatial relations, saying, ‘Not dinner time yet, wait until they are CLOSER.’ To support young children’s spatial understanding, teachers need to talk about the spatial world, thus enhancing children’s spatial language and thinking (Pruden et al., 2011). Taking the above position in joint play allowed teacher Deb to explain the rules, mathematical ideas and language as it was apparent that the toddlers did not yet have the capacity to understand these. This aligns with the argument by Disney and Li (2022) that teachers might shift their pedagogical positions to enrich children’s play and support their mathematical reasoning and thinking as the situation demands. This study also showed that very young children can engage with much more complex mathematical concepts if their teachers’ support responds to their intentions.

Third, this study found that co-teaching approaches in play need to acknowledge and respond to children’s play needs and intentions, which also allows teachers to assess children’s ZPD and shift the pedagogical positions in intentional teaching. As van Oers (2013, p. 194) argues, ‘adult engagement in children’s play should primarily enhance the play format of children’s activity and answer the children’s need for help to improve their participation in the current role play.’ To meet the demands of a group of toddlers’ ‘Mr Wolf’ game, their teachers’ collaborative relationship was shaped through the different roles they adopted. Teacher Sally was invited to join by teacher Deb, as shown in Vignette 2. This action both continued and enriched the toddler-initiated play. By being inside the game, the co-teachers were able to assess the toddlers’ challenges and intentions in play and make pedagogical decisions accordingly. Teacher Sally first took the above position, holding the children’s hands and demonstrating counting using steps. In Vignette 3, teacher Sally took the below position to offer the toddlers the possibility to explore counting their own steps, and in an exaggerated fashion asked the toddlers what the next step was: ‘Now what to ask?’, while suggesting a louder voice as Mr Wolf was sleeping. Teacher Sally’s dynamic shifts in positioning aligned with the toddlers’ needs and challenges. By being inside the play, co-teachers were able to take active play roles with the children that allow them to assess the children’s ZPD and adjust their co-teaching positions accordingly. The toddler-initiated play was extended to exploring mathematical concepts and rules within the collective imagination and help them become competent players. This is consistent with Chaiklin (2003), who argues that teaching should focus on maturing children’s psychological functions, and thus teachers are required to assess which functions to develop. The co-teachers collaboratively assessed the children’s needs and potential, demonstrating and narrating the Mr. Wolf game as a higher form of play to the group of toddlers. This study argues that collaborative relationships between co-teachers can be formed while assessing the children’s ZPD. Their collaborative engagement did not hinder or take over the children’s initiative but rather extended their joint play through their affective involvement in the game and by communicating their play actions (Hannikainen and Munter, 2019). This study argues that co-teaching approaches increase the potential for identifying challenges in play and assisting children within their ZPD, thus enhancing intentional teaching. Most studies reported in the literature, however, focus on the ‘one teaches/leads, one assists’ approach (Hsieh and Teo, 2021) or a single teacher’s interactions with children in early childhood education. What these studies miss is how co-teachers dynamically position themselves to support children’s exploration of mathematical concepts such as one-to-one correspondence and spatial sense and relations through joint play.

Finally, the findings of this research suggest that intentional mathematics teaching can be meaningfully merged into joint play when new developmental conditions are formed by co-teachers’ responses to children’s challenges. The co-teachers used their dynamic positions to communicate mathematical thinking to toddlers. Using imaginative play with rules contributed to the quality of their teaching, providing meaningful opportunities for the toddlers to actively explore mathematical concepts such as one-to-one correspondence, time, and spatial relations. In Vignette 1, the toddlers showed the challenges they faced in playing the Mr Wolf game due to their lack of mathematical ability. When teacher Deb realised these challenges and invited teacher Sally to support this play engagement, the children’s mathematical understanding was extended and enriched. Subsequently, in Vignette 2 teacher Sally guided the toddlers in counting steps, and the toddlers later demonstrated initiative and capability in this new skill, as shown in Vignette 3. In this process, the toddlers were invited to use a one-to-one correspondence counting principle (one step per each number counted), and they used it progressively, showing their growing competence in associating the steps with corresponding values of time. In line with van Oers (2010), this study argues that teachers taking action to enhance children’s mathematical play by narrating mathematics concepts and explaining mathematical implications enhances toddlers’ exploration of mathematical concepts. In this instance, through the co-teachers’ intentional actions, the toddlers realised the mathematical meaning of their own actions by counting their steps and calling the numbers/time. This study enriches the argument that toddlers’ mathematical learning is a matter of experiencing them bodily (Franzen, 2014, 2021). The co-teachers’ active and affective involvement in the children’s mathematising activities such as the Mr. Wolf game extends children’s experience and adds values to their play, furthering mathematical exploration. In accordance with Bjorklund et al. (2018), this study argues that mathematics education for toddlers is not about promoting and directing counting, recognising time, or using measures, but rather extending their play and solving problems to introduce mathematical concepts in a meaningful way.

7. Conclusion

The potential for drawing broad conclusions from this study is limited as it is based on only one hour of observations of a single class at an early learning centre in Australia. Other research has produced visual data showing similar co-teaching positioning while teaching toddlers. But despite the small data set, the three levels of theory-driven data interpretation provide a thorough analysis by using cultural-historical concepts. The data show the potential for a co-teaching approach to support toddlers’ understanding of basic mathematics. Through the in-depth analysis of one instance of joint play, it is argued that co-teachers can work collaboratively to create conditions that orient toddlers to explore mathematical concepts and rules in joint play. This study maintains that the co-teaching approach creates the conditions to support toddlers’ collective play within institutional practices as the teachers can work collaboratively by taking different pedagogical positions to support children engaged in mathematical concepts exploration. With the support of co-teachers, toddlers’ joint play becomes more complex and play rules are regulated to help children explore mathematical concepts, thus enhancing their play.

8. Acknowledgments

Monash University Human Research Ethics Committee (Project ID: 0413) and the Department of Education and Training (Project ID: 2017-003278) granted approval for the project, A study of adults’ engagement in babies-toddlers’ play. Special thanks to the participating teachers, children, and parents for giving permission to undertake this research and their participation in the project. We also acknowledge the research assistance from Dr Judith Gome, Dr Junqian Ma and Dr Victoria Minson. The author is very grateful to the reviewers and editors whose thoughtful inputs considerably improved this paper.

9. Disclosure Statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

2019 Advancing Women’s Research Success Grant at Monash University, and Faculty of Education Seeding grants.