By Beatriz T. Font Strawhun
IFL Mathematics Fellow
Mariel* got up from the back of the classroom reluctant to take a seat next to her working partner for the day. Mariel is a native Spanish speaker early in her journey with English and she knew that today’s lesson would involve some new English math vocabulary. She was assigned a partner who knew some Spanish, but she was, nevertheless, reluctant.
When a teacher encounters a student like Mariel in their classroom, there are several choices they can make. Which of these actions would you try?
- Appoint a bilingual student to act as translator for Mariel.
- Activate prior knowledge so that Mariel can engage in the task.
- Provide opportunities to work with physical and/or pictorial models.
- Give worksheets for Mariel to practice basic skills until she knows more English.
- Engage in an activity that creates need for the use of new English academic vocabulary.
- Encourage student-developed definitions of academic vocabulary.
Let’s look at what Mariel’s teacher chose to do.
Mariel’s teacher passed out the task then asked that all students turn over the paper and write down what they thought the word “similar” meant in English or Spanish. Mariel thought to herself, “Esto si lo puedo hacer. Suena como ‘similar’ que quiere decir algo como ‘igual.’” (“This I can do. It sounds just like the word ‘similar’ which means something like the same.”)
Once students had called to mind what they thought the word similar meant in their Quick Write, the teacher asked them to look at some shapes cut out of paper that were in fact similar and name why and how students thought they were similar. The teacher encouraged the students to communicate in whatever language they chose. They were then asked to find shapes they believed to be not similar and explain why. After the sharing of examples, non-examples, and the listing of attributes of similar shapes, the students returned to their Quick Writes to refine their initial definitions written on the back of their papers.
So, which of the pedagogical choices above did Mariel’s teacher employ?
In their Fall 2021 position statement TODOS, an educational organization dedicated to equity, excellence, and social justice for all math students, states that
Regardless of what stage multilingual learners are in their language development, teachers can afford opportunities for them to engage in cognitively demanding tasks that provide multiple entry points and leverage bilingualism to facilitate mathematical meaning making (Chval & Khisty, 2009; Khisty, 1995; López Leiva, Torres, & Khisty, 2013; Moschkovich, 1999; Turner & Celedón-Pattichis, 2011).
Mariel’s teacher allowed this to happen for her by using four specific pedagogical choices:
1. Activate prior knowledge.
The multilingual learner brings a wealth of knowledge to the classroom that many teachers do not or cannot tap into (i.e., a lack of common language, assumption that a multilingual learner does not know the mathematics the way we know mathematics, etc.). Asking students to engage in a Quick Write of what they know about a particular term, gives the teacher an opportunity to identify the assets that the student brings to the classroom. For all students in the classroom, calling to mind what they knew about the word similar, helped them with a starting point to further think about what the term might mean in a math context. In Mariel’s case, she was also able to use the cognate ‘similar’ to think about the meaning of the word.
2. Provide experiences with models.
The teacher gave the class several examples of similar shapes that were cut out and could be manipulated. Having several examples and non-examples allowed the students to manipulate the figures to further identify the attributes of similar figures. In this class, some students placed their figures one on top of the other to see that the shapes had the same-sized angles but different side lengths. In other instances, the use of tables, graphs and or drawings could also provide a common “language” for discussion in students’ small groups. By providing a common concrete anchor for students to use as a basis for discussion, the multilingual learner has a tool to facilitate conversation.
“Inviting students to use multimodal representations and resources such as gestures, drawings, diagrams, manipulatives and technology will support them as they represent their mathematical solutions and communicate their thinking. Doing so can enhance multilingual learners’ participation” (TODOS Position Statement, Fall 2021).
3. Engage in an activity that creates need for the use of the word.
In a previous article about strategies for multiligual math classooms, we reference the idea of a shingle on which to hang the new word those students have learned in the classroom. Because the term ‘similar’ was part of the students’ social language and even a cognate in the case of many of the students in his class, the teacher was able to start with what the students knew. In many cases in the mathematics classroom the academic vocabulary is completely new for every student, but particularly those who first language is not that of instruction. When academic language is being acquired, it is especially essential to provide an experience that creates a need for the term.
4. Encourage student developed definitions.
Textbook definitions are often dry, highly word-smithed versions of word meanings. We often see students copying the words down from the glossary only to continue to be confused because the words were presented in a contextual vacuum. When students explore a concept that leads to the development of a definition in their own terms, the term becomes their own. The students in Mariel’s class had a starting idea for their understanding of the term “similar,” through their interactions with the shapes and their work to refine their idea, the students were able to develop their own definition of the term. Students realized that the shapes all had proportional corresponding sides and angles that were equal in measure, or congruent. Testing and retesting their ideas through the use of examples and non-examples allowed students an opportunity to revise and even discard initial ideas about a concept. Mariel and her classmates all initially thought that the term similar meant that something was the same, but upon examination of the shapes their teacher gave, they discarded that initial idea realizing that similar meant something very different in the math classroom.
Why didn’t Mariel’s teacher use a student translator or given Mariel a skills worksheets?
It is doubtful that Mariel would have had the same success in a class where she had been assigned a series of worksheets full of basic fact practice. Without formative assessment (preferably in her native language), it would have been merely an assumption on the part of the teacher that Mariel was not yet ready to engage in a lesson on similarity. Those assumptions would have prevented Mariel from gaining access to the grade-appropriate high-level task for the day and it would have sent the message to Mariel that she is not a mathematician simply because she is a multi-lingual learner. (Additionally, those computationally-based worksheets are actually not a precursor for determining similarity!)
And employing the help of a student translator requires the translating student to focus on translating and not engaging in the math while simultaneously diminishing the contact between the teacher and the student whose first language is not English. It is the job of the teacher, not another student, to provide the access point/differentiated scaffold for every student. If a student was used as translator, there is no guarantee that what is being conveyed to the non-native English speaker is accurate to the task, nor is it a guarantee that Mariel’s thinking was accurately translated to English for the class. Leveraging Mariel’s thinking via her Spanish definition and her use of the cut-out polygons empowers her to express her thinking mathematically, regardless of language, and to solidify her identity as a doer of mathematics. It also allows Mariel to try out the English she does know rather than pigion-hole her into an isolated world of Spanish in an English-dominant classroom.
“Multilingual learner success requires establishing environments in which teachers and students respect one another, consider agency and identity, value partnerships, and position multilingual learners as leaders.”
TODOS Position Statement, Fall 2021
Had the four pedagogical choices above not been made, would Mariel have experienced her learning environment in the same way? Would the opportunities to grow as a doer of mathematics been equal? Working on creating an environment that honors students’ lived experiences, raises up and builds on their assets, and treats every student as a mathematician, inviting students of all backgrounds into doing the math.
*student name has been changed for privacy
With thanks to Jaime Montelongo, whose practice was featured in this article. Mr. Montelongo is a middle school math teacher in Fabens Independent School District in Texas. Mr. Montelongo’s classroom story gave us insight into the ways of celebrating students and supporting them in becoming mathematicians who can express and build on their knowledge in whatever language works for them.
Reference
Chval, K., & Khisty, L. L. (2009). Bilingual Latino students, writing and mathematics: A case study of successful teaching and learning. In R. Barwell (Ed.), Multilingualism mathematics classrooms: Global perspectives (pp. 128–144). Clevedon, UK: Multilingual Matters.
Khisty, L.L. (1995). Making inequality: Issues of language and meanings in mathematics teaching with Hispanic students. In W. G. Secada, E. Fennema, & L. B. Adajian (Eds.), New directions for equity in mathematics education (pp. 279–297). Cambridge, UK: Cambridge University Press.
López Leiva, C. A., Torres, Z., & Khisty, L. L. (2013). Acknowledging Spanish and English resources during mathematical reasoning. Cultural Studies of Science Education, 8(4), 919-934. doi: 10.1007/ s11422-013-9518-3
Moschkovich, J. (1999). Supporting the participation of English language learners in mathematical discussions. For the Learning of Mathematics, 19(1), 11–19.
NCSM and TODOS. (Fall 2021). Positioning Multilingual Learners for Success in Mathematics: A joint position statement from NCSM: Leadership in Mathematics Education and TODOS: Mathematics for ALL. Retrieved from https://www.todos-math.org/assets/images/NCSM-TODOS%20Multilingual%20Learners%20Position%20Paper%202021.pdf
Turner, E., & Celedón-Pattichis, S. (2011). Mathematical problem solving among Latina/o kindergartners: An analysis of opportunities to learn. Journal of Latinos and Education, 10(2), 146-169.