By Haiwen Chu and Leslie Hamburger
Ideal conditions for learning exist when students take up opportunities to engage in meaningful interactions and discourse with fellow learners. This need is true across disciplines from mathematics to the humanities: meaningful peer discussions, as orchestrated by teachers, place students at the center of mathematical learning. For English Learners, such opportunities are especially critical as they develop content knowledge and language together. For English Learners to participate fully in activities and learning, their teachers will have to think carefully about how to include structures that invite and support English Learners’ meaningful interactions with their peers.
For example, teachers may find that it is useful at the beginning of a new lesson to have students engage in a Which One Doesn’t Belong? task. Students are shown four objects, for which they are asked to form an opinion and argument for which one doesn’t belong. The four objects are selected by the teacher so that students could plausibly make an argument for any one of them. Teachers will need to ensure the examples they select or create are related to the main goals and ideas of their lesson. To foster meaningful interactions, it is important that English Learners have some time to think individually and jot down their personal reasons and ideas, in bullet-point form. This time to reflect on their own will support the richness of their subsequent conversations.
One simple way to offer more structure is through a “Think-Pair-Share”. After students have had time to think individually, they then pair up and discuss with their partner which object does not belong, and why. After they partner with each other, however, we ask that students are prepared to share not what they just said, but rather what their partner thought. This structure encourages students to listen carefully and think about how they will represent the ideas of others, a key element of intersubjectivity.
A second option would be to have students “take their corner” in the room based upon the object they think does not belong. Everyone in that corner will already agree on the shape that does not belong, but their reasons may differ. In that corner, students share in a “Round Robin” format. That is, each student shares their reasons without interruption or discussion, even if their reasons are exactly the same. The goal in each corner is to identify two or three of the best reasons for why that shape does not belong. Afterwards, they pair up with a student from a different corner and try to convince each other.
The carefully designed structures (such as Think-Pair-Share and Round Robin) facilitate both sustained talk, in which students are able to elaborate upon their ideas in depth and reciprocal interactions, leading students to build upon, expand, or challenge each others’ ideas and reasons.
Additional approaches and resources regarding this practice are explored in the full “Integrating Language While Teaching Mathematics” brief. Click here to learn more.
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