Texas Comprehensive Center

Previous Work
October 2005 through September 2012

These resources were published under a previous TXCC funding; therefore, information contained therein may have changed and is not updated.

English Language Learners Materials

What Can a Mathematics Teacher Do for the English Language Learner?

Interactive Lessons

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Description - The 5 E's


  • Begin with an application or demonstration that allows students to use their prior knowledge and experiences.


  • Use concrete experiences before moving to the abstract.


  • Ask students to explain the connections orally.
  • Provide students with an explicit overview of the key concepts and vocabulary with a graphic organizer. Encourage students to speak and write mathematically to enhance mathematical learning.


  • Correlate the oral language to the new academic language, allowing students to work in cooperative groups or with partners.
  • Provide explicit and intensive instruction in the basic mathematics concepts and skills. Provide supplemental intervention to subgroups of children with sustained difficulty. Interventions should be a precise match with the source of difficulty the students are experiencing. Avoid overemphasizing teaching basic skills to the point of inhibiting the development of higher order thinking skills.
  • Model and provide guided practice before beginning pair work.
  • Independent practice after paired work develops deeper concept understanding.


  • Set high expectations, evaluating responses for clear reasoning, not allowing simple sentences or errors in grammar and spelling to mask student learning.
  • Informally check student comprehension and performance throughout the lesson.
  • Provide assessments tailored to the students' level of proficiency (see assessment).

(Adapted from Bybee, 1997.)


Example (Engage, Explore, Explain)

Mr. Torres teaches a high school math class with some ELLs. He begins the lesson on the interior angles of a polygon by distributing several geoboards to student groups and asking them to make shapes on the boards. He asks students to show their shape to the class, identify it, and tell where they might find it outside. Separating the class into two groups, he gives each group a card, one with the word "polygon" and the other with the word "non-polygon." He asks the students to work with partners to create a definition of polygon. As they share their ideas, Mr. Torres writes the attributes of a polygon on the board—closed shape, no curves. To check for understanding, he asks students to create a polygon on their geoboards. As Maria holds up her polygon, Mr. Torres writes "polygon" on the board and pronounces it for the class. He asks the class to copy the drawing and name of the shape in their notebooks. Now that the class understands the concept of polygon, Mr. Torres can go on to connect the geometric vocabulary with the corresponding math content. The concept of interior angles will now be easier for the ELLs to comprehend. Mr. Torres then uses a large demonstration compass to measure one of the interior…


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