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Math Sticky Notes for Students

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Reflections on Teaching English Learners

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In many classrooms today, the emphasis has shifted from students solving math problems to learners explaining solution processes, describing their ideas and reasoning, presenting arguments, and proving their conclusions. There are many creative, effective approaches to teaching mathematics but one common denominator (pun alert!) in them all is the important relationship between language and mathematics. Language is at the heart of teaching math. For English learners, the relationship is critical because these students are learning mathematics while they are acquiring the language in which mathematics is being taught.

Equity is one of the themes reflected in NCTM math standards. As stated, " Excellence in mathematics education requires equity-high expectations and strong support for all students."

So, what does strong support for English learners look like? Would you recognize it - or its absence?

Here are a few suggestions.

Explicitly teach vocabulary. Math has its own language and English learners must master it in addition to the general academic language they are acquiring. Explicit teaching involves selecting a set of math terms for each unit of study Ask yourself: What are the essential key terms students must know to be successful in this lesson/unit? How will I ensure key terms are not only introduced by me but also processed, used, and reviewed by my students? How can I encourage students to use the terms when working in partners?

Vocabulary for a 2-day lesson on the meaning of integers might include positive integers, negative integers, number line, opposites, and absolute value. Make sure students are provided multiple exposures to the words to deepen understanding. For example, write the words on the board or word wall, pronounce the words, point to a word on the board when it is encountered in the text or during instruction, play a vocabulary game, encourage students to use the terms in their answers and discussions. In other words, consistently make students aware of those words and how they are used. Students also need to use and practice the words in a variety of contexts such as peer discussions, individual activities, and teacher-led instruction. It is said that students need to use a word meaningfully around 15 times before it becomes part of their vocabulary. Getting that many encounters takes planning on the teacher's part with a focus on vocabulary.

Scaffold instruction. Since listening to oral instruction can be challenging for students who don't yet speak English fluently, English learners require additional supports.

Model the procedure step-by-step to demonstrate how a problem is solved. Remember that you may need to model more than once.

Speak clearly and at a pace that is understandable. Often teachers inadvertently speak too rapidly for English learners (and other students) to follow. Use a pace that is slower but natural. Use visuals. Technology offers innumerable ways to help English learners comprehend instruction. White boards, document readers, online resources, and the like provide the visual support these students need.

Link teaching to their background knowledge and experiences. For example, a lesson on the meaning of integers might be more meaningful if it begins with, Think of a time when you borrowed money. Tell a partner using the sentence frame, "One time I borrowed money __________." (10 seconds to share) Then discuss the symbol in math that can be used to represent borrowed money making the connection between negative integers and borrowed money. Use a number line to show on which side of the number line borrowed money is represented. Linking the content to students' own lives makes it more meaningful and easier to learn.

Provide opportunities for discussion. English learners benefit from discussing math concepts and procedures with peers, as well as in whole group. When posing a question to the class, consider having students turn to a partner and answer the question first, before reporting out to the whole class. Speaking to a peer may be less threatening since it allows students to share their answer or idea with one classmate instead of many. As students are talking together, the teacher may circulate to monitor student responses and get an idea of who understands and who might need more instruction and/or practice. Taking time to have students talk about math is a productive use of time because it....

Is a means for students to express their thinking, and to clarify and fine-tune their ideas;

Gives each student time to process information and hear what others are thinking;

Provides opportunities for English learners to participate as equal contributors to the class;

Offers the benefit of repetition of academic language terms and thinking processes.

When interacting with students, go beyond responses such as, "Good job!" or "You're right" by encouraging elaborated responses with comments like, "Can you tell us more about that?"

Try some of the following comments and see how the interaction in your class changes.
Prompt Thinking

You're on the right track. Tell us more.

That's a great start. Keep thinking and I'll get back to you.

What made you think of that?

Justify a Response

That's a good probable answer. . . How did you get to that answer?

Why is what you said so important?

Please explain how you figured that out.

Other Points of View

If you were solving the equation, what would you have done?

Would you have done (or said) it like that? Why or why not?

Did anyone else have that answer?

When teachers and students interact together, it fosters a supportive environment which builds teacher-student rapport and a sense of community.

It may occur to you that the suggestions here would likely benefit all of your students. Right! Many of the supports that provide access - and equity - for English learners are good teaching for all. However, these supports are essential for English learners to achieve academically.

Based on: Echevarria, J., Vogt, M.E., & Short, D. (2010). The SIOP Model for Teaching Mathematics to English Learners. New York: Pearson.

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Supporting English Learners in Mathematics Classrooms

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In many classrooms today, the emphasis has shifted from students solving math problems to learners explaining solution processes, describing their ideas and reasoning, presenting arguments, and proving their conclusions. There are many creative, effective approaches to teaching mathematics but one common denominator (pun alert!) in them all is the important relationship between language and mathematics.

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https://portal.wida.us/GetResource/2404

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Teaching and Learning Cycle of Genre Writing

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