Preservice teachers learning from teaching mathematics in multilingual classrooms
Toril Eskeland Rangnes and Tamsin Meaney
As a response to calls for more research about mathematics teacher education for multilingual students (see e.g. Aguirre et al., 2013; Essien, Chitera, & Planas, 2016; McLeman, Fernandes, & McNulty, 2012; Thompson, Kersaint, Vorster, & Webb, 2016), we investigate preservice teachers’ stories about implementing a modelling task on practicum. By analysing what the preservice teachers noticed about how multilingual students used multimodalities to make meaning, we were able to identify when their expectations about the students’ learning were disturbed or confirmed.
In Norway, education for teachers of Grades 1-7 became a compulsory Master programme in 2017. The consequent revision of programmes allowed for more emphasis to be placed on teaching mathematics in multilingual classrooms, which are common in Norway. Previously, preservice teachers (PTs) had complained that they had not received adequate input about how to teach subjects, such as mathematics in multilingual classrooms (Thomassen, 2016). However, research suggests that this can only be done when teacher educators make a concerted effort (Eikset & Meaney, 2018). Initial investigations indicated that, on practicum, our preservice teachers recognised the resources that multilingual students used to communicate mathematics.Yet, when reflecting with others on multilingualism in the mathematics classroom they tended to adopt a deficit perspective (Rangnes & Eikset, 2019). Similarly, de Araujo, Smith, I and Sakow (2018) found that preservice teachers focused on the students’ lack of the language of instruction, rather than on alternative possibilities for communicating and interpreting mathematical meanings. This was the case even though the PTs adjusted their own communication to include a range of multimodal representations, such as gestures and diagrams. Although not to the same degree as some of Fernandes’ (2012) preservice teachers who continued to hold strong beliefs about the students’ lack of English as being responsible for a lack of mathematics learning, the PTs in de Araujo et al.’s (2018) study seemed to hold deficit beliefs about their students’ potential to learn mathematics.
Moving beyond fluency in the language of instruction to consider other ways to support meaning making in multilingual mathematics classrooms can be done through considering super-diversity. In reviewing Barwell (2016), Meaney and Rangnes (2017) summarised the main ideas about super-diversity as:
Super-diversity highlights how individuals identify themselves with different groups in the current globalized world. Differences between languages and the fluency that speakers have with them can no longer be tenable research objects when the focus changes to communicating meaning, something that can occur in a range of different ways. Instead, recognising super-diversity requires researchers to view concepts around languages, language groups, speakers, and community differently.
Thus, we consider that a recognition of the range of semiotic resources used by students may contribute to preservice teachers changing their expectations about mathematics learning in multilingual classrooms. Therefore, the aim of this chapter is twofold. The first is to find out within an innovative teaching situation which multimodal resources the preservice teachers noticed. The second is to investigate whether the teachers’ noticing of multimodal resources disrupted or confirmed their existing understandings about multilingual students’ learning.
To conduct this investigation, we adapted theoretical perspectives on multimodal social semiotics (Bezemer, Diamantopoulou, Jewitt, Kress, & Mavers, 2012). In alignment with super-diversity, a multimodal social semiotic approach can provide insights into how the semiotic resources within an interaction contribute to the mathematical learning possibilities and the identities of the participants. Bezemer et al. (2012) stated that multimodality is particularly suitable for studying learning as it considers how resources, such as gestures, body language, speech, screenshots, concrete materials, and books, are used to create meaning and facilitate the organisation of a learning environment. Jewitt and Henriksen (2016) described multimodality as highlighting the relationship between meaning making and the meaning makers in regard to: meaning production; communication; how people develop representations for their understanding of the world; and the power relationships between people. In summarising the key components of a multimodal semiotic approach Bezemer and Jewitt (2018) described three aspects: (1) Meaning is made with different semiotic resources, each offering distinct potentialities and limitations; (2) Meaning production involves the production of multimodal wholes; (3) To study meaning, we need to attend to all semiotic resources being used to make a complete whole (p. 282)
Viewing mathematics teaching and learning as multimodal involves considering how the combination of semiotic resources (the multimodal whole) influences the potential meaning making available to students. Jewitt and Henriksen (2016, p. 147) reinforced van Leeuwen’s (2005) description of“a meaning potential, based on their past uses, and a set of affordances based on their possible uses, and these will be actualized in concrete social contexts where their use is subject to some form of semiotic regime” (p. 285). Semiotic resources have meaning potentials that emanate from their previous use, which carry meanings into new situations (Jewitt & Henriksen, 2016). In multilingual classrooms, there could be differences in what resources are seen as appropriate depending on different groups’ previous interactions with them. When there is no shared history of using or interpreting specific semiotic resources, then the meanings attached to them will also not be shared (see for example, Planas, 2018).
To illustrate how semiotic resources can carry (extra) meanings, Kress and van Leeuwen (2001) introduced the ideas of provenance and connotation (O’Halloran, Tan, Smith, & Podlasov, 2011). Provenance describes how meanings are imported with the use of signs/semiotic resources from one context (culture, social group, etc.) to another, which can give them new connotations.This process can add input to the meanings being produced (O’Halloran et al., 2011). In describing a button turning green in a digital balance game when the pans had equal amounts, Meaney (2015) suggested that the provenance from using actual balances and from situations where green meant “go” supported young children to make sense of when they had solved a problem correctly.
Connotational signifiers are the socio-cultural values and backgrounds that participants use to understand and interpret the meanings being produced in a particular situation (O’Halloran et al., 2011). An example is when in an interview, teachers described technology as only being for “strong” students (Li, 2007). Technology' carried the connotation that it required time and effort to master and the term “weak students” was connected to the need to complete exercises correctly to learn the basics. The connotations connected to “technology” and “weak students” led to an assessment that technology' was only for “strong students”.This was the case even though the “weak” students had previously lacked success in traditional tasks, such as completing textbook exercises. Connotational signifiers include positive or negative assessments of what is being interpreted, although the assessment can change depending on the situation (Kress & van Leeuwen, 2001).
Kress (1996) discussed the potentials and limitations of “representational resources” and “their effects on subjectivity”. He referred to two different multimodal newspaper covers, one from Frankfurter Allgemeine and one from The Sun. “It seems to me that radically different transformative potentials are employed in the two cases; radically different transformative potentials made available; radically different subjectivities projected” (Kress, 1996, p. 27). Whereas one newspaper expected the reader to engage with the story' by giving them the opportunity to critically evaluate the multimodal front page, the other newspaper front page only used colours and headlines to provide an overview, seemingly suggesting that the reader need not spend time on it. Kress (1996) referred to Bourdieu’s concept of habitus to suggest that various multimodal representations are offered on the basis of the expected habitus of their readers. Using a different set of multimodal representations can promote an alternative habitus that expects more from recipients and so affects their perception of themselves and their possibilities to act, or, in other words, their agency. In relationship to mathematical learning possibilities, the semiotic resources that are made available to students could affect what they see as their identities, which are related to how they see their possibilities to act. Their actions could then reinforce teachers’ perceptions of them as either competent or not competent, in the same way that newspaper editors did of their readers.
Inspired by Jewitt and Henriksen’s (2016) description of the potential of social semiotic multimodal analysis as a tool for understanding social function and complexity of a text, we developed Figure 12.1 to show how a sign is linked to the sign maker and what a focus on multimodalities would make possible to study, within a specific context. In Figure 12.1, the oval symbolizes the environment which surrounds a specific interaction and its available multimodal semiotic resources.The oval is dotted because semiotic resources from other environments could be included if participants identify them as having a possible use. Thus, participants’ agency can be considered as being affected by the environment and its potential resources.
The social context can be studied by investigating how the preservice teachers viewed the sign makers’ (the students’) choice of modalities in producing signs that carried meaning. By analysing the modalities identified in the PTs’ descriptions of the modelling investigation, it is possible to investigate how these PTs considered that communication, potential for learning and the available identities of the students affected, and was affected by, their meaning making in a social context.
Drawing on understandings about super-diversity (Barwell, 2016), we considered communication to be what occurs in interactions between people and between
FIGURE 12.1 Multimodalities, signs and signs-maker in a social context people and artefacts. For example, textbooks provide a monological communication, in that readers have no possibility of changing what is written. Thus, a textbook, even though it is multimodal with written words, diagrams and pictures, strongly constrains how the communication between it and people can develop. In contrast, a discussion, for example, between two students about measurement units, which allowed them to consider new aspects such as the need for them to be exactly the same length or area, etc., would be considered a dialogical communication because they can change and adapt each other’s contributions. By examining which “signs” are used and how the recipients respond, the function of semiotic resources in the communication can be studied.
Using Jewitt and Henriksen’s (2016) “meaning potential”, we consider communication to be linked to learning potential in that it is through interactions that there is a potential to meet and engage with new ideas. The integration of multimodal representations as a multimodal whole can make some ideas easier to learn. For example, “many mathematical concepts which are confusing or resist easy explanation and learning in natural language alone become far clearer with visual representations and manipulatives combined with natural language” (Lemke, 1998, p. 292). In our study we do not investigate what the students learnt, but instead identify in the PTs’ stories instances where learning may or could have occurred.
Similarly, we consider available identities offered to be the possibilities that the PTs present to the students about being multilingual students, mathematics learners, group members, etc. This definition builds on Kress’ (1996) description of how semiotic resources made available to newspaper readers could have shaped their self-understanding. Consequently, identities can be seen as being determined by those that are offered by others. Thus, the provenance and connotation of the signs used to suggest possible identities can co-opt what is available, as in the earlier example of the connotation between technology and strong students. However, we also acknowledge that students can use different learning potentials to develop critical thinking, argumentation and through this, also, identity. Sign-makers have the opportunity to shape their identity as someone who acts, participates and who can contribute. In that way, sign-makers have agency.