Experiencing Tensions When Integrating Language Diversity into Mathematics Teacher Education

ABSTRACT

Mathematics teacher educators experience tensions when developing their practices in order to integrate social justice issues, such as language diversity. Research on what in fact causes the experiencing of these tensions and how to navigate them to improve professional practice is yet limited. As part of an action research project, I investigate my reflections on planning to integrate language diversity issues into mathematics teacher education. I discuss three main tensions to do with: focusing on my teaching or the pre-service teachers’ teaching; wanting to change my practices but struggling to let go of control; identifying alternative activities but struggling to choose from them. The analysis revealed that each of these tensions was connected to different moments of my planning and to the uncertainties of wanting to achieve multiple aims simultaneously. Understanding the characteristics and implications of the tensions I experienced provides insights into the complexities of planning, such as the blind spots of aiming to be responsive to pre-service teachers’ needs, whilst at the same time contradicting my assumptions about good practice. Knowledge about these complexities can support future research about what aspects of practice might influence the improvement of integrating language diversity issues into mathematics teacher education.

KEYWORDS:

• Action research
• tensions
• mathematics teacher education
• language diversity

Previous research has highlighted the need to integrate understandings about language diversity, such as utilizing students’ multiple languages as a resource, into mathematics teacher education, rather than being an add-on to it (Chitera, 2012; Essien et al., 2016). However, this research has also shown that teacher educators (TEs) may struggle to make pre-service teachers (PTs) aware of how to utilize students’ language resources when teaching mathematics. Instead, TEs tend to prioritize mathematical understandings (e.g., Chitera, 2012; Eikset & Meaney, 2018; Essien et al., 2016). When TEs are aware of the struggle between what they want to achieve and what actually happens, they can be said to be experiencing tensions. In Berry’s (2007) self-study as a biology TE, tensions were conceptualized as:

feelings of internal turmoil experienced by teacher educators as they found themselves pulled in different directions by competing pedagogical demands in their work and the difficulties they experienced as they learnt to recognize and manage these demands (p. 119).

Berry (2007, 2008) identified six main areas of tensions: telling/growth, confidence/uncertainty, action/intent, safety/challenges, valuing/reconstructing experience, and planning/being responsive. In mathematics teacher education, Jaworski (2006) also referred to tensions as conflicts, challenges, or struggles with respect to a range of issues and contradictory feelings, such as confidence, power, and control as opposed to discomfort, underachievement, and disappointment and related them to the complexities of TEs’ practice.

Based on this notion of tensions, Berry (2008) identified areas of uncertainties influencing her pedagogical practices, such as between her plans and her need to deviate from these plans in her emergent interactions with PTs in order to be responsive to them. Discussing tensions experienced around planning and being responsive, allowed Berry (2008) to recognize missed opportunities where her intended plans restricted her from identifying alternative possibilities and making decisions to respond to unplanned situations. In mathematics teacher education, Erbilgin (2019) investigated her own and another TE’s reflections on their planning, as part of an action research project. Although not focusing on tensions, Erbilgin (2019) described that they experienced feelings of anxiety and uncertainty at different moments of their pedagogical planning, such as when responding to PTs and designing appropriate tasks in a mathematics education course. Discussing their plans supported these TEs to improve their professional skills as they dealt with challenges and complex decision making.

The recognition and management of tensions in teacher education can be challenging. According to Jaworski (2006), addressing tensions does not mean that they are automatically removed from the practice, but identifying them is necessary for building understandings about the complex, sociopolitical systems in which a practice develops. Therefore, identifying and addressing tensions is important for understanding teacher education practice as well as for the professional development of TEs (Jaworski, 2006; Nolan & Keazer, 2021). Similarly, Casey (2012), who engaged in an action research project on his teaching of physical education (PE), described how his self-study of his teaching practices allowed him to identify how institutional understandings about being a PE teacher affected both what he was initially able to identify as changeable and then what he was able to change within these institutional constraints.

Apart from Berry’s (2008) self-study, little research in STEM teacher education has discussed the role of tensions in the planning aimed at improving practice. Planning, as the first phase of an action research cycle, is considered to require reflection in order to improve practice (Kemmis et al., 2013). Consequently, planning can provide insights into the complexities that produce the tensions experienced by TEs, while making decisions about their future practices. As was the case in Erbilgin’s (2019) study, this could lead to better understanding of how to improve the practices.

Therefore, in this article I discuss the tensions that I experienced in my planning around the integration of language diversity issues into mathematics teacher education. The study is part of a wider action research project (Kasari, forthcoming), where I investigate mine and other TEs’ work on raising language diversity issues in mathematics teacher education. The research question is:

How does identifying tensions in planning mathematics teacher education, which integrates language diversity, contribute to understanding the complexities of improving practices?

To address the research question, I analyze my reflections, as a TE, on planning six workshops of integrating language diversity in a mathematics education course for second-year PTs of grades 1–7. To do this, I draw on methods also used in self-study and action research (e.g. Casey, 2012), to gain insights about integrating language diversity issues, as a new practice, into mathematics teacher education.

Tensions in Mathematics Teacher Education Integrating Social Justice Issues

Tensions in mathematics teacher education practice have rarely been the focus in previous research on the complexities of TEs’ planning to integrate issues of social justice, of which language diversity is part. Although tensions were mentioned by Barwell et al. (2016), their focus was on language use, for instance the tension between using students’ home language or the language of instruction in school classrooms. The nature of these tensions was thus different to those mentioned by Berry (2007, 2008) or Jaworski (2006), as they did not refer to TEs’ uncertainties about their own practices.

According to Cochran-Smith (2010), issues of linguistic, cultural, racial or ethnic diversity, gender, religion, and disability are some of the social justice issues which teacher education has been concerned with. Social justice issues aim: to shift deficit-oriented discourses around students’ backgrounds and abilities to discourses that consider their knowledge and backgrounds as resources; and to advocate for equalizing educational opportunities (Cochran-Smith, 2010). Consequently, I have synthesized previous research on these issues, as a way of understanding how I could improve the integration of language diversity into my mathematics teacher education practices. I identified three strands of issues that were connected to TEs experiencing tensions, as understood in this study: 1) the relationship of TEs with their PTs, 2) wanting to be socially-just TEs but being uncertain about how, and 3) focusing on teaching mathematics or social justice issues.

Strand 1: Relationship of TEs with PTs

In previous related research, the relationship between TEs and PTs has been identified as important, yet challenging (e.g., Keazer & Maher, 2021; Livers & Willey, 2023; Meaney, 2013). Berry (2007) had described this relationship as a central source of tensions, stemming from TEs’ need to fulfil educational aims while simultaneously responding to PTs’ specific needs and interests. For example, Livers and Willey (2023) discussed how a TE experienced a tension arising from a need to meet PTs’ expectations for learning more mathematics, while integrating issues of equity and equitable practices.

In several studies in mathematics teacher education with social justice concerns, the relationship of TEs with PTs involved feelings of uncertainty and discomfort (e.g., Eikset & Meaney, 2018; Livers & Willey, 2023; Meaney, 2013; Nolan & Keazer, 2021). This can be related to knowing and not knowing one’s students, which Gutiérrez (2009) had identified in connection to PTs experiencing tensions when teaching mathematics through equity in school classrooms. She described this tension as appearing when PTs were considering students’ backgrounds, resources and needs in practices, such as planning, but were also struggling to avoid making assumptions about them.

Although Gutiérrez (2009) described the tension as being experienced by PTs in school classrooms, rather than herself as a TE, Meaney (2013) and Eikset and Meaney (2018) described similar struggles for a TE providing challenging activities to PTs. The TE had concerns about not being familiar with the cultural background of the PTs and, thus, not being able to build common understandings about social justice issues in mathematics education. Tensions arising from cultural differences also appear in other studies, such as those of Nolan and Keazer (2021) and Keazer and Maher (2021). In these studies, the tensions arose when the TEs considered if they could or should model cultural-responsive practices which were respectful of PTs’ needs and backgrounds. Keazer and Maher (2021) found that the culturally-relevant mathematics tasks they used in their teacher education practice were reproduced by PTs in their reflections about such tasks in their everyday lives. This made the TEs uncertain about whether their choices and practices restricted, rather than modelled, culturally-relevant tasks and PTs’ possibilities for identifying their own. Nolan and Keazer (2021) were concerned about the extent they pressured PTs to reflect on cultural-responsiveness and change their practices. They considered that the PTs were pushing back on the requirements to reflect on social justice issues.

In these studies, the tension experienced by TEs was identified from looking retrospectively at the TEs’ interactions with PTs. They have indicated that TEs may experience tensions when providing challenging activities to PTs while simultaneously responding to PTs’ needs or background, either perceived by the TE or explicitly stated by the PTs. It is likely that a similar tension could arise in TEs’ planning, although the focus of planning being on forthcoming practice could produce differences.

Strand 2: Wanting to Be Socially Just TEs but Being Uncertain About How

In previous research, TEs were uncertain about how to introduce social justice issues to PTs. For example, in studies related to issues of culture and cultural-responsiveness (Keazer & Maher, 2021; Meaney, 2013; Nolan & Keazer, 2021), the TEs realized they needed to go beyond sharing ideas around these issues with PTs, to improving the ways they incorporated them into their own teacher education practices. However, the TEs expressed uncertainties about whether the tasks they chose would achieve these results. Baker and Bitto (2022) identified that they were conflicted about wanting to change their practices as TEs beyond a ‘surface level’ (p. 88, 92), while being uncertain about what these changes could be so that they would avoid harming or disrespecting students of color. They realised that a lack of explicitness about social justice issues could mean that their expectations for socially-just practices may have gone unnoticed by PTs.

The uncertainties around raising social justice issues through socially-just practices seemed to be related to TEs needing to change their own understandings about these issues. Gutiérrez (2009) had identified similar uncertainties in PTs’ work, to do with being and not being in charge of the classroom. As teachers, PTs were responsible for what happened in the classroom. Yet, the students were ‘authors’ (p. 13) of their learning. The PTs’ commitment to equity required them to acknowledge that, although they provided opportunities, they could not force students to take up authorship in ways that the PTs expected. TEs committed to social justice issues have to deal with similar institutional responsibilities and complexities, as mentioned in the study of Baker and Bitto (2022), while wanting PTs to take ownership of their learning.

These tensions arose in studies which reflected retrospectively on what had occurred (Baker & Bitto, 2022; Keazer & Maher, 2021; Nolan & Keazer, 2021). The TEs recognized their uncertainties when reflecting on what they could change and what alternatives were available. Thus, it is also likely similar tensions would emerge when planning future practices. However, because planning involves making decisions to explicitly change previous practices, there may be differences in how this tension emerges.

Strand 3: Focusing on Mathematics or Social Justice Issues

A third strand of tensions comes from when TEs had to choose between focusing on teaching mathematics or social justice, in adapting established teacher education courses addressed to all PTs (e.g., Eikset & Meaney, 2018; Livers & Willey, 2023), rather than courses designed exclusively about those issues (e.g., Baker & Bitto, 2022; Nolan & Keazer, 2021). In a survey, many TEs expressed that they faced challenges when selecting appropriate materials and tasks that could potentially support PTs to develop both their mathematical and social justice understandings (Vomvoridi-Ivanović & McLeman, 2015). This was because the course design and the PTs’ multilingual backgrounds contributed to TEs experiencing this tension. Similarly, Meaney (2013) described how her experiences of this tension varied in three different contexts and was partly influenced by the opportunities provided in each teacher education program.

In mathematics teacher education aimed at integrating language diversity, this tension has been documented frequently (e.g., Chitera, 2012; Eikset & Meaney, 2018; Essien, 2021; Essien et al., 2016). This suggests that it may also arise when planning, because TEs need to select tasks that incorporate both demands. However, the complexity of planning teacher education practices might mean that TEs find that other aspects and demands contribute to feelings of uncertainty.

Methodology

In analyzing my reflections on planning my teacher education practice, I identified where I felt uncertainty or confusion about what I was planning, as a way of recognizing when tensions occurred. I then used an analytical tool, adapted from Pierson (2008), to consider how the tensions in my planning were related to how I anticipated giving and demanding intellectual work, in which language diversity issues were integrated into mathematics education.

Action Research Cycle, Reflection, and Change

In keeping with previous research, I anticipated that tensions would appear in reflections in action research (e.g., Keazer & Maher, 2021) or similar approaches where TEs investigated their own practice, such as self-study (e.g., Baker & Bitto, 2022; Casey, 2012) and autoethnographic research (e.g., Meaney, 2013). Although these approaches are connected, according to Feldman et al. (2004), self-studies in teacher education often focus on issues of the self in practice whereas action research uses different methodological processes with the aim to understand and improve the practice itself. However, studies such as Casey (2012) showed how a self-study during an action research project led to an understanding of how the context and expectation of being a PE teacher affected what he could change in his practice. Using action research to identify tensions could therefore provide insights not only into the complexities of my practices but also into how those practices could be improved in the next action research cycle.

The action research cycle, or spiral, involves multiple cycles of planning-acting-observing-reflecting and replanning (Kemmis et al., 2013). Planning and replanning are to do with making decisions about what to change and how, so that practices could be improved. This can lead to experiencing several dilemmas (Winter, 1982), which can cause TEs to feel uncertain. As well, being an ‘insider’ in researching one’s own practice can make the recognition and management of the uncertainties and their resulting tensions challenging, as was identified by Casey (2012). However, according to Feldman et al. (2004), in self-studies in action research, the TE as a self is inseparable from the research and the practice. Therefore, they argued that the practice experiences of the TE are utilised as a resource for the investigation of that practice within these approaches. In my study, the use of the analytical tool provided a possibility to shift between the perspective of the insider (the TE) and the ‘imagined outsider’ (the action researcher), as part of improving understandings about practice (Kemmis et al., 2013). Doing so meant that the experiences from being a TE could be used as a resource, as Feldman et al. (2004) indicated. Although individual reflections as well as the experience of tensions are often personal, using self-study can support TEs to move beyond this level, as Berry (2008) noted in the studying of her tensions. Using self-study features in my action research allowed me to analyze my reflections beyond the personal level by challenging the assumptions that I had made for my teaching practice in the beginning of the action research cycle and sharing the processes as well as the new understandings I developed.

Analytical Tool

To investigate the research question, I needed to identify the characteristics of the tensions. In my planning, I used a tool based on Pierson (2008) that had been developed with a colleague in a pilot study (Kasari & Meaney, 2023). Our aim was to identify practices that needed improving when integrating language diversity into mathematics teacher education. Therefore, it seemed sensible to use the tool to analyze my reflections on planning to do with Pierson’s (2008) key notion of intellectual work and how I anticipated giving intellectual work to or demanding intellectual work from the PTs (see Figure 1).

Figure 1. Adapted flowchart for intellectual work.

Pierson (2008) distinguished between giving and demanding intellectual work and between different levels of giving or demanding in mathematics classrooms. In Kasari and Meaney (2023), the focus on intellectual work allowed the TE to evaluate how PTs were supported to engage with language diversity as part of mathematics education.

According to Pierson (2008), the relationship between giving and demanding intellectual work is complex and involves two assumptions: that high levels are generally better than lower ones (assumption 1), and that high-level demands are potentially more beneficial for students’ learning than high-level giving (assumption 2). This is because demanding intellectual work seems to require more cognitive activity and responsibility from students, as making themselves understood when discussing a task is more challenging than just receiving information and following a teacher’s own thinking. In my planning and in the initial stages of the analysis, I included similar assumptions in reflecting on my practices in the teacher education context. However, Pierson (2008) also stated that requesting only high-level demands did not mean that practice was always more effective, suggesting that some caution in decision-making was necessary.

To plan the focus of the intellectual work for integrating language diversity issues with the mathematical content of the courses, I drew on ideas from the language-responsive teaching framework (see Table 1) of Lucas and Villegas (2010, 2013). My third assumption was that high levels of giving or demanding intellectual work would be when I explicitly integrated aspects of language diversity with mathematics education stimulated through this framework. On this basis, I adjusted the framework into the levels of intellectual work and was able to distinguish them.

Table 1. The aspects of the language-responsive teaching framework (adapted from Lucas & Villegas, 2010, p. 302; 2013, p. 103).

Language-responsive orientations	1	Sociolinguistic consciousness and the role of additional languages in schools
	2	Value for linguistic diversity
	3	Inclination to advocate for language diverse students
Language-responsive pedagogical knowledge and skills	4	Learning about students’ linguistic and academic backgrounds, and experiences
	5	Identifying the language demands of classroom discourse in particular disciplines
	6	Knowing and applying key principles of second language learning
	7	Scaffolding instruction

Initially, I considered that giving information which did not integrate language-responsiveness and mathematics was low level (see Figure 1). Giving information about language diverse students’ activity was classified as medium level, while information about teachers’ language-responsive practices (Lucas & Villegas, 2013) as high level. This was because my focus was on how to support PTs to take up this work in classrooms and raising the perspectives of language diverse students could be considered as an initial step to achieve this. For demanding intellectual work, I considered whether the activities required the PTs to consider how to integrate language-responsive teaching (Lucas & Villegas, 2013) with the mathematical topic which was at hand. Activities which did not integrate PTs’ orientations and pedagogical knowledge about language-responsiveness with mathematics education were classified as low demand. To distinguish between medium- and high-level demands, I considered whether the demand for PTs in the activities was implicit or explicit, following the distinction made in the pilot study (Kasari & Meaney, 2023).

Data Collection and Context

The data came from my reflection journals, kept during two consecutive action research cycles. The first cycle focused on the mathematical topic of modelling and the second on functions and functional thinking. In each cycle, I had three workshops on the same topic, with three groups of PTs, as part of a compulsory course for second-year PTs for grades 1–7. The course included a period of school practicum, where PTs had to implement a modelling activity, utilizing the structure of modelling in three-acts (Wallace & Jensen, 2017), and then write an assignment about its implementation.¹ The workshops on modelling occurred before PTs’ practicum, while the workshops on functions were after. Between workshops, I discussed my plans and their improvement with two colleagues as critical friends (CF1, CF2), who were also engaged in improving their practices related to language diversity as part of our action research work (see, for example, Kasari & Meaney, 2023). Casey (2012) had found that his critical friends provided him with insights about his emotional responses to the challenges he faced in trying to improve his practices within the existing understandings about what teaching PE entailed. Therefore, I considered that discussions with critical friends would contribute to my understandings of the tensions that I would face.

The main aspects of language-responsive teaching, from Table 1, that I aimed to integrate with modelling were to: develop sociolinguistic consciousness (1); learn about students’ backgrounds (4); and identify language demands of classroom discourse (5). In the workshops on functions the main aspects were: valuing diversity (2); identifying language demands of the topic (5); and scaffolding instruction with representations and visuals (7).

The reflections were mainly written in English, with some exceptions when I used Greek, my native language. I chose to write in English because it was the main language I used with the PTs, as I had recently immigrated to Norway. All the PTs who participated in the course were fluent Norwegian speakers, but some had second language backgrounds.

Data Analysis Process

To analyze the data, I used the assumptions from the analytical tool. If the three assumptions were realized in my planning, then I considered that I had made appropriate decisions to integrate language diversity through socially-just practices (Kasari & Meaney, 2023). If they were not, then I identified the situations and contexts that led to the uncertainties and tensions I experienced when they were not achieved. This identification provided insights into how the planning could be improved in future action research cycles. In describing the analysis of dilemmas, Winter (1982) set out similar steps about clarifying goals or assumptions, identifying contradictions, and moments of awareness. By using the same analytical tool for my planning and the analysis of my planning I was able to consolidate this process.

To analyze my reflections on my planning, I used the flowchart in Figure 1 to identify the levels of giving and demanding intellectual work I seemed to focus on. This was not straightforward, as many reflections could be connected to multiple levels and differed in explicitness. I also identified the aspects of language-responsive teaching, from Table 1, that were part of the intellectual work that I was anticipating giving or demanding.

As my reflections were messy, there was a need to be consistent and transparent in the analysis. Therefore, I identified the verbs that indicated whether I was considering giving or demanding intellectual work (see Table 2). For instance, considering ‘how am I going to show relations’ (see Reflection 3.1.) was classified as giving intellectual work, since I, as the TE, was responsible for showing the relation, while there was no mentioning about what actions the PTs should engage in. Depending on how they were situated in the reflection, some verbs (e.g., see, bring, notice) were associated with actions indicating that, in my plans, I anticipated actively or passively involving PTs in the intellectual work. As a result of this process, actions connected to PTs’ doings, such as noticing and seeing (see, for instance, Reflection 1.1. and 2.1.), were classified as the TE anticipating giving intellectual work. This was because the PTs seemed to be expected to passively receive the intellectual work from me as observers, without necessarily being expected to share their ideas of what they have seen or noticed. This was in contrast to other actions, such as anticipating PTs to ‘identify’ (see, for example, Reflection 2.2.), which were classified as I, as the TE, was planning to demand intellectual work from the PTs, since they indicated an explicit requirement of PTs engaging in an activity.

Table 2. Verbs indicating the kind of intellectual work planned.

	Teacher educator’s actions	Pre-service teachers’ actions anticipated by the TE
Giving intellectual work	say, tell, explain, show, connect, introduce, emphasize, summarize, give, use, bring, start, build on, support, show examples, talk about	notice, see, bring up, make clear
Demanding intellectual work	ask, relate, demand, request	see, reflect, discuss, note, think, focus, bring, realize, do, work, identify

The verbs in Table 2 allowed me to identify when the actions were not focused on actively engaging the PTs with the intellectual work (e.g., the TE is telling but not asking, the PTs are noticing but not doing). This allowed me to evaluate the levels of intellectual work, related to my three assumptions about my practice. For example, planning to demand low levels of intellectual work (see, for example, Reflection 3.2), meant I had not included demanding high levels of intellectual work, indicating that I had not fulfilled my second assumption. Identifying the verbs and what they meant about the level of intellectual work that I was expecting supported me to shift between ‘insider’ and ‘imagined outsider’ perspectives as a TE action researcher. The insights gained from this analysis informed me about how the complexities, related to the factors, or competing demands in Berry’s (2007) terms, embedded in teacher education practices when social justice concerns were to be integrated, were affecting my planning.

Presenting the Findings

As Berry (2007) had done, I used features of self-study to identify from my reflections, three broad areas of tensions:

1. My relationships with others

2. Researching my practice while planning my practice as a TE

3. My teacher education practice as a whole

Table 3 sets out the features and descriptions of each area in which I experienced tensions. As was the case with Berry (2007, 2008), the issues that provoked the tensions were not independent, definite, distinct or equally intense, but overlapped, interacted and coexisted.

Table 3. Areas and features of my experienced tensions.

Areas that prompted tensions	Features	Descriptions
Relationships with others	Focusing on my teaching (as a TE) and focusing on the PTs’ teaching My goals and my relationship with the course content Wanting to respond to my critical friends’ feedback but not knowing how Wanting to align my goals with those of my colleagues but being uncertain	Having goals for my practice but not knowing whether they corresponded to PTs’ needs for their teaching Considering research literature but being uncertain about its suitability for my goals Discussing with my critical friends, ideas about my practice and its changing but not knowing what ideas to pursue Discussing with my colleagues about our practices but being unsure about how to support each other
(b) Researching my practice while planning for it as a TE	My identity as a TE and as a researcher Planning to give and planning to demand intellectual work Wanting to change practice but struggling to let go of control Being aware of my assumptions but also being uncertain of the degree to which I respond to them Planning forward to another action research cycle but not knowing what to expect from the current one	Wanting to combine my experiences as an insider TE and as an outsider-researcher but having difficulties doing so Wanting to demand intellectual work but not knowing how to connect it with giving intellectual work Planning changes in my practice based on assumptions but struggling to consider them simultaneously Responding to some assumptions of the analytical tool and rejecting others Wanting to make connections between the topics in both cycles but also wanting to do things differently
(c) My teacher education practice as a whole	Previous practices and new practices Being explicit and not knowing how Planning to integrate language-responsiveness but needing to focus on the mathematical content as well Teaching about language-responsiveness and being a language-responsive TE Ideas for my practice and their applicability Identifying alternative activities but struggling to choose	Wanting to implement new practices but struggling to let go of previous ones Wanting to use explicit practices but struggling to do this for language-responsiveness Identifying activities related to language-responsiveness but not knowing how to balance them with the mathematical topic Planning to use language-responsive practices with PTs but not knowing how to exemplify them Having ideas about practice but not knowing how they can be applied in my context Imagining alternative ideas for my practice but not being able to decide

The table shows the complexity of areas which I navigated in my planning which caused me feelings of uncertainty and struggle. In the next section, I elaborate on three situations of uncertainty, one from each area, highlighted in bold in Table 3. Two examples from different parts of the journals are provided in each case to illustrate how my reflections were connected to uncertainties and experiencing tensions. In these examples, I use square brackets ‘[]’ to indicate that a personal pronoun or real name was replaced; parenthesis ‘()’ to indicate that additional information was added to clarify some meanings and contextual references; ellipsis ‘ … ’ to indicate that text which did not provide additional information was removed; and angle brackets ‘< >’; to indicate that long periods of text were summarized into shorter descriptions.

Findings and Discussion

In this section, I analyze and discuss some of the tensions I experienced. I do this by describing the experiences connected to each tension, before providing examples of reflections on planning about giving and demanding intellectual work, taken from my reflection journal. I then compare and contrast them with previous research, under each example, to better understand the complexities that influenced my planning processes as a TE.

To do this and inform my research question more deeply, I decided to focus here on three tensions, one from each area from Table 3. These were chosen because they appeared frequently in my reflections and seemed to be connected to different moments in the planning and replanning of the action-reflection cycle:

• Making initial decisions around utilizing resources/materials

• Considering how to change my practices

• Reflecting on whether my plans were appropriate

A fourth set of moments connected to planning intellectual work was also identified, to do with connecting goals or specific examples from the resources/material with PTs’ learning about language-responsive mathematics teaching. However, I did not experience uncertainties during this fourth set and so they are not included in Table 3.

Focusing on My Teaching as a TE – Focusing on PTs’ Teaching

When I was making initial decisions about the resources and material to use in the workshops, a tension emerged when the aims for my teaching about integrating language-responsiveness into mathematical topics seemed not to be in alignment with what I considered relevant for the PTs’ practicum teaching. As this was related to the TE-PTs relationship, it was categorized within the first area in Table 3.

An example of my uncertainty about how to negotiate the different demands came from planning the second workshop of mathematical modelling. I was considering using a video about modelling in three acts (Wallace & Jensen, 2017), which was set in a second-grade, English-speaking classroom with language diverse students (Video title: “Three-Act Tasks: Modeling Subtraction”, source: https://www.teachingchannel.com). The video had been recommended to the PTs for the compulsory course assignment (arbeidskrav).

I also saw the three-act videos of modelling activities that are recommended for the arbeidskrav and I choose to show [PTs] the one for second grade. The classroom (in the video) is clearly multilingual and there are many representations. Kids’ use of language is also very interesting. There’re many things to tell [PTs] which I can relate to theory. … Probably they will also notice different things every time they watch it. The activity is not the best from the perspectives of modelling activity, but I especially like that it is second grade and many PTs have struggles to see modelling in the earlier grades and also many of them usually implement such kinds of modelling in their practicum (Reflection 1.1. – Action research cycle 1, p. 7).

In this reflection, I justified the decision to use the video of mathematical modelling (‘I choose to show’). In accordance with Table 2, the phrases ‘to tell PTs’ and the expectation that PTs would ‘notice different things’, indicate that I focused on giving, rather than demanding, intellectual work. The phrases ‘clearly multilingual’ and ‘Kids’ use of language’, which highlight the student population without explicitly mentioning implications for teachers, indicate a medium level of giving intellectual work. The language-responsive teaching aspects I attended to for giving intellectual work seemed to generally concern PTs developing sociolinguistic consciousness (Table 1), by inviting them to become aware of the multilinguality of the classroom and multilingual students’ language use (Lucas & Villegas, 2013).

Although I justified the video as being suitable for my aims of discussing language-responsiveness (e.g., ‘clearly multilingual’, ‘Kids’ use of language is also very interesting’), the mathematical content in the video was considered problematic (‘The activity is not the best from the perspectives of modelling activity’). Yet, I also considered that the video was relevant for PTs learning about teaching modelling in the lower grades (‘it is second grade … practicum’).

The analysis suggested that I experienced a tension when trying to manage achieving the two aims about wanting to discuss language-responsive mathematics teaching and what I thought that the PTs needed for practicum. The choice of resources or material, such as the video, was judged against these competing aims. My focus on how this resource would be relevant for PTs’ teaching of modelling resulted in me not considering how it would be relevant for their teaching in multilingual classrooms, beyond that it had been filmed in one. I, thus, missed an opportunity to evaluate the intellectual work to consider if it could be raised to a higher level. This confusion about how to manage the different aims connected to my assumptions shows similarities to the findings of Meaney (2013) and Eikset and Meaney (2018) when it comes to the TE’s struggles to be responsive to PTs’ needs while providing challenging activities to them.

Another example came from the beginning of the second action research cycle, when I reflected on choosing a video from the Norwegian broadcaster for schools (NRK-skole), on the concept of functions. The video’s narrator described the concept and representations of functions, through a problem about the monthly cost of a mobile phone subscription. To illustrate the application of functions in everyday activities, the video used an example of getting refunds for returning plastic bottles (called ‘pant’ in Norwegian), and of playing adventure games on a tablet. Prior to this excerpt, I had considered including an activity for demanding intellectual work about the meanings and uses of the word function in everyday life as well as in mathematics.

I like how [the video] introduces the concept of functions and the applications in everyday life because that can link to the meaning of the word functions in everyday life. The examples are interesting. The gaming and technology, the pant (refunds) which is a quite cultural example…The phone example then might not be the best but it is nice for the representations and I like how each time [the narrator] talks there is a sign to where he would point, circling in red (see Figure 2), zooming in, emphasizing the words… it is very multimodal and brings all the representations together. I also know that many [PTs] like using NRK videos a lot, so that would bring something that is familiar to them and that they value. Most importantly it is in Norwegian and it is better than me introducing such things in my English (Reflection 1.2. – Action research cycle 2, p. 3–4).

Figure 2. Screenshot from video about functions with the focus of the narration being highlighted (source: NRK-skole, https://www.nrk.no/skole-deling/22179).

As with the previous example, demanding intellectual work was not part of the planning and the focus was on how the video provided opportunities for activities relevant to my teaching (e.g., ‘I like how, … because’, ‘The examples are interesting’), and on how, even though it included content which was less relevant (‘The phone example then might not be the best’), it would be relevant to PTs’ teaching experiences (‘I also know … value’) and language backgrounds (‘Most importantly it is in Norwegian’). The difference with reflection 1.1. is that I highlighted that the PTs valued familiar resources for their teaching and they would benefit from having those resources in Norwegian, their native language. In this reflection, I described the video as a way to ‘introduce’ PTs to the concept of functions, indicating the choice was connected to giving intellectual work. This was classified as low level of giving, as the focus was on the mathematical content, with little connection to language-responsive teaching in multilingual classrooms, apart from a general point about representations (‘very multimodal’).

In both reflections 1.1. and 1.2., making initial decisions to utilize resources and material, such as the videos, did not focus on designing challenging activities to support PTs’ intellectual work. In these reflections, there was no explicit mentioning of PTs pushing back, as in the study of Nolan and Keazer (2021). However, my expectations about PTs’ teaching needs related to practicum seemed to influence my planning. In particular, I seemed to have restricted considerations about intellectual work, especially to do with designing high demand tasks. In previous research, the TE in Eikset and Meaney (2018) and Meaney (2013) also experienced confusion and uncertainty when the aims for integrating language diversity seemed to be in contrast to PTs’ perceived needs for mathematical knowledge. This may be because the TE in these studies had a different cultural background from the PTs, as did I, which added to the complexities of integrating social justice issues into mathematics teaching. In my reflections, this uncertainty was most obvious during the initial decision making, rather than any other phase of planning. Decisions taken about resources, which I considered responded to PTs’ needs for teaching, seemed to direct my focus away from planning to demand high levels of intellectual work about language-responsive mathematics teaching.

Wanting to Change Practice – Struggling to Let Go of Being in Control

When I was reflecting on my earlier decisions and considering whether improvements were needed for the next workshop in the same action research cycle, I experienced a tension to do with wanting to improve the level of intellectual work about language-responsiveness that I demanded of PTs, but struggling to let go of being in control of the intellectual work. Although I wanted to be more consistent in achieving my assumptions about good teacher education practices, it was challenging to respond to all of them simultaneously. The issues that led to this tension were classified as being connected to researching my practice while planning it (Table 3).

In some of these reflections, I seemed able to focus on planning high, rather than low or medium, levels of intellectual work (assumption 1), but not on planning to transfer the intellectual work from giving to demanding (assumption 2). For example, after the second modelling workshop, I reflected on how some information I had given could be provided again and improved in the next workshop. To do this, I focused on a situation in the video of modelling in three acts (Wallace & Jensen, 2017), when a linguistically-diverse student explained a mathematical strategy of decomposing numbers, both visually and verbally, as a way to add or subtract them (see Figure 3):

I also realized that I talked about the (multilingual) student who did the decomposing strategy and I discussed it with [CF2], so I think that I could make that explicit and use it in a (PowerPoint) slide so that [PTs] notice how language and representations and mathematics were used from a multilingual kid very successfully. … That only became possible because the teacher gave [the students] the opportunity. … How is that then relevant to teaching? It is not enough to say and show it as something that happened, but to use it to talk about <implications for teachers’ classroom practices> … (Reflection 2.1. – Action research cycle 1, p. 10).

Figure 3. Student’s decomposing strategy from the video “Three-Act Tasks: Modeling Subtraction” (Video source: https://www.teachingchannel.com).

In reflection 2.1., I considered changing the way I gave information about a multilingual student’s use of ‘language and representations and mathematics’, by providing additional information about the implications for teachers (‘How is that then relevant to teaching?’). The plan focused on giving intellectual work, where my role would be to ‘say and show’ or ‘talk about’, and PTs’ role to ‘notice’ or ‘see’ (Table 2). I classified this, first, as medium level of giving intellectual work, since I initially focused on the student (the ‘multilingual kid’) being represented as a capable mathematics doer (‘very successfully’), and then as high level concerning implications for teachers (‘because the teacher gave them’, ‘relevant to teaching’). The language-responsive teaching aspects were related to sociolinguistic consciousness in terms of recognizing multilingual students’ success (‘very successfully’) and identifying language demands of classroom discourse (‘language and representations’) (Table 1).

By reflecting on how to include a focus on teachers’ practices, I was intentionally considering actions to improve my practice, based on the first assumption of the analytical tool. However, I did not consider activities that would demand intellectual work from the PTs, according to the second assumption. This suggests that I struggled with demanding intellectual work about language-responsiveness from the PTs, so that the PTs would have more control of the learning, even though I initiated other changes in my plans.

In other reflections, I considered changing the kind of intellectual work from giving to demanding (assumption 2), but not changing the level of intellectual work from low/medium to high (assumption 1). For example, after the first workshop of functions, I discussed with a critical friend about demanding intellectual work from the PTs in the next workshop. I referred to the same video as in Reflection 1.2. about the concept of functions.

I discussed with [CF1] about demanding PTs to bring from the video the different representations of functions that they could identify. I think it is important to understand that these different representations have different uses and different meanings, they bring different information and that is important to realize mathematically and pedagogically. This is something I could demand and relate to the video, instead of me giving the information about the different representations of functions (Reflection 2.2., Action research cycle 2, p. 7).

In this reflection, I considered changing the task for the PTs from one of giving low levels of intellectual work ‘about the different representations of functions’, to demanding intellectual work (‘demanding PTs to bring’, ‘I could demand … , instead of me giving’). However, I classified it as low level of demanding, because the task focused on the mathematical content, without making connections to language-responsive aspects of teaching functions.

Therefore, despite clarifying the assumptions about good teaching, it seemed difficult to fully realize them in my planning. This may have resulted in providing fewer possibilities for PTs to discuss issues of language diversity from their perspectives. My struggles resonate with tensions TEs experience when aiming to use socially-just practices, such as those mentioned in Baker and Bitto (2022). Similar to what they found, I become aware that I seemed to have planned superficial changes, as my assumptions were not visible. The difficulties in my planning around these assumptions produced uncertainties similar to those of Nolan and Keazer (2021). However, my analysis allowed me to identify what aspects of my planning caused these uncertainties and when. In particular, it showed that they were connected to managing the relations between giving and demanding intellectual work and creating more space for PTs to discuss language diversity issues.

Identifying Alternatives – Struggling to Choose Between Them

As was noted earlier, Feldman et al. (2004) highlighted that in self-studies in action research the TE as a self is inseparable from the research and the practice. Therefore, it was perhaps not surprising that when I was reflecting on whether my decisions for my future practice were appropriate, I experienced a tension to do with choosing one idea from a set of alternatives. These uncertainties emerged only in the second action research cycle regarding functions, with the exception of one example in the first cycle. I considered that they were connected to the teacher education practice as a whole (Table 3), because they concerned uncertainties about addressing language diversity as part of my mathematics teacher education professional practice.

An example came from my reflections on planning the first workshop of functions, where I considered asking PTs about who might be multilingual students in Norwegian school classrooms. However, I was uncertain about how this would support PTs’ learning about language-responsive teaching of functions and challenging deficit views of multilingual students, which was considered important in earlier research (see, for example, Rangnes & Eikset, 2019):

I don’t think there is a common understanding of who in the end is a multilingual student … Maybe that could be a question to bring into the session and see what PTs think, and why … But what does that have to do with functions? How am I going to show relations? I don’t find anything in the content to bring the language perspective, other than the language demands of the content (the word functions …) … and of the representations. But the focus on representations I’m afraid that is not enough to show a non-deficit perspective, and to focus on the multilingual students’ needs, because representations are useful for all students -so what examples can I show? What aspect would then make it important to talk about multilingualism specifically in functions? (Reflection 3.1. – Action research cycle 2, p. 2).

In this reflection, I was uncertain about bringing PTs’ attention to aspects of language-responsive teaching of functions (‘what does that have to do with functions? How am I going to show relations?’). I considered two alternatives: asking PTs which students they considered to be multilingual; and the usefulness of representations for responding to multilingual students’ needs. The first alternative was classified as low level of demanding (‘could be a question … and why’) because it did not explicitly show how PTs’ knowledge for teaching mathematics in multilingual classrooms could be supported. The second alternative is classified as giving intellectual work (‘how am I going to show relations?’, ‘what examples can I show?’), of medium level, since I focused on ‘multilingual students’ needs’ in working with representations of functions. The language-responsive teaching aspect in this case seemed to be about scaffolding instruction with representations and visuals, and valuing linguistic diversity from ‘a non-deficit perspective’ (Table 1).

The analysis indicates that alternating planning between different kinds and levels of intellectual work was associated with shifting my attention between the issues of language-responsiveness and functions, which were in alignment with my third assumption. Therefore, having alternative ideas for intellectual work did not lead to me making a decision, perhaps because of the complexity of finding a balance between language-responsiveness and the mathematical topic of functions.

Another example was when I was planning the first workshop on functions and was uncertain whether my potential tasks would achieve my aims of connecting representations of functions and language diversity. Prior to the following reflection, I had reflected on utilizing a mathematical task to talk about students’ early functional thinking.

Maybe I could ask [PTs] how representations (of functions in the mathematical task) could look like for lower grades 1–4 vs. 4–7 or I could wait and see if they bring it up themselves… Again, I am losing the language (diversity) perspective…I want [PTs] to understand that we (as teachers) don’t just use representations and visuals just to make [mathematics] look interesting or to make it easier, because they should be there for a reason … But then that is useful for all students, so what is it that makes it important now? … How can I demand PTs to work on those things instead of me giving? I don’t think it would be enough to ask if they think representations are important and why, but I can give it a try (Reflection 3.2. – Action research cycle 2, p. 5).

My alternatives were associated with different levels of demanding intellectual work. At first, I considered to involve PTs in working with representations of functions (‘Maybe I could ask … 4–7’), which I classified as low level of demanding, because it lacked linkages to language diversity. Then, I focused on the role of representations (‘to ask if they think representations are important and why’), which I considered as medium level of demanding. This is because I had previously provided some indications about how I could support PTs’ learning about language-responsive teaching of functions (‘I want PTs … reason’), particularly through scaffolding instruction with representations and visuals (Table 1). Nevertheless, the connection to language diverse classrooms is not made explicit. Although I considered alternatives in my planning, I experienced feelings of uncertainty about choosing between the alternatives and questioned whether they were sufficient to achieve my goals (e.g., ‘I don’t think it would be enough’).

Consequently, in reflections such as 3.1. and 3.2., I experienced a tension from having to choose between possible activities, because of a lack of balance between my joint aims for language diversity and mathematics. My uncertainty was similar to the tension experienced by other TEs in previous research (e.g., Baker & Bitto, 2022; Essien et al., 2016; Nolan & Keazer, 2021) to do with the degree of integration of language diversity or social justice issues into the mathematical topics. In their survey results, Vomvoridi-Ivanović and McLeman (2015) found that TEs described similar challenges of selecting tasks that would support PTs to engage in reflections on both mathematics and social justice. However, my difficulties with balancing the aims of mathematics and language diversity when selecting tasks seemed to be related to selecting tasks to do with raising non-deficit perspectives of multilingual students and their learning of mathematics.

In Meaney (2013), the TE experienced a tension between a focus on mathematics or on social justice connected to the context in which she operated. In my reflections, the context did not initially seem to contribute to feeling uncertain. However, the analysis showed that these feelings emerged mostly in my planning of the second action research cycle connected to the topic of functions. This suggests that that there might have been aspects of functions which were more complex than modelling, particularly in regard to focusing on non-deficit views of language diversity. Therefore, the mathematical topic may have played a contextual role in my planning about integrating language diversity.

Conclusion and Implications

In this article, I investigated the research question, ‘How does identifying tensions in planning mathematics teacher education, which integrates language diversity, contribute to understanding the complexities of improving practices?’ Following Berry’s (2007) definition of tensions, I focused on three situations in which tensions arose more often: focusing on my teaching or the PTs’ teaching; wanting to change my practice but struggling to let go of control; and identifying alternative activities but struggling to choose between them. These issues had some similarities with those identified in retrospectively considering the implementation of teacher education in earlier studies (e.g., Baker & Bitto, 2022; Nolan & Keazer, 2021). However, focusing on planning provided new insights into the complexities around the issues that affected my decision-making and the difficulties I had to reach my goals of improving my practice. Based on the three situations, I was able to unpack some of the complexities in my work as a TE and make sense of how different factors affected my decisions more broadly. Therefore, considering as well that multiple factors can overlap and relate to different tensions at the same time (Berry, 2007, 2008), similar issues regarding my difficulties to improve practice could emerge from a deeper analysis of the other tensions and uncertainties I experienced (Table 3), although less intensely.

In particular, I became aware of the blind spots in my planning, such as overlooking PTs’ actual needs for learning about language diversity and limiting opportunities for them to be in charge of discussions around language diversity, due to navigating multiple aims for my practice. This illustrates an aspect of complexity in my work as a TE because, even though my focus was on language diversity issues as the intellectual work, balancing this with my responsiveness to PTs’ perceived, rather than actual, needs was challenging. This resonates with some of the challenges faced by Casey (2012), when he found that expectations about being a PE teacher held by students and the school affected his possibilities to have students take more responsibility for their own learning.

It was also clear that different moments in my planning and the mathematical topics influenced my uncertainties as a TE. Knowing when tensions are likely to arise in planning can contribute to TEs, including myself, anticipating how complexities are entangled in their practices. In her reflections on planning her mathematics teacher education practices through action research, Erbilgin (2019) also identified similar phases, but not all of them were connected to feelings of uncertainty or confusion. In my case, tensions may have arisen because my focus was on integrating language diversity, as an aspect of social justice, into my mathematics teacher education work, which has been connected to such feelings in previous research (e.g., Eikset & Meaney, 2018; Nolan & Keazer, 2021).

The assumptions that were built into the analytical tool allowed me to recognize what contributed to the tensions arising. Without a clear understanding of my aims for improving my practice, based on the analytical tool, it would have been difficult to unpack specific complexities in my planning. In this study, I had focused on the aims regarding the intellectual work, yet other issues of the analytical tool, such as my responsiveness to PTs as a TE (see Kasari & Meaney, 2023), could provide other insights.

Although recognizing tensions and uncertainties can support TEs’ further planning and decision-making, it may not always be the case. This study has begun the identification of some of the complexities, to do with integrating language diversity into mathematics teacher education, yet there is a need for future projects about TEs’ work. As it may not always be possible to resolve tensions, even after recognizing them (Jaworski, 2006), future research could address how these might influence the interactions of TEs with PTs about issues of language diversity and social justice or whether new tensions emerge. Considering that TEs might set unrealistic expectations of an ‘ideal practice’, as did I, more insights from their own research undertakings, through self-study and action research, could add on the existing knowledge in the field of mathematics teacher education. Such knowledge could be useful to shift our understandings, as both TEs and researchers, towards what possibilities might actually exist within mathematics teacher education practice including issues of language diversity or social justice.

Disclosure statement

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

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

This study is part of the Research Council of Norway funded project 273404 “Learning about Teaching Argumentation for Critical Mathematics Education in multilingual classrooms” (LATACME) at Western Norway University of Applied Sciences.

Notes

1. For ethical reasons, other than teaching these workshops, I was not further involved in marking PTs’ assignments or exams, and was not part of the practicum mentorship.