A Deceiving Counting System
Michael Bahi, Niles West High School
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Imagine yourself stranded in a random location somewhere on this planet. You walk endlessly to find any sign or form of communication, when you suddenly come across these symbols:
Looking at these signs, you can infer the first one looks like a decimal or period, the second one looks like the number “1”, the fifth one looks like a backwards “3”, the next three symbols look like “0”, “7”, and the letter “V”, respectively, and the last one a “9”. So, there you are, stranded in the middle of nowhere with nothing but a list of symbols in which seven look somewhat familiar. Hopefully, you wouldn't go with your presumptions and take these symbols for what they appear to look like. If you did, however, you would be upset to know that only two of those assumptions were correct (the ones that look like a “1” and “9”). The symbols are the Arabic numerals from 0 to 10, shown above in numerical order. Yes, that “backwards 3” is a 4, the zero is a 5, that “7” is a 6, and the “V” is a 7. But enough daydreaming about being in the Middle East where the weather is five times warmer than the Midwest; that wasn’t the point of this discussion.
The purpose of this paper is to recognize a fraction of the difficulties emergent English language learners face when coming to this country. In this discussion, we will focus on the Arabic counting system and how its appearance, written order, and phonetics cause confusion to students learning the English counting system. Although our counting system is technically called the Hindu-Arabic numeral system, it will be referred to as the English counting system to prevent confusion.
We can already concur that the looks of Arabic and English numbers can be deceiving (i.e., their number five looks like an English zero, six looks like our seven, etc). It’s safe to say it’s even more confusing with double- and triple-digit numbers. Imagine a Middle Eastern student coming across the number “70”, for example, in the United States. This would appear as “65” according to the student’s native language! Numbers are everywhere in this country: cellular phones, street signs, kitchen appliances, automobiles, medication, calendars, and clocks (to name a few). For a newcomer to encounter these numbers on a daily basis, it can become confusing and aggravating. Now, picture this newcomer in a mathematics classroom. American teachers are used to citing numbers effortlessly. However, for an emergent English language learner it will take some time to process simply looking at certain numbers. Imagine an algebra classroom, where “X” is no longer the symbol used to represent multiplication. Instead, a decimal is used that is placed a bit higher. Take a look at the following problem:
This problem that is so simple to most people can be baffling for a newcomer. If the English number system is new to them, they could see that problem as “15063 = ?”, which can cause frustration and lower self-esteem. When working with English language learners, we must keep in mind how our number systems can look similar, but in a misconceiving way.
Apart from looking different, numbers are also said differently. No, we are not going to discuss how numbers are said in Arabic, but rather the way they are said. In the English number system, we say any number left-to-right, regardless how high the number is or whether or not it has a decimal value. With our numbers in the teens, they are said slightly differently - i.e. “17” is not said “ten-seven”. In Arabic, unless there is a decimal, the number in the tens place is said last. For instance, “25” would be said “five -twenty”, “77” would be said “seven-seventy, and so forth. Working with several Intro to ELL students, I have noticed how much distress this can cause. I have seen them open their textbooks to page 26 when I asked them to turn to page 62. With triple-digit numbers and beyond, the number in the tens place is still said last. For example, the number “1,284” would be translated to “one thousand two hundred four eighty” in Arabic. Again, this can cause great difficulty and bewilderment for emergent English learners, especially since we teachers have a tendency to rapidly cite numbers.
Numbers can be easily misinterpreted. Teachers must keep in mind that these misinterpretations are from linguistic language, not conceptual language. When we think it is the latter, student Zone of Proximal Development (ZPD) (Brown and Eisterhold, 22) can be underestimated, thus affecting the student’s education.
The Arabic language has another feature that differs from English: it is read right-to-left. Fortunately for all Middle Easterns, numbers are written left-to-right. For instance, “159” would be written as “109” in Arabic. This is also true with phone numbers. However, when listing counting numbers (0, 1, 2, 3,…) in Arabic, they are listed right-to-left (..., ۳, ۲, 1, ∙). Although this is a minute difference, it can still cause initial confusion for a student who is just beginning to learn the English counting system.
What We Can Do
From the preceding sections, we can speculate on the caliber of difficulties emergent Middle Eastern students face when coming to the United States. Nevertheless, most professionals in education assume that only their vocabulary and grammar need to be progressed. From this project - and working individually with many ELL students from the Middle East - I have learned much about the subtle differences in our cultures that have a huge impact on ELL students. Keeping in mind the differences in number appearance and pronunciation, we teachers must help ease their transitions into a new country and number system.
In ELL Algebra classrooms, I have seen a variety of learning activities used in the initial weeks of class. One activity was handing out worksheets with a table titled “Numbers 1-10”. Students would write each of the first eleven numbers - counting zero - in English, spell it, and write that number in their native language. This sheet can be used at all times during the first few weeks of class, including quizzes and in-class assignments. It really helped the students understand the subtle differences and quickly become accustomed to them. This activity was repeated for numbers in the tens, hundreds, and thousands.
Another notable activity was in an Intro to Reading class, where students created their own customized clocks and practiced telling time. Behind this paper clock, the numbers 1 through 59 were written along with their spelling. Students would be encouraged to set the clocks at a random time and tell the time of their peers’ clocks, without looking at the back of the sheet for assistance.
Teachers working with ELL students should always remember to speak slowly and concisely with numbers. We have a tendency to shorten 3- and 4-digit numbers, like saying “one thirty-four” instead of “one hundred thirty-four”. Because it is second-nature to us, we don’t realize the many differences in other cultures’ number systems that can cause an ELL student to take some time in processing numbers. Teachers also need to inform them when it is okay to shorten verbal expression of numbers (i.e., saying the year is “twenty-thirteen” rather than “two thousand thirteen”).
At Niles West, there are four primary introductory classes for emergent language learners: Intro to ELL Reading, Intro to ELL Vocabulary, Intro to ELL Grammar, and ELL Algebra. Intro Reading and ELL Algebra are the only two classes that put emphasis on number pronunciation and spelling, since the other two classes use so much time to build English vocabulary and strengthen grammar. While understanding numbers is just as vital as building vocabulary, ELL teachers should collaborate and discuss how both vocabulary and the English number system can be incorporated into curriculum. They should also be encouraged to record what works well and delivers the transition in the most efficient and effective way.
As Brown and Eisterhold point out, any translation is difficult to accomplish; some are more difficult than others (41). From appearance to verbal expression, there are vast differences between the Arabic and English number systems that can cause misinterpretation and confusion to emergent English language learners from the Middle East. Bearing this in mind, teachers can make several minimal adjustments and incorporate a slew of activities that will ease student transition into the English number system.
Brown, S. & Eisterhold, J. (2004). Topics in Language and Culture for Teachers. Ann Arbor: University of Michigan Press.
Eastern Arabic Numerals. (2014). In Wikipedia. Retrieved April 7, 2014, from http://en.wikipedia.org/wiki/Eastern_Arabic_numerals
Michael Bahi is an American Assyrian born in Chicago whose parents migrated here from Iraq. He teaches mathematics at Niles West High School. He was intrigued by English Language Learning since English was not his first language and because his highly diverse student body consists of many English Language Learners.
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