It is tough learning two new languages at once. In the case of English Language Learners (ELL), the two “languages” are often English and mathematics. Young children in classrooms where the language of instruction is not their dominant language can have challenges when it comes to learning math language, particularly positional words. These children are not only learning concepts about relationships in space, which are challenging on their own account, but they also have to respond to the demands of comprehending in a new language.

The difference between “through” and “between,” for example, could be a difficult distinction for ELLs. Teachers can help students learn these distinctions by amplifying language.

Here is an idea. With small groups of children, create an obstacle course in your classroom where children would need to do the following: walk between two chairs, go under a table, skip around the water table, climb over a cardboard box, and crawl through a tunnel. As you model each movement, use language to describe what you are actually doing: “What am I doing? I am walking between two chairs,” putting an added stress on the positional word “between” and the word “two.” When it is their turn to go through the obstacle course, you can continue to ask all the students what each child is doing.

Then you can invite the students to verbally repeat the sentences, describing their movement as they go through each obstacle in the course. When everyone has completed the entire obstacle course, you can ask, “What did we do in this obstacle course?” They would say: “First we went between two chairs, then under the table, then we went around the water table, then over a cardboard box.” On another day, you can ask the children to create a different obstacle course and once again intentionally amplify language to help them learn the labels for the positional words.

Once children have experienced the action and been exposed repeatedly to the label for each prepositional word, you can continue to amplify the language by matching those words with drawings that illustrate the concept they represent.

Using the above activity enables ELLs to learn not only the labels for the positional words but gives them the linguistic context they need to use them. Doing the language activity with children answering all together provides differentiation in terms of levels of English proficiency. For children who are in the very early stages of English language development, techniques that combine language with action provide repeated exposure to conventional models of English. For children who are more fluent, the verbal component gives them the opportunity to use English in a conventional fashion without fear of being singled out.

Once children have experienced the action and been exposed repeatedly to the label for each prepositional word, you can continue to amplify the language by matching those words with drawings that illustrate the concept they represent. You can make these drawings into cards that can be used for games or to give students directions for lining up or during other transitions throughout the day.

These strategies to make content comprehensible and promote language development are beneficial to all students, but they are essential to ELL students in order to learn foundational concepts and the language we use to describe them.

Watch a lesson like the one described here and check out these other resources for ELL teachers.

Tana Hoban and Ann Morris are both gifted children’s book authors who combine minimal text with wonderful photos that beg to be pored over again and again. Many of them are organized around ideas that call for mathematizing. For example, just the cover of Hoban’s Shapes, Shapes, Shapes or Cubes, Cones, Cylinders, and Spheres will make it easy to engage children in wondering what regular geometric shapes they can spy in the classroom or on a walk around the school. Be sure the children record their findings by drawing or making tally marks so that they have data to analyze when they get back to the classroom. As you guide a discussion into asking what shape seems to be the most common, be sure to include the all-important follow-up: Why? Why do you think that is so? Why do you think you found many more rectangles than triangles?

In the same way, Ann Morris’s Shoes, Shoes, Shoes and Bread, Bread, Bread can jumpstart a survey of the different kinds of shoes the children are wearing or the kind of bread they like, as well as encourage some serious thinking about good ways to categorize them. Make sure you have them show the results. Once again, the best thinking comes as the children and teacher converse together about what questions they have and how they see the data making sense.

Sharon Hogan and her preschool class at Peterson School had all kinds of fun with the way Eric Carle’s The Secret Birthday Message plays with the two main faces of geometry—shapes and spatial sense. The group made up their own treasure map to correspond with the one in the story and then brought the map to life as they set up an obstacle course. Throughout the process, the children were surrounded by two- and three-dimensional shapes and involved in recognizing, naming, drawing, and building with them.

They also got lots of practice using directional language such as “down the stairs” or “through the opening” and relative words like “near to.” Sharon knew that both first- and second-language learners need many repetitions of these terms. These words can describe a relationship between two objects that shift. For example, one person pointing left looks like they are pointing right to someone facing them, or just as a bush that might have been in front of you at one point soon is behind you as you continue along a path.

A Triangle for Adaora by Ifeoma Onyefulu is a delightful book that emphasizes several Big Ideas in geometry, including that comparing attributes of shapes helps define and classify them and that two- and three-dimensional shapes can be used to represent and understand the world around us.

Adaora doesn’t want to eat her paw-paw fruit because she loves the shape inside – a star. The conversation with her cousin that ensues sets the stage for an exploration of shape and the search for one shape in particular – a triangle. As Adaora sees that her world is full of shapes and learns the names of these shapes, we also learn about life in a Nigerian village.

As we journey with Adaora and her cousin, we see the rectangle of Uncle Eze’s robe, the circular tops of the elephant drums, and many other beautiful shapes in her world. We see the shapes, but we also see the culture and hear the life of the village. We are drawn in with Adaora on the search for the elusive triangle, and when she finds it, we are able to celebrate with her. Her exploration invites the reader to search their own world for shapes and to see that geometry is all around us.

This book is a wonderful way to connect mathematics with children’s lives. Teachers can explore the culture of the children in their classrooms from a geometric perspective by encouraging the children to identify different shapes unique to their family and discuss the shapes that they have in common. Having collected all this data, don’t forget to graph it to answer the question, “Which shape is most common in everyone’s family?” The results will be both fun and enlightening. Children may eventually be able to come up with additional questions this data can answer.

A student gives and receives orders about where to put a stuffed animal.

Focus on the Child videos are taken from one-on-one interviews with individual children. The interviews are designed to elicit evidence of children’s mathematical thinking. They are not teaching episodes or formal assessments.

A student uses blocks to recreate arrangements of shapes.

Focus on the Child videos are taken from one-on-one interviews with individual children. The interviews are designed to elicit evidence of children’s mathematical thinking. They are not teaching episodes or formal assessments.