Today’s posts wraps up a three-part series on English-language learners and math instruction.

## Total Physical Response for Math

*Jody Nolf is an associate language and literacy specialist at Vista Higher Learning**. **For more than 20 years, she taught English and reading to middle and high school students. Six years ago, she transitioned into the world of ESOL as a full-time coordinator and advocate for multilingual learners, creating professional development and working with educators around the United States:*

“Math is a universal language.” This is a common belief, and there is *some* truth to it. Educators need to understand that not all cultures use the same numerical symbols and function signs, and some ELs, like their English-speaking classmates, lack the basic number facts to succeed in their math classes, especially at the secondary level. However, there are some strategies and scaffolds teachers can implement to ensure success with their EL students.

An important step for math teachers in ensuring that their EL students are grasping content as well as language is to break down the mathematical steps in comprehensible language. Some EL students enter the classroom with a wealth of math proficiency in their home language, depending upon education background. These students only require language assistance, perhaps the use of a heritage dictionary or academic glossary, to be successful in class.

However, other students have not learned the basics of computation; therefore, language will be just one part of their journey to math proficiency. This is one reason why teachers should not be misled into believing that math is a universal language. While it is true that 5×5=25 in all languages, the symbols differ from culture to culture. For example, Chinese students must first understand that the English letter “x” also signifies “times” and that the English word “times” signifies multiplication as well as chronology. Many ELs need to be taught that the term “colon” is not only a grammatical symbol *and* a body part, but it also is a mathematical symbol.

Even students with a strong foundation in math can find the language daunting at first. I had a student from Israel a few years who was quite proficient in math. However, she struggled to get accustomed to the United States customary units system, using the metric system her entire life. Her heritage dictionary was of little help when she looked up the term “yard.” Her Hebrew dictionary only defined “yard” in terms of a “garden,” not as a unit of measurement. Eventually, these expressions and symbols become relatively easy to master to those with strong math skills. However, students lacking the basic foundations must first learn concepts such as number facts, multiplication tables, long division steps, etc.

Therefore, one way to break down the mathematical steps is through pictures and graphics. Word problems can be daunting for any student of math. Teachers can scaffold for ELs by using pictures to accompany the language. Visual cues can be invaluable tools for EL learners, especially newcomers. For example, if students are presented with a word problem asking them to find the area of a soccer field, the teacher can scaffold by inserting a picture of a soccer field, complete with shading of the inside and arrows directing the student to focus on the entire inside of the field. Once the students understand the task, the teacher can continue with the steps of calculating the area.

Another recommendation is to show a model response to a math problem. For example, if a math problem requires students to express their answers as a ratio, teachers should consider writing an answer expressed as a ratio as an example, a gentle reminder to students not to write the answer as a fraction or a decimal.

I encouraged a math teacher in my school to use this strategy, and she remarked that the students were more successful as a result. It should be noted, however, that ELs needed to understand the correct connotation of the term “colon” before continuing with the steps.

**Here is how the answer should have looked: **

1:4 (used as an example on the assignment for the students to model)

Teacher Explanation: “1, colon, 4” (Teachers can then have students repeat in choral form to practice oral fluency.)

A final strategy for teaching math to ELs is to employ TPR whenever possible: the Total Physical Response technique. Some educators might feel that this method is more appropriate for younger children. However, all children, especially ELs, can benefit from this strategy.

To teach the concept of slope intercept, it is far more effective to demonstrate gradual ascension (climbing stairs) rather than to merely define it in words. To teach addition, use students themselves as “numbers.” Five students in a group equals 5 (or 5×1). Two groups of five students equals 10 (or 5×2). The TPR method also encourages student engagement, thus resulting in greater understanding and retention of information.

## ‘Your Attitude Matters’

*Laleh Ghotbi is a 4th grade educator in a Title I school in the Salt Lake City school district. She came to the United States in August 2000 and earned two master’s degrees in English, her second language:*

One reason I love mathematics is because math operations are the same across the globe, making it easier for English-learners to learn math compared with other subjects. I am an elementary educator from a diverse background and work in a Title I school. Two years ago, I was recognized by Utah Leading through Effective, Actionable, and Dynamic Education (ULEAD), as one of the four most effective 4th grade math teachers in my state. Through my experience, I have learned a few tips and tricks for teaching math to students whose first language is not English.

1- **Your attitude matters.** I love math, and my students can tell. Over the years, my students have told me, “Math is not hard anymore” or “Math is my favorite subject now.” I believe that teachers’ positive attitude toward math is crucial in engaging students and helping them to fall in love with math.

2- **Create a safe learning environment**. The first step in teaching any subject effectively is having a classroom culture where kids feel comfortable enough to make mistakes and learn from them. When students feel safe, they take risks and become more creative. This is when we see students coming to the board, solving problems in new ways, and teaching the answers proudly to their peers.

3- **Use data effectively**. I always start the year by preassessing my students’ background knowledge on different math concepts. Every year, we inevitably have students who move to a higher grade level of math concepts without mastering the math skills from the previous grade. This learning gap has been especially true for the pandemic era when academic gaps have widened.

4- **Access prior knowledge**. When I teach math, I always start with examples from previous grades. This instructional strategy has two benefits: Kids remember that they have learned the concept before, so it isn’t an unfamiliar topic. And because we start with easier examples, students feel more confident in their problem-solving skills. For example, to teach the addition of four-digit numbers, I start with adding single-digit numbers and I say, “Let’s start at 1st grade.” I even joke with them by saying, “Little 1st graders, here is your first problem.” They laugh and start adding.

When I make sure everyone knows basic strategies such as counting up and modeling like number bonds, I move to the next grade-level skills and keep moving higher. I don’t stop longer than a few minutes on each lower-grade concept unless I see several kids showing signs of struggle. Math skills are built over years, and if our students don’t have the prerequisite skills, we cannot successfully teach them the new ones.

5- **Use a variety of teaching strategies**. When I teach, I use several visual models and manipulatives, so students can master the skills by moving from concrete to abstract learning. For instance, while teaching +/- of numbers that need bundling and unbundling, I use base 10 blocks and the language of a story that is easier for English-learners to understand. To illustrate, if we are solving 3425 – 1218 = I say, “Do we have enough ones to take away 8 from?” They say no, so I say, ”Ok, this number is poor, it goes and knocks on the closest neighbor’s door to borrow some more ones.”

My work on the board follows what I do with base 10 bocks. After whole-class instruction, my students get to practice with a partner that I intentionally chose for them based on different assessments. My students are my helpers; they teach one another, and both parties learn better in the process.

Using life examples and playing math games are other effective strategies to solidify what students have learned. Sometimes, I play one of my childhood games with my students. It was how my dad taught multiplication facts to me. Students skip count by any single digit that we are practicing. When they get to the number that is a multiple of that digit, they don’t say the number, they say “beep.” For example, learning the multiples of four would sound like 1, 2, 3, beep, 5, 6, 7, beep. My students love playing this game, even those who are struggling at multiplication facts.

I hope every teacher can fall in love with teaching math. Teaching math to students learning English does not have to be intimidating. Create a safe learning environment where making mistakes is allowed, recognize students’ current math abilities, unlock prior knowledge, and use a variety of teaching strategies such as visual models, manipulatives, peer support, and math games to enable English-learners to become successful mathematicians. Math is fun, play with it!

## ‘Content and Language Objectives’

*Lisbeth Banales is an elementary bilingual specialist and multilingual students’ advocate:*

There are different strategies to make math classes comprehensible for our English- language learners. The ones I used with my students and recommend to my teachers are using visuals with labels, sentence stems, sketching, manipulatives, pair-share.

Before you even start your lesson, the students need to see, understand, and own the content and language objectives. You can help by showing it using kid-friendly language and visuals that represent unfamiliar vocabulary and having students recite them.

Use visuals with labels that represent academic vocabulary. You can preview this vocabulary in their primary language before any lesson and then demonstrate the same visuals in the language of instruction to make a connection.

Sentence stems are perfect to facilitate the process of using the academic vocabulary. This particular strategy will depend on the students’ linguistic level. Some students will be able to produce simple sentences while other students will be able to use more complex sentence structures or frames.

Sketching has been one of my favorite strategies. It allows students to slow down to pay attention, especially during word problems, and show what they think it means while teachers can check for understanding and clear misconceptions.

Manipulatives should be always the first step students take when learning a new concept. As part of the CRA (concrete, representation, and abstract) model, using manipulatives helps students connect and understand by doing and practicing the concept. One thing to be aware of is that many newcomers have never used them before. Teachers need to name manipulatives and model how to use them for students to comprehend better.

Pair-share is also a very important strategy to use with our multilingual learners. It helps students lower their affective filter while also allowing them to use their linguistic repertoire to communicate their understanding. Teachers need to provide a word bank with the academic vocabulary needed as well as sentence stems to help students practice conversation using a more academic tone. I always let students practice pair-share before I even start asking them to share aloud to the whole class; it provides support for them to know what to say.

Thanks to Jody, Laleh, and Lisbeth for contributing their thoughts!

The new question of the week is:

*What instructional strategies do you recommend using with English-language learners in math classes?*

In Part One, Isabel Becerra, Beth Skelton, Tan Huynh, and Jim Ewing contributed their suggestions.

In Part Two, Cindy Garcia, *I*vannia Soto, Theodore Sagun, Michael Beiersdorf, and Kimiko Shibata offered their ideas.

Consider contributing a question to be answered in a future post. You can send one to me at [email protected]. When you send it in, let me know if I can use your real name if it’s selected or if you’d prefer remaining anonymous and have a pseudonym in mind.

You can also contact me on Twitter at @Larryferlazzo.

Education Week has published a collection of posts from this blog, along with new material, in an e-book form. It’s titled Classroom Management Q&As: Expert Strategies for Teaching.

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