English Language Learners

Using CMP in Linguistically Diverse Classrooms
Original Rebus Technique
Diagram Code Technique
Chart Summary Technique
Rebus Scenario Technique
Enactment Technique
Visual Enhancement Technique
Summary

Using CMP in Linguistically Diverse Classrooms

Students at different levels of English proficiency can successfully participate in CMP. Moreover, English learners should receive the same content as their peers as no part of the program is diluted for them.

Many lessons in CMP require no modification, as they are already rich in comprehensible input. With these lessons, English learners easily understand information and concepts by participating in hands-on learning activities that incorporate visuals and manipulatives. For other lessons, we offer six simple techniques for making information accessible. Places to implement these techniques are suggested throughout each Teacher's Guide under the heading, "Tips for the Linguistically Diverse Classroom." However, these suggestions should be considered only examples of when a particular technique might be appropriate.

Offering general techniques rather than providing specific modifications accomplishes several goals. First, CMP Teacher's Guides do not become inundated with extraneous material unrelated to math. Second, teachers are not led to believe that cited modifications are the only times English learners might need assistance. Third, these general techniques acknowledge and address the wide range of English proficiency among English learners, thus enabling teachers to present modifications at every level. Last, the combination of detailed explanations of techniques in this section along with cited examples throughout each Teacher's Guide provides an enrichment tutorial for teachers working with English learners. Not only can these techniques be used anywhere in the CMP program, but they are equally effective in other areas of the curriculum.

The primary guideline we used when developing these techniques was simplicity. Most can be implemented with no preparation; a few require minimal time to gather visual aids or props. References to a particular technique are accompanied by a specific example related to a question or section on the page. These references and examples can be found at the bottom of various pages in each Teacher's Guide under the title Tips for the Linguistically Diverse Classroom. Initially, teachers may refer to the detailed explanations in the Teacher's Guide to review how to implement a referenced technique. However, due to the simplicity of these strategies, teachers will soon find that references and examples in the Teacher's Guide are all they need to make specific modifications for that page. Furthermore, as teachers become familiar with these techniques, they will also begin to choose appropriate strategies for unreferenced parts of the program as well.

A detailed explanation of each technique follows.

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Original Rebus Technique

On a sheet of paper, students copy the text from all or part of a page before it is discussed. During discussion, students then generate their own rebuses for words they did not understand as the words are made comprehensible through pictures, objects, or demonstrations.

This strategy ensures that English learners benefit from written communications in the same way as their English-proficient peers. While written text summarizes key concepts, includes background information, and provides directions for completing tasks, English learners often do not benefit from such communication.

In the past, English learners have been traditionally paired with English-proficient students who are asked to read aloud written text. However, this approach does not provide English learners with access to written communication. For example, English learners are asked to rely on memory when trying to recall the written information—something not required of their peers. Furthermore, simply reading information aloud does not ensure that the words are made comprehensible to the English learner. Therefore, the Original Rebus Technique offers a strategy that makes written communication meaningful to English learners, without depending on peer cooperation or memory.

1. Teachers identify text perceived to be difficult for English learners to comprehend. Examples of such text may be questions appearing in Mathematical Reflections, Applications, and Connections sections of the program.
2. English learners receive a copy of the rewritten text when the corresponding page is introduced to the class. As the information from the student book is read aloud, teachers make key words understandable. For example, a teacher may demonstrate the word "snapshot" by showing a photo of a pet.
3. After students comprehend the word, the teacher writes it on the board so English learners can connect the written word with a specific meaning. At this time, English learners create an original rebus over that key word on their sheet of paper. This rebus will then help the English learners recall the meaning of the word when referring back to the text during independent work.

Note: It is essential that English learners draw their own rebuses. This ensures that whatever symbol they choose to draw has meaning to them. The problem with providing professional or teacher-drawn rebuses is that simple drawings, by themselves, do not often convey a universal understanding of the words. For example, many English-proficient students were not able to correctly identify a rebus when the word below was covered, yet could do so when they were able to view both the word and rebus. This suggests that the written word, not the rebus, conveyed the meaning in such situations. Moreover, if English learners are required to create their own rebuses, they then choose which words need to be coded. Depending on the level of English proficiency, the number of coded words can vary greatly among students.

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Diagram Code Technique

Students use a minimal number of words and drawings, diagrams, or symbols to respond to questions requiring writing. Learning to organize and express mathematical concepts in writing is a skill students develop over time. If English learners are not given this same opportunity, they miss an important component of the math curriculum. This strategy provides alternate ways for students not yet proficient in writing English to express mathematical thinking on paper. While their responses will not be in the same format as those of their English-proficient peers, English learners still have the same challenge: they must record and communicate mathematical ideas so that someone else can understand their thinking.

1. At the beginning of the program, teachers model and encourage English learners to use this approach when writing answers to questions presented in the program.
2. To introduce this approach, the teacher writes several questions requiring written responses on the board. These questions should be simple with obvious answers.
3. The teacher then shows the English learners how to answer each question without writing complete sentences and paragraphs. At the end of this session, the teacher should have modeled answering questions by using and/or combining minimal words, drawings, and diagrams. (Not every question needs to be answered by using all of these approaches.)

Note: This approach can be used for any written response in the program, but it is especially useful for responding to questions found in Mathematical Reflections. Since this part of the program provides a vehicle for assessing how well students have understood key concepts of the unit, this approach enables teachers to evaluate their English learners' progress, as well.

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Chart Summary Technique

This technique involves presenting information by condensing it into a pictorial chart with minimal words. This extension of the Diagram Code technique offers English learners another way to organize and express mathematical thinking with a minimal amount of writing.

1. At the beginning of the program, the teacher shows various charts on any subject. The charts need to be simple, include pictures, and have a minimal number of words.
2. The teacher then creates and writes a question on the board that relates to each chart. For example, the teacher might show a chart of the life cycle of a plant divided into four sections. For this chart, the teacher could ask this question: What are the growth stages of a plant?
3. The teacher continues by showing how the chart answers this question by pointing to the drawings in each section, showing the seeds, roots, stem, and flower. The teacher also points out how each section has been labeled.
4. At the end of this session, English learners should be able to respond to a question by creating a chart with pictures and minimal words.

Note: This approach may be an alternative for English learners when responding to some of the Unit Projects requiring detailed writing.

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Rebus Scenario Technique

Teachers make use of rebuses on the chalkboard during discussions and when presenting information. While modifications for primary mathematical concepts may be perceived as necessary for English learners, there may be a tendency to omit such techniques for "enrichment" information, such as text appearing under "Did you know?" However, if programs offer English-proficient students such information, then English learners should also have an opportunity to acquire the same knowledge. Therefore, the Rebus Scenario offers teachers a simple way to ensure that all students have access to both the core and enrichment aspects of the Connected Mathematics program.

The teacher assesses what key words may not be understood by the English learners. As each of those words is presented, the teacher simultaneously draws a rebus on the board.

Note: If there are English-proficient "artists" in the classroom, teachers may opt to implement this approach in a slightly different way. Prior to the lesson, a teacher can ask an artistic student to come to the chalkboard to draw rebuses for targeted words. When using this approach, the teacher can then just point to the appropriate drawings during the lesson. If there is no time prior to a lesson, the artistic student can be asked to draw the rebuses as key words are presented. With this latter approach, it is important that the artist knows which words to represent as rebuses and to draw quickly.

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Enactment Technique

Students act out mini-scenes and use props to make information accessible. This technique ensures that all students comprehend hypothetical scenarios presented throughout CMP. With this technique, English learners are not excluded from lessons involving situations reflective of real-life scenarios.

1. Teachers decide which simple props, if any, will enhance the enactment. These props are gathered prior to teaching the lesson.
2. At the time of the lesson, students are selected to assume the roles of characters mentioned in a CMP problem or scenario.
3. These students then pantomime and/or improvise speaking parts as they enact the written scenario presented in CMP.

Note: There may be a tendency to select only English-proficient students for mini-scene roles; however, many parts can also be given to English learners. For example, roles such as pantomiming shooting baskets or pretending to ride a bicycle can be easily enacted by English learners, as these kinds of parts do not require students to speak English.

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Visual Enhancement Technique

The Visual Enhancement technique uses maps, photographs, pictures in books, and objects to make information understandable by providing nonverbal input. This technique is most helpful for conveying information that is unlikely to be understood through enactment or creating rebuses. When pictures or real objects are added to lessons, English learners have the opportunity to receive the same information presented to their English-proficient peers, who are able to understand the written text without visual aids. This approach ensures that English learners equally acquire and benefit from descriptive and/or background information sections of the program.

1. Teachers decide if information on a page is unlikely to be understood with a rebus or by having students create an enactment. For example, maps are often used with this technique to help students understand what part of the world an informative section or investigation is centered around. In contrast, a mere rebus "outline" of the same country would not be likely to be understood by anyone. Likewise, topics such as video games, different kinds of housing, and newspaper advertisements are more easily comprehended by merely showing examples than by trying to draw something representative of the topic.
2. When teachers decide visual aids are the best approach for making information accessible, examples are sought prior to teaching the lesson.
3. Teachers then show the visual aid at the appropriate time during the lesson.

Note: In the first year of implementation, English-proficient students can earn extra credit by finding appropriate visual aids for targeted lessons. Teachers can then keep the pictures, objects (if possible), and book names (with page number) on file for use in subsequent years.

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Summary

The six techniques (Original Rebus, Diagram Code, Chart Summary, Rebus Scenario, Enactment, and Visual Enhancement) ensure that English learners will receive the same mathematics curriculum as their English-proficient peers. Although the techniques differ in implementation, they all offer ways for English learners to acquire and express the mathematical ideas presented in CMP.

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These ideas were taken from the CMP Web site hosted by Michigan State University.