Research in Brief - March 2008 - Volume 108 (3)

Language Proficiency and Mathematics Learning

Xi Chen & Yeping Li

Mathematics is important for success in school, not just for some students but for each and every student (National Council of Teachers of Mathematics [NCTM], 2000). However, learning mathematics is not an easy task for many students, especially those who also need to overcome the language barrier (e.g., Winsor, 2007). At a time when we recognize and enjoy the advantages of cultural and linguistic diversity made possible in this great country, an achievement gap in school mathematics seems evident across groups of students whose language proficiency in English differs (e.g., Abedi & Lord, 2001; Cocking & Chipman, 1988; Mestre, 1988). Although it is not quite clear yet how our brain processes language and mathematical information, findings from recent studies suggest that people's arithmetic processing in the brain is shaped by different language experiences as well as other cultural factors, such as mathematics teaching and learning (e.g., Tang et al., 2006). A better understanding of students' language and some other cultural experiences thus becomes very important to mathematics educators and teachers, when we consider and develop possible interventions for improving our students' mathematics learning.

Language, used to define mathematical concepts and express mathematical ideas, plays a key role in mathematics learning and teaching. Children with different language backgrounds may think about mathematics differently, and it may also influence their mathematics performance (e.g., Miura, Okamoto, Kim, Chang, Steere, & Fayol, 1994). For example, some researchers indicated that the number naming systems of languages like Japanese, Korean, and Chinese are held to endow speakers with an inherent advantage in understanding place value concepts and the Base-10 system (e.g., Miura & Okamoto, 1989; Miura et al., 1994). In other words, they found that number naming in Asian language is organized with structures of tens and ones and place value can be viewed as an integral part of that cognitive representation. On the other hand, non-Asian language speakers (e.g., French, English, and Swedish) may lack such an advantage in understanding the meaning of place value. Some researchers also indicated that mathematical terms in Chinese have been developed in a descriptive and conceptually clear way, and can “express concepts through a combination of everyday words, just like the ordinary written and spoken Chinese language“ (Han & Ginsburg, 2001, p.204). Thus, the results led researchers to argue that “the more Asian schooling, the greater the competence in Chinese language, and hence, the higher the performance on the mathematics test” (p.217).

In the United States, educational researchers identify students whose first language is not English in multiple ways (e.g., ESL students, ELL students, LEP students or bilingual students). Here we use Hofstetter's term of English Language Learner (ELL) students to identify those who come from places where English is not spoken at all or where limited English is spoken (Hofstetter, 2003). A number of studies have focused on ELL students' mathematics performance (e.g., Bernarodo & Calleja, 2005; Clarkson, 1991; Mestre, 1988). Relevant results showed an achievement gap in mathematics between ELL students and non-ELL students (e.g., Cocking & Chipman, 1988; Mestre, 1988). These results suggest that students' language competencies impact their mathematical performances over a number of different contexts including word problems. Thus, educational researchers also tend to agree that language proficiency (or competency) is one of the important factors influencing ELL students' mathematics performance (e.g., Bernarodo & Calleja, 2005; Clarkson, 2007).

In order to reduce the mathematics performance gap between ELL students and non-ELL students, researchers have studied possible relationships between language proficiency and cognition. Cummins (1979, 1981) put forward the idea of common underlying proficiencies (CUP). According to Cummins (1981):

(B)ilingual proficiency is represented by means of a ‘dual iceberg’ in which common cross-lingual proficiencies underlie the obviously different surface manifestations of each language. In general the surface features of first language and second language are those that have become relatively automatized or less cognitively demanding whereas the underlying proficiency is that involved in cognitively demanding communicative tasks. (p. 38)

Based on this idea, Cummins hypothesized that if students understand academic concepts in a discipline and express those concepts in their first language, the concepts and language would serve as a bridge or as common underlying proficiencies for the ELL students to learn the English needed to express those underlying concepts. Cummins and other researchers pointed out the importance of the language proficiency in their first language for ELL students' academic achievement (e.g., Clarkson, 1991; Clarkson & Galbraith, 1992; Cummins, 1979, 1981). Consistently, research showed that ELL students highly competent in two different languages were mathematically superior to their monolingual peers and to other ELL students who master one language. ELL students who are weak in both languages are also mathematically weak (Clarkson, 2007; Secada, 1992). Secada confirmed such a finding in the United States with Spanish/English bilinguals.

Applying Cummins' theory, early studies of ELL students' mathematics learning emphasized students' vocabulary understanding and language comprehension skills (e.g., Cuevas, 1984). In particular, researchers argued that ELL students would face more difficulties in solving word problems, understanding vocabulary, or translating from English to mathematical symbols (e.g., Bernardo, 2002). They may also have difficulties when the conceptual relationships expressed in the text do not map on the quantitative relationships in the problems (Riley & Greeno, 1988). For example, Clarkson (1991) found that 39% of the errors that ELL students made in his study were related to language (e.g. reading mistakes, comprehension errors). Bernardo conducted the study to determine “whether the language of word problems in arithmetic would have an effect on how the language minority students understand and solve word problems” (p.293). The results showed that ELL students' performance in solving arithmetic problems was poorer with word problems presented in either the first or second language than the case with the same problems presented in a purely numeric format. Moreover, Bernardo found that ELL students had better comprehension of the word problems when it was written in their first language. Abedi and Lord (2001) also found that linguistic modification of test items results significant differences in mathematics performance. Therefore, at least for word problems, “a task that has a clear linguist component, the application of mathematical knowledge and skills is affected, possibly even constrained, by whether the students is able to effectively undertake the requisite linguistic processes” (Bernardo, 2002, p. 294). Thus, studies indicated that students' vocabulary acquisition and language comprehension skills are central issues that ELL students need to grapple with when learning mathematics.

According to NCTM standards (1989, 2000), students are now expected to communicate mathematically, both orally and in writing, and to participate in mathematical practices such as, explaining solution processes, describing conjectures, proving conclusions, and presenting arguments. Therefore, researchers noticed that vocabulary understanding and comprehension skills are only limited to the surface level and not enough for bilingual students' mathematics learning (e.g., Campbell, Adams, & Davis , 2007; Moshkovich, 2002). The relationships between language proficiency and mathematics education become more complicated, and researchers now tend to address how ELL students are affected by this emphasis on mathematical communication and how classroom instruction can support these students' learning to communicate mathematically (e.g., Brenner,1994; Winsor, 2007). Learning to communicate mathematically (e.g., Moshkovich, 2002) is now seen as a central aspect of what it means to learn mathematics, and language is taken to play an important role in shaping students' mathematics thinking.

Moschkovich (1999) emphasized the need for ELL students to experience the development of mathematical content and argumentation practices, as well as to experience the process of vocabulary building. Therefore, the students must be encouraged to participate in mathematical discussions that focus on justifying thinking and interpreting meaning in mathematics classroom. Moreover, students' sociocultural experience also needs to be considered (e.g., Campbell et al., 2007; Moschokovich, 2002). According to Moschkovich (2002), ELL students' learning of mathematics can be described as constructing multiple meanings for words rather than acquiring a list of words. This perspective takes mathematics as another language, and considers differences between the every day language and mathematical registers for the same concept (Moschokovich, 2002). It aims to describe how students' language use can move closer to the mathematical register of the concept. Moschkovich (2002) indicated that the “multiple-meanings perspective certainly adds complexity to our view of how language and learning mathematics intersect” (p. 195). Nevertheless, this perspective can help uncover possible misunderstanding in classroom conversations and be useful in pointing out ways to support ELL students in developing their mathematical communication, by “clarifying multiple meanings, addressing in the conflicts between two languages explicitly, and discussing the different meanings students may associate with mathematical terms in each language” (Moschkovich, 2002, p.206).

Some other mathematics educators also explored different approaches to support students' mathematical communications. For example, Barwell (2003) studied how elementary ELL students make sense of mathematics through the interaction with their monolingual peers. Winsor (2007) developed an approach that builds upon Brenner's (1994) framework for the forms of mathematics communication: (1) communicating about mathematics means that students can describe their own problem-solving processes and their thoughts about those processes; (2) communicating in mathematics means that students effectively use the language and symbols of mathematical convention; and (3) communicating with mathematics means using mathematics as a tool in solving meaningful problems. In order to help students learn mathematical vocabulary, Winsor suggested using Word Squares. In particular, students need to write the mathematical term in their own language on one side and write the mathematical term in English on another side. Students are asked to write the definition of the mathematical term in whichever language they understand best. But the definition needs to be in the students' own words, not just copied from the textbook. In the lower right quadrant of the Word Square, students include a representation of the mathematical concept. The teacher encourages students to first develop the mathematics concept related to their first language understanding. Moreover, cooperative learning is a strategy that is often suggested for ELL students' learning of mathematics (e.g., Barwell, 2003; Winsor, 2007). Students within a group are not homogeneous in their language ability. Therefore, students with different language proficiencies can interact in order to improve the group's mathematical communication. Varying the group's composition can further provide students the chance to gain possible insights from many different students' mathematical points of view. Certainly, group learning can also allow students to learn collaborations and participations that can support their own mathematics learning in this culturally and linguistically diverse community.

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