# Teaching Math to ESL and EFL Students

*Paul has spent many years teaching English as a foreign and second language. He has taught EFL in Taiwan and Thailand, and ESL in the U.S.*

## Mathematics

## Difficulties in Teaching Math to ESL and EFL Students

Teaching math to ESL and EFL students in school immersion programs is much more difficult than you might think. In reality, the teacher has two challenges. The first is making sure the student understands the English used in math instruction. The second is ensuring that the student understands and uses math concepts to perform basic arithmetical and algebraic computations and then applies this knowledge to solve real-world word problems. This article will examine the two challenges and suggest ways the teacher can help students meet them.

## English Used in Math Instruction

There is very much English math vocabulary encountered in textbooks and speech which all students enrolled in English immersion programs must know. It includes words like **add and plus; minus and subtract; multiplied by or times, and divided by**. It also encompasses more specialized vocabulary such as **equals, quotient, fraction, decimal, percentage, formula, a power of, squared, cubed, square root, differential, integral,** and many others. Before a teacher gives any meaningful math instruction, he must make sure his students understand and can use this specialized math vocabulary.

One of the greatest difficulties most students have is understanding English word problems where they must apply certain arithmetical and algebraic principles to get an answer. As an example, consider the following real-life word problem:

June works as a sales clerk in a clothing store. She has four days off each month and earns a basic wage of 250 Thai baht per day. She also receives a 15 percent commission for each sale she makes. In September June earned a total of 9,500 baht from basic wages and commissions. What was the total amount of sales she made in September?

In this word problem the student must understand the following words and phrases: ** sales clerk; four days off; earns a basic wage; per day; receives a 15 percent commission; and total.** if the student does not know the meaning of these words and what is asked in the problem, the teacher must first explain the meaning of the unknown vocabulary and the problem before expecting the student to solve it.

## Algebra for ESL Students

## Understanding Math Concepts and Principles as Well as Applications

The second challenge is helping the student understand math concepts and principles so that he or she can first do basic computations, and then apply this knowledge to solve real-world application problems. During my three months of experience teaching math to EFL eighth graders, I learned that some students still needed remedial help in doing basic computations such as adding, subtracting, multiplying, and dividing. Many students also struggled with understanding the concept of fractions, decimals, and percentages, and using these in computations to solve problems. A lot of practice exercises and homework were needed so that the students could grasp the use of all of these concepts.

The biggest part of this second challenge was guiding the students to apply the acquired concepts and principles in the solving of everyday word problems. A picture is worth a thousand words. In helping my students solve application problems, I always told them to visualize the problem and write down first the information given. In the commission and sales problem involving June mentioned earlier in this hub, I had the students first find out what is known from the given information. Well, in this problem, we know that September has 30 days. June had off four days, so she worked a total of 26 days during that month. We also know that each day she worked she received 250 baht. For the 26 days she worked in September, she received 26 x 250 baht or a total of 6,500 baht. These are her basic wages for September. We also know that June received a total of 9,500 baht from both basic wages and commissions. Representing this as an equation we have: basic wages + commissions from sales = total money (baht) received. Substituting the figures into the equation we get: 6,500 baht + commissions from sales = 9,500 baht. By solving this simple equation we get 3,000 baht as the commissions from sales that June received. Finally, we know that June got a 15 percent commission from each sale she made. Percent means hundredths, so 15 percent is the same as 0.15. Now, what does the problem ask us to find? We are asked to find June's total amount of sales for September. By letting "x" equal the amount of sales, we can set up the simple algebraic equation 0.15 (x) = 3,000 where (x) means 0.15 times "x", and then solve for "x". In solving the equation by dividing both sides by 0.15 we get an answer of 20,000 baht as the total amount of sales

In doing any kind of word problem I always insisted that my students show all of their work and logic in getting a solution. Merely writing the answer to a problem or showing a computation with no explanation was unacceptable.

Understanding math instruction in English and the use of arithmetical and algebraic concepts and principles in computations and applications will remain challenges for ESL and EFL students in school immersion programs. Through a better understanding of English and visualization of word problems, students through extensive practice should start meeting the challenges.

## Teaching Math to EFL Students

## Teaching Math to ESL Students

*This content is accurate and true to the best of the author’s knowledge and is not meant to substitute for formal and individualized advice from a qualified professional.*

**© 2011 Paul Richard Kuehn**