Magazine article Teaching Children Mathematics

Helping English-Language Learners Develop Computational Fluency

Magazine article Teaching Children Mathematics

Helping English-Language Learners Develop Computational Fluency

Article excerpt

Students who are computationally fluent can solve problems accurately, efficiently, and with flexibility. These students draw on a repertoire of strategies when solving problems, and their choice of strategies often depends on the type of problem they are solving and the numbers involved.

Although we can define computational fluency and explain how it can be nurtured, the challenge is to ensure that all students attain fluency. How can we help all students, especially English-language learners, develop computational fluency if they have experienced mathematics as quiet, solitary practice of standard procedures? How do we make communication the focus of mathematics class so that mathematical conversations are productive and accessible to everyone? What sensitivity, awareness, and skills do teachers need when working with students from diverse backgrounds with differing experiences and skills who may be learning English as a second language?

Computational fluency is rooted in an understanding of arithmetic operations, the base-ten number system, and number relationships. Communicating mathematical ideas is fundamental to developing computational fluency. When students share their solution strategies with others, they learn that there are many ways to solve problems and that some strategies are more efficient than others.

Communication: An Instructional Feature That Can Promote Fluency

Research in mathematics education identifies specific instructional features that promote conceptual understanding of mathematics and are associated with higher levels of performance. One such feature is communication. Many researchers of mathematics learning have found that students benefit from communicating their mathematical ideas (Cobb et. al 1997; Heibert and Wearne 1993; Khisty 1995; Lampert 1990; Wood 1999). When teachers ask effective questions, they prompt students to articulate their various solution strategies, which can create a cross-pollination of ideas. Students become flexible problem solvers, and through shared dialogue they begin to build computational fluency. But what happens when students learning English as a second language are expected to communicate mathematical ideas in English?

Communication in mathematics class has the potential to facilitate understanding and develop computational fluency, but the practice of discussing ideas in English may place children who are learning English as a second language at a distinct disadvantage. For example, English-language learners can become confused during a discussion if the mathematics vocabulary has different meanings in everyday usage, as with column, table, and rational. They also may be confused if the same mathematical operation can be signaled with a variety of mathematics terms, such as add, and, plus, sum, and combine. A word such as left--as in "How many are left?"--can be confusing when the directional meaning of the word is most commonly used in everyday English. The words sum and whole also can cause confusion because they have nonmathematical homonyms. Furthermore, a symbolic statement such as 9-4 = 5 can be expressed verbally in several different ways, such as "Nine take away four is five" or "Four from nine leaves five." Unles s teachers thoughtfully construct conversations that are intended to promote an understanding of mathematics, English-language learners are less likely to benefit from mathematical discussions.

If students talk about their mathematical ideas in order to develop their computational fluency, teachers must make sure that communication does not result in inequity for English-language learners. The Equity Principle in Principles and Standards for School Mathematics (NCTM 2000) states that all students, regardless of their personal characteristics, backgrounds, or physical challenges, must have opportunities to study and learn mathematics. NCTM recognizes that equity requires an accommodation of differences. …

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