Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

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Insights Into Algebra 1 - Teaching For Learning
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Topic Overview Lesson Plans Student Work Teaching Strategies Resources
Workshop 3 Systems of Equations and Inequalities Teaching Strategies
Teaching Strategies:

Strategies for Teaching English Language Learners

Building Understanding
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Strategies for Teaching English Language Learners

High Expectations
Developing Meaning and Understanding
Building Bridges Between Cultures
Using Contextual Problems
Using Comprehensible Communication

According to the U.S. Department of Education, if the population of children in this country were evenly distributed geographically, the typical American classroom would look like this:

  • 10 students would be from racial and ethnic minorities
  • 10 would be poor
  • 6 of the above 10 would be from families where a language other than English is spoken
  • 2 to 4 of the above would be English language learners
  • 50 percent of this last subgroup would be immigrant students.
Source: U.S. Department of Education, NAEP 1996 Mathematics Report Card for the Nation and the States.

The demands of teaching in diverse classroom environments are both challenging and rewarding. Fortunately, researchers have identified strategies and pedagogical practices teachers can employ to enhance student learning in these heterogeneous settings. They include:

  • Having high expectations of all students
  • Focusing instruction on developing meaning or understanding
  • Building bridges between the various student cultures and the culture of the classroom
  • Using contextual problems to help alleviate language barriers
  • Using comprehensible communication to facilitate the learning of English and the learning of mathematics in tandem.
Teacher Patricia Valdez and her students in the video are all native Spanish speakers. However, this isn't true of all of her classes, just as it may not be the case for yours. Here she offers some advice on overcoming language barriers.


Read transcript from teacher Patricia Valdez
I did have a student last year who spoke Swahili and I don't speak Swahili. Read More

High Expectations

Recent studies suggest that teachers who hold high expectations of their students actually contribute to their pupils' success in school. For example, researchers found that working-class Latino students made substantial academic progress in classrooms where teachers assigned rigorous, intellectually challenging work and assumed they were capable of handling it. It is important that teachers communicate their high expectations to students and provide a variety of activities so students with different strengths can experience success in mathematics.


Listen to audio clip of teacher
Patricia Valdez
I had a student in my class who failed my class. Read More

Reflection:
What do you do in your classroom to communicate to students that you have high expectations of them? Highlight two ways in which you will try to communicate to your class that you know they "can do it."

record your thoughts in your journal



Developing Meaning and Understanding

Several studies have found that minority students have greater success in classrooms where they're expected to participate actively, work collaboratively with their peers, and develop their own understanding of concepts. They have less success with teachers who expect students to memorize rules and practice skills without a context.

When students work with data and devise their own ways of solving challenging problems, they see that mathematics is relevant to their lives, and they begin to recognize and develop their intellectual power. Advocates of mathematics education reform agree that these are important goals for all students. In the video for Part II of this workshop, Patricia's students tackled a real-world problem with two variables and several constraints and discovered how to maximize profit. Throughout the year, she's used a variety of strategies to help her students develop their understanding of new concepts.


Read transcript from teacher Patricia Valdez
Any time you use a new word or concept - like area of a triangle... Read More

Engaging students with hands-on activities helps enhance understanding, particularly for English language learners. It's also significant that Patricia has her students work on these activities in small groups. This gives them a chance to develop their mathematical understanding and their language skills at the same time. Patricia circulates around the room, encouraging students to help teach and explain concepts to one another.


Listen to audio clip of teacher
Patricia Valdez
In order to get to all the groups - especially when you have nine ... Read More


Read transcript from teacher Patricia Valdez
For the first few years that I've been teaching mathematics, I taught it the way that I was taught. Read More


Reflection:
Think about a lesson that you have taught that focuses on developing meaning and understanding. What are the components of that lesson? Can you think about another lesson you teach that focuses on skill development but is somewhat decontextualized? How can you improve this lesson?

record your thoughts in your journal


Building Bridges Between Cultures

Classrooms in which teachers have high expectations and give students opportunities to make meaning of relevant mathematics are rich learning environments. However, this style of instruction requires sophisticated use of language. First, the students have to read a problem and be sure they understand what it asks them to do. They then have to carefully consider the information presented in the text and identify what parts of it are relevant to solving the problem. Throughout their investigation, they must be comfortable exchanging ideas with their peers and the teacher. Students who aren't prepared to participate will be left struggling. Therefore, "bridge building" is a critical component of activity-based instruction in multicultural classrooms. The goal is to enable students to bridge the gaps between their home and classroom cultures.

An effective way to do this is to choose activities and contexts that have relevance to students' own cultures. Another is to listen carefully to what students say so you can build on their common sense and their informal approaches to solving problems.

In order for students to understand the culture of your classroom, you may find that they need explicit instructions about the types of interactions and behaviors you expect. Some of these behaviors include appropriate talk, peer collaboration, mathematical reasoning and justification, and participation and effort. Focusing on the process involved in students' mathematical activities lets them know that how they work on a problem is as important as the solution itself. Patricia Valdez monitors her class to ensure that students are engaged in the mathematical activities, and she provides more support for students who aren't involved at expected levels.


Read transcript from teacher Patricia Valdez
I've been working on how do I get these kids to focus ... Read More

Reflection:
Patricia made it a point to contact parents to keep them informed, and to solicit support from them. Think about how you can structure time and activities to help build more bridges in your classroom.

record your thoughts in your journal

Using Contextual Problems

In general, learning a mathematical topic in context is particularly helpful to English language learners. Consider using real-world examples whenever possible, and physical models to make sure all students understand the context. When students apply new concepts to familiar situations, they build a stronger understanding of the mathematics and improve their language skills. Patricia Valdez elaborates on this idea:


Read transcript from teacher Patricia Valdez
We can look at algebra and how it can help us solve a real-world problem. Read More

Reflection:
How often do you use contextual problems in your teaching? Describe some ways in which you could incorporate more of this into your regular classroom lessons.

record your thoughts in your journal

Using Comprehensible Communication

One way to describe what English learners are doing as they learn mathematics is that they are mapping the meaning of words and expressions between two languages. This mapping model (though admittedly oversimplified) focuses on how students learn to use new mathematics vocabulary and everyday vocabulary. For example, the word "set" has a mathematical meaning, such as in "a set of objects," and an everyday meaning, such as in "set the table." English language learners need to learn to match the expressions in their native language with the different ways in which an idea can be expressed in English. Because the associations among words, meanings, and concepts are different in each language, students are making multiple connections and mapping meanings from everyday language in their native language to mathematical language in English. Words and phrases with multiple meanings in either language can lead to misunderstandings in mathematics conversations. Sorting out these differences is something English language learners have to do continuously in an English-speaking classroom.

The following tips for effective communication with English language learners were adapted from Supporting Children's English Language Development (Focus on the Learner) by Scott D. Enright (Prentice Hall, 1992):

  • Use clear, normal speech in communicating with English language learners.
  • Moderate your speed if you are a fast talker. It may be necessary to repeat yourself or rephrase what you said.
  • Help to shape what the student wants to say.
  • Use non-verbal cues (such as gestures, pictures, and concrete objects) in your teaching to assist comprehension.
  • Make sure that English language learners are seated where they can see and hear well. Give them maximum access to the instructional and linguistic input that you are providing. Involve them, in some way, in all classroom activities.
  • Fill your classroom environment with print and with interesting things to talk, read, and write about. Creating a language-rich environment will allow your English language learners to learn even when you aren't directly teaching them.
  • Keep in mind that the English to which English language learners are exposed in your classroom is of crucial importance to their language development.
  • Encourage English language learners' efforts to participate by celebrating their contributions and searching out opportunities for them to take part directly in learning activities. But allow for the "silent period" that some students go through.
  • Correct the content of what they say if necessary.
  • Provide opportunities for English language learners to use the language and concepts you are teaching them in meaningful situations. Include a variety of ways of participating in your instruction - in cooperative groups, for example. Encourage all students to work with and help English language learners.
  • Treat English language learners as full members of the classroom community.
  • Help them to feel comfortable, and integrate them as quickly as possible. Refer to them often and make it clear to them (and to the class) that you expect them to work and learn just like everyone else. Then, ask for more and more participation and work as these students become better able to accomplish it.
Another strategy Patricia Valdez uses is having students read or restate problems out loud in class.


Read transcript from teacher Patricia Valdez
Today is Monday, so it's been a few days since Friday... Read More

Reflection:
Why might comprehensive communication be a useful teaching strategy for all students? What new ideas are you willing to try with your students to improve communication and understanding?

record your thoughts in your journal


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