Dean has a recipe for lemonade. To make 14 servings, Dean will need 4 cups of lemon juice. How many ounces of lemon juice will Dean need if he wants to make 35 servings?
Students in the United States are taught to complete the following steps when solving a word problem like this:
- Read the entire problem.
- Determine what the question is.
- Find the information needed to solve the problem.
- Determine what operation is necessary to answer the question.
- Solve the problem.
- Check to make sure the answer is reasonable.
The steps seem clear, but English language learners often struggle with steps one and two. This is particularly true when the problem revolves around non-metric measurements such as cups, quarts, or inches. Consequently, the remaining steps are lost in translation.
English language learners are hard workers and strive to be successful, yet the language of mathematics often frustrates them. In the word problem above, an English language learner may understand that a cup is used to drink from, but may not understand a cup as a means of measurement.
Mathematics books in the students' native language are helpful, but the help is enhanced when English language learners are paired with more fluent English speakers who can translate and explain in the native language. With the help of a partner, the limited English speaker can discuss and understand the rationale behind the words and their meanings. They can solve problems together.
Neither ELL nor English-proficient students like word problems because they find them to be long and confusing with vocabulary that doesn't make sense. It is easy enough for ELL students to distinguish between add, plus, and minus, but when confronted with words like quotient and product, they are likely to have trouble.
A foldable is an interactive graphic organizer students can use to become more familiar with difficult math terms. Students fold a piece of paper such that the vocabulary word is written on the “tab” and is visible. The definition of the word is hidden beneath the tab. (See http://newsouthvoices.uncc.edu/files/nsv/institute/Foldables.pdf for sample foldables.)
By creating their own foldables, students can reinforce key topics in the math curriculum. Not only are students seeing a math word in context, they are also writing the words (which reinforces learning) and referring to them as a study aid.
Today's math class is not about simply solving a two-step equation; it's about reading for meaning, identifying a situation, finding the information for the problem, setting up the equation, and then solving the equation.
How many middle grades teachers does it take to help all our students learn and understand math? All of us!
Previously published in Middle Ground Magazine, October 2010
Diana Picchi Cwynar is a math teacher at Harris Road Middle School in Concord, North Carolina. E-mail: Diana.firstname.lastname@example.org
Susan Hewett, is a math teacher at J.N. Fries Middle School in Concord, North Carolina. E-mail: Susan.email@example.com