What role does vocabulary instruction play in the math classroom?
It plays a foundational role serving all students, especially English learners, according to Rita Paolino, an English-as-a-second-language lead teacher at Falling Creek Middle School in the Chesterfield County district in Virginia, and Mary LeFebvre, a virtual math instructor in the district.
Paolino and LeFebvre co-teach at a school where English learners account for nearly half of the student population. The duo recently presented at this year’s WIDA conference, a national gathering of teachers and administrators working with English learners. Their session highlighted how all teachers can help make math more accessible through targeted vocabulary instruction.
“As teachers, oftentimes we tend to focus on the content and forget a very important part of it, which is language. Content is delivered through language. If we don’t focus on how to deliver the content, we will make learning extremely challenging for our students,” Paolino said.
Equitable teaching of math involves recognizing language in math
To intentionally teach vocabulary in a math classroom, teachers must first understand that every student is a language learner and every teacher is a language teacher, Paolino said.
Part of that mindset shift includes recognizing the distinct language of math, which contains specific vocabulary terms, punctuation and grammar rules, and its own alphabet.
“The further you go in math, the less numbers you see,” said LeFebvre during the conference presentation.
Math is all about patterns, she added. Language is also about patterns, and it can help students use context to understand problems in any subject area.
“As teachers, we want to condition ourselves to think less of ‘I teach a subject, like I teach math,’ and think more along the lines of ‘I teach students how to think and communicate like subject matter experts, like mathematicians,’ ” LeFebvre said.
Vocabulary is the building material students need to participate in academic learning, Paolino said. And in math, vocabulary and broader language development occur across three levels or dimensions: word or phrase, sentence, and discourse.
For example, at the word or phrase level, a student in a math class might say: “These two ratios are the same.” Teachers should instead help students use the specific math term needed—in this case “equivalent.”
Next, students need to learn how to communicate relationships between ideas at the sentence level. For example, students might say: “The ratios are equivalent because both ratios represent the same relationship between the number of red tiles and blue tiles.”
In math, it’s important for students to be able to prove and explain why they got their answer and how they went about getting it, LeFebvre said. Teaching students subordinating conjunctions in math class such as “because” or “therefore” helps students reach this level of communication.
Finally, students must then also learn at the discourse level how to put precise mathematical vocabulary and complex sentences together into a complete, organized thought. For example, a student might say: “First I compared the two ratios. I multiplied both quantities in the first ratio by the number two, which gave me the second ratio. Therefore, the ratios are equivalent because the relationship between the two quantities stays the same.”
Educators share strategies on teaching language in math
To intentionally teach vocabulary in math class, LeFebvre and Paolino offer strategies such as using a structured vocabulary routine.
In this activity, teachers introduce a word; have students repeat it; provide a formal definition and a student-friendly definition; provide a special characteristic of the word, just as the prefix “-bi” often means two; and have students participate in turn and talk where they use the word in sentences.
Repetition of vocabulary is key, and it’s especially important for English learners to practice academic language verbally and in writing whenever possible, LeFebvre said.
For instance, teachers can assign pair or group work, and teachers can repeat aloud key words they hear students use, offering praise while reinforcing the words for the rest of the class. In the event that ESL teachers and content teachers can co-teach as LeFebvre and Paolino do, both teachers can also model the types of conversations students should be having in group or pair work.
Teachers can also allow students to help write out word problems to help get practice in writing. At the end of an assessment, LeFebvre also includes a questionnaire that says, “Write anything else you know about this topic.”
“Get students writing out their thinking, because when we write things down, it’s just another form of being able to retain that information,” LeFebvre said.
There are also some key mistakes to avoid in all this, Paolino said. For instance, teachers shouldn’t teach too many vocabulary words at once; they shouldn’t limit vocabulary instruction to simply repeating a definition, as students need opportunities to put terminology into practice; and teachers shouldn’t slip into casual, simplified language. The goal is to make language accessible with scaffolds, not simplify it.
The co-teachers also advise all educators working with immigrant students in math class to recognize cultural differences in math language. For example, some countries use commas to denote decimal points.
