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It’s interesting, I observe a lot of math lessons, strategies, and procedures being taught. However, in terms of vocabulary being taught, I most frequently hear the terms numerator and denominator. Yet, other than hearing teachers describe that the d in denominator stands for down, I rarely ever see or hear mathematics vocabulary being explicitly taught and used as part of the classroom vernacular. How do we get students to understand the language of mathematics, take it up and use it as a part of their everyday language?

Monroe and Orme (2002) indicate that the language of mathematics is similar to reading comprehension; students must know the vocabulary to understand what they are reading; however, several obstacles can interfere with vocabulary acquisition. One such obstacle is the rarity in which students are provided the opportunity to speak mathematically outside of the classroom. Additionally, many mathematics teachers mistakenly disregard teaching vocabulary in the classroom further limiting students’ ability to learn, build and broaden their individual vocabularies.

If the research from Monroe and Orme still stands true today, then we as educators must hold ourselves accountable, so that we can hold our students accountable for using the language of mathematics. Why use the word phrase “number sentence”  or the word “answer” with young students when we can just as easily integrate the terms equation and unknown value into our discussions?

Monroe, E. E., & Orme, M. P. (2002). Developing mathematical vocabulary. Preventing School Failure, 46(3), 139-142.

Mathematical vocabulary in our warm-ups.

I often, but not always like to stay with one type of warm-up for a whole week. The focus upon one type of warm-up allows the class and I to delve deeper into a strategy, use practice to strengthen our skills and connect the language of mathematics to the work we are doing together.

For example, if we are describing everything we know about a particular number we can identify and discuss place value (ones, tens, thousands). We can talk about rounding a number to a specific place value, and we can introduce and use the word decompose when describing place value, or in the case of choral counting we can connect numbers like 8 to units of measure like cups, ounces, and quarts.

With warm-ups, we have multiple opportunities to say, “I used the commutative property because I ____ . or I used the associative property because I _____.” I can notice and name when I see students decomposing a number by place value or compensating to make an operation easier and then ask them to “try” using those same words themselves.

Instead of insisting on mastery of the language on days 1 and 2, I can instead facilitate multiple opportunities to discuss the mathematics being addressed on any given day, notice and name the language when I see an opportunity for it and encourage and recognize students when they implement the language of mathematics.

*By the way, the language of mathematics is an excellent topic for parent engagement workshops.

Mathematics language in our problem-solving.

The language of mathematics must run through every area of our mathematics instruction. For years I have worked with schools, many of which had high populations of English learning students and many without, and again and again, with both types of student populations the language of mathematics stood in the way of success for many students.

For many students, it was not until they took the state assessment that they had to solve problems with the words one-tenth or one-hundredth. In class, many, many students had only heard and been expected to use the words (zero- point -one to describe situations involving one-tenth or zero- point- zero-zero one to describe one-hundredth, you can see how this wording can make decimals slightly more confusing).

Students are also often taught to say add a zero to a number to go from 42 to 420 when in actuality they are multiplying by ten and would benefit from repeating the phrase ” ___ is ten times as much as ___” over and over again. Students who have had limited exposure to the language of mathematics are in for quite a rude awakening when they sit down to take state tests.

Word problems often present a challenge to both students and teachers not solely because of the mathematics involved, but the language used within the word problems. For example, compare problem types such as

“Mary has 15 balloons. That is 7 more than Michael. How many balloons does Mary have?

Many students cherry-pick the word “more” from the problem and automatically add the two values (15, 7) together. When solving word problems reading comprehension must play an equal role in instruction in order for students to build true meaning and have success.

Additionally, a reoccurring part of the state SBAC or CAASP test (depending on where you live) is matching an equation to the correct word problem.  I have included an example from the state practice test below to give you an idea of the stamina, reading comprehension, and model making students will face.

CAASP, 5th Grade Sample Problem, 2019 Practice Test

Understanding how mathematics connects to language must play a consistent role in the mathematics classroom for all students, but especially for students who are just learning the English language. The everyday use of mathematics vocabulary in the classroom accomplishes 3 major goals of the California English language Development standards: 1) it’s collaborative, students can exchange ideas with one another, 2) it’s interpretive, students can read and listen in for key ideas,  analyze and learn from the work of others, and 3) it’s productive, students can express their ideas while advocating for their own strategies and strategies of others.

Mathematics language in our explanations.

A simple number or a value is not a thorough answer to a mathematics problem. In fact, I tell students all the time, no engineer, designer, chef, or scientist is standing in a laboratory or conference room yelling out 10. The answer is 10. Professionals have to explain what the 10 represents, is it 10 inches, 10 decibels, or 10 degrees. Professionals must also explain how they came up with their final number and why it’s the best choice. I believe that if Elon Musk has to explain his reasoning that so should your students.
An explanation that includes a given value should be the norm in the mathematics classroom because it ensures students understand the concept at hand and it provides an opportunity for students o position themselves as adding value to the mathematics community, students are seen by themselves, their instructors, and peers as more credible, and the classroom has an opportunity to learn from one another and perhaps see a problem or solution from a different perspective. Explanations are opportunities for students to apply the language of mathematics.

Do students need to explain everything every day? No. Nobody has time for that. Explanations should be used in situations where the teacher is unsure of the student’s current understanding of a topic. Good student explanations should be used as a teaching source for other students, and explanations can and should be used at least 2-3 a week as a part of the mathematics problem-solving routine.

Mathematical language is not an extension of the mathematics classroom, it is a mainstay of the mathematics classroom. If we as educators commit to using the language of mathematics ourselves, we can hold our students to the same high standard. Additionally, exposure to mathematics is an equity issue because without explicit instruction and practice our students will in no way be prepared for the assessment they face. Lift mathematics vocabulary off of the page and into the minds and mouths of students.