Students who generally perform well in mathematics often have difficulties solving word problems. By the time they reach high school, most students will say that they hate word problems—and many dislike math as well. What can teachers do to transform their view so more students are successful in problem solving and encouraged to learn more mathematics?

National test results (NAEP 2005) confirm that our students are, for the most part, successful in computational skills or routine exercises or problems, but show deficiency in the area of problem solving. Historically, there wasn't an emphasis on communication in the math classroom, but we now know that in order to learn mathematics students must learn to communicate mathematically (NCTM 2000, NRC 2005). This means listening, speaking, reading, and interpreting. It means explaining how a problem is solved, and explaining the problem and its solution using a variety of representations: words, symbols, graphs, charts, visuals, models, and manipulatives. Word problems are a challenge for all students. Being fluent in English is far from being fluent in the math classroom.

Mathematics is a language with its own symbols, syntax, and grammar—it can be represented in many ways. Students must learn this language and become proficient in translating within the mathematics and English languages. For example, we use the word "right" both in English and in mathematics when we speak to students. Hear the following set of instructions given by a teacher to her class:

"We have just finished the reading about the first flight of the Wright Brothers. Now for your math task, please take out a piece of paper, and write your name on the upper right hand corner. Draw an airplane design that uses right triangles and other angles. Write a paragraph describing your design. Do it right and do it right now." 

No wonder words present a problem in problem solving. There are many other words in math that baffle students. For example:

• prime number vs. prime rib
• irrational number vs. irrational behavior
• sum, total, altogether, and add, which are taught incorrectly as implying addition

Other complications arise when using symbols such as the equal sign. Many children think that the equal sign commands them to perform the operation expressed: such as in 2+3= where students may say that the equals means "we must do it,  add 2 and 3!" It's not surprising then that they're confused when presented with:
Show that 4 x 3 = 4 x (2 + 1)

The role of reading and understanding
Read the following problem:
The ferris wheel cars hold 3 children each. If there are 16 children, how many cars are needed?

Following are some of the barriers presented with this problem:

• What is a ferris wheel?
• How are the 16 children related to the cars?
• What kind of cars are these?
• What are the cars needed for?

Even when students are native English speakers, they have difficulty with language. The problems are compounded when students with different backgrounds, home culture, or language are in the same class. The diversity of today's classrooms mandates that teachers address the language as well as the math concept and skills. Also, the situation described in the word problem must be part of the students' common experiences. In this case, teachers must discuss the context of problem. For example, "the fair is coming to town, and it has a ferris wheel."

The role of visuals
A picture is worth a thousand words. Showing a picture of the ferris wheel during class discussion makes a complicated word problem simpler. Whenever possible, problems must be described with visuals, manipulatives, pictures, models, or even the "real thing." The benefits include students increasing their vocabulary as they learn and collaborate in mathematics.

The role of language
The original problem needs to be rewritten as the vocabulary is understood and discussed:

• 16 children are going to ride on the ferris wheel.
• Each car on the ferris wheel holds 3 children.
• There are 6 cars on the ferris wheel.

Now say, "What question would you ask?" and proceed to lead class discussion before putting students in groups.

The role of group work
We can provide a powerful problem-solving opportunity by asking students to make up their own problems in small groups, and then discuss and solve them. Later, they exchange papers and do each other's problems. Instead of ten routine problems that are likely unrelated, students can work on five rich problems in familiar context.

Students team up in small groups that rotate depending on the situation or problem. Each group is asked to use the data to pose a ferris wheel problem, write the problem on the front of their paper or index card, and then solve and describe the solution on the back. They can proceed to work each other's problems in groups or to do it as individuals in a station activity. While forming groups, teachers must take into account that some students work better with specific peers, that some second language learners should have someone who can help them with the language, etc. Teachers must use a creative approach in collaborative work to benefit all students and to differentiate instruction. Is it possible to enlist students from higher grades to work with your class? Or enlist the bilingual teacher? Or invite an adult that speaks the language of one of the English language learners to assist with the class?

The teacher must take this opportunity to walk around the classroom, hear the discussions, and anticipate or identify obstacles or barriers. This is also a window to assess individuals and groups. Assessment is not a test that happens at the end of the year, but a daily occurrence in successful teaching. Teachers must make sure that they're assessing the mathematics knowledge of each student and that they're aware of their language skills.

The role of communication and reasoning
Students should complete the problem by explaining the process and justifying their answers. This means that students must communicate their understanding effectively with pictures, models, words, and other representations. They have to address the following questions: what did you do, why did you do it, and why do you think the answer makes sense?

Implications for teachers
Teaching mathematics used to be much easier, but it was also ineffective and outdated for today's technological world. In the past, students imitated what the teacher did, in many cases without fully understanding the problem and its solution. Today, the focus is on approaches that force students to reason and communicate. As a result, we open the doors of opportunities to all students, help them to function in their world, and expose them to high-quality mathematics that give them access to all professions. We must prepare students for their present and future—not for our past.

References
The nation's report card: NAEP 2005. Washington, DC: U.S. Department of Education, National Center for Education Statistics.

National Council of Teachers of Mathematics (NCTM). 2000. Principles and standards for school mathematics. Reston, VA: NCTM.

National Research Council (NRC). 2001. Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.