Universal Language Lost in Translation

The Challenges of Teaching

Mathematics to ELLs

By: Marlon Marmolejo.

Introduction If teachers really want to help their ELLs (English

Language Learners) in any particular content area, they must begin by understanding the challenges that ELLs face, not only in mathematics, but also in all content areas.

We must begin by understanding that math is not just adding or subtracting numbers arithmetically. It involves higher levels of reasoning or abstract thinking, before translating into figures and equations. Moreover, there are also many challenges that teachers must deal with.

Preparing for success

As we all know, for the first time in our small community district, we have an increase population of ELLs (English Language Learners) in each of our schools. This represents a challenge when teaching all the different subjects, especially math in the middle school, which must become the solid foundations for the secure transition into the upper grades. It is for this particular reason that I decided to target the middle school grades with this training.

I think this workshop will be not only beneficial for the math teachers, but also for all of other content area teachers who will be working in the district this year. After all, these students are expected to take and succeed in the other content areas too.

Most importantly, it has be proven that the strategies and techniques utilized to teach ELLs also benefit in great deal native English learners who might not be at the same level of their native peers’ performance.

Objectives

1. to avoid misunderstandings and teachers’ frustration build-up when teaching our ELLs, because “English language learners can not demonstrate their mastery of content without having already attained a high degree of English fluency.”

2. To demonstrate the importance of providing different alternatives of assessment so that your English language students have the chance to show their knowledge and teachers to evaluate it more appropriately.

3. To illustrate the importance of scaffolding (jump-starts) to help content language development in the area –a crucial tool for success.

4. To look at the different challenges of teaching math to ELLs that be might overlooked due to false assumptions. For example, “we all understand the universal language of math.”

U niv ersa l La ng ua g e Lo s t in T ra ns la tion

M isu nd e rs tan d in g s a nd fru stra tion

V oca bu la ry d ev e lo pm e nte .g . ju m p -sta r ts

D iffe re n t a lte rna tive s o f assessm e ntS e lf-a sse ssm e nt

M o st im p or tan t ch a lle n ge s o f te a ch ing m a thto E L Ls

M a th fo r E L Ls

Misunderstandings and frustrations Many ELLs use different processes to arrive at

answers due to their diverse ethnic backgrounds in which the reasoning might be more important than the specific correct answer;

or perhaps where placing more emphasis to the final product in complete disregard to the process, becomes the priority. Unfortunately, many teachers do not value other systems and prior mathematical knowledge – my modus operandi is the only correct way. This can create a big conflict for those ELLs who may be more concerned with getting the correct response than with the process or vice versa.

Different alternatives of assessment for ELLs.

Even when ELLs can communicate with fluency with their peers and teachers in a social context (BICS), it doesn’t mean that they can do the same academically (CALP). It takes from 5 to 7 years for an ELL student to achieve this level of competency. Therefore if you only evaluate your ELLs based only on oral explanations of their mathematical problems, they are destined to fail.

Common practices that will affect your ELLs’ performance and assessment Grading based on the final product, i.e. the

answer. Placing all the emphasis on the linearity of process

and disregarding the final answer. Accepting only one procedure as the appropriate

when evaluating the students. Being condescending by reinforcing the students’

belief that math is only about numbers and can not be verbalized.

Suggestions for assessment Use various test forms that call for the use of

different strategies such as making lists, tables, drawings pictures, finding patterns, working backwards, and guess and check.

Use tests that call for identification of the problem, the components of the problem, or just the right procedure that can lead to the answer.

Use of simple calculations that the students will have to theorize into a problem. This will help with the development of the academic language in your content area. For example, 200x20=4000

(continue)

…If Mary needs to save $4000, but she can only save $200 a week, it will take her 20 weeks to come up with the money.

Create assessments or assignments that consist of different levels of difficulty. For example, 12 different problems where the first 6 are specially designed for ELLs (with language prompts or diagrams) and the rest are made to target the mainstream learners. Of course, always encourage the Ells to do more if they can. This is a great scaffolding device that builds confidence in ELLs and also helps them to save face. The rest of the class does not need to know how much they struggle.

Encourage the creation of portfolios for assessment.

Use rubrics (set goals and expectations).

Self assessment

Self assessment is critically important in using problem-solving strategies successfully. As students reflect on the problem-solving approach they have used to succeed or the difficulty in using it, they gain an awareness of the types of strategies they can bring to similar problems in the future.

One way of doing this is by using a simple checklist or inventory list that ELLs can complete after finishing a lesson or unit in mathematics.

Vocabulary development “Math classes can present extra challenges for ELL

students because they must learn the specific content vocabulary and expressions, along with their second language acquisition. Help your ELL students by directly teaching math vocabulary. Use the following guidelines to plan your vocabulary building activities”.

Topical Terms. Identify and teach specific vocabulary that must be understood for each assigned activity.

Common Math Terms. Teach the meanings of common math terms that have other definitions outside of the context of math-for example root, face, mean, and prime.

Solutions. Create a plan for how you will help ELL students acquire the language of mathematics.

Visual Aids. Consider using visual aids, multiple examples, and student explanations as possible techniques to help your ELL students grasp unfamiliar math terms.

Note Cards. Encourage your ELL students to keep note cards to record math terms and vocabulary in their own words, sometimes with the use of their native language. Remind your ELL students to reference these note cards and to add to them as their understanding grows.

• Math Journals. Use journals to practice and strengthen new language skills and math terms in a non-threatening manner. Some ELL students may feel comfortable using their native language in their journals as a way to help solidify their understanding of math concepts.

Challenges of teaching math to ELLSFor some students, math seems to be a foreign language, consisting of words and concepts that do not converge with their everyday experiences. For these students, successful teachers find ways to make math understandable, relevant, and familiar. In some ways, it is all about finding a common language. Other cultures have different approaches to mathematics that even the ELL may be unaware of.

Among the most important difficulties that ELLs and teachers face when working with math, we should consider the following compilation of ideas that I found in different sources on the Internet.

1. Formation of numbers varies from culture to culture: While the decimal system is nearly universal, the shapes

(or glyphs) used to write numbers are not. The Arabic numeral shapes of 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are used in most of the world, either alone or in addition to other numeral shapes. For example, Indic numerals are used in many Arabic countries instead of, or in addition to, the Arabic numerals. These Indic numeral shapes are:

India, like the Arabic countries, has a parallel decimal system using different numeral shapes. What is more interesting is that each of the different scripts officially recognized in India have different numeral shapes. For example, the Devanagari script (used to write Hindi, Marathi, etc) has these numeral shapes:

China, Greece, Israel, Japan, Korea, and Thailand all have alternate glyphs used for counting or numbering, but they are not commonly used to express decimals, and some traditional number systems do not even provide a way to express zero. In computer operations, the difference in glyphs doesn't generally need to be recognized except at the time of entry or presentation. Quantities are invariant, regardless of the glyphs used to indicate them.

2 Use of decimal point and comma vary from culture to culture.

Not all cultures use the decimal system, a numeration system based on powers of 10, in which a number is written as a row of digits, with each position in the row corresponding to a certain power of 10. It is believed that the decimal system is based on 10 because humans have 10 fingers and so became used to counting by 10s early in the course of civilization.

3 Students have no experience with our measurement system:

This means that it is too abstract for the students. Science and technology involve, to a great extent, measuring. The scientific community world wide long ago realized the necessity for standardization of units of measure. It was largely for this reason that the metric system was developed. Today, almost every major nation in the world and the vast majority of all nations, have officially adopted the metric system. The United States is the only major exception. We continue to use the customary, or English, system which goes back to about the 1200’s.

4 Math is not spirally taught in many cultures:

Students might not know about geometry, for example, if they are in the 3rd grade. The curriculum might be different due to the number of years that is required to graduate. In Colombia, for example, it only takes 11 years to graduate from high school. Therefore, the Math sequence might take a different sequence.

5 Many students have never worked with manipulatives:

They may not take lessons involving manipulatives seriously. Teachers have known for years that hands-on manipulatives lead to longer retention of concepts but students may not have been told why that is true. It is a simple plan to reach both memory systems in the brain. Unfortunately, most students have been trained over the years to solve math problems mentally without any concrete visualization.

6. Students learn math by rote memory:

Memory has been always been praised. The faster students can multiply, add or subtract the better. But how many students actually know why 7 times 5 is equals to 35?

7. Math curricula in their countries may be primarily calculation:

Mathematics teaching in some countries may place greater emphasis on basic calculation and less on other aspects of mathematical knowledge, skills and understanding.

Word problems might not be introduced until much later. They lack mathematical discourse.

8. Estimating, rounding, and geometry are not often taught as early in other cultures:

This also depends on the number of years that students are required to attend school to graduate, which will directly affect the pacing of the curriculum.

9. Mathematical terms do not always translate well:

The word factors always signifies multiplication. And again, we speak of the "product" abcd, even though we do not name an answer. Sometimes students get lost in the multiple meanings of the key words in math. “Mathematics operations can often be signaled by more than one word or phrase; for example, plus, add, combine, sum, and increase by all indicate addition” (Corasaniti Dale &Cuevas, 1992).

10. Mental math may be norm:

Students may not show their work in addition, subtraction, multiplication and division or they may show their work in a different way.

11. Math might be gender dominated in some cultures where the men manage the family’s finances or vice versa. Traditionally in Vietnam women run businesses and men are professionals

12. Math language favors language structures that might be difficult for ELLs, e.g. passive voice.

13. Students’ misconceptions that math is only about numbers and cannot be verbalized.

14. Students are learning both math and English at the same time. Math can be the most challenging content area to teach, but it does not mean that is not possible, nor that it cannot be fun for the students. It is very important to be aware of the students’ and teachers’ shortcomings to secure the students’ success.

ConclusionAs concerned math teachers and educators, our instructional goal should be to facilitate full participation in all aspects of a rich mathematical educational experience for all students. I think we should not lead the ELL students into just a functional math (gatekeeping)leaving them semi-literate in math. That is, math knowledge that is compartmentalized and students who never learn to make connections between math and other disciplines. Therefore, it is crucial to identify these difficulties and find a way to address them.

We can do this by lessening or removing some of the barriers to learning that are connected to the process of second language acquisition. Keeping a few of these instructional strategies and techniques in mind can help us make our math instruction better for not just ELLs, but for all of our students.