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Using Two Languages When Learning Mathematics
Abstract
This article reviews two sets of research studies from outside of mathematics education to consider how they may be relevant
to the study of bilingual mathematics learners using two languages. The first set of studies is psycholinguistics experiments
comparing monolinguals and bilinguals using two languages during arithmetic computation (language switching). The second set
of studies is sociolinguistic research on young bilinguals using two languages during conversations (code switching). I use
an example of a mathematical discussion between bilingual students to illustrate how sociolinguistics can inform analyses
of bilingual mathematical conversations.
... Something is considered resourceful when it can create useful and unique solutions in challenging conditions. Research has long acknowledged the perspective of language-as-resource (Adler, 2001;Setati, 2005;Planas & Setati-Phakeng, 2014, Moschkovich, 2007McLachlan & Essien, 2022). Research has also shown the role of language in education, especially in challenging contexts such as multilingual mathematics classrooms (Adler, 1999;Barwell, 2009;Mostert & Roberts, 2020). is research points to the fact that in these contexts, language can be used as a resource to aid learners' understanding of mathematics and to enable teachers to convey the mathematics content meaningfully. ...
... Research reporting on the practice of code-switching in multilingual African and international contexts, emerged in the 1990s and is still ongoing (e.g. Adler, 1999Adler, , 2001Aineamani, 2018;Bunyi, 1997;Essien, 2010Essien, , 2013Essien, , 2018Kaphesi, 2002;Langa, 2006;Moschkovich, 2007;Poo & Venkat, 2021;Setati, 2003). Codeswitching (an alternation between two or more languages of expression) is seen as useful for both teachers and learners when mathematics is taught in multilingual contexts. ...
Research has acknowledged the complexity of mathematics teaching and learning in linguistically diverse contexts where, commonly in most African classrooms, teaching and learning happen in a language other than the home language of the majority of students. In such contexts, language use is neither trivial nor straightforward. What immediately comes to mind are Ruiz’s three language planning orientations: – language-as-problem, language-as-right, and language-as-resource. A wealth of research exists on how language can be harnessed as resources or source of meaning in different linguistic contexts. Drawing on the concepts of language-as-resource, and language as sources of meaning, and given the complex nature of multilingualism across different linguistic contexts in Africa, we argue for the potential of translanguaging as a discursive practice for enabling meaning making in mathematics and the attainment of broader language roles.
... The statistics register, for example, includes words unique to statistical communication, but also specialised uses of everyday words, which take on unique meaning in statistical contexts. To succeed in a statistics classroom, students need to be not only familiar with and competent in their ordinary English register, so they can communicate with their classmates, but also fluent in multiple mathematical registers (Kazima, 2006;Moschkovich, 2005). ...
... ELLs are known to employ code-switching to clarify their understanding and to express their arguments and ideas generally (Clarkson, 2007;Moschkovich, 2005). Code-switching involves the movement between languages in a single speech act. ...
There are challenges making connections between language use and mathematics in mathematics education. A lack of connections between the two domains can have negative consequences on student learning and performance. The challenges in statistics classrooms, where language and contexts are important as a medium of instruction, have received little scrutiny. This article reports on collaborative research carried out in three largely Pasifika-dominated year 12 classes. Specifically, we explored the language resources and strategies that appear to enhance the statistical understanding of Pasifika students. Findings from the teacher reflection aspect of the study indicated that some strategies to incorporate student language and communicative resources in their learning worked better than others. Teachers may need to re-evaluate their teaching practices, especially if part of their population is learning English as a second language.
... In a review outlining bilingual mathematics learning, Moschkovich (2006) questioned whether the subtle millisecond differences reported in previous psycholinguistic studies would even appear in natural classroom settings at all, especially if bilinguals are allowed to choose the language in which they perform arithmetic. Moschkovich (2006) argues that switching between languages occurs naturally for bilinguals during mathematical thinking and discourse, and should not be viewed as a deficiency or sign of "semilingualism." ...
... In a review outlining bilingual mathematics learning, Moschkovich (2006) questioned whether the subtle millisecond differences reported in previous psycholinguistic studies would even appear in natural classroom settings at all, especially if bilinguals are allowed to choose the language in which they perform arithmetic. Moschkovich (2006) argues that switching between languages occurs naturally for bilinguals during mathematical thinking and discourse, and should not be viewed as a deficiency or sign of "semilingualism." This argument suggests that bilinguals might not necessarily lack mathematical competence across languages, but instead simply struggle to convey their knowledge in a weaker language. ...
In 2020, 21.5% of US preschoolers spoke a language other than English at home. These children transition into English‐speaking classrooms in different ways, often handling foundational concepts in two languages. Critically, some knowledge may be dependent on the language of learning. For instance, both bilingual children and adults typically prefer, and exhibit higher performance on arithmetic in the language in which they learned math (LA+) compared with their other language (LA−). The typical interpretation is that arithmetic facts are accessed from memory more efficiently or solely in LA+. However, recent research suggests that bilingual arithmetic is not restricted to one language in memory, and that language experience plays an important role in performance. Moreover, evidence suggests children and adults process arithmetic fundamentally differently. Thus, bilingual arithmetic memory may manifest differently across the life span. This review outlines evidence to date at the intersection between the brain basis of bilingualism, arithmetic processing, and development.
... Mathematics education research has gone a long way to employ and integrate a more asset-based perspective on languaging (Moschkovich, 2007;Planas, 2018) and to acknowledge linguistic discrimination within mathematics education research (Barwell, 2003(Barwell, , 2018. However, research on language that shapes the field and the view on mathematical concepts still largely sidelines and even excludes important categories of languages, linguistic resources and students with certain linguistic backgrounds by not truly engaging with languages that do not fall into western-and modalnormativity 1 . ...
... Special potential might lie in the multilingual classroom, where mathematical terminology can be an obstacle for learners who learn mathematics in an additional language. Research acknowledges the benefit of integrating multimodal resources in engaging and supporting multilingual students (e.g., Castellon & Enyedy, 2006;Domínguez, 2005;Moschkovich, 2007;Shein, 2012;see Robutti et al., 2022 for an overview). The more surprisingly, methods for using gestures as linguistic resource coupled with spoken and written language to support multilinguals' learning of mathematics as well as their language skills have not yet been systematically elaborated. ...
Research on language in mathematics education is largely dominated by a ‘normalcy’ of spoken languages. This modal hegemony does not only affect a whole group of learners in failing to provide access that is epistemologically equitable—those using sign language as their preferred mode for mathematical discourse—it also obscures our view on the roles language can play in mathematical thinking and learning. As a field, we can only win from seeking to understand Deaf learners of mathematics beyond a disability, as learners of mathematics with a specific linguistic background that influences mathematical thinking and learning in peculiar ways. In this contribution, I suggest a shift in mindset towards a more inclusive view on language in mathematics education research and practice. I propose basic principles to inform a perspective for reconsidering the role of language in mathematics thinking and learning, inspired by work of philosopher Francois Jullien. This perspective counters a perspective that merely integrates sign language into existing research and instead searches for dialogue between linguistic modalities in learning mathematics, looking beyond language as spoken or written. This approach will be illustrated by the case of the modal affordance of iconicity foregrounded in signed mathematical discourse, its role in Deaf students’ mathematics thinking and learning, and how this can inform existing research and practice dealing with language in mathematics education.
... English is positioned as a "high status" language associated with "gaining access to social goods" (Planas & Setati, 2009, p. 39). Other languages, like Spanish in the United States, are positioned as lower status (Moschkovich, 2007) and can even be viewed as hindering access to social goods like education. ...
Active learning practices, like groupwork, are becoming more widely used in post-secondary mathematics classrooms. These practices are often talk-intensive and require interpersonal interactions. As such, it remains an open question the extent to which practices like groupwork equitably support students with different social identities, including identities that center language. The goal of this paper is to use critical quantitative methodology to analyze the experiences of students in introductory college mathematics courses, particularly in courses that require peer collaboration. The data for this paper stems from surveys completed by 464 undergraduate students with different language backgrounds. The analysis identifies relationships that existed between the identities students brought to the classroom and the identities they developed in introductory mathematics courses. Using linear regression models, the study found that students’ comfort speaking during class and the language they preferred to do mathematics in were associated with practice-linked identities, like sense of belonging among peers. Findings also suggest an interaction between these variables and the frequency that students engaged in peer collaboration. This study contributes to the growing body of literature documenting how students with marginalized identities may have differential experiences with active learning practices, like groupwork.
... This led me to thinking about the mathematics register and mathematical discourse (Moschkovich, 2002(Moschkovich, , 2007a. I worked with bilingual students and this led me to exploring the role of language in learning mathematics, documenting how bilingual students communicate mathematically (Moschkovich, 1999(Moschkovich, , 2007b. Moschkovich (2002) was my first attempt to understand and use the concept of register. ...
This invited lecture summarized my work on language and learning mathematics. I described a theoretical framework for academic literacy in mathematics (Moschkovich, ABCDa, ABCDb) that can be used to analyze student contributions and design lessons. The presentation included a classroom example and recommendations for instruction that integrates attention to language. Although the example is from a bilingual classroom, the theoretical framing and the recommendations are relevant to all mathematics learners, including monolingual students learning to communicate mathematically.
Mathematics education in India is offered in one of the 22 officially recognized state languages or in English even though there are at least 270 languages with more than 10,000 speakers each. Caste, a deep-rooted structure that stratifies Indian society, is integrally linked to shaping state languages. There is minimal research from India that looks at language and mathematics education and practically none that factors in caste. Focusing on Tamil Nadu, a state with a history of anti-caste movement on the one hand and pure Tamil movement (a movement that sought to create a Tamil language with no words from other languages) on the other, this conceptual paper seeks to explore this dimension. More specifically, by using caste as an analytical framework, and by drawing on examples from the mathematics textbooks published by the Tamil Nadu State Board of Education and the experience of a few teachers and learners, the paper seeks to make a theoretical argument that the use of pure Tamil in mathematics textbooks has negative implication for socio-culturally and economically marginalized students who are solely dependent on textbooks as the only source for learning mathematics. There is a strong need for carrying out empirical work that would highlight the nuances and complexities involved in realizing ‘mother tongue’ education in mathematics, particularly for those who belong to marginalized caste-class backgrounds, and we hope that such work would emerge in the future.
This work presents landmark research concerning the vital dynamics of childhood psychological development. It’s origin can be traced to the late 1970s, when several psychologists began to challenge existing notions of cognitive development by suggesting that such functioning is bound to specific contexts and that cognitive development is based on the mastery of culturally defined ways of speaking, thinking, and acting. About the same time, several translations were made available in this country of the seminal work of Vygotsky, the noted theoretician, offering a conceptual base on which these workers could build. This volume, with contributions from many of the scholars who pioneered this area and translated the work of Vygotsky, looks at the complex mechanisms by which children acquire the cultural and linguistic tools to carry out cognitive activities and explores the implications of this research for education. The book is organized around three main parts: Discourse and Learning in Classroom Practice, Interpersonal Relations in Formal and Informal Education, and The Sociocultural Institutions of Formal and Informal Education. An afterword by Jacqueline Goodnow suggests new directions for sociocultural research and education. The intended audience is composed of developmental, educational, and cognitive psychologists, along with advanced students in developmental and educational psychology.
To understand the role of language in public life and the social process in general, we need first a closer understanding of how linguistic knowledge and social factors interact in discourse interpretation. This volume is a major advance towards that understanding. Professor Gumperz here synthesizes fundamental research on communication from a wide variety of disciplines - linguistics, sociolinguistics, anthropology and non-verbal communication - and develops an original and broadly based theory of conversational inference which shows how verbal communication can serve either between individuals of different social and ethnic backgrounds. The urgent need to overcome such barriers to effective communication is also a central concern of the book. Examples of conversational exchanges as well as of longer encounters, recorded in the urban United States, village Austria, South Asia and Britain, and analyzed to illustrate all aspects of the analytical approach, and to show how subconscious cultural presuppositions can damagingly affect interpretation of intent and judgement of interspeaker attitude. The volume will be of central interest to anyone concerned with communication, whether from a more academic viewpoint or as a professional working, for example, in the fields of interethnic or industrial relations.
This book is a collection of papers that explore the ways in which bilingual children cope with two language systems. The papers address issues in linguistics, psychology, and education bearing on the abilities that bilingual children use to understand language, to perform highly specialised operations with language, and to function in school settings. All of the papers provide detailed analysis about how specific problems are solved, how bilingualism influences those solutions, and how the social context affects the process. Finally, the implications of these findings for policy-setting and the development of bilingual education programmes are explored. This will be an important and useful volume at the forefront of topical research in an area which is exciting increasing interest among linguists and cognitive scientists.
The ethnic and linguistic diversity of U.S. schools has grown significantly in the last two decades. Such diversity provides distinct new challenges for school reform efforts. New policy and federal programs, particularly exemplified in Title VII of the 1994 reauthorization of the Elementary and Secondary Education Act, attempt to address this challenge. This act calls for integrated and comprehensive programming based on a new empirical and conceptual knowledge base, which has emerged in the last decade. This article addresses the demographic circumstances of student diversity, the emerging knowledge base, and the related federal educational reform policy changes related to these issues.
