Language diversity and mathematics education: new developments

Language diversity has become a feature of education more or less everywhere. The idea of the unilingual nation state is being steadily eroded in the places where it did exist, with minority language speakers often claiming the right to education in their languages. Internal and external migration is leading to superdiverse classrooms in urban centres around the world. The ability to live and work in multiple languages is seen more and more as a social and economic asset.

This shift – as much a change of awareness as a sociolinguistic or demographic one – has important implications for education. If language rights are recognised, what is the consequence for mathematics education? What issues arise in teaching mathematics in minority language contexts? Or plurilingual contexts? If mobility and superdiversity are prevalent, what is the consequence for mathematics teaching? Or the preparation of mathematics teachers? Or mathematics curricula?

The domain of research that focuses on mathematics education in relation to language diversity is starting to mature. In principle, this topic covers a wide range of situations arising in the context of societal multilingualism, migration, colonisation, Indigenisation, language immersion and education, and often several such situations at the same time. As little as twenty years ago, however, it was still possible to read all the extant literature on this topic, and the active researchers working on it would have fit round a large table.¹ In recent years, the maturing of the field is apparent in several respects.

First, there has been a series of review activities and writings, including an International Commission in Mathematics Instruction (ICMI) Study and accompanying volume (Barwell et al., 2016), at least one new book (Halai & Clarkson, 2016), at least one journal issue (Prediger & Schüler-Meyer, 2017) and a handbook chapter (Barwell, Moschkovich, & Setati Phakeng, 2017). Conference activities on this theme have also gone from strength to strength; the contributions in this special issue of Research in Mathematics Education were all initially presented to Topic Study Group 31 on mathematics education in multicultural and multilingual contexts at the 2016 International Congress on Mathematics Education (ICME) in Hamburg. This expansion shows a field of research that is becoming more and more mainstream, as countries around the world wake up to the increasing diversity (or superdiversity) of their school systems, and turn to researchers to develop mathematics education practice, policy and curriculum in response.

Second, a corollary; there are now many more researchers working on questions related to language diversity in mathematics education, from many more countries. For example, at a recent European Research in Mathematics Education (ERME) Working Conference held at the Technische Universität Dortmund, in Germany, there were researchers representing Germany, Denmark, Norway, Sweden, Finland, Catalonia, the Netherlands, Canada, the USA, Colombia, and India. A glance through the publications mentioned above similarly shows a great geographical diversity. There were, for example, 51 contributing authors in the ICMI Study volume, representing 26 different countries.

Third, there is an increasing diversity of research foci, theoretical perspectives, and research styles. The trajectory of the domain so far has been summarised in three phases (Barwell et al., 2017):

• cognitive research, looking at individual mathematical thinking in relation to, for example, learners’ languages or degree of bilingualism or multilingualism;

• discursive research, looking at collective mathematical thinking and classroom interaction in multilingual classrooms;

• socio-political research, looking at the relationships between language, power and privilege in relation to mathematics learning, teaching and assessment, as well as education policy.

While these phases are listed in chronological order of appearance, they all remain active areas of work. More recently, however, we see increasing innovation and diversification, so that some researchers or groups have adopted approaches like topic-specific design research (Prediger & Kuzu, 2019; Schüler-Meyer, Prediger, Kuzu, Wessel, & Redder, 2018), linguistic anthropology (Edmonds-Wathen, 2019), ethnography (Barwell, 2016), decolonising methodologies (Borden, 2013; Parra & Trinick, 2018) and others.

Finally, we feel that the overall treatment of language within this domain of research has become increasingly sophisticated, with much more thorough application of linguistic theory and methods than in the past.² With the increased use of theories such as comparative linguistics (Edmonds-Wathen, 2019), interactional discourse analysis (Wessel & Erath, 2018), systemic linguistics (e.g. Planas, 2018) or Bakhtinian translinguistics (Barwell, 2018), language is now routinely problematised and built into methodological and theoretical thinking. The same goes for mathematics, with the emergence of studies that focus on language diversity with respect to specific aspects of mathematics (beyond the long-standing work on word problems), including fractions (Wessel, Prediger, Schüler-Meyer, & Kuzu, 2016; Prediger & Kuzu, 2019), undergraduate mathematics (Durand-Guerrier et al., 2016), probability (Kazima, 2007) and linear functions (Zahner, Velazquez, Moschkovich, Vahey, & Lara-Meloy, 2012).

This special issue illustrates these new developments very well. It includes a mix of established and new researchers, geographical diversity, and a range of theoretical and methodological perspectives. This special issue presents 6 papers covering several aspects of the research on language diversity in mathematics education. All of them deploy an interest in overcoming compartmentalised perspectives on language diversity that used to conceive of the different languages as independent or separated; instead, the selected papers show an interest in theories of translanguaging, in which grammar, lexicons and resources from different languages are continuously entangled to make meaning. Another common interest in some of the papers is the study of how teaching activities can build common languages, by combining multiple ways of communicating, aiming to apply distal knowledge to situational knowledge.

The exploration of these concerns covers two aspects: studies of classroom practice (Assaf & Graves, Prediger & Kuzu, and I & de Araujo) and the development of theoretical notions to enhance research (Edmonds-Wathen, Barwell) on linguistic diversity. The paper by Ryan and Parra fits in to both of these groups.

In the first group, Assaf and Graves focus on the use of multiple resources to address open-ended problems and well-defined collaborative mathematical problem-solving activities in non-scholarly environments. They show how children’s reasoning is deployed through generalisation and self-reflection on their own experiences, and how such reasoning evolves and depends on the context in which mathematical activity is situated. Specifically, Assaf and Graves find that children’s use of multiple resources can facilitate the development of a mathematical argument, and because of that, they invite educators, when posing open-ended activities, to encourage children not only to communicate their answers, but to listen, evaluate, elaborate, and re-voice statements made by others.

Also within the first group, I and de Araujo inquire into the instructional strategies implemented during task set-up by monolingual preservice teachers. They find strategies in which the assessing of different student understandings (of languages, context and mathematics) can have a positive impact on emergent bilingual students’ solving of cognitively demanding tasks. The authors present cases of two preservice teachers, examining teacher-student interactions in one-on-one settings. These cases allow them to identify common themes, which can be taken into account when building a common space of understanding between a monolingual teacher and bilingual students. The paper shows teachers’ strategies that exemplify the themes: systematic reference to students’ prior experiences about the topic and the seeking of unfamiliar words (to establish a baseline of understandings); and the use of verbal explanations and supplemental tasks (when building a common space). The authors defend the need to invest enough time for assessing each student’s understanding of language, context, mathematics, and the problem itself.

The research by Prediger and Kuzu addresses how students in a bilingual teaching intervention adopt and combine language-related conceptualisations of the part-whole concept in or across languages. By following a perspective on multilingualism that studies dynamic and interconnected multilingual repertoires in multilingual communication, these authors document the existence of connection and complementarity between linguistic codes that allows Turkish-German-speaking students in Germany to achieve a deep conceptual understanding of the part-whole concept of fractions.

Within the second group of papers, Edmonds-Wathen provides important insights regarding different stages of the research process (the framing of research questions, eliciting mathematical language and presenting data in different languages) involved when researching the creation of mathematical registers. Here, the aim is to increase the interaction with trained linguists. Edmonds-Wathen defends the utility of a typological approach from linguistics when researching the enactment and explanation of the same mathematical process through different languages. This is important because it provides a broader mathematical frame, in which deficit views on language are surpassed. Elicitation tools are also explored in her paper, in order to produce targeted data in contexts and situations in which direct translation is not enough to capture intended meanings. Interactive mathematics elicitation tasks can emulate seminal works in cognitive linguistics, and therefore collaboration between linguists and mathematics educators is encouraged.

Barwell invites us to re-view the notion of resource and to expand it with the idea of repertoires of sources of meaning. This draws on Bakhtinian approaches to language that guide the author to examine the discourses, voices and languages used by students in three second language mathematics classrooms. Barwell describes the repertoires deployed by several students in close relationship with the sociolinguistic context of each class. Sources of meaning is a notion that embraces multiple and varied forms of languaging, and can provide evidence of the situational–distal dimension of language use in the mathematics classroom, a potentially significant aspect of students’ meaning-making.

In the intersection of the two groups, Ryan and Parra take data from diverse Swedish and Colombian educational practices in order to illustrate the existence of a theoretical dimension scarcely problematised in current research: the epistemological dimension of multilingualism. The philosophical theory of inferentialism is used to analyse the data and introduce a problematisation of the assumption that mathematical knowledge is fixed, pre-established and out of discussion when linguistic diversity issues are recognised. The authors observe such an assumption in several “language-as-resource” approaches and propose a re-examination of the usual aim to “improve the transitions” between formal and informal language use in mathematics classrooms, which implicitly demarcates certain points of departure and arrival.

The two areas of exploration covered in this special issue – studies of classroom practice and the development of theoretical notions to enhance research on linguistic diversity – further expands and evolves the growing body of descriptive research on language diversity in the mathematics classroom. However, the shortage of contributions concentrating on teaching designs (as a result of research-based design development of learning trajectories) for fostering students’ multiple languages for learning mathematics might reflect the overall tendency of researchers to firstly better understand before developing research-based teaching-learning arrangements. Although the increased use of theories in this body of research has generated elaborate frameworks and methods for data analysis, so far this work has paid limited attention to changes in classroom practices or curricula and assessment innovations. In terms of equity, this is problematic, especially for students whose language repertoires do not correspond to usual or normative expectations in mathematics classrooms.

In times of migration, with increasing numbers of students and teachers who learn and teach mathematics in multilingual contexts, important and necessary research questions about how to initiate fruitful mathematics learning by making use of multiple resources have come to the forefront. This is case for researchers, as well as for teachers, who express their urgent need for answers and approaches about how to react and change their teaching. Consequently, the developmental perspective of how to design teaching learning arrangements that intertwine multiple resources or sources of meaning for developing mathematical understanding has to be taken into account more systematically as part of the next phase. We see a connection between a design-based approach to research, and prior work in the cognitive, discursive, and socio-political phases outlined above. All three phases are necessary conditions for such developmental work and provide a basis for design research to formulate and experiment with design principles; they build the theoretical background from which design principles can be drawn.

Summing up, although multilingual learning has been analysed thoroughly (but not yet thoroughly enough), there is still a gap in research-based knowledge on teaching practices, task designs, design principles and evaluated teaching-learning arrangements by which mono- and multilingual learners’ language repertoires can be activated and developed in order to achieve deeper mathematics learning. This gap has to be overcome by more scientific exchange – not only between researchers from different language contexts but also between teachers and researchers – involving both theoretical elaboration and dissemination of theoretical ideas.

This leads to a number of questions: If language rights are recognised, what is the consequence for the preparation of mathematics teachers or teacher professional development? What are the beliefs of (future) teachers when it comes to teaching in superdiverse language contexts? What do (future) teachers have to learn about teaching in multilingual contexts? These questions are not yet acknowledged in research on teaching that recognises language rights. Similarly, questions such as “How can we design professional development? How can we design university mathematics education courses or teacher training at schools?” are not at yet satisfactorily answered in many multilingual contexts which brings us to the question If language rights are recognised, what is the consequence for research and development?

As an important overarching research focus, we see a need for theoretical development in the domain of mathematics teacher education that focuses on mathematics teaching and learning in relation to language diversity. This work would contribute to better understanding language-specific aspects of teachers’ pedagogical content knowledge. Of course, along with this in-depth understanding of teachers’ learning processes, we can also examine teachers’ beliefs, which is highly relevant when aiming to change teaching practices. We need to theorise teaching practices and teachers’ beliefs in different language contexts to inform the future work of teachers, researchers and teacher educators, which requires further research in this area.

Apart from working on the identified research and development gaps, we would add that there are also many challenges for mathematics education researchers with first languages other than English. The production of research in many different languages and in different contexts (e.g. shared first language and not shared first language) is of course a great achievement. However, there can also be drawbacks when seeking to publish our research in international research journals. For research carried out in non-English speaking countries, it can be very challenging to translate data transcripts or student work. Moreover, presenting the data in two (or more) languages takes up space (see Barwell, 2003; Geiger & Straesser, 2015). The majority of contributions in this special issue, such as those by Prediger and Kuzu from Germany, and Ryan and Parra from Sweden, are examples from European contexts that are still very privileged; the challenges may be bigger and more serious for researchers from contexts in which local or regional languages of academia are not widely used internationally.

In conclusion, in light of the research questions and methodological approaches we have outlined here for future research, we suggest extending the trajectory of the domain as follows:

• cognitive research, looking at individual mathematical thinking in relation to, for example, learners’ languages or degree of bilingualism or multilingualism;

• discursive research, looking at collective mathematical thinking and classroom interaction in multilingual classrooms;

• socio-political research, looking at the relationships between language, power and privilege in relation to mathematics learning, teaching and assessment, as well as education policy;

• design research at the classroom level for filling the gaps in research-based knowledge on teaching practices, task designs, design principles. This also involves evaluating teaching-learning arrangements and curricula by building on the theory that has been developed in the first three phases;

• design research on professional development including teacher pre- and in-service professional development;

• research in methodological settings of randomised controlled trials (efficacy studies) or field trials (effectiveness studies) for testing instructional approaches and designs;

• theory development: integrating and networking of theories.

The field may be maturing, but there remains much work to be done.

ORCID

Aldo Parra http://orcid.org/0000-0001-9503-0648

Correction Statement

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

Notes

1 Indeed, in a series of pre-conference sessions organised at PME annual meetings starting in 2002, this is exactly what happened.

2 We realise that this statement is to some extent an over-generalisation; some sophisticated linguistics was used in some early work.