Abstract
Alongside the increased presence of students classified as English learners (ELs) in mathematics classrooms exists a persistent pattern of the marginalization of ELs. Educators have sought research to identify how to provide ELs with high-quality mathematics education. Over the past two decades, education researchers have responded with increased attention to issues related to the teaching and learning of mathematics with ELs. In this review we analyzed literature published between 2000 and 2015 on mathematics teaching and learning with K–12 ELs. We identified 75 peer-reviewed, empirical studies related to the teaching and learning of mathematics with ELs in Grades K–12 and categorized the studies by focus (Learning, Teaching, and Teacher Education). We synthesize the results of these studies through the lens of a sociocultural perspective on language in mathematics. We then discuss avenues for future research and calls to action based on the extant body of literature.
The linguistic diversity of students in schools is expanding worldwide. In many schools a significant proportion of students’ first languages (L1s) differ from the language of instruction (LOI). Yet, in many countries in which transformations in students’ language backgrounds are occurring, educators struggle to meet the needs of an increasingly diverse student population. For example, decades of research reveal that U.S. schools have served English learners 1 (ELs) poorly as evidenced by assessment scores, course-taking patterns, and measures of educational attainment such as high school graduation rates (Gándara & Contreras, 2009; Menken, 2013).
One commonsense assumption is that mathematics should be a safe harbor for students learning the LOI because, for the most part, numbers and mathematical symbols do not differ across national contexts. However, this assumption does not account for the central role of linguistically complex practices such as defining, explaining, and justifying in school mathematics (Moschkovich, 2015). In the United States, these practices are central to the Common Core State Standards for Mathematics (National Governors Association Center for Best Practices & Council of Chief State School Officers, 2010), a document modeled after the mathematics standards of top-performing countries. Thus, the implementation of the Common Core, in conjunction with associated accountability mechanisms, has placed additional pressures on ELs and their teachers (Moschkovich, 2015). This is not only a U.S.-based phenomenon; the question of how to educate students learning the LOI affects mathematics educators worldwide (Barwell, Moschkovich, & Setati-Phakeng, 2017).
These demographic trends and curricular shifts, together with long-standing evidence that schools have failed to meet the needs of ELs, raise a question: What research evidence provides guidance for educators of ELs who are responsible for the teaching and learning of mathematics? The purpose of this review is twofold. First, we synthesize extant empirical literature regarding the teaching and learning of mathematics with ELs in K–12 schools. Second, with regard to that literature, we examine the research context, methods, and theoretical perspectives in an attempt to understand the current state of the field. After summarizing the current state of the field, we propose new directions of research for the field to consider and call for a collective move beyond harmful practices, deficit narratives, and ideologies that have flavored past literature on ELs.
Theoretical Perspectives on the Mathematics Education of ELs
Over the past 30 years, the perspectives framing researchers’ examination of the mathematics education of ELs have expanded from their examining the role of language in individual cognition to examining the sociocultural and sociopolitical dimensions of language in mathematics education (Barwell et al., 2017). New theoretical perspectives have not necessarily replaced older ones. Rather, contemporary researchers draw on these perspectives, with some using a blend of theoretical perspectives and others firmly rooted in a single perspective.
Early researchers, grounded in cognitive and information-processing theories, examined how language might be a barrier for ELs’ mathematics learning. In research grounded in cognitive theories, language and language acquisition are treated primarily as a cognitive issue that may be distinguished from mathematics learning and the social contexts of schooling. Researchers drawing on this perspective often explain the linguistic influence on ELs’ mathematics performance as a result of higher cognitive-processing loads. This perspective has also been used to argue, conversely, that depending on their L1, some ELs face lower cognitive-processing loads in mathematics than in other subjects because of the parallel structure of number names in some non-English languages and in the base-ten system (e.g., Miura, Okamoto, Kim, Steere, & Fayol, 1993).
Over the past two decades, researchers who study ELs in mathematics have begun to incorporate insights from sociolinguistic theories of language (e.g., Halliday, 1978; Schleppegrell, 2007) and sociocultural perspectives on learning mathematics (Moschkovich, 2002; Razfar, Khisty, & Chval, 2011). Schleppegrell (2007) argued that “each subject area has its own ways of using language to construct knowledge, and students need to be able to use language effectively to participate in those ways of knowing” (p. 140). This insight is built on Halliday’s (1978) theory that each social sphere, including school mathematics, has a unique linguistic register. One implication of this theoretical stance is that language and mathematics are not easily separated. Pimm (1987) provided numerous examples and descriptions of how speaking mathematically requires appropriating the mathematics register. Schleppegrell (2007) reviewed the subsequent body of research on language and mathematics and characterized the features of the classroom mathematics register, identifying the major categories of multiple semiotic systems as well as key grammatical patterns used in school mathematics. These sociolinguistic perspectives on language in mathematics have led to research on ELs in mathematics classrooms to examine how ELs gain access to the mathematics register through teaching and learning processes (e.g., Khisty & Chval, 2002).
Moschkovich (2002) extended the work of linguists, such as Halliday, by incorporating Gee’s (2015) notion of Discourse practices in her analysis of how ELs engaged in classroom mathematical discussions. Gee’s concept of Discourse goes beyond the use of verbal language to include “ways of being” in the world, ways of using language, and social signifiers to identify with socially meaningful categories. This definition of Discourse practices led Moschkovich to argue that understanding issues related to language and communication in multilingual classrooms requires an analysis of how students, particularly ELs, construct identities in and through discourse. In Moschkovich’s (2015) more recent Academic Literacy in Mathematics framework, she has continued expanding the focus in research on language in linguistically diverse classrooms by incorporating mathematical proficiency, mathematical practices, and mathematical discourse as interrelated aspects of literacy in mathematics.
Finally, researchers in a number of recent studies on language and mathematics have adopted a sociopolitical stance, highlighting how students’ and teachers’ use of language(s) and discourse practices is connected to societal power and language ideologies (e.g., Planas & Setati, 2009; Razfar & Rumenapp, 2012; Setati & Adler, 2000). Gutiérrez (2013) outlined how the sociopolitical perspective draws on critical perspectives in education research, such as critical race theory and LatCrit (Latinx critical theory), to examine the intersection of racism, language ideologies, economic inequality, and the politics of immigration with the study of mathematics teaching and learning for nondominant students, including ELs. In the United States, work situated in the sociopolitical perspective often highlights how the use of nondominant languages in schools reflects ideological struggles tied to contentious issues, such as immigration policy and identity development among youth from historically oppressed communities (Gutiérrez, 2013; Razfar, 2012a). Outside the United States, researchers have also described how the challenges facing students learning the language of teaching and learning in school mathematics classrooms are often inextricably tied to social hierarchies, challenges related to patterns of immigration (e.g., Barwell, 2005a; Planas & Civil, 2013), and colonial histories (e.g., Setati & Adler, 2000).
Focusing and Framing This Review
This review is focused on studies of teaching and learning in which K–12 students are learning mathematics in English while simultaneously learning English in school. Worldwide, the population of these students is incredibly diverse, and this diversity makes framing this review challenging. In the United States, ELs are often immigrants or the children of immigrants, and about 80% of ELs in the United States speak Spanish as their home language (McFarland et al., 2017). In contrast, in countries with more than one official language, some ELs are domestic students learning English in school. In yet another contrast, in many countries with more recent colonial histories (e.g., Botswana, South Africa, and Micronesia), the LOI is English, whereas pupils speak local languages at home. Across these cases, the invariant challenge for teachers of ELs is creating opportunities for students to learn mathematics while simultaneously learning the LOI.
From a sociocultural perspective (Moschkovich, 2002), learning mathematics in English while learning English implies that ELs are learning to participate in academic discourse practices that may differ from home or community discourse practices. From the sociocultural perspective, this learning challenge is not purely cognitive but includes dimensions of learning to participate in valued sociocultural practices and communities. Furthermore, from a sociopolitical perspective (Gutiérrez, 2013), the social and political status of ELs’ home communities may also be critical mediators of their learning opportunities. For example, in the United States, where immigration policy is being debated in racialized terms, understanding mathematics learning in contexts with ELs may lead to investigating the sociopolitical dimensions of immigration and language policies in schools (e.g., Battey et al., 2013; Razfar & Rumenapp, 2012). Similarly, in postcolonial countries, language policies are inextricably tied to colonial histories as well as related issues surrounding race and social class (e.g., Planas & Civil, 2013; Setati, 2002, 2005).
In what follows, we generally use a sociocultural lens (Moschkovich, 2002; Schleppegrell, 2007) to frame our synthesis. In using a sociocultural lens, we highlight how teachers and students use language(s), symbolic tools, and multiple semiotic resources to learn mathematics and mathematical discourse practices in settings where students are learning the LOI (i.e., English). In the discussion we revisit this issue of framing literature on ELs in mathematics classrooms to consider how adopting a more explicitly sociopolitical perspective may extend the current boundaries of literature on ELs in mathematics.
Method
Phase 1: Article Identification Process
We compiled a list of keywords (Figure 1) using prior literature reviews by established scholars (e.g., Janzen, 2008; Lee, 2005). We limited our search to articles published between 2000 and 2015 in order to align with research published in the wake of the influential National Council of Teachers of Mathematics’ (2000) Principles and Standards for School Mathematics, which highlighted communication as a central strand of K–12 mathematics. 2 We used the ERIC database, a database frequently used in literature reviews of a similar nature, for the initial search. We searched abstracts of peer-reviewed, scholarly articles published in English with the parameters listed in Figure 1. After removing duplicates, we had amassed 831 articles.
Initial ERIC search results including duplicates.
We then searched individual journal websites using the same search terms to ensure that we identified articles from leading mathematics education, education, and bilingual education venues (Figure 2). We drew on Williams and Leatham (2017) to identify the top peer-reviewed research journals in mathematics education. This search yielded an additional 60 articles not previously included in our ERIC search, bringing the full list to 891.
Individual journal sites searched.
Phase 2: Identifying Relevant Articles
After identifying our initial list of articles, we formalized our inclusion criteria for this review. We included only original studies in peer-reviewed journals situated in K–12 mathematics teaching and learning contexts, in which English was the LOI. For a study to be included, both ELs and mathematics had to be central foci, not just part of the context. We excluded studies that included data on ELs only as demographic data and studies of ELs in which mathematics teaching and learning were not central. We also limited our review to empirical articles with clearly articulated research questions, or research purposes, and methods sections. After we had agreed on the inclusion criteria, we clearly defined exclusion criteria (Table 1).
Exclusion criteria
Note. EL = English learner.
The authors independently evaluated each title and abstract to decide whether to include an article. If two authors chose to exclude an article, it was excluded from the set. When an article was marked for inclusion by two authors, it was listed for further review. In instances in which authors disagreed, the remaining authors made their decisions, and the team discussed the issue until they reached agreement. In cases of uncertainty, the article was included for further examination in the subsequent round of review. From the newly winnowed list, two authors read each article to identify the research questions and other key information such as the context, theoretical perspectives, and participants. We used this information when we met again to resolve disagreements.
Phase 3: Organizing the Literature Through Identifying Themes
Categorization of Articles
To organize the literature, we adopted an iterative approach to building categories. We started with the classifications used in Lee’s (2005) review of science education literature related to ELs, a scheme later used by Caswell, Martinez, Lee, Berns, and Rhodes (2016) in categorizing National Science Foundation–funded projects related to the mathematics education of ELs, which includes the following categories: learning, curriculum, instruction, assessment, and teacher education. Two authors independently coded the focus of each article using these schemes and noted any questions or points to discuss with the full team.
Following this initial round of coding, we met to compare codes and to refine our initial scheme. For example, one of Lee’s (2005) categories was curriculum. We found, however, that articles tentatively labeled as curriculum also fit well into our teachers or learners categories because curriculum papers focused on either teachers’ interactions with curriculum or learners’ interactions with curriculum. We identified two additional potential categories during this process when we found articles that did not fall clearly into any of the initial categories: schooling structures referred to articles that addressed student course-taking patterns and immigrant students’ schooling experiences, and parents/families related to examinations of immigrant parents’ perspectives of their children’s schooling experiences. However, we found few articles in these categories (three and one, respectively) and chose to address them as part of the discussion rather than in the results, bringing our list of articles included in the results to 75 (see Table 2 for a summary and Tables 3–5 for the full list of articles). Using this revised scheme, two authors again individually identified the primary categorization of each article, and then a third author verified the classification. In cases without unanimous agreement, we discussed the categorization until we reached consensus.
Overview of synthesized articles
Articles had multiple contexts.
Learners and learning articles
Note. EL = English learner; SC = sociocultural; C = cognitive; SP = sociopolitical; EAL = English as an additional language.
Teachers and teaching articles
Note. EL = English learner; ESL = English as a second language; SC = sociocultural; C = cognitive; SP = sociopolitical.
Teacher education
Note. EL = English learner; PD = professional development; PST = preservice teacher; SC = sociocultural; C = cognitive; SP = sociopolitical; PACT = Performance Assessment for California Teachers.
Synthesizing the Literature
We conducted a synthesis of literature within each category using an inductive and iterative process. For the articles within each category, we identified the context, theoretical framing, methods, findings, and language background of the ELs (see categorizations in Tables 3–5). We used these characterizations to create initial observations across each category (Maxwell, 2013). We also characterized the theoretical orientation toward language in each article using the predominant theoretical categories outlined above: cognitive, sociocultural, and sociopolitical. We looked at patterns and trends within each category (learners and learning, teachers and teaching, teacher education) for similarities and dissimilarities in the data to understand each set of literature. For example, in the teaching/teachers category, we identified the framing of each article and then coded it as sociocultural, sociopolitical, or cognitive. We then looked at the findings for each article and categorized them by themes such as mathematics and language proficiency, drawing on linguistic resources, and drawing on cultural resources. Using these descriptive substantive categories, we considered also how the articles were categorized theoretically (cross-categorizing the substantive categories with our sociocultural, sociopolitical, and cognitive categories to understand the nature of the literature). Authors shared their summaries with the group for further discussion and refinement. The full literature identification process is summarized in Figure 3.
Overview of methodology.
Limitations
Any effort to synthesize the body of literature related to a topic necessarily has limitations. In choosing to focus on empirical studies published in peer-reviewed venues, we acknowledge that we have neglected studies found in books, monographs, and conference proceedings. One drawback of this approach is that the work of scholars who examine issues of equity, including ELs in mathematics, has appeared in book chapters or other venues outside of peer-reviewed research journals. Nonetheless, we chose to search journals because we have no systematic way to search book chapters and conference proceedings. Additionally, peer-reviewed articles hold a place of privilege in the academy, so focusing on these outlets gives researchers in the field insight into where this literature is (and is not) being published. Another limitation is that a number of studies that, although not focused on ELs in particular, were highly relevant to issues of language and mathematics. For example, studies from the TEACH MATH project (e.g., Turner et al., 2012) were excluded from this review because ELs are not the primary focus of TEACH MATH’s work. Because of this decision, several commonly cited articles were excluded, but we consciously made this decision to bound our review. Finally, we limited our review to articles focused on ELs in mathematics. We also acknowledge that many mathematics education scholars who examine language learners other than ELs have made meaningful connections to this body of literature. We selected studies in which English is the LOI for practical purposes; it is the context in which we work. We are aware that this is a limitation of this review because of the continued dominance of English in the research literature on multilingual mathematics classrooms (Barwell, 2005a).
Results
Learners and Learning
Learners and learning articles were focused on K–12 ELs’ learning and participation in mathematics. In this section, we discuss the following themes that arose from our analysis: the relationship between mathematics performance and language proficiency, ELs’ use of linguistic resources to learn mathematics, and ELs’ use cultural resources in mathematics learning.
Mathematics and Language Proficiency
ELs’ language proficiency, in both their L1s and their second languages (L2s), is related to their mathematical performance (Bautista Verzosa & Mulligan, 2013; Clarkson, 2007; Ríordáin & O’Donoghue, 2009; Vukovic & Lesaux, 2013). In particular, studies have shown that ELs with high language proficiency in both L1 and L2 performed better on mathematical assessments than students with low proficiency in both languages (Clarkson, 2007; Ríordáin & O’Donoghue, 2009). Thus, supporting ELs’ proficiency in L1 and L2 may correlate with stronger mathematical proficiency and understandings.
Adding further to the interrelatedness of mathematics and language is the notion that more sophisticated mathematical solutions are associated with more complex uses of language (Sigley & Wilkinson, 2015). Bailey, Blackstock-Bernstein, and Heritage (2015) examined 62 elementary ELs while they completed a task designed to elicit students’ “language for mathematical understanding” (p. 12) and found that the sophistication of children’s mathematical strategies related to the linguistic complexity of their explanations. For example, the explanation by a student using a one-by-one counting strategy to solve a counting task contained simpler vocabulary and fewer words than an explanation by a child who used a multiplication strategy.
Further evidence supporting the interconnected nature of learning mathematics and language for ELs came from studies of the language of tasks, curriculum materials, or both. Several researchers found that textbook and task terminology, unfamiliar problem contexts, grammar, and syntax can be challenging for ELs (Jhagroo, 2015; Kazima, 2007; Lager, 2006; Novotná & Moraová, 2005; Ríordáin & O’Donoghue, 2011; Zahner, 2012). For example, Lager (2006) found that the use of technical terminology such as show and pattern affected ELs’ performance on generalization tasks. Kazima (2007) found that students who imported meanings for probability terms from L1 to L2 often interpreted the terms differently than intended, and similar to a conclusion by Moschkovich (2002), Kazima argued that this evidences the need to focus on developing the meaning of mathematical terminology in conjunction with the understanding of the relevant concepts. In addition to the challenges created by the misalignment of tasks and students’ language, the use of English for mathematics instruction related to ELs’ negative self-perceptions of their mathematical abilities because they had difficulty demonstrating their mathematical understandings in L2 (Jhagroo, 2015).
Although language proficiency is related to mathematical performance, researchers have cautioned teachers to avoid putting ELs’ mathematical learning on hold while they acquire English. Even while they are learning English, ELs can engage in mathematical activity and participate in some forms of discourse in the mathematics classroom (Barwell, 2003, 2005b; McGraw & Rubinstein-Ávila, 2009; Sigley & Wilkinson, 2015). For example, Barwell (2005b) examined the ways in which students attended to language and mathematics while they worked on word problems and found that students’ attention to narrative experience served a number of purposes, such as developing shared meaning of the task context and developing a social relationship among students. This attention to narrative experience contributed to students’ abilities to “work together to write and solve word problems with relative ease and with little sign of language being a major issue” (p. 345). One of Barwell’s recommendations was that teachers should recognize ELs’ strengths and that they should support ELs in communicating about and engaging with rich word problems in mathematics classrooms. These findings indicate that putting students’ mathematical learning on hold while they acquire English is unnecessary because academic language can develop in the context of mathematical learning.
Note that the previously discussed studies were conducted in contexts in which students were exposed to English outside of school. In contrast, Bautista Verzosa and Mulligan (2013) studied 17 second-grade Filipino students, for whom English was the LOI but who had little exposure to English outside of school. They too found that the language in which problems were presented affected students’ solution strategies; however, they cautioned that although students may have developed particular mathematical solution strategies, “they still need to develop their English language skills before they can solve problems in English” (p. 239). This statement seemed to contradict the notion that ELs can develop mathematical proficiency at the same time they develop English proficiency, perhaps reflecting the influence of the different national-language contexts. However, we also approach Bautista Verzosa and Mulligan’s results with caution, as a single study does not necessarily hold the same weight as the prior studies that reached the opposite conclusion. More research is needed in this area.
Drawing on Linguistic resources
Below, we discuss research related to the ways ELs communicate their mathematical understanding using resources beyond written and spoken English. We also discuss mathematics curricula designed to capitalize on ELs’ resources.
Multimodal communication
Researchers have highlighted the importance of acknowledging and encouraging ELs’ use of nonverbal communication such as gestures, particularly with young children (Dominguez, 2005; Shein, 2012). Dominguez (2005) examined the ways in which second-grade ELs used gestures to communicate their mathematical reasoning and concluded that teachers should attend to nonverbal communication in conjunction with speech to gain more complete understanding of ELs’ mathematical knowledge.
Several researchers have built on such evidence regarding the benefits of multimodal communication for ELs in designing activities and curricula to support ELs’ mathematics learning (Cho, Yang, & Mandracca, 2015; Crawford, 2013; Freeman, 2012; Miller & Warren, 2014; Warren & Miller, 2015). One such project was Help With English Language Proficiency (HELP) Math, a technology-based mathematics curriculum that was designed to support middle-grades Spanish-speaking ELs with multimodal learning opportunities (Crawford, 2013; Freeman, 2012). Another curriculum-focused project, Representations, Oral Language, and Engagement in Mathematics (RoleM), was also designed to support ELs in mathematics through emphasis on multimodal communication (Miller & Warren, 2014; Warren, Harris, & Miller, 2014; Warren & Miller, 2015). Both curricula were focused on visual representations. Miller and Warren (2014) assessed both ELs and non-ELs who experienced mathematics lessons focused on representations and oral language and found that ELs’ mathematics test scores improved such that “they were achieving at the same level for mathematics achievement as the national cohort of students” (p. 800). Furthermore, ELs in the study “made significantly greater gains than the mainstream students” (p. 801). Together, findings from projects such as these indicate that the use of curricula that incorporate multimodal communication may hold promise.
Primary language as a resource
In considering language beyond spoken and written English, evidence has been found for purposefully supporting ELs in drawing on their L1 in the mathematics classroom (Civil & Hunter, 2015; Clarkson, 2007; Planas & Civil, 2013; Rubinstein-Ávila, Sox, Kaplan, & McGraw, 2015). For example, in examining students in Papua New Guinea, Matang and Owens (2014) found that, in early arithmetic, children who learned traditional counting systems in their primary language of Tok Ples outperformed children taught in English. The authors stated that students’ early mathematical learning in Tok Ples not only promoted knowledge ownership among school children but, most importantly, also provided the missing link between the abstract ideas learnt in school mathematics and the practical meanings provided by the out-of-school informal mathematics found in children’s own sociocultural environment. (p. 549)
In addition to possible increases in learning for ELs taught in their primary language, drawing on a student’s L1 is beneficial because ELs naturally draw on it when engaging in mathematical reasoning (Clarkson, 2007; Rubinstein-Ávila et al., 2015). The process of students’ moving between L1 and L2 is commonly referred to as code switching in the mathematics education literature, although more recently researchers are transitioning to the use of translanguaging (e.g., García & Wei, 2014) in a bid to move away from the deficit framing of much of the early research on code switching (Moschkovich, 2007). For consistency we use the term code switching here to parallel the articles we reviewed. Several researchers have tried to understand why language learners code switch (Clarkson, 2007; Parvanehnezhad & Clarkson, 2008). Clarkson (2007) found that elementary, Australian Vietnamese students’ switching between languages was unplanned, although students tended to draw more heavily on their L1 when tasks were more difficult and some students did not draw on L1 during problem-solving interviews. The lack of code switching in interviews might have been due to the contexts in which the interviews occurred, students’ maturation, or affective reasons such as their having greater confidence in L1. Regardless of the reason for hybrid language use, researchers have found that when teachers fail to draw on the ideas underlying students’ speech, in English or otherwise, students’ mathematical understanding is constrained (LópezLeiva, Torres, & Khisty, 2013). One conclusion from this work is that teachers of ELs can confidently draw on all their students’ language resources and embrace students’ use of hybrid language practices.
Some types of mathematics tasks may create more opportunities than others for ELs to draw on their existing linguistic resources, and teachers of ELs can select such mathematical tasks to facilitate learning opportunities in linguistically diverse classrooms (Barwell, 2005b; Razfar, 2013; Rubinstein-Ávila et al., 2015; Turner & Celedón-Pattichis, 2011). For example, Razfar (2013) examined bilingual Latinx students’ mathematical engagement with open-ended tasks during an after-school program and found that such tasks allowed for students’ use of their L1, which, in turn, helped facilitate students’ meaning making. Similarly, Turner and Celedón-Pattichis (2011) found that when kindergarten teachers provided students repeated opportunities to engage in challenging mathematics tasks and drew on students’ primary language as a resource, low-income Latinxs performed similarly to their White, middle-class peers. ELs can and should engage in deep mathematical reasoning, and they should also be encouraged to do so while drawing on their linguistic resources, including their L1s.
Despite the benefits of using ELs’ L1s in teaching mathematics, evidence shows that strong social and political forces in place continue to privilege English in mathematics classrooms with ELs (e.g., Setati, 2008). Barwell (2014) found that a number of tensions arose for Cree ELs in Canada, and he explained that these tensions arose from conflicts between what Bakhtin referred to as centripetal and centrifugal forces in language. Centripetal forces in this case referred to institutional pressures to maintain instruction in English, and centrifugal forces included the desire to allow students to draw on Cree. Barwell concluded, “The requirement to speak in English contributed to the challenges [students] seemed to face, leading them to draw on a range of resources, not dissimilar to those highlighted by Moschkovich (2008), including gesture and deictic language” (p. 921). Planas and Civil (2013) suggested that although language-as-resource has been widely taken up, we must move beyond this idea. They proposed the addition of language-as-political, which captures the “potential for transformation through processes that place certain languages and their speakers at a distinct disadvantage” (p. 363). Setati (2002) has similarly confronted the implications stemming from the historic use of English and Afrikaans in South Africa as the LOI and identified language as a carrier of symbolic power. In her work, Setati-Phakeng (Planas & Setati-Phakeng, 2014; Setati, 2005, 2008) examined the power of language as well as its contribution to hegemony and the continued marginalization of students through larger structural or institutional influences. She contends that using students’ home languages is a human right that creates mathematics learning opportunities.
In classrooms in which English is the LOI, students may draw on their L1 as a means of retaining agency in the classroom (e.g., Planas & Civil, 2013; Setati & Barwell, 2006). Zavala (2014) found that when English was the LOI, Latinx bilingual students in the United States used Spanish to resist the dominance of English and to communicate more productively. Her findings evidence the ties among students’ mathematical, racial, and linguistic identities in that “racial and linguistic identities do matter to learners in the classroom and impact their engagement” (p. 80). This and other studies (e.g., Setati & Barwell, 2006) provide evidence of the affordances of allowing ELs to draw on L1 and furnish reason for teachers to carefully consider the effects of the English-only narrative that dominates many classrooms serving ELs.
Drawing on Cultural Resources
Language and culture have deep connections to one another. Thus, in addition to examining students’ linguistic resources, researchers have examined the ways in which drawing on students’ cultural resources might support their mathematics learning. In several studies (Dominguez, 2011; Dominguez, LópezLeiva, & Khisty, 2014; Razfar, 2012b), researchers have examined the use of tasks that drew on students’ funds of knowledge (Moll, Amanti, Neff, & Gonzalez, 1992) to engage ELs in mathematical meaning making. For instance, Razfar (2012b) discussed the importance of drawing on children’s cultural and linguistic resources in creating a third space between formal and informal mathematical activity. Relatedly, Dominguez (2011) examined how students’ familiarity with task contexts and the language in which a task was given affected their mathematical activity. He found that in tasks with familiar contexts, students were able to undertake actions that promoted meaning making while they solved them, rather than simply relying on procedures. Together, and in conjunction with prior work on funds of knowledge (e.g., Moll et al., 1992), these findings underscore the importance of allowing ELs to use their cultural and linguistic resources while they engage with mathematics.
Reflections
The learners and learning research is the richest area of research related to ELs and mathematics. We found a number of research foci in this area as well as several cross-cutting themes. A number of authors attended to the need to value ELs’ ideas and resources (LópezLeiva et al., 2013; Matang & Owens, 2014; Setati, 2008), the role of providing ELs with quality mathematics experiences (e.g., Dominguez, 2011; McGraw & Rubinstein-Ávila, 2009; Razfar, 2012b; Turner & Celedón-Pattichis, 2011), roadblocks placed in ELs’ learning experiences (Barwell, 2014; Bautista Verzosa & Mulligan, 2013; Cho et al., 2015; Lager, 2006), and ways ELs supported their own learning through such practices as code switching (Clarkson, 2007), gesturing (Dominguez, 2005), and using other language strategies, like using a silent phase or a translation dictionary (Jhagroo, 2015).
This section of research is the most evenly split among type of research, type of setting, duration of studies, and number of participants. More than half the work related to learning took place at the elementary school level, with the rest evenly split between middle and high school. More than half the studies were also qualitative, with the rest of the studies either quantitative or mixed-methods studies. Whereas most of the studies were small, with fewer than 50 participants, more than a fourth had more than 200 participants. Finally, when we focused on learning in this section, we considered attending to how authors measured learning or attended to learning in their research to be important. In 13 of the studies, researchers used a test of some sort; for example, Miller and Warren (2014) developed three mathematics tests that were aligned with national and state tests in Australia. Tasks or task interviews were similarly common, with researchers in 14 studies using tasks such as word problems (e.g., Barwell, 2003, 2005a, 2005b) or a task interview (e.g., Turner & Celedón-Pattichis, 2011) to document student learning.
Across the research on ELs in mathematics focused on learners and learning, we saw evidence of multiple theoretical perspectives framing the research, sometimes leading to contradictory findings. The analyses of the relationship of learners’ proficiency in L1 or L2 and their mathematics achievement largely grow from cognitive perspectives on learning (Clarkson, 2007; Ríordáin & O’Donoghue, 2009; Vukovic & Lesaux, 2013). Similarly, in some studies of code switching, researchers frame this practice in purely cognitive terms. In contrast, much of the research on ELs’ linguistic resources is rooted in a sociocultural approach to language and thinking. From a sociocultural framework, mathematical thinking is not separable from language and the semiotic tools used to do mathematics (Moschkovich, 2002; Schleppegrell, 2007). Researchers adopting sociocultural or sociolinguistic stances argued for ELs to have opportunities to learn, talk, and interact in mathematics classrooms. The frameworks used to understand the mathematics learning of ELs may explain the contradictory findings we noted related to whether ELs can learn mathematics in English while learning English (e.g., Barwell, 2005b; Sigley & Wilkinson, 2015) or whether ELs should learn English before completing tasks in English (Bautista Verzosa & Mulligan, 2013). Another plausible explanation for the apparently contradictory findings is the differences in linguistic-policy contexts of the research.
Research focused on ELs’ use of their primary languages and research related to drawing on ELs’ cultural resources in mathematics draw on sociocultural concepts and simultaneously move the field in a more explicitly sociopolitical direction by relating languages, mathematics learning, identity development, and relationships of social power. For example, Zavala (2014) framed ELs’ use of the primary language as a form of resistance, reflecting the notion that teaching mathematics in English only may restrict ELs’ rights to use their language as a resource (Planas & Setati-Phakeng, 2014; Setati, 2005, 2008). This stance represents a shift from the earlier work in which researchers examined ELs’ use of languages as a cognitive phenomenon.
Teachers and Teaching
Articles in this section are focused on the ways in which teachers attended to ELs in their mathematics instruction and to the ways teachers have enacted instructional practices for ELs. In this section, we discuss the following themes from our analysis: teachers’ histories and teaching contexts and teachers’ practices, which include practices that promote access to content and practices that support mathematical discourse.
Teachers’ Histories and Teaching Contexts
We begin with an overview of several studies related to teachers and teaching in which teachers’ personal histories and the contexts in which they work were considered. Hansen-Thomas and Cavagnetto (2010) captured teachers’ prior experiences, or histories, working with ELs, noting that the mathematics teachers they surveyed believed that mathematics should be easier for ELs than other subjects, that ESL training for teachers is needed, and that ELs fail in mathematics because of issues with reading and comprehension of oral language. This study provided the type of background information that many teachers may bring to a classroom when working with ELs, much of which is laden with deficit perspectives with respect to ELs and what they can achieve.
Other researchers studying teachers’ contexts highlighted the realities of teachers. For instance, teachers often face the challenge of implementing new curriculum. Celedón-Pattichis (2010) examined the work of a mathematics teacher of ELs while she implemented a new reform-based curriculum. She found that in the shift from a traditional curriculum, she needed long-term professional development (PD) for supporting ELs. Zahner (2015) explored additional external forces beside curriculum that teachers face. He found that assessment pressure can lead teachers to adopt a procedural focus when teaching mathematics classes including ELs. These studies demonstrate some of the external challenges teachers face and some of the perceptions of ELs they bring to their mathematics instruction.
Teachers’ Practices 3
In a number of studies aspects of teachers’ practice that affect ELs’ mathematical learning were examined. We identified two broad categories of teacher practices to enhance ELs’ learning of mathematics: practices that promote access to the mathematics content and practices that support ELs’ entree into mathematics discourse.
Practices that promote access to content
Practices that promote ELs’ access to mathematics content often include visual and speech strategies (Pray & Llieva, 2011) but could also include technology supports (Ganesh & Middleton, 2006; Zahner, Velazquez, Moschkovich, Vahey, & Lara-Meloy, 2012). In their study of 11 secondary teachers, Pray and Llieva (2011) drew on the Sheltered Instruction Observation Protocol (Echevarria, Vogt, & Short, 2007) and found that visual and speech strategies were the most influential in supporting ELs in the earliest stages of English proficiency. Relatedly, researchers have studied supports for ELs when accessing mathematical ideas and solving word problems in English (Orosco, 2014a, 2014b; Orosco, Swanson, O’Connor, & Lussier, 2013). Orosco et al. (2013), for example, assessed a mathematics comprehension strategy for word problems for Latinx ELs at risk for math failure/math disability and found structured reading an effective intervention. These studies illustrate the role of discrete practices to support ELs, sometimes in limited settings (e.g., solving word problems).
Practices that support mathematics discourse
We identified four broad categories of practices that support ELs to develop or access mathematics discourse: (a) eliciting, (b) modeling, (c) revoicing, and (d) recognizing and valuing ELs’ multiple resources.
As Hansen-Thomas (2009) described, “Eliciting discourse draws students into the verbal interactions” (p. 94). She studied three middle school teachers’ elicitation of ELs in class and found that the teacher who was most successful in her elicitations used a variety of practices, including choral responses, modeling standard forms, and encouraging the use of mathematical language in small and large groups. Researchers have shown that eliciting ELs’ contributions in mathematics discussion is a function of honoring students’ lived experiences and being cognizant of their evolving identities (Celedón-Pattichis & Turner, 2012; Takeuchi, 2015; Turner, Dominguez, Empson, & Maldonado, 2013; Turner, Dominguez, Maldonado, & Empson, 2013; Warren & Young, 2008). Teachers’ interests in students’ experiences enable them to recognize the resources students bring to the classroom and to affirm students’ identities. This affirmation, in turn, can provide increased opportunities for ELs to participate in the mathematical discourse.
The second practice we identified for supporting mathematics discourse was through modeling. Teachers sometimes model discourse directly (Khisty & Chval, 2002) or through structured reading of the text, calculating, or solving problems orally and repeating or emphasizing algorithms, concepts, formulas, and definitions (Hansen-Thomas, 2009). Researchers discussed the practice of modeling mathematical discourse both independent of (e.g., Khisty & Chval, 2002) and in conjunction with other practices, like revoicing (Enyedy et al., 2008) or eliciting (Hansen-Thomas, 2009).
Revoicing is the third practice that supports discourse. At one level, teachers use revoicing to “positively acknowledge or redirect students to correct forms” (Hansen-Thomas, 2009, p. 94). At another level, revoicing involves “explicit verbal, gestural, and other non-verbal positioning moves by the teacher that . . . explicitly plac[e] the original speaker in relation to other people, the task, or the original speaker’s interpretation of his or her own utterance” (Enyedy et al., 2008, p. 141). Enyedy et al. (2008) labeled this practice as revoicing to position, and one can infer the potential effect of this positioning on ELs’ formation of identities related to mathematics.
The fourth category of a practice to develop discourse is recognizing and valuing ELs’ multiple resources. As previously mentioned, several authors in this section also acknowledged the importance of drawing on students’ L1 as a tool to help ELs comprehend oral or text-based mathematics discourse (Enyedy et al., 2008; Hansen-Thomas, 2009; Khisty & Chval, 2002; Tavares, 2015), allowing students to code switch (Salehmohamed & Rowland, 2014; Setati & Adler, 2000), and using students’ funds of knowledge (Lipka, Sharp, Adams, & Sharp, 2007). Additionally, researchers have found that code switching on the part of the teacher is useful in supporting ELs’ engagement in classroom talk, to draw on ELs’ L1 resources, and to acknowledge political realities of language (Salehmohamed & Rowland, 2014; Setati, 2005; Setati & Adler, 2000).
Though supporting ELs’ mathematical discourse is important, in several studies researchers also documented ways in which teachers’ practices can unintentionally impede ELs’ mathematics discourse (LópezLeiva & Khisty, 2014; Pinnow & Chval, 2015). For example, Pinnow and Chval (2015) described how classroom members regularly positioned Roberto, an EL, as less competent than his peers. In multiple interactions, students both physically and verbally moved to exclude Roberto from participating in the classroom discourse. The authors concluded, as do many other researchers, that teachers played a key role in shaping the classroom structures and interactions needed for ELs to draw on and gain access to the discourse.
Reflections
Collectively, the literature illustrates how teachers are located squarely at the complex intersection of language education (although often not certified or prepared for it) and mathematics curriculum and instruction. The articles in this section were, overall, focused on teaching practices for working with ELs, such as using teacher discourse moves like modeling and eliciting language (Hansen-Thomas, 2009), using rich language (Khisty & Chval, 2002), revoicing (Enyedy et al., 2008; Shein, 2012), and recognizing and valuing students’ resources (Lipka et al., 2007; Takeuchi, 2015). Many of these studies evidenced how teachers’ instruction is largely based on their personal histories, training, relationships with curriculum, and the professional support they receive. We also found studies related to topics such as curriculum implementation (Celedón-Pattichis, 2010), caring (Lewis et al., 2012), microaggressions (LópezLeiva & Khisty, 2014), and the effects of external forces on teachers’ instruction in mathematics classrooms with ELs (Zahner, 2015). Elementary school contexts were most prevalent in this category, with 19 of the 28 studies conducted at the elementary school level. As with most of the studies we reviewed, the majority of these were small qualitative studies; 20 of the 28 studies used qualitative methods, and 13 studies took place in a single classroom, with an additional 6 studies taking place with two to three teachers.
Sociocultural perspectives were most represented in this section, with attention to teachers’ supporting emergent bilingual students’ mathematical discourse through technology (Ganesh & Middleton, 2006), modeling (Hansen-Thomas, 2009), providing opportunities for interaction and using rich mathematical words with students (Khisty & Chval, 2002), and using gestures, questioning, and revoicing (Shein, 2012). Studies grounded in cognitive perspectives were focused more on word problem solving accuracy (e.g., Orosco, 2014b) and the use of particular visual and speech strategies (Pray & Llieva, 2011). Research that highlights teaching practices enumerated as strategies (e.g., structured reading in Orosco, 2014a, 2014b) is largely rooted in cognitive perspectives on language and mathematics learning. One drawback of this perspective is that its proponents can reduce language in mathematics to a barrier, and they do not acknowledge the valuable resources to be found in ELs’ emergent thinking. In contrast, teaching-practices researchers who emphasize ELs’ access to mathematical discourse or discourse practices (e.g., revoicing by Enyedy et al., 2008) highlight the sociocultural aspects of mathematics learning and focus on identifying and building on ELs’ resources. Researchers taking this perspective avoid contributing to deficit perspectives on ELs (Moschkovich, 2002). We note that few works in this section were based explicitly on a sociopolitical perspective. Exceptions include LópezLeiva and Khisty (2014) and Pinnow and Chval (2015), both of which highlighted how ELs might be shut out of mathematics classrooms. Also, researchers on teachers’ code switching noted that teachers’ use of ELs’ L1 might be a political act challenging language policies (Salehmohamed & Rowland, 2014; Setati, 2005; Setati & Adler, 2000).
Teacher Education
We identified just 12 studies that were focused on teacher education and met our inclusion criteria. Among this set of articles, five were focused on in-service teacher education and the remaining seven related to aspects of preservice teacher (PST) education (Table 5). In the following sections, we provide a brief synthesis of these studies.
In-Service Teacher Education
Given the evidence that teachers continue to view mathematics and language as fundamentally separate (e.g., Battey et al., 2013), teacher educators in the United States have emphasized experiences designed to build awareness of the relationship between mathematics and language and developing practices to support ELs’ understanding of mathematics alongside their language development. Related to in-service teachers, research on these experiences tend to be focused on collaborative, classroom-based experiences with a small number of teachers (e.g., Musanti, Celedón-Pattichis, & Marshall, 2009). For example, Chval, Pinnow, and Thomas (2015) found that longitudinal collaboration between a mathematics teacher educator and a teacher involving lesson-planning meetings focused on language use and development helped the teacher develop a specialized knowledge of language planning and development. Over the course of several months, these efforts translated into “marked improvements in [one EL’s] willingness to participate in whole-class discussions and the academic quality of his contributions over time” (p. 111). In studies such as this, collaborators helped teachers shift from conceptions of mathematics and language as separate to a more integrated notion of how mathematics and language are intertwined and must be developed together.
Despite the promise of these findings, a separate study based on a survey of 181 K–12 U.S. teachers showed that teachers continue to feel unprepared to teach mathematics with ELs, especially as compared with teaching non-EL learners, and that more opportunities to participate in PD related to teaching ELs does “not correlate significantly to enhanced teacher self-efficacy” (Ross, 2014, p. 96). Although the specifics of these PD efforts were not given, this finding indicates that experiencing additional PD may not improve teachers’ feelings about teaching ELs and shows a need to develop evidence as to which practices and structures support in-service teachers in learning to teach mathematics with ELs effectively and increase their self-efficacies for teaching ELs.
In addition to studies of EL-specific PD, two studies were focused on aspects of policy related to teacher education. Both studies were conducted in the United States, and the researchers examined the effects of policies regulating language instruction. Neither was a study of PD specific to mathematics and ELs; rather, the focus was on the ways in which mathematics PD is influenced by the policies. In both instances, the authors found that the availability of PD opportunities was subject to changing federal, state, and school policies focused on language instruction (Battey et al., 2013; Kaufman & Stein, 2010). The policies examined in these studies were found to regulate language instruction from a deficit perspective. Moreover, because race and language are often intertwined, policies related to language may further marginalize students of color and students from nondominant-language backgrounds. Thus, studies such as these problematize such policies and document their ramifications on teaching.
PST Education
Studies of PST education in relation to the mathematics education of ELs broadly fell into one of three categories: studies to examine PSTs’ perspectives related to teaching mathematics with ELs, studies to examine PSTs’ practices related to teaching mathematics with ELs, and studies of PSTs who were themselves ELs.
In studying PSTs’ perspectives related to teaching mathematics to ELs, the researchers documented existing views; they did not conduct interventions. For example, McLeman, Fernandes, and McNuttly (2012) surveyed 292 PSTs and concluded, “Exposure to EL issues is one of the most important factors to helping PSTs have non-deficit views” (p. 125) about ELs and “When PSTs have had exposure to EL issues, they are more likely to understand the language demands of mathematics” (p. 125). In contrast, in a small qualitative study, Bunch, Aguirre, and Téllez (2015) found that exposure to EL issues did not guarantee meaningful change in PSTs’ conceptions; PSTs continued to hold unsophisticated notions of academic language. Thus, even when teacher learning related to mathematics and ELs is provided, the extant research is not conclusive on whether or how it may affect teachers’ perspectives of mathematics and language.
Researchers have also documented PSTs’ and teacher educators’ practices related to teaching mathematics when working with ELs. Essien (2010) examined teacher educators’ practices for preparing PSTs to work in multilingual classrooms and found that teacher educators focused on the use of code switching and the use of linguistic metaphors. These practices were similar to those Kasmer (2013) documented in a study of practices that U.S. PSTs implemented when teaching mathematics in a study-abroad experience in Tanzania. In a later study, Essien (2014) found that despite teacher educators’ awareness of the multilingual context in which their PSTs would teach, their practices centered on developing PSTs as learners of mathematics rather than teachers of mathematics in multilingual classrooms. The lack of focus on the latter resulted in PSTs being underprepared to teach in multilingual contexts.
In seeking to support ELs, educators commonly assume that having teachers who are former ELs or who speak ELs’ primary languages would benefit ELs. Research does not necessarily support this assumption. PSTs who speak the language of their students are not necessarily readily able to use that language effectively when teaching mathematics (Vomvoridi-Ivanović, 2012), and they may feel uncomfortable teaching in that language because of a lack of academic language or because of societal norms that uphold English as the language of schooling (Chitera, 2011; Thornton, Giles, Prescott, & Rhodes, 2011). The continued dominance of English in schools has resulted in “an environment where maintaining a language other than English is considered an obstruction to developing proficiency in English” (Vomvoridi-Ivanović, 2012, p. 105). In response to bilingual PSTs’ lack of preparation to use their L1 resources, researchers (e.g., Chitera, 2011; Thornton et al., 2011; Vomvoridi-Ivanović, 2012) have suggested that programs include coursework to address the connections between language and mathematics and work to support bilingual PSTs’ in expanding their academic language in L1.
Reflections
Teacher education research specific to teaching mathematics with ELs remains sparse and varied in foci, resulting in a lack of depth in any one area of teacher education. This shortcoming is particularly true of research related to purposeful preparation of teachers, both in-service and preservice, in strategies for teaching mathematics with ELs. Just two of the articles we surveyed (Chval et al., 2015; Musanti et al., 2009) were focused specifically on PD related to teaching mathematics with ELs; both were at the elementary school level and had sample sizes of just one teacher. The need to understand how to support the thousands of in-service teachers, including secondary school teachers, in effectively teaching this quickly growing population of students is great, particularly given the documented lack of preparation specific to teaching ELs (Ballantyne, Sanderman, & Levy, 2008) and given teachers’ continual feelings of being unprepared to work with ELs (Ross, 2014).
Moreover, most of the articles documented existing perspectives and practices regarding the mathematics education of teachers. Although these studies provide an understanding of teachers’ work with ELs absent intervention, we, in the field, have little understanding of specific practices necessary to teach teachers how to teach ELs mathematics effectively. Moreover, given the articles we reviewed, understanding what is effective in what context is difficult to understand because the contexts were not always clearly defined. Furthermore, contexts of only small numbers of ELs with a variety of L1s are not well represented in the literature.
Although we found variation in the researchers’ theoretical perspectives, attention to sociopolitical power and policy is evident across much of the work in this section. Several researchers (Battey et al., 2013; Kaufman & Stein, 2010) highlighted the need to examine the particular political context in which studies are conducted, particularly because school and district leaders continue to view mathematics as detached from language. Moreover, the prevalence of sociocultural perspectives among these authors reinforces the need to account for local social contexts and discourses in development of teacher education programs. This research shows that teachers bring ways of being that often inhibit their abilities to acknowledge, value, and leverage ELs’ multiple mathematical knowledge bases (Turner et al., 2012). Devising and understanding processes that support teachers to bridge this political divide is critical.
Discussion
We leveraged a sociocultural perspective to synthesize the literature, and this perspective led us to interrogate the ways in which language and context were considered in each category. Below, we discuss the various perspectives in the literature, assertions based on key findings of the review, with calls to action for teachers and researchers engaged in this work.
Perspectives Across the Domains
The work we reviewed was conducted within a political landscape; it is not isolated from larger political trends. Researchers have concluded that unproductive language ideologies, broadly (e.g., Gonzalez & Melis, 2014) and specifically with teachers (e.g., de Araujo, 2017), as well as beliefs about what is best for ELs are often rooted in deficit notions of children and families who might speak other languages at home (Razfar, 2012a). These ideologies inhibit implementation of optimal pedagogy for ELs. Researchers have begun to explore how shifts in language ideologies and discourse about ELs intersect with mathematics teaching and learning. Such shifts may lead to new social arrangements for ELs’ engagement, participation, and learning in mathematics.
Most of the recent research on the mathematics education of ELs is based on sociocultural perspectives. Given the sociopolitical landscape researchers have responsibility to carefully frame research on the mathematics education of ELs to avoid deficit framing of learners. One way to begin such framing is to explicate and acknowledge the perspective(s) on language that undergird our studies. Such clarity on theoretical commitments and assumptions will enable others to interpret research more meaningfully. A second, and perhaps more difficult, way forward is to acknowledge not only the sociocultural dimensions of language in mathematics (Moschkovich, 2002) but also the sociopolitical dimensions of language in school mathematics (Gutiérrez, 2013). The interconnected nature of language and mathematics brings us to a point at which debate regarding the usefulness of theoretical frames in research on ELs in mathematics is needed. Consequently, researchers should critically examine the collective discourse related to ELs and promote frameworks that are free from tacit deficit framing and make recommendations to fundamentally transform mathematics teaching and learning arrangements for ELs.
Assertions Based on the Literature
Our analysis enabled us to assess the state of the field and to propose opportunities for advancing the teaching practices and research related to ELs in the mathematics classroom. Below, we discuss these assertions in connection with our findings.
Research Contexts Matter, but Some Contexts Are Missing
Across the studies (Table 2), most (about 66%) were conducted in the United States, and from these, the majority were conducted in urban contexts and settings such as California, where ELs have a long history in schools. However, in the United States, we know that the numbers of ELs are currently growing fastest in rural contexts and in states that were not traditional destinations for new immigrants (McFarland et al., 2017). Therefore, in the future, research should take place in these contexts. We also noted that researchers have described the location of the research, the student population, and the teachers using widely varying terminology and levels of specificity. This variation made our task of synthesizing research findings and identifying general trends across studies challenging. To make researchers’ efforts more cumulative, we suggest that, moving forward, researchers consistently describe the following in as much detail as possible: study setting (e.g., school, district, etc.), student demographics, student language background, and teacher demographics including language/educational background. These specific descriptions will enable researchers to build on and extend one another’s work.
Labels for Linguistically Diverse Students Can Impede Mathematical Learning
Schools, classrooms, and teachers must value the resources that ELs bring to their mathematics learning (e.g., Civil, Planas, & Quintos., 2005; Razfar, 2012b; Turner & Celedón-Pattichis, 2011). Researchers have started to challenge assumptions implicit in the terminology used to describe students who are learning the LOI. The label English learners implicitly highlights what these students lack and, consequently, frames them as deficient (though English learners is preferable to the older term limited English-proficient that explicitly uses deficit framing). Furthermore, the label obscures the resources linguistically diverse students bring to school and may reinforce harmful policies focused on developing English proficiency above learning in content areas.
With Support, ELs Can Thrive in School Mathematics
Our findings bring to light the importance of building for ELs intellectual spaces that have long been denied to this population of students (e.g., participation in group work in mathematics, Esmonde, 2009). Participation in rich mathematical communication in classrooms is not only possible for ELs but also vitally important for their development of mathematical understandings (Zahner et al., 2012). Although not included as a distinct category in this review, research on schooling structures shows that schools provide intellectual spaces for ELs to participate and engage with higher level mathematics (Gutierrez, Willey, & Khisty, 2011), highlight the often harmful effects of tracking and course placements (Mosqueda, 2010; Mosqueda & Maldonado, 2013), and identify persistent inequities in everyday schooling experiences that affect ELs’ mathematics learning (Barajas-López, 2014). Additionally, schools can value and leverage insights provided by families of students who are ELs (Civil et al., 2005).
Mathematics Teachers Need Additional PD and Support to Teach ELs
When mathematics educators propose ideas for supporting ELs in mathematics, the supports are often framed either as technical assistance (i.e., eliminating unnecessary linguistic complexity) or as sets of tips and tricks for engaging ELs. Those recommending such strategies may ignore additional sociopolitical elements related to teaching immigrant students or students from nondominant communities. Moving forward, researchers must continue to examine these experiences to generate an evidence base on which practice can be built. The field needs more studies of effective teacher education for teachers of ELs focused specifically on mathematics. Given our focus on studies specifically related to mathematics, we did not address studies and program evaluations of initiatives to support teachers of ELs that have a wider focus across content areas (e.g., WIDA, QTEL [Quality Teaching for English Learners]). We note that these content-general efforts and efforts of those who work specifically with preservice and in-service teachers are often disconnected. Thus, one area in which the literature base and teacher education efforts can be strengthened is in relating research from these larger, EL-focused efforts with mathematics-specific efforts.
Calls for Action
We acknowledge that educating ELs is still an emergent field of research, and we hope that this review prompts a conversation in the field of mathematics education and education more broadly. In alignment with the research to date, we call for action in the areas discussed below.
Expansion of Research on Learning Experiences for Teachers
Currently, we in the field have no extensive knowledge base on the preparation of mathematics teachers who teach ELs, and divergent findings point to the complexity of teaching mathematics with ELs. On one hand, case study researchers highlight that teachers’ mathematics instruction with—or perceived ability to teach—ELs is directly influenced by access to, and content of, PD opportunities (e.g., Celedón-Pattichis, 2010). On the other hand, larger scale survey-based research indicates that PD opportunities to develop efficacy with mathematics instruction of ELs were not significantly correlated with teachers’ perceived abilities to teach ELs compared to their perceived abilities to teach non-EL learners (Ross, 2014). Overall, research results are not conclusive as to what form of PD might help teachers feel more comfortable teaching ELs. Moving forward, a key commitment is needed to determining what teachers need to learn and experience to support students learning the LOI in their instruction. This commitment may necessitate difficult discussions about the sociopolitical dimensions of education (Gutiérrez, 2013). Relatedly, teacher education programs cannot simply be imported from one location to another; contexts must be considered in designing learning opportunities for teachers (Essien, 2010). Additionally, this work needs to be grounded in research rather than debated in ideologically charged terms lacking connection to students’ and teachers’ experiences. Creating curriculum is not enough; we educators need longitudinal studies to determine whether the curriculum is helping students and teachers be successful, with success defined in myriad ways beyond standardized-test scores.
Use Diverse Forms of Evidence in Research
The majority of studies in this review were conducted using qualitative methodologies. As researchers who use qualitative methods, we do not accept the general critiques of qualitative methods; we do, however, see a need to draw on more diverse forms of evidence beyond individual case studies. We do not discount qualitative research: If students are learning through talk, then qualitative studies may be best suited for describing their learning processes. However, we also recognize a critical need to make the research on ELs in mathematics more cumulative and to produce the kinds of research policymakers use to craft policies (Burkhardt & Schoenfeld, 2003). Research evidence is necessary to design equitable learning environments, develop teaching practices, and design instruction for ELs in mathematics classrooms that align with current social theories of learning. Although we recognize the difficulty in, for example, assessing classroom discourse, we know that what is assessed is also what is taught. Thus, because research included in this review highlights the centrality of participation in rich mathematical discourse, we must find diverse forms of evidence aligned with theory and practice for the sake of new forms of belonging, participation, engagement, and success in mathematics teaching and learning spaces among ELs.
Conclusion
Issues of language learning have long been part of teaching and learning, including within mathematics. Yet, as educators, we tend to operate on faulty, or incomplete, assumptions about ELs, language, and mathematics learning, and as a result, we continue to provide insufficient opportunities for ELs to thrive in mathematics. Our disheartening past, coupled with an increasing diversity of students in schools worldwide, necessitates further research incorporating asset-based discourses and practices to support ELs in mathematics. In highlighting the advances related to the mathematics education of ELs and presenting avenues for continued study, we have outlined a robust rationale for this work.
Footnotes
Notes
Authors
ZANDRA DE ARAUJO is an associate professor of mathematics education at the University of Missouri, USA; email:
SARAH A. ROBERTS is an assistant professor of mathematics education at University of California-Santa Barbara, USA; email:
CRAIG WILLEY is an associate professor of mathematics education at Indiana University-Purdue University Indianapolis (IUPUI), USA; email:
WILLIAM ZAHNER is an associate professor of mathematics at San Diego State University, USA; email: