1 Emergent Bilinguals in Math Class

• Answer the following questions. Make sure you answer all four questions.

* Source: Adapted from Celedon-Pattichis & Ramirez (2012).

“Of greatest importance, in relation to placement for STEM learning, is their prior knowledge about STEM subjects, but children are not typically assessed for their content knowledge when entering U.S. schools. Instead, their identification and course placement, at least at the secondary level, is typically determined by their level of English proficiency.” (NASEM, 2018, p. 27)

Mathematics course placement should depend on students’ mathematical knowledge and performance, but in reality, other factors interfere with the decision of class placement of EBs (and many other marginalized students). For EBs in the United States, their course placement is typically determined by their level of English proficiency (NASEM, 2018). Placing EBs in math classes by their English proficiency harmfully impacts their learning because EBs in low-track mathematics courses are not usually provided with enough opportunities to learn rigorous mathematics. If EBs achieve English proficiency and move to non-ELL status, they are often placed in low-track mathematics classes again because they did not learn grade-level math up until that point (Umansky, 2016). We need to break this negative cycle that systemically fails our students. We must not withhold a rigorous math curriculum from EBs until they achieve English proficiency. Mathematical learning and English development must be pursued simultaneously in math classes. This chapter discusses how we can work towards these dual goals.

Dual Goal Challenges

These dual goals are not only EBs’ challenge but their teachers’ challenge as well. Mathematics teachers may feel burdened when they encounter EBs struggling to understand the language used in a math lesson or worksheet because teaching language is not their expertise (however, many states, including Iowa, require all content teachers to be equipped with disciplinary literacy methods). When we recommend math teachers improve EBs’ learning in both math and English, we do not mean that math teachers should teach English grammar. Rather, we encourage teachers to step away from correcting grammatical and spelling errors and instead focus on EBs’ mathematical ideas. To do so, we support following Moschkovich’s (2010) recommendations:

1. Treat students’ language as a resource, not a deficit: When your EBs use their home language, their everyday language with their own accents and/or emergent pronunciation, do not perceive it as a deficiency or obstacle for those who cannot use English well. Instead, use students’ languages as a resource to support their growing proficiency in their home language, English, and mathematics.
2. Address much more than vocabulary and support EBs’ participation in mathematical discussions as they learn English: Math teachers teach mathematical terminologies, such as function, variable, or fraction. But when they do, they should not just teach these words. Instead, they need to build the mathematical concept or meaning of a term with how to read and write the term and how to use it successfully in a sentence. The process for building a conceptual understanding requires various language activities, such as discussion, explanation, justifying, comparison, etc. Through these high-level language activities, rather than simply memorizing words, EBs can develop their English proficiency while they learn mathematics.

These two principles are based on a common view: EBs are capable. They can do rigorous mathematics, and they can do high-level language activities. Hence, teachers should focus on EBs’ mathematical ideas and reasoning, allowing them to productively grapple with high-level language activities while they make sense of mathematics. In other words, math teachers should provide EBs with ample opportunities to engage in both challenging mathematics tasks and high-level language activities. Math teachers teach mathematical concepts and procedures, but they do not have to focus on English itself, especially low-level linguistic skills such as accurate pronunciation, vocabulary, or spelling. You probably have seen EBs (and non-EBs too) become silent after their spelling or pronunciation is corrected because they do not want to make more mistakes. Note: if you really want to help EBs with their English spelling or pronunciation, you can model good examples rather than directly correcting their mistakes.

To engage EBs in mathematical reasoning and high-level language skills, setting learning objectives for both mathematical and language learning is essential. The next section explains what a language objective is and how to write an effective language objective for EBs in math classrooms.

Language Objective

Each lesson has its objectives or learning targets that a teacher aims for students to achieve at the end of the lesson. A mathematics lesson has mathematics objectives, such as “students will be able to distinguish a function from non-function relationships by using graphs.” For EBs, teachers can also have language objectives (Echevarria, Vogt, & Short, 2004), such as “students will be able to explain that a function is a relationship between two sets where one input corresponds to only one output by engaging in a class discussion, writing about functions, and drawing graphs.” To pursue dual goals for teaching math to EBs, setting objectives for both content and language is necessary.

Jennifer Himmel explains what a language objective is and how to write it as follows (for an in-depth look please, refer to Colorin Colorado),

Language objectives are lesson objectives that specifically outline the type of language that students will need to learn and use in order to accomplish the goals of the lesson. Quality language objectives complement the content knowledge and skills identified in content area standards and address the aspects of academic language that will be developed or reinforced during the teaching of grade-level content concepts (Echevarria & Short, 2010).

These objectives involve the four language skills (speaking, listening, reading, and writing), but they can also include:

1. The language functions related to the topic of the lesson (e.g., justify, hypothesize)
2. Vocabulary essential to a student being able to fully participate in the lesson (e.g., axis, locate, graph)
3. Language learning strategies to aid in comprehension (e.g., questioning, making predictions).

The idea of language objectives initially came from the SIOP Model. SIOP stands for the Sheltered Instruction Observation Protocol, which is a framework for organizing and assessing instruction specially designed for EBs

Here are some more tips for writing effective language objectives for EBs from Colorin Colorado:

1. Include high-level language activities where students discuss or justify, instead of only focusing on vocabulary learning (Moschkovich, 2010). This does not mean you cannot include any vocabulary learning in the objectives – teachers sometimes need to teach unknown terms. It means do not have only low-level language activities in the lesson.
2. Include productive language modes (speaking and writing), instead of just passive modes of language activities (listening and reading). By being able to see and hear students’ responses, this will also help teachers assess students learning in both mathematics and language.
3. Consider an extended view of discourse, such as drawing, representations (graphs, charts, tables, etc.), and gestures.

Mathematics is NOT a Universal Language 

To discuss how we can support EBs to succeed in learning both mathematics and English in a math class, we need to talk about what mathematics is. The traditional view of mathematics is that mathematics consists of numbers and symbols, and learning mathematics requires a huge amount of memorization. A common student complaint about mathematics is that mathematics is not related to their lives or the real world. This view is in the same vein as this common saying, “mathematics is a foreign language” or “mathematics is an alien language.” Some may say this due to the abstract appearance of mathematics. Others may say this because they feel they will never understand mathematics. This perception also reflects their belief that mathematics has nothing to do with the language they use every day. This belief also connects to the common assumption that mathematics is culture free and language free. This false view toward mathematics is one of the reasons why EBs face difficulties in math class, as there is no reason for a teacher to differentiate a math lesson for EBs if mathematics is language free. So, here is a question for you:

Is mathematics really free from culture and language?

As you might expect, the answer is NO. The quotes below emphasize how language has an important role in mathematical learning.

It is important to recognize that the content taught in STEM subjects is not separable from the language through which the content is presented (Schleppegrell, 2007). There is no language-free content; language use always presents some content, and most representations of content require some language use, even with multimodal resources for meaning-making (NASEM, 2018, p. 58).

One contributing factor to the difficulty ELs [EBs] experience is that mathematics is more than just numbers; math education involves terminology and its associated concepts, oral or written instructions on how to complete problems, and the basic language used in a teacher’s explanation of a process or concept (Echevarria, Vogt, & Short, 2010, p. 1)

When teachers say EBs are doing fine in their math class, it may imply that the EBs already learned the specific math concepts in their home country. In that case, they might perform well on certain mathematical tasks­–if the task does not include text-heavy content–although they may not understand what their teacher says and may not be able to verbally explain how and why they solved the task in that way. However, when EBs learn a new mathematical concept that they have not learned in their home countries, language then becomes a huge barrier because it is through language that the meaning of the new concept is delivered. If a verbal explanation is the only instructional tool, EBs will not understand the new concept, and they will soon fall behind in their math class unless their parents hire a bilingual tutor for them.

Language is not the only factor that influences EBs’ learning in mathematics. A few years ago, one high school EB student, let’s call her Sunni, explained what happened in her math class. She had learned how to solve quadratic equations by factoring in her home country, and the method was different from the common method used in the U.S. When she had a test on this concept, she used the method she learned in her home country. After receiving her test back, Sunni was shocked to discover that, her math teacher marked her answers wrong although the answers were correct. Even after Sunni explained how she solved the problems (she could not explain herself very well in English), the math teacher insisted she must use the method taught in the class.

You may or may not agree with Sunni’s math teacher, but regardless of the teacher’s decision, this is an example of the fact that mathematics is not a universal language. Not only are there different ways to read the term quadratic equation, but there are also different methods for solving quadratic equations in different cultural communities. People say 1+1=2 in any language or country, but in English, you will read the equation as “one plus one equals two” but in Korean, for instance, it will be read as “일 더하기 일은 이,” which does not make any sense to non-Korean speakers.

Even writing and reading numeric symbols are different in different cultures. Perkins and Flores (2002) show many examples of the differences between the US notations and Mexican notations and the reference document provided by TODOS: MATHEMATICS FOR ALL shows the differences between the U.S. and Latin American ones. Here are some examples:

Different notations in Asian countries and European countries also exist. For Asian countries’ mathematical notations, refer to the following table and for European notations, refer to this link:

The Algorithm Collection Project (Long Division Algorithms Collected in the European Union)

Table 1.2: Comparison of mathematical notation between the U.S. and Asian countries (I & Yu, 2017)

U.S.	Asian Countries
[latex]24/6[/latex]	[latex]\frac{24}{6}[/latex] or [latex]\text{24 ÷ 6}[/latex]
[latex]3.\overline{234}[/latex]	[latex]3.\dot{2}3\dot{4}[/latex]
May 15, 2007 5/15/2007	2007/5/15 or 2007.5.15. or more commonly used, 2007 년 5 월 15 일 2007 年 5 月 15 日
[latex].1[/latex]	[latex]0.1[/latex]
[latex]\text{6:4}[/latex], [latex]\text{6 to 4}[/latex], [latex]\frac{6}{4}[/latex]	Only [latex]\text{6:4}[/latex]

Can you see how complicated the challenges are that many EBs face in their math classes? When they cannot provide an explanation of their thinking process in English, their mathematical knowledge and performance are often devalued or not recognized, as you saw in Sunni’s case. As mentioned earlier, navigating the teaching and learning of EBs is complex for both student and teacher alike, but a language objective acts as a reminder to ensure mathematics and language development can happen at the same time. The benefits of language and being able to communicate mathematically for EBs will also be discussed in later chapters.

References

Celedon-Pattichis, S., & Ramirez, N. G. (Eds.). (2012). Beyond good teaching: Advancing mathematics education for ELLs. National Council of Teachers of Mathematics.

Echevarria, J., Vogt, M., & Short, D. (2004). Making content comprehensible for English learners: The SIOP Model. Allyn and Bacon.

Moschkovich, J. N. (Ed.). (2010). Language and mathematics education: Multiple perspectives and directions for research. Information Age Pub.

National Academies of Sciences, Engineering, and Medicine (NASEM). (2018). English Learners in STEM Subjects: Transforming Classrooms, Schools, and Lives. Washington, DC: The National Academies Press. doi: https://doi.org/10.17226/25182.

Schleppegrell, M.J. (2007). The linguistic challenges of mathematics teaching and learning: A research review. Reading & Writing Quarterly, 23(2), 139–159.

Umansky, I. M. (2016). Leveled and exclusionary tracking: English learners’ access to academic content in middle school. American Educational Research Journal, 53(6), 1792–1833. https://doi.org/10.3102/0002831216675404