Magazine article Teaching Children Mathematics

Cooperative Problem Solving: Using K-W-D-L as an Organizational Technique

Magazine article Teaching Children Mathematics

Cooperative Problem Solving: Using K-W-D-L as an Organizational Technique

Article excerpt

Cooperative learning continues to prove its effectiveness in many facets of mathematics education. Not only does cooperative learning promote achievement with many levels and types of students (Slavin 1991), but as students work together in groups, communication and interpersonal-relations skills are refined (Greenes, Schulman, and Spungin 1992; AAAS 1989, 1993). Students in small groups are more involved with the subject matter and with one another than they are in whole-group mathematics contexts (Mulryan 1992).

Inherent in cooperative work are such valued processes as clarifying, comparing, and defending ideas as well as the social skills of listening, compromising, and reaching consensus (Rees 1990; Yackel, Cobb, and Wood 1991). Collaborative-group work affords diverse opportunities for engaging students in meaningful discourse (NCTM 1989, 1991). It contributes to a sense of mathematical community as recommended in Everybody Counts (National Research Council 1990).

Implementing Cooperative Learning in Mathematics

At the request of teachers in a Professional Development School (PDS) site for the University of Mississippi's teacher-education program, we initiated a cooperative-learning project with fourth-grade teachers and their students. In this rural school district, the teachers had not previously, incorporated much organized cooperative learning in their mathematics lessons, and they were eager to find out more about using cooperative-learning strategies effectively.

Students in two classrooms at the PDS site participated regularly in cooperative-learning groups for mathematics and other subjects. Students in two other classrooms worked only occasionally in groups. In the classrooms where cooperative learning was a regular practice, students engaged in group problem solving in mathematics two to four times each week. Often cooperative-learning sessions followed large-group introductions to topics.

In their groups, the students worked mathematics problems using their textbook materials, exercises from Cooperative Learning Resource Activities (Haubner, Rathmell, and Super 1992) (see fig. 1), material adapted from AIMS (1987) (see fig 2), real-life situations suggested by their teachers. and materials furnished by university personnel (see fig. 3). We introduced and reviewed several specific problem-solving strategies, such as guess and check, make a chart, and use a picture. In addition, as students initiated, developed, and shared other strategies, these approaches became part of the repertoire of problem-solving strategies that were available. The students worked in groups on problems using problem-solving strategies; they also created and shared similar problems of their own. The students' favorite types were logic problems and open-ended problems developed from everyday-life situations, such as the one shown in figure 4.

K-W-D-L: A Technique for Organizing and Recording Work

To guide the children's work, we used a modification of Ogle's (1986) K-W-L technique (fig. 5). Originally developed for improving reading comprehension, the technique guides readers through steps that mature readers take as they read expository material. The technique is widely used for reading, but it also holds much potential for use in mathematics investigations. Explanations of K-W-L and the ways it was used for mathematics problem solving follow.

K - What I know

In this step, readers brainstorm and discuss what they already know about a topic. The teacher lists their responses and helps the students categorize the pieces of information of which they are already aware. He or she then helps the students identify anything, such as possible misconceptions, that they want to check or clarify as they proceed.

For group mathematics problem solving, the "K" step involves students' reading, paraphrasing, and discussing the problem to see what information is provided. It may also include other strategies, such as acting out the problem, drawing pictures, or making a chart so that students begin to understand the problem and recognize what they already know about it. …

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