Learner-centred education and English medium instruction: policies in practice in a lower-secondary mathematics class in rural Rwanda

ABSTRACT

This paper shows how one mathematics teacher, in a government secondary school in rural Rwanda, re-contextualises learner centred education (LCE) and English medium instruction (EMI) policies in classroom practice. Data are drawn from an ethnographic, critical case study and include lesson transcripts and teacher and student perspectives. The study indicates the importance of including non-verbal language in investigations of classroom interaction, and problematises the tendency to equate LCE with student talk in groups. In these lessons, whole-class interactions are managed by the teacher and student verbal participation is limited. Nevertheless, students co-construct and participate in activities and communicate mathematical meanings. The teacher observes and responds to students and enables students to access the English and mathematics they need for examinations. EMI limits student verbal participation and access to the textbook. The study indicates the importance of learning from and responding to classroom realties rather than pedagogical and linguistic ideologies.

KEYWORDS:

• English medium instruction
• Learner-centred education
• mathematics education
• secondary education
• Rwanda

Introduction

Learner-centred education (LCE) and English medium instruction (EMI) are typically investigated separately in studies of policy implementation. Here the two policies (and two literatures) are considered together in relation to a single teacher’s pedagogical approach and classroom context. We show the value of grounding policy analysis in ethnographic understanding of how lessons work, and the benefits of drawing descriptive and explanatory concepts from education and linguistics. We begin this paper with a review of the literatures in these two areas and in relation to Rwanda, indicating the gap in understanding which the present study addresses.

Learner-centred education (LCE)

In 2015, a competence-based curriculum (CBC) was introduced in Rwanda as a means of achieving the national development vision to become a regional hub for entrepreneurship, science and technology through human resource development (MINECOFIN 2000; REB, 2015). The CBC can be understood in relation to the international trend of learner-centred education (LCE) policy (Schweisfurth 2011; Van de Kuilen et al. 2020). There has been substantial debate around LCE in sub-Saharan Africa (SSA) over several decades, in response to the perceived failure of reforms to impact classroom practice (Chisholme and Leyendecker 2008; Guthrie 2018). LCE is criticised for lacking conceptual clarity, resulting in simplistic ‘ready-made prescriptions’ for practice directed at teachers (Schweisfurth 2015, 261). LCE reforms are seen by some as a form of soft power associated with international development agenda, where the aims are as much ideological as pedagogical (Tabulawa 2003). Finally, concerns are raised around the contextual (in)appropriacy of LCE for under-resourced education systems with content-heavy curricula and high-stakes examinations (Altinyelken 2010; Barrett 2007), and in societies which value received knowledge and authority (Guthrie 2018; Tabulawa 2003).

A number of studies have lent nuance to this debate by indicating the hybrid nature of pedagogy, where teacher- and learner-centred elements combine e.g. Barrett (2007), Altinyelken (2010), Lattimer (2015) and Brinkman (2019). Such studies also shed light on the ways in which the social and material context of classroom interaction enable and constrain different forms of pedagogy. For example, in Tanzania, Barrett (2007) notes that large class sizes, limited numbers of textbooks, closely defined timetables and high stakes examinations result in predominantly ‘performance-mode’ pedagogy, but that this includes aspects of quality. As a result of her investigation of LCE attitudes and practices across three states in India, Brinkman (2019) concludes that teacher CPD should engage teachers with LCE principles connected to their beliefs and support them to develop contextually feasible and appropriate pedagogies. To this end, Schweisfurth (2013, 2015), presents seven LCE principles. The principles are distinct from any single form of classroom organisation and reflect the theoretical and research-based roots of LCE and the human-rights/value agenda. The principles include constructivist approaches, that consider learners’ previous knowledge and skills the basis for new learning (Chisholme and Leyendecker 2008); socio-cultural theory, which highlights the centrality of guided participation in social activity for learning higher-order thinking skills (Vygotsky 1978); and the rights of learners to be respected and participate in education.

In Rwanda, teacher continuous professional development (CPD) has been a central strategy for curriculum implementation (REB 2015, 2017). Following the introduction of the new curriculum, Rwandan teachers received CBC training, through a nation-wide cascade, along with a school-based in-service program (REB 2017). However, training appears to have focused on LCE methods over teacher engagement with LCE principles. Van de Kuilen et al. (2020) report that following training, primary and secondary school teachers interpret the CBC (as a form of LCE) as group-work and group-work was included in all lessons observed in their study. The authors question the pedagogical value of the group-work they observed, due to limited textbooks, large groups and the limited cognitive challenge of group-work tasks. Interestingly, despite the fact that primary and secondary teachers received the same generic training, there are differences in how the two groups interpret LCE. Secondary teachers maintain a more instructive role than primary teachers, which leads to more effective pedagogy in secondary classrooms than in primary classrooms (Van de Kuilen et al. 2020). There is a need to better understand how teachers re-contextualise LCE in distinct classroom contexts in order to inform teacher CPD, which enables teachers to strengthen teaching and learning in relation to the resources and constraints of their classroom contexts.

English medium instruction

English Medium Instruction (EMI), as part of basic education in under-resourced and postcolonial education systems, is highly controversial (Milligan and Tikly 2016). In Rwanda and elsewhere, policy makers portray English (and EMI as a means to learn English) as necessary for regional and global opportunity (MINEDUC 2013), whilst critics point to the severe, negative effects of EMI on educational quality and equity (Milligan, Desai, and Benson 2020; The World Bank 2021). The Rwandan model of EMI can be described as early-exit and subtractive, because English (L2, i.e. the additional language) is introduced in the first phase of primary¹ at which point Kinyarwanda (L1, i.e. the language of early years education, and the main out of school language for the vast majority of children) is officially removed (Erling, Adinolfi, and Hultgren 2017). Subtractive, early-exit language in education policies assume that use of L1 undermines L2 and L2-medium subject learning, based on notions of linguistic purity and that time using L2 increases L2 learning (May 2017).

These assumptions are refuted by research-based evidence. Multilingualism is recognised as a single integrated psycholinguistic system rather than two language silos (Herdina and Jessner 2002), and higher proficiency in L1 is found to transfer to L2 (Bialystok 2001). Judicious use of L1 can enable multilingual learners to transfer cognitive and linguistic skills and use their metalinguistic skills for language and subject learning (Cummins 2017). Increased time using L2 does not necessarily improve the quality of language learnt, especially in classroom contexts where the range of language may be limited (Genesee 2013). Early transitions to L2 do not equate with increased learning gains over later transitions, and instead undermine language and subject learning, years at school and home-school relationships (Laitin, Ramachandran, and Walter 2019; Seid 2019; McEachern 2019). Large-scale, longitudinal studies repeatedly show the benefits of additive models of multilingual education over subtractive models on language and subject learning (Collier and Thomas 2017; May et al. 2017). There are widespread calls for additive, bilingual models of EMI (e.g. Ssendanda and Wenske 2021; Bowden and Barrett 2022). Nevertheless, subtractive early-exit models continue to be widespread in SSA (Trudell 2016).

In Rwanda, the model is evident in textbooks and examinations which, past the point of transition, are written ‘as if’ for monolingual English users (Milligan et al., 2016). Since the policy was introduced, teacher CPD has focused on training secondary subject teachers in English, through courses which are reportedly basic and generic (Pearson 2014; Williams 2017). Classroom communication in Rwanda and comparable EMI contexts is multilingual (Pearson 2014; Williams 2017). However, teachers and other school stakeholders consider classroom use of L1 undermines official policy and students’ access to English and restrict L1 as a result (Pearson 2014; Williams 2017; Early and Norton 2014; Probyn 2009).

There are a range of drivers associated with EMI in Rwanda, including the geo-political shift towards Anglophone alliances; the need to accommodate returning diaspora post-genocide (Steflja 2012); regional alliances within the East African Community (REB 2015); the interests of the ruling political elite (Samuelson, Freedman, and Policy 2010); and the popular appeal of English, which secures the political legitimacy of the government (Williams 2017). These factors indicate that EMI likely to remain in place at secondary level, and a recent focus of research and advocacy has been on strengthening EMI teaching and learning (Milligan and Tikly 2016). ‘Language supportive pedagogy’ (LSP) describes a strategies, including the judicious use of L1, which support EMI subject learning (Barrett, Juma, and William 2021; Milligan and Tikly 2016; Opanga and Nsengimana 2021). ‘Pedagogical translanguaging’ refers to the use of two or more languages for subject learning, and has been shown to improve subject learning, critical awareness of language hierarchies and student motivation (Banda 2018; Charamba 2020a, 2020b; Makalela 2015, 2019; Probyn 2015). In contrast to LSP, which is predominantly a means to enable EMI, pedagogical translanguaging aims to develop literacy in two (or more) languages through the alternation of languages for receptive and productive communication tasks (Bonacina-Pugh, da Costa Cabral, and Huang 2021; Rubagumya 2021). Researchers in both traditions tend to dismiss teachers’ multilingual classroom communication as haphazard, and adhoc (Probyn 2015; Rubagumya 2021). They emphasise the role of student talk in groups as a core pedagogical strategy, which may not be feasible in many African classrooms (Msimanga 2021). There is a need to learn from actual classroom practice, about the pedagogical resources and constraints that teachers and learners operate with, in order to identify how to strengthen LCE EMI mathematics lessons in Rwanda and comparable contexts (Milligan and Tikly 2016).

Research design

A case study design was adopted as an approach suited to investigate complex social phenomena in context (Duff 2008). The case of ‘these mathematics lessons’ was assembled using data on classroom interaction, teacher and student perspectives, and the social and material context of the school, the local community and the wider education system. The focus on a single class enabled a rich and detailed data set for extensive inductive and deductive analysis. We see this case as at once unique and applicable to other similar cases (Blommaert and Dong 2010).

A fully government owned and funded combined primary and secondary school was purposively sampled in order to investigate classroom practice and the impact of policy in relation to marginalised students (Williams 2019). Mathematics was selected because it is a high-priority subject in Rwanda, while student achievement and the numbers of students who opt to pursue mathematics and related subjects at upper secondary are disappointing (Uworwabayeho 2009). The mathematics teacher is in his late twenties, has a bachelor in mathematics education from the university of Rwanda, and has worked at this school for 6 years. He expresses concerns about his salary, which is low in relation to other kinds of public servant in Rwanda (and teachers in neighbouring countries). Like all public servants, he works a minimum of 40 hours a week, with most hours timetabled for teaching. There are 52 students aged between 12 and 16 years old in this senior one mathematics class, of whom 33 are female.

Data included 10, double-period (80 minute) mathematics lessons recorded over a 5-month period in 2018; a week of participant observation in school; post-lesson interviews with the teacher and groups of students; an in-depth interview with the teacher; and two focus groups with students. Data were gathered by a cross-national, multilingual research team. Rachel, a European researcher, designed and led the study as part of her PhD. The Rwandan researchers (Alphonse, Innocente and Jean Claude) assisted Rachel to identify a research site, gain informed consent from research participants, and to collect and translate data. Where possible, research participants were invited to choose language/s for communication. Most interviews were conducted in Kinyarwanda and translated to English, with some teacher interviews conducted in English and French. Student focus groups were conducted in English and Kinyarwanda. Recorded lesson observations were conducted by all researchers. The Rwandan researchers translated Kinyarwanda to English. Rachel transcribed English, paralinguistic features (e.g. pause, word stress and intonation), non-verbal language (e.g. movement, gesture, gaze and facial expression), written language and drawings from the board.

The study raises a number of ethical issues, given the power imbalances between adults and young people, European and Rwandan researchers, and Rwandan researchers and the teacher (Bond and Tikly 2013; Hultgren, Erling, and Chowdhury 2016). To mitigate these issues, information and consent forms were translated into Kinyarwanda, and presented orally and in writing to staff and students. All interviews and focus groups were conducted out of lesson time, and students opted in for interviews and focus groups and were able to sit off-camera during recorded lessons. The teacher reviewed and commented on tentative conclusions. Publications from the study are co-authored by all researchers.

In total, 13 hours of lesson recordings were transcribed, multilingually and multimodally (Heller, Pietikaeinen, and Pujolar 2018). Classroom interaction was analysed ethnographically, through the identification of contextualisation cues, speech acts and speech events (Gumperz and Hymes 1986). The following hierarchical units of interaction were identified: ‘Instructional units’, roughly equivalent to a single lesson period, were defined as having an explicit pedagogical objective presented by the teacher at the start and end of the unit, and ‘activities’, which repeat within across instructional units. Activities are defined as bounded units of interaction, with distinct roles for teachers and students and communicative objectives, serving the purpose of the instructional unit (Lemke 1990). In the data set overall, six activity types were categorised. These were:

1. Preparation

2. Presentation

3. Demonstration

4. Summary

5. Student questions

6. Individual and groupwork

Of these, the first four were present in all instructional units in the data set while the last two were less frequent, with instances of individual and group work (6) least frequent of all.

Critical analysis comprised tracing connections between classroom discourse and discourses and ideology at school and in the wider education system and society (Fairclough 2013). Interview, focus group and participant observation data were coded and connections were traced between classroom practice, teacher and student comments and texts, discourses and ideology from the school and wider education system (Heller, Pietikaeinen, and Pujolar 2018). For example, the teacher’s claim that ‘language is not that important for mathematics’ (05.09.18 fieldnotes), was associated with claims made by Ministry of Education officials and the introduction of EMI for mathematics and science before other subjects (Pearson 2014); the teacher’s focus on showing and doing mathematics and his omission of textbook student talk-based activities. Inevitably, the researchers were part of the lessons observed (Blommaert and Dong 2010). Analysis of lessons involved researcher reflexivity about our role as co-constructors of lessons.

Findings and analysis

In this section, we present findings and analysis to illustrate how the teacher and students construct and participate in lessons and construct LCE and EMI as part of lessons. We begin with three lesson extracts which show how the teacher uses routines and responds to students using multilingual and multimodal semiotic resources. Then we consider teacher and student perspectives on LCE and EMI.

The three extracts are from the activity ‘student questions’, which is the final activity of an instructional unit we term ‘surface area of cuboids’, after its mathematical focus. The teacher regularly uses ‘student questions’ at the end of instructional units, and in roughly half of the instructional units in the data set students ask questions. ‘Surface area of cuboids’ is a typical instructional unit in the data set in terms of the activities included and their sequence. It begins with ‘preparation’, where the teacher writes text from the textbook on the board, which students copy into their notebooks. In ‘presentation’, the teacher reads the text with students, highlights key terms and concepts and presents an exercise that the class will do together. In ‘demonstration’ the teacher invites students to complete the exercise on the board, whilst he stands to the side and offers support or guides seated students to provide support in a way which makes the example and support available to seated students.

It becomes clear in this lesson that the teacher and students have distinct methods for calculating the surface area (SA) of cuboids. The teacher’s method, taken from the student textbook (Ndyabasa et al. 2016, 221–2), is based on the understanding that a cuboid consists of three pairs of rectangles. His method, which he tells, shows and demonstrates to students in the lesson, is to calculate the SA of the three different rectangles and multiply each answer by two before adding the three numbers together. In the course of the unit, students share three different methods for calculating the SA of cuboids, individually and collectively. The first and last methods are accepted by the teacher, and a number of students, with the last being the most popular. This final method, which students report that they learnt in primary school (09.17.SGIT) consists of calculating the ‘surface of base’ (SB) which is the surface of the two square ends of the cuboid and then calculating the ‘lateral surface’ (LS) which is the surface area of the four sides of the cuboid. The method for obtaining the SA of the cuboid is to calculate one SB and multiply by two, to get the total SB. Then, to calculate one LS and multiply by four to get the total LS. Finally, the total SB and total LS are added together to get the SA of the cuboid. As the teacher points out at the end of this unit, both his preferred method and the method preferred by students can be used to calculate the SA of a cuboid. While the teacher sees the cuboid as consisting of three pairs of equal rectangles, the students see the cuboid as consisting of one pair of base rectangles, and a set of four lateral rectangles.

These extracts demonstrate how students shape interactions and activities and communicate mathematically in these lessons; the extent to which the teacher enables them to do so; and the way in which he uses student contributions to build their understanding. More broadly, the extracts demonstrate how the teacher constructs lessons using routines and by responding to students, and how the teacher and students use multilingual and multimodal semiotic resources to construct and participate in lessons and to communicate mathematically. The full activity ‘student questions’ lasts 5 minutes and 7 seconds.

Extract one

In the first extract, the teacher invites students to ask questions using a familiar routine and responds to students’ contribution. He signals the activity by raising his own hand, and only allows students who raise their hands to ask a question. He listens to a student’s question, and checks his interpretation of the question, before informing the student that the method they propose is correct.

The teacher raises his right hand and says:

Abantu batari kubona aho turi kubikura ni hagire umanika…Hands up (If you don’t how we are doing it, please…)

A student calls out. The teacher doesn’t accept the student, but raises his hand again, as he says:

SSS! Kumva aho turikubivana Hands up (How we are doing it) ……….

(Lines 124–5)

In the 10 second pause that follows, several students call out, but what they say is unclear. The teacher gestures around the room with his arm extended. Three students raise their hands. One calls out:

Teacher! teacher! …

The teacher gestures with his right arm towards a student. She starts talking, but what she says is inaudible. The teacher walks toward her as she is talking. He raises his arm, as he says:

eh?

(Lines 127–9)

The student speaks again, louder:

Ikibazo. Waretse tukabikorera icyarimwe kugirango tubone uko tubikora neza? Biriya biratujijisha tukabikorera icyarimwe nkuko formule ibitwereka Eh! Eh! (That’s a problem. Why can’t do all at the same time so that we do them properly? That method confuses us and we end doing all of them as the formula shows. Eh! Eh!)

(Line 130)

The teacher responds:

Eh! Ukabikorera icyarimwe? (Are you doing it altogether?)

Several students raise their hands and call out:

iiih (yes) Yes eh! Teacher! Teacher!

The teacher moves to the far-right of the board saying:

Buretse turebe (Wait a moment)…

He stands to the right of the board and says:

Ukabiteranyiriza hamwe? (Are you adding them all together?)

At least three students answer, loudly:

YES YES YES

The teacher gestures towards the formula in the middle of the board as he says:

Nabyo nta kibazo, Sibyo? Ubwo ni, ni total y izi surfaces zose tubonye, Sibyo? (That’s fine too. That’s the total of all of these surface areas we got. Isn’t it?) ………… (12 seconds)

(Lines 134–7)

Extract two

In the second extract, the teacher repeats the textbook method for calculating SA of cuboids, using a new example. He guides students through the example, by writing it ‘lock-step’ with pauses to allow students to work and by gesturing through each step of the calculation with his chalk, before he elicits the answer from the class.

The teacher looks at the class, then begins writing on the board. In the 12 second pause that follows, one student calls out, although only part of what he says is audible:

Eeeh……….surface…./unclear/

Meanwhile, the teacher writes:

S.A = 36 cm² + 24 cm² + 12 cm² =

Then he points to the calculation and asks:

Turagira kangahe? (What do we get?) ….

Several students reply in the four-second pause he leaves, but nothing is distinct. The teacher faces the calculation he has just written and says:

Mumbwire..dufite kangahe? (Tell me..what do we get?) ………..

In the 11 second pause that follows, several students call out, louder than before. Of these, two utterances are distinguishable:

S1:

Ntago ndi kubyumva! Bon nyine … (I don’t understand)

S2:

Mirongo itandatu na gatandatu uteranyije..Mirongo irindwi na kabiri (Sixty six plus seventy two)

The teacher moves his chalk across the calculation he has written on the board, from left to right, then writes at the end of it:

72 cm²

He looks up to the class and says:

Eh? …..

In the five second pause, the teacher looks at the students

(Lines 137–142)

Extract three

In the third extract, the teacher allows students to show their method, using the familiar format of ‘demonstration’. He stands to the side and allows seated students to guide the student working at the board. Finally, he presents the textbook method alongside students’ example and shows them that the two methods are the same.

The teacher points towards a student seated at the back right of the room. He says:

Hagire uza yandike iye nawe (Who can come and write theirs? Let him try)

The student walks over to the teacher and takes the chalk from him. The teacher smiles as he hands over the chalk, saying:

Come and write your formula

(Line 151–3)

In the five second pause that follows, the volunteer starts writing on the board. The teacher stands to the side. He faces the student, as do most students in the class. The student at the board is re-directed three times by other students. When the student at the board (and the seated students) are finished, the teacher takes the chalk back from the student, he moves to stand in the middle of the room, faces the class and says:

How many surface of base?

He raises the model cuboid and touches the two square ends, saying:

Dufite bases ebyiri.. sibyo? Sibyo? (We have two bases.. isn’t it? isn’t it?)

The teacher steps back and begins to write on the board. He writes under the calculation that the last volunteer wrote. He writes, below the ‘S.B’ that the volunteer wrote:

= (2LW) +

As he does so, he says:

Sibyo?..Singizi? …..Si izingizi?(isn’t it?.. it’s this? ….Is it this?)

(Lines 163–5)

Teacher steps to the side and turns to the class. He shows students the four long sides of the model cuboid as he talks.

Noneho lateral surface .Si ibihande, bine? … Si bine? (Now … not four sides? not four?)

(Line 165)

Teacher steps back to the equation, on the board as he continues:

Nese urabona hari aho bitaniye n’ ibi? (Is there any difference between these sides?) …

A student calls out:

Ahubwo Iyongiyo (You can use that)

The teacher exclaims:

Eh?

Another student calls out:

Niyo yaba nziza (That one is much better)

(Lines 167–170)

In the 22 seconds that follow, the teacher writes the textbook formula below the students’ formula on the board (see Figure 1 below).

Figure 1. The students’ and the teacher’s formula on the board.

He says:

Ahubwo iyi niyo yaba nziza (But this is one is better)

Then the teacher points to his equation and says:

Ibi nibyo bya….Iyi niyo lateral surface.. Sibyo? (That is….that is the lateral surface. Isn’t it?)

As he speaks, beneath 2LH + 2WH, he writes:

L.S.

He continues to talk:

Ikaba surface of base.. (This is …)

As he speaks, beneath 2LW, he writes:

S.B.

He says:

Si ibi se? Turi kubireba? (Isn’t it? Do you see that?) … byo mwize ntaho bitaniye n ibi, Sibyo? …Sibyo? (There is no difference between these and what you learnt Isn’t it? Isn’t it?)

Three different students answer, in agreement now:

S1:

Yes.

S2:

Yes.

S3:

Yes.

(Lines 171–5)

Teacher’s perspective on the CBC

The teacher’s perspective on the CBC/LCE suggests that he interprets LCE in relation to mathematics, based on his professional education and experience. Initially, the teacher talked about the new curriculum in general terms which echoed other teachers at the school and official discourses. For example, he stated that the new curriculum is ‘better’ because before teachers were ‘just teaching knowledge’ (Fieldwork notes, 03.09.18). He described the CBC as follows:

The students are more active. The students do 80% of the lesson and the teacher 20% (Fieldwork notes, 04.09.18).

A similar phrase is repeated by two other teachers at this school in separate conversations (Fieldnotes, 05.09.18). These comments echo discourses around pedagogical transformation in the curriculum framework document (MINEDUC 2013; REB 2015).

However, in later interviews the teacher talked about the CBC in a more nuanced way in relation to mathematics. For instance, in the extended interview, he commented that the CBC is not always appropriate for mathematics:

The CBC also has some challenges for mathematics. The approach works well for languages and humanities but not for science subjects and mathematics (06.09.TIN)

He said this was because ‘knowledge is more important for mathematics’ and ‘groupwork does not work well in mathematics lessons’ (06.09.TIN). Further, in the extended interview the teacher stated that the learner centred approach of the new curriculum is not new for him because it was a part of his bachelor of mathematics education (Fieldnotes, 06.09). These qualifications of his earlier comments indicate the ways in which the teacher has ‘recontextualised’ the CBC (Bernstein 1996) in relation to his professional education and experience of mathematics teaching and learning.

Lesson transcription and analysis reveals that the teacher constructs lessons purposefully and to some extent effectively, but differently from the lessons presented in the textbook where units begin with student group or pair work tasks (Ndyabasa et al. 2016). The teacher refers to his lessons as ‘CBC lessons’ (Fieldnotes, 04.09, 06.09), based on two criteria: 1) Students are active in lessons; and 2) students learn by helping each other (Fieldnotes, 04.09; 06.09). These two aspects are evident in the extracts above and across lessons. In addition, the teacher listens and responds to students and scaffolds their participation and understanding, which are key LCE principles (Schweisfurth 2013, 2015). On the surface, these lessons do not look learner centred but close analysis reveals principles of learner centred education.

Teacher and student perspectives on EMI

Next we consider the teacher and students’ perspectives on EMI. It is striking that, on various occasions, the teacher (05.TIN; 06.13.TIT; Fieldnotes 05.09, 06.09) and students, in groups and individually, (05.09.SFGN; 19.09.SGIT), describe students’ preferred language policy in similar terms. For example, when groups of students were asked to list the qualities of a good teacher, one group said that a good teacher should:

Teach in English and explain maths in Kinyarwanda

(05.09.SFGN)

On a different occasion, in answer to the question of which language they prefer using in mathematics lessons, one student responded:

I like studying mathematics in English but with some explanations in Kinyarwanda for understanding mathematics and English too.

(19.09.SGIT)

The teacher describes his language policy as follows:

When I teach I prefer to use English only but students do not understand maths without explaining in Kinyarwanda (…) students like me to use both Kinyarwanda and English (05.TIN)

A similar phrase is reported from a Rwandan primary school teacher working in a rural, government school (Williams 2019, 654). The notion of teaching in English and explaining in Kinyarwanda merits further investigation. On the surface, the comments suggest that the teacher ‘switches’ from verbal presentation in English, to verbal explanation in Kinyarwanda. However, lesson data indicate that English and Kinyarwanda are used flexibly as part of a multilingual and multimodal semiotic repertoire in these lessons (Garcia 2009; Garcia and Li, 2014).

The teacher and students consistently use English for mathematical terms. Written texts on the board and in student notebooks are in ‘English only’, as is teacher talk in ‘presentation’, when his purpose is to show students mathematical terms and texts. However, when the focus is mathematical meaning English is frequently ‘meshed’ with Kinyarwanda, along with other non-verbal and mathematical forms. For example:

The teacher gestures towards the formula in the middle of the board as he says:

Nabyo nta kibazo, Sibyo? Ubwo ni, ni total y izi surfaces zose tubonye, Sibyo? (That’s fine too. That’s the total of all of these surface areas we got. Isn’t it?) …… …… (12 seconds)

(Line 137)

Thus, while this strategy may be described by the teacher and students as explaining in Kinyarwanda, the ‘explanation’ is multimodal and multilingual. Indeed, ‘explanation’ in these lessons includes showing and doing mathematics. This is reinforced by student post-lesson comments after ‘surface area of a cuboid’:

I:

Tell us what you learnt today?

S5:

I was happy today because the teacher gave us good explanations.

I:

What did he explain to you?

S5:

He explained to us how to find the surface and we have understood.

(09.17.SGIT)

The student describes the strategy that helped them to understand as ‘explanation’. The interactions above, show the teacher ‘repeating’ the method for calculating surface area of a cuboid in various forms, engaging students to do a calculation as a class, and guiding a student to demonstrate a calculation on the board.

The teacher seems to use the subtractive and monoglossic model of EMI in Rwanda to enable his focus on mathematics, and English only in so far as it is part of mathematics. He considers teaching English the responsibility of primary school English teachers (Fieldnotes, 04.09.18; 05.09.18). For himself, he states:

I am a mathematics teacher, not an English teacher (Fieldnotes, 04.09.18)

Students are also focused on the English they need to get through school and pass exams, as one group comment:

Learning English helps us to pass the exams of subjects taught in English (05.18 Student focus group notes)

The English students learn is the English they need to pass exams, where they must read, comprehend and respond to mathematical English.

In contrast to the teacher, students indicate that they experience difficulties using English. Rather than questioning the logic of the policy, they perceive the problem as their own lack of skills. As one student puts it:

The issue is the lower level of English skills we have (19.09.18 Student group interview transcript, S3)

Students seem to compare their proficiency with the monolingual textbook and examinations, and perceive themselves to be lacking. This perception impacts students’ confidence to communicate in lessons, as described by one student, below:

The language issue that I had it was to ask questions but it was due the lack of confidence. I did not have enough confidence to ask in English. (19.09.18 Student group interview transcript, S1)

Discussion

At first glance these lessons may not appear learner centred or English medium, and yet closer analysis of classroom interaction shows the teacher’s re-contextualisation of LCE and EMI in response to his subject, learners and classroom context. The data indicate that the teacher constructs mathematics lessons through routines and by responding to students. The familiarity of routine activities means they can be signalled, set up and managed with minimal verbal instructions. As reported by Bernstein (1996) and Barrett (2007) this is a means of saving time before and during lessons. Therefore, the use of routines is appropriate in settings with short lesson periods in strictly defined timetables, and where teachers have limited time to prepare lessons (Bernstein 1996; Barrett 2007). As the extracts above indicate, familiar routines enable students to communicate mathematical meanings. Considerable pedagogical value is attributed to enabling students to express their thinking (Lemke 1990). It is notable here that students do so multimodally. The teacher builds on the students’ contributions to represent his own method. This reflects ‘constructivist pedagogy’ (Chisholme and Leyendecker 2008), and judging by student responses in the lesson and post-lesson comments (09.17.SGIT), is effective for some students at least.

This finding suggests that routine activities not only restrict classroom communication, as suggested by Alidou et al. (2006) but can also be a resource for classroom communication. This resonates with Barrett’s (2007) application of Bernstein’s (1996) pedagogical modes. Barrett found that lessons were overall in the performance mode but, within this mode, teachers continually observed and responded to students. Likewise, we find that these mathematics lessons are overall in the performance mode, and that the teacher responds to students in this mode. He is most responsive to students during ‘demonstration’ and ‘questions’, activities which he constructs with students in the lead. Notably, the data from this study indicate that routine and responsive elements of these lessons work together as part of holistic instructional units. For example, the highly routine activities of ‘preparation’ and ‘presentation’ enable ‘demonstration’ and ‘questions’ to proceed. This finding indicates the importance of investigating lessons in pedagogical wholes, and not drawing conclusions from the analysis of parts. It also confirms the insight that teacher and student agency are not binary qualities, but are closely inter-related (Schweisfurth 2013, 2015). This is significant, given reports that that learner-centred pedagogy is interpreted in Rwanda as the teacher doing less, and ‘groupwork’ (Van de Kuilen et al. 2020). It suggests that rather than learner centred or even learnING centred pedagogy (Brinkman 2019; O’Sullivan 2004), ‘teaching and learning’ centred research, policy and teacher CPD programmes may be more appropriate.

The teacher uses multilingual and multimodal semiotic resources to construct these lessons and to communicate mathematically. This finding resonates with the concept of translanguaging (García and Li 2014) and a number of studies of classroom practice in multilingual contexts (e.g. Cincotta-Segi 2011; Early and Norton 2014; Probyn 2009, 2015). The present study contributes by highlighting the central role of non-verbal semiotic forms in classroom communication. The finding is significant, indicating that researchers should include non-verbal linguistic resources in their data and analysis of classroom communication and indicates the need for sustained and detailed explorations of classroom interaction in order to identify situated forms and meanings.

The present study provides detail on the teacher’s systematic and flexible use of linguistic resources. The teacher consistently uses English for mathematical terms and register (Schleppegrell 2007) and this resonates with earlier findings (Early and Norton 2014; Setati 2008, 2003). He uses English, as a visible language (Adler 1999; Setati, Molefe, and Langa 2008) for mathematical terms and registers (Schleppegrell 2007); and to signal authority (Setati 2005, 2008), to signal the CBC, and to gain, maintain and direct student attention (Probyn 2009). He uses English as part of a broader multilingual and multimodal semiotic repertoire, and combines ‘English’ with ‘transparent’ linguistic resources, to make mathematical forms, meanings and practices accessible students (Adler 1999; Setati, Molefe, and Langa 2008). We propose the term ‘meshing’ to describe this practice, of combining visible and transparent linguistic resources in single utterances. This finding resonates with the language as a resource orientation taken by Setati, Molefe, and Langa (2008), Probyn (2015), and Moschkovich (2002, 2015) and indicates that ‘English’ does not present problems of proficiency, when it is used flexibly by teachers and students as part of a multilingual and multimodal semiotic repertoire.

The integrated ways in which the teacher uses his semiotic repertoire in this study contrasts with proposals for linguistic practices in multilingual classrooms. For example, the proposed model of ‘pedagogical translanguaging’ (Heugh et al. 2019; Makalela 2015, 2019; Probyn 2015), which promotes the separate use of ‘languages’ with the aim of bi/tri -literacy. One apparent reason for the difference here, is that this teacher’s aim is to teach mathematics and not language. This is evident in his statement that he is a mathematics and not a language teacher. He teaches English only in so far as it is part of mathematics, as the language of mathematics (Barrett and Bainton 2016; Early and Norton 2014), along with other semiotic resources/mathematical modes (O’Halloran 2015). He uses Kinyarwanda as a transparent language for teaching and learning, along with other semiotic resources (Barrett and Bainton 2016; Setati, Molefe, and Langa 2008). Thus, pedagogical translanguaging may not be appropriate in this classroom, because this teacher is aiming to teach mathematics and English as part of mathematics and not literacy in two languages. This finding resonates with Jasper’s call for classroom language policy researchers and advocates to appreciate the complex concerns which teachers’ work with, beyond their concern with verbal language and literacies (Jaspers 2018). At the same time, we find that the teacher uses language systematically and responsively in relation to his pedagogical aims. It is systematic, in the shared policy of ‘teaching in English and explaining in Kinyarwanda’, his use of English as a visible resource, and the consistent use of English as the language of mathematics. It is responsive, in that the teacher flexibly ‘meshes’ modes and shifts between modes, to enable students’ access to language and mathematics. As such, the teacher’s use of multilingual and multimodal semiotic resources is an indicator of pedagogical quality in these lessons (Barrett 2007; Schweisfurth 2013, 2015).

Conclusion

This paper provides a situated account of mathematics lessons in a government secondary school in rural Rwanda, with a focus on the teachers’ construction of lessons and student participation in lessons, and the construction of LCE and EMI as part of lessons. The study indicates that the teacher’s purposeful pedagogical approach is a pragmatic response to contextual constraints. His approach involves the combined re-contextualisation of LCE and EMI, and differs from LCE and EMI as formulated in official policy and curriculum documents. The study suggests that subtractive EMI undermines the implementation of LCE, making it necessary for the teacher to mediate the textbook for students, reinforcing the teacher’s pedagogical approach of showing students mathematics (rather than fostering mathematical talk) and restricting student verbal participation. Teacher CPD which legitimises multilingual communication as a pedagogical resource may enable this teacher to encourage students to communicate verbally in lessons. However, EMI is part of a complex of interactive factors which shape this pedagogical nexus (Schweisfurth, 2019) and change to a single factor is unlikely to transform classroom interaction. This study indicates the limitations of prescribing ‘ideal’ pedagogical and/or linguistic practices to teachers and suggests that engaging teachers with educational principles, and providing ongoing and situated support to interpret principles into practice may be more effective. Finally, we suggest there is much to learn from reading between academic fields in relation to practice.

Disclosure statement

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

Notes

1. Since the introduction of EMI in 2009, the transition has shifted from primary 1, to primary 4 and back to primary 1 again.