Math

=== The academic language of math has been a challenge for many of the Level 1-3 ESL students at Manheim Twp. Math math be a universal language but accessing the math through the prompts, word problems, and verbal instructions is a different matter. Terry Lee is consistently using "Math Minutes" with his Level 1/2 class to embed academic language into his class. Additionally, students work at explaining their solutions to the problems in English as well as questioning each other's solutions in English. Improving Speaking and Listening skills, while also supporting math, is one way that departments can partner with our ESL teachers. All we need to know is what consistent themes exist that we can support. ===

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By [|Mary Ann Zehr] Modifying the English on math test items doesn't change the math knowledge assessed, concluded a [|study] on math testing accommodations conducted by the [|Regional Educational Laboratory West] and released this week by the Institute of Education Sciences.

Mathematical Notations in Arabic
===MTHS has seen the enrollment of two Arabic speaking ELLs this E, each with varying degrees of experience in English. One piece of background information that may prove helpful is being aware of how challenging it can be for an Arabic student to recognize notations in English. As you can see below, its quite different. This is just from Wikipedia but pretty enlightening about some of the challenges our Arabic students face in learning math at MTHS. Clicking on the image will take you to the main page where you can read more. I have also included a pdf to provide more insights. If you are teaching a Level 1/2 Arabic speaking student it may serve as an excellent resource to help sort out what you may be seeing in the classroom. ===



Incorporating Math Into ELL Classes
===One initiative in ELL this year has been to work at being responsive to what ELL students are learning in their content classrooms and incorporating those concepts into ELL lessons. Below you will see two of this years Level 1/2 ELLs working on describing math notation symbols.===



Key Math Terminology
====**One of the most challenging aspects of word problems for ELLs is the variety of different words used to indicate operations for students. ELLs do not pick up on the variety of operational words as quickly as out other students and sometimes they need to be directly shown the relationship to the word and its operation.**====

increased more than total of sum added to together plus || minus less than less fewer than difference decreased take away || product of times of || divided by into per quotient of percent (divided by 100) out of ratio of ||
 * ~ **Addition +** ||~ **Subtraction -** ||
 * combined
 * ~ **Multiplication x** ||~ **Division ÷** ||
 * multiplied

PDE Standards Aligned Systems Provides ELL Scaffolding Strategies
The most recent update of the PDE Standards Aligned Systems website launched on Monday 12/7. It now offers content specific scaffolding strategies on a students level of language acquisition. For example: State recommendations for how a student should be able to express their Geometry knowledge in writing.

Teaching Mathematics: Strategies to Reach All Students
Joseph M Furner; Noorchaya Yahya; Mary Lou Duffy Intervention in School and Clinic; Sep 2005; 41, 1; Education Module


 * I hope am not overstepping our limits on this article but it proposes 20 strategies for differentiation, inclusion students, as well as for ELL students. I included the article if you are interested in looking at more of its suggestions. A few strategies include:**

2. Relate //math// problems and //vocabulary// to prior knowledge and background. Especially for teaching students from diverse backgrounds, teachers can assess the current strategies used by their students to learn //math//. For instance, Chinese students may be familiar with the use of an abacus to do their calculations. Teachers can perhaps ask these students to show the others in class how an abacus is used. Honoring and recognizing students' knowledge will boost their self-esteem because students will feel that they, too, have something to contribute to the //learning// process despite their limited English abilities. Students with //learning disabilities// in the area of //math// can be powerful teachers to other students when they explain how they learned to accomplish specific skills or concepts (Mastropieri et al., 2001, p. 23). In addition, teachers can prompt students to talk about their experience in //learning// some of the //math// concepts in their country. By capitalizing on students' prior knowledge, teachers who are empathetic to their students' needs and backgrounds bridge the new knowledge to the old, making //learning// new //math// concepts more manageable for these students. In some cases, by understanding how students solve problems, teachers can troubleshoot or fine tune the individual student's process and make him or her more efficient learners.

4 Use manipulatives to make problems concrete. Best practices in special education call for you to teach concepts with concrete examples, and once the vocabulary and process is understood, then move to more abstract problems (Mercer & Mercer, 1998). The same practice is equally effective when considering the needs of Limited English Proficiency (LEP) or learners from diverse backgrounds. Teachers can obtain commercial manipulatives, or their students can make their own manipulatives (e.g., paper money, buttons, blocks, rods, tangrams, pattern blocks, algebra tiles). The use of manipulatives provides teachers with a great potential to use their creativity to do further work on the math concepts instead of merely relying on worksheets. Consequently, students are learning math in an enjoyable way, making connections between the concrete and the abstract. I recently saw this being done my Trina Hess and Molly Reinhardt in their pre-Algebra classes.

5 Encourage drawings to translate and Visualize word problems. The Natural Approach (Krashen, 1985; Terrell, 1981) is used extensively with ELL students. One of the four principles of this approach is that the teacher understands that the student will need to have a silent period before being expected to speak English. **One of the subsequent strategies of the Natural Approach is to allow students, especially those at the beginning level of their English language developmental stage, to use drawings and symbols in solving some of the math problems.** The same techniques are employed with students with learning disabilities to allow them to process auditory information before making a verbal response. In fact, as a comprehension strategy, teachers can use students' drawings and verbal rehearsals as testimony of their understanding of math concepts. This approach can alleviate frustrations for both teachers and students.

6 Have ELL/special education students pair with typical students for computer/cooperative activities. According to Krashen, language is acquired in an "amazingly simple way-when we understand messages" (1985, p. vii). He termed this understandable language as "comprehensible input." Peer interaction between native and non-native speakers of English is one means of promoting "comprehensible input" or understandable language.

Here are a few new resources for Geometry as well as a website with various math flash card aids.
Geometry flashcards Geometry Vocabulary with images. Not much different than what may be found in a text but another source for use with students. Ex: Point to identify an example of adjacent angles, etc.

Academic Vocabulary Games has countless vocabulary tools and aids for all subjects, math included.
= Math Cognates = 5 pages of Math Cognates that may be of assistance to Spanish speaking ELL students. Consider printing a copy for your student to keep in their math folder to help with decoding directions within your assignments.

= = = = = Challenges for ELLs in Mathematics =

Difficulties that ELLs face when learning mathematics:

 * formation of numbers varies from culture to culture
 * use of decimal point and comma vary from culture to culture
 * Students have no experience with our measurement system, It is an abstract to them.
 * Math is not spirally taught in many cultures. So students may not know a lot about geometry, for example.
 * Many students have never seen or worked with manipulatives. They may not take a lesson using manipulatives seriously.
 * Students learn math by rote memory.
 * Math curricula in their countries may be primarily calculation.
 * Word problems may not be introduced until much later.
 * Estimating, rounding, and geometry are not often taught as early in other cultures.
 * Mathematical terms do not always translate well.
 * Mental math may be the norm. Students may not show work in addition, subtraction, multiplication and division or they may show work in a different way,

from

[|Challenges for ELLs in Content Area Learning]
by Judie Haynes

= Mathematics: The Universal Language? =

by Sharon B. Hoffert
= = = Teaching Math and Science to English Language Learners = This very brief reading points out some of the challenges that ELL students face in mathematics and science. While their properties and laws may be universal, communication breakdowns still occur and their prevention can be planned for in advance.

"Today’s emphasis on problem solving and communication in mathematics means, more than ever, that students must be skilled in using at least the basic language of mathematics."