By Jim Ewing, PhD
There is a belief that math is math and there is no language involved (Ewing, 2020). Thus, if English learners (ELs) are not doing well, it must be because they are not that capable. This is wrong on both accounts. We can challenge these misunderstandings and encourage teachers to meet the real needs of ELs so they can be successful.
There is also a belief that we need to learn strategies, but it is not enough just to plug in strategies for meeting the needs of ELs in math. In addition to learning strategies, we can help teachers change their mindsets. Read on to learn four mindsets, each with three accompanying strategies. The acronym PATH will help you remember the mindsets—Position ELs to be successful; provide culturally responsive Access; Teach language; and learn from researchers like Hattie.
Mindset 1: Position ELs to be successful
Consciously or not, day in and day out, teachers position their students by their actions and words. It is not a matter of whether teachers position, but whether they do so in ways that are inclusive and fair to all students (Chval et al., 2021). If a teacher reads a book or tells a story students can relate to, she is positioning those students positively. However, other students who do not relate are probably being positioned negatively.
It is challenging to learn math in a second language and therefore we need to be intentional about positioning ELs to be successful. We can help teachers reflect on how ELs are being left out or negatively affected by our positioning. Below are three strategies for positioning Multilingual Learners to be successful.
1. Use the term “Multilingual Learner” or “MLLs.”¹
The terms “English Learners (ELs)” and “English Language Learners (ELLs)” are examples of deficit language. Calling students “ELs” focuses on their weakness—they are not yet good at speaking English. However, in many ways ELs are language experts. They speak at least one language and are learning another. Calling our students “MLLs” honors them for their talents. When schools and districts are intentional about calling students “MLLs” it can be a reminder of how capable these students are. After all, if MLLs are capable of learning another language, they are also capable of learning math. We can model calling students MLLs and watch the snowball effect—the teachers raise their expectations, classmates raise their expectations, and MLLs themselves raise their expectations about learning all subjects, including math.
2. Revoice MLLs.
MLLs are often ignored because they do not speak English well enough to explain their ideas, but by revoicing their ideas teachers can position them as capable. If teachers say, “Juan Jose says 1/3 is bigger than 1/4; turn and talk to your partner about why Juan Jose is correct,” this positions Juan Jose as a capable mathematician.
3. MLLs help too.
If teachers consistently call on other students to help MLLs, the class may get the impression that the MLLs are not good at math. They may need the linguistic support, but it is imperative that we are reciprocal with this support. Teachers can position MLLs as being mathematicians by asking MLLs to help other students. For example, if MLLs are familiar with the metric system, teachers should ask MLLs to be the expert in the room and help other students (Kersaint, Thompson, & Petkova, 2014).
Mindset 2: Access—Culturally Responsive
Access is essential, and visuals, sentence stems and gestures can help provide it, but if the material is not culturally responsive, MLLs are not going to feel they belong. We want MLLs to visualize themselves in the curriculum. MLLs are not only learning to be bilingual (or multilingual), they are also learning to be bicultural (or multicultural.) Thus, it is not enough to use visuals and sentence stems to provide MLLs with linguistic access. We need to consider our students’ culture too.
1. Culturally responsive counters.
For Spanish speaking MLLs — 90% of MLLs in Texas — teachers can use frijoles instead of plastic counters. This simple adjustment helps MLLs feel special. Or teachers could give Mexican MLLs (the biggest group) an authentic experience by asking the class to draw or make the Mexican flag out of colored cubes. Then ask what fraction of the flag is white.
2. Make word problems about MLLs’ lives.
How many of us have solved fractions using pizza? How about also asking questions about enchiladas verdes? Instead of asking word problems about Halloween, we can also ask word problems about Quinceañera Parties. Of course we have to be careful of stereotypes, but we can ensure that the word problems used in their schools are culturally responsive for MLLs.
3. Role Models.
Think of as many superheroes as you can in a minute. How many of those superheroes were Hispanic—the biggest group of MLLs? Students need positive role models. In math, we can provide access that is culturally responsive by introducing students to role models that relate to them. For example, we can discuss how the Aztecs were successful mathematicians. Calling students “mathematicians” is an effective way to develop students’ mathematical identities, but we can take this a step further. We can be culturally responsive for Hispanic MLLs by saying things like, “Today, let’s be successful mathematicians like the Aztecs.” When the content relates to students’ identities, it provides them access because they will be more inclined to persevere to solve the problems.
Mindset 3: Teach Language
Not only should we provide MLLs with real access to the content, we also need to develop their language. Attempting to help MLLs succeed in math, many teachers provide MLLs with pure arithmetic, but this deprives them of practice developing their language. MLLs need to be challenged mathematically as well as linguistically. In order to develop language, teachers need to offer students opportunities to listen, speak, read and write. MLLs tend to do too much listening and do not have enough opportunities to speak and write (Ewing, 2020). When observing teachers, we can encourage them to give MLLs many opportunities to speak and write in math class.
1. Ask more questions.
When we ask questions, not only do students learn concepts more deeply, but they also have opportunities to develop their language through speaking. When MLLs are at the beginning stages of English proficiency, teachers can ask yes/no math questions—MLLs can justify their mathematical reasoning with the help of manipulatives (Bresser, Melanese, & Sphar, 2009). As MLLs become more fluent, teachers should be encouraged to ask more open questions that require them to explain their answers in greater depth.
2. Small group discussion.
Instead of having students solve math problems independently followed by whole group discussions of how they did it, students will flourish working through the problems together in small groups, discussing as they go, with particular benefit for MLLs.
3. Children’s books and storytelling before math lesson. The key is to find books and tell stories that MLLs can relate to. When we do, we can tie the books to the mathematics and develop their language. When students hear stories they can relate to, they will write their own stories and even their own word problems (Ewing, 2020).
Mindset 4: Hattie and MLLs
John Hattie has not researched Math and MLLs directly, but we can benefit from his research by using best practices. The key message from Hattie is that we should be using teaching approaches that are effective according to the research (Fisher, Frey, & Hattie, 2020). Hattie gives teacher practices quantitative scores according to their effectiveness. We should know our teachers’ impact on student learning and encourage them to adjust their teaching accordingly. Below are three effective practices, according to Hattie, applied to teaching math to MLLs.
1. Teacher Clarity for MLLs in Math.
Hattie stresses the importance of students knowing what they are supposed to be learning and what success looks like. We can ask teachers to include in their lesson plans how to teach MLLs what they need to know to be successful for each math lesson. Teachers should be encouraged to pre-teach MLLs not only to develop vocabulary, but also to discuss the purpose of the lesson and what they can do to be successful.
2. Reciprocal teaching.
When students tutor each other, they learn more deeply and that is the idea behind reciprocal teaching. This approach is more than students just learning in groups—each student in the group has a defined role. This makes it easier on MLLs because it is structured so that they too can participate. In addition, one student in each group can be responsible for making sure that each student, including the MLLs, understands the vocabulary in the math problems. However, as the name implies, the teaching and learning are reciprocal. Thus, the MLLs are positioned to teach others as well as being taught.
3. Collective Teacher efficacy.
Hattie claims this teacher practice is the most effective so we should use this finding to position MLLs for success in math. When teachers collectively believe they can positively influence students, learning shoots up. We can work with teachers to encourage them to have high expectations for MLLs in math. When teachers have deep understanding of both mindsets and strategies for meeting the needs of MLLs, they will have strong “Collective Teacher Efficacy.”
We can take the right PATH to ensure success for MLLs in mathematics. Let’s position our MLLs to be successful; be culturally responsive when we provide access; teach language in each subject, including math; and use Hattie or other research-based strategies.
Dr. Jim Ewing is an associate professor at Stephen F. Austin State University and an education consultant. He has presented at TEPSA conferences and the TEPSA Presents series, and is on a focus group with TEA and Columbia University on meeting the needs of ELs in Texas.
Apart from writing four books for teachers, Dr. Ewing is the lead author of a position paper about teaching math to multilingual learners for NCSM (National Council of Supervisors of Mathematics). Learn more on his YouTube channel “Teaching Math to English Language Learners (ELLs)” and via his book “Math for ELLs. As Easy as Uno, Dos, Tres.”
Bresser, R., Melanese, K. & Sphar, C. (2009). Supporting English language learners in math class: Grades 3-5. Math Solutions Publications.
Chval, K.B., Smith, E., Trigos-Carrillo, L. & Pinnow, R.J. (2021). Teaching math to multilingual students: Positioning English learners for success. Corwin Press.
Ewing, J. (2020). Math for ELLs. As easy as uno, dos, tres. Rowman & Littlefield.
Fisher, D., Frey, N. & Hattie, J. (2020). The distance learning playbook: Teaching for engagement and impact in any setting. Corwin Press.
Kersaint, G., Thompson, D. R. & Petkova, M. (2014). Teaching mathematics to English language learners. Routledge.
TEPSA Leader, Fall 2021, Vol 34, No 4
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