How to teach math to ESL students

Useful strategies for teaching mathematics to non-native English speakers while also teaching new math vocabulary in English

• mathematics (noun): the study of numbers, quantity and space
• maths (British), math (American): mathematics

When I first started teaching ESL in a foreign country, one of the first classes that I taught was a math class for ESL learners. This is quite common in schools that have an intensive English program (IEP) where many different subjects are taught in English to students who are learning it as a second language. Despite some initial apprehension, I learned the following strategies early on that greatly helped me, which I continue to use to this day.

Build on existing knowledge

When introducing math topics to your students, try to do so along with topics, words, or concepts that they’re already familiar with. Don’t just leap into teaching new math-based English words to your students without some background support.

Instead, start the lesson with the words they’ve already learned and are comfortable with, then slowly introduce any new words or concepts into the lesson.

This is known in linguistic circles as “activating prior knowledge,” and it can enhance both English and math skills in many ways.

Activating prior knowledge:

• Builds on what students already know: Students are learning how to connect things they know to new concepts, which teaches them how to use prior knowledge in different contexts.
  
• Improves vocabulary memorization: When previously learned vocabulary is paired with new vocabulary words, word associations are formed, which makes it easier to remember the new words.
  
• Makes new concepts less intimidating: Incorporating concepts and vocabulary terms that students are both familiar and comfortable with helps to make new concepts less intimidating.

Incorporate visual aids

When introducing new math concepts to your students, you should do so with visual aids. While math problems are typically written on a board in front of the class, which is a type of visual aid that allows plus and minus signs to be seen by all, it’s simply not enough when you’re teaching both math and English at the same time.

You should therefore use visual aids that not only show math problems and the signs that go with them (plus, minus, multiply, divide, etc.), but also the spellings of words. Both the numerical and the written forms should always be shown to ESL students since they need to learn both.

When showing a plus sign on the board or a flash card, it should have the word “plus” spelled out below it, and for younger students, you should be walking them through how to spell it by reading each letter aloud (e.g. “P-L-U-S, plus!”).

Example of a math problem with both numerical and written formats:

• 1 + 1 = 2
• One plus one equals two

Create English-based math problems

This approach builds on the previously mentioned one but is more appropriate for more advanced students. Once they’re able to write full English sentences, you can have them write sentences that incorporate both math problems and English.

Example: write 3 – 2 in a sentence and solve it.

1. You could demonstrate this to your class by first showing students the numerical math problem (e.g. 3 – 2 = ?).

2. You could then write a sentence on the board, such as, “Doug had three apples and ate two. Now, he has one apple left.”

3. Next, you would give your students a new numerical problem on the board, then ask them to create a sentence with it.

This activates many different skills, including critical thinking skills, and will help your students learn both English and math more quickly with a single activity that combines both. While the example given is a simple one, you can make it more advanced with multiplication, division, or just about any other type of math problem.

Use cardinal and ordinal forms

You should also always be showing your students both the cardinal and ordinal forms of numbers when there’s an opportunity to do so. Cardinal refers to amounts and ordinal refers to positions.

They should know that both “one” and “first” correspond with the number 1, and they should be able to spell these words while also understanding them when they’re used in math problems.

As a versatile teacher, there are many times when you’ll need to use ordinal words in both your English and math lessons (e.g. “What is the third word in the sentence?”).

Your students will therefore need to eventually know these words when speaking and reading English, so you might as well teach them this while it’s relevant to both the subjects of English and math, which can enhance the learning of both.

Warm up with vocabulary words

You should start every lesson with a quick five-minute warm-up activity where you write both new and old vocabulary words on the board and have students repeat them.

The words should all be math-based words, with a mix of vocabulary that you’ll be covering for the first time in the current lesson and some of the words that have already been taught in previous lessons.

Examples of math-focused vocabulary words:

• add
• sum
• plus
• times
• divide
• minus
• equals
• product
• subtract
• multiply

This helps to familiarize the students with new words while jogging their memory when it comes to old words so they don’t forget what you’ve already taught them.

This should be a traditional vocabulary listen-and-repeat exercise where you simply point at the words, say the word aloud, then have your students repeat. You can also spell out the word after saying it aloud and have your students do the same.

Utilize English-based worksheets

While most of the previous tips can be helpful in the classroom, you’ll still want your students to practice their English and math skills at home as well. In this case, you can use English-based math worksheets, which are those that are specifically designed to teach both English and math skills. 

You can find these types of worksheets on many sites online and then print and download them for free. ISL Collective is one such site, which offers plenty of pre-made worksheets specifically for this purpose.

If you want worksheets that incorporate a specific topic or concept that you can’t find in pre-made worksheets, you can always make your own. You can do this either from scratch using Microsoft Word or by using free online tools, like Canva or EnglishClub Worksheet Maker.

Require sentence frames

As a form of scaffolding, which is any type of temporary support given to students while they’re learning, the use of sentence frames can help teach students how to blend both math and English in a practical way.

When carrying out activities that involve speaking, such as posting a problem on the board and then calling upon students to answer with the solution in front of the class, you should provide a sentence frame for students to answer with. This is a type of template that requires the student to respond in a specific format using the English words that you’d like them to practice with.

Sentence frame examples (from basic to more advanced):

• “The sum of ___ plus ___ is ___.”
• “The total is _____ because we add _____ to _____.”
• “_____ plus _____ equals _____ because we add _____ to _____.”
• “The answer to the problem is _____ because we divide _____ by _____.”

As your students solve solutions and answer in front of the class, you should encourage them to format their answers by using a sentence frame that’s written on the board so that every response is not only an opportunity for the responding student to practice both English and math, but for those listening to them to hear a repetition of how these two topics can be used together.

Support with manipulatives

While visual aids can help to show students both math symbols and their English spellings, this can be enhanced by also providing some manipulatives, which are physical, interactive materials that correlate with the topics. Many learners are kinesthetic learners, which means they like to learn with hands-on activities.

While teaching your math lessons, you can incorporate hands-on activities, such as by providing students with items that they can use to subtract, add, multiply, and divide, whether it’s blocks, toys, or even pieces of candy.

Although this doesn’t directly teach ESL skills, it makes it easier for you to appeal to all types of learners, and helping your learners learn the math aspect of a lesson more quickly allows them to also maintain their focus on the language aspect.

Parting advice: challenge your students

While you’re teaching, your students are learning what math problems look like and how to solve them. You can always help them refine these skills by encouraging them to create their own math problems instead of simply solving the ones that you provide.

Once they can make their own numerical math problems and solve them, you should then challenge them to do the same by writing their math problems as words in English. By sharpening both creative- and critical-thinking skills, you’re enhancing their math and English skills as well.