Collaborative Problem Solving in Mixed-Language Groups. (Research, Reflection, Practice)
Edwards, Laurie D., Teaching Children Mathematics
An important goal of mathematics teaching is to help all students, including students whose first language is not English, become effective problem solvers. Yet English-language learners face obstacles that may not apply to native English speakers because they must make sense of mathematical situations while interpreting a new language. The purpose of the research described in this article was to investigate mathematical problem solving involving both native English speakers and native Spanish speakers working in small, collaborative groups. The work of psychologist Lev Vygotsky provides a theoretical justification for having students solve problems in groups. A central tenet of Vygotsky's theory is that people first develop cognitive activity socially, through interaction with others, and later internalize it (Vygotsky 1978). Therefore, we wanted to investigate whether students who worked together to solve mathematical problems would later be more adept at solving similar problems on their own.
This research was funded by the University of California Office of the President, through a program in which teachers collaborated as co-researchers with university faculty (Edwards 1999). All the teacher-researchers teach in California schools that have high proportions of English-language learners. In designing the study, we wanted to give students the opportunity to communicate authentically about mathematics and to practice solving challenging, open-ended problems. We hoped that interaction in groups with students of varying levels of English proficiency would provide support for students who were trying to understand both the mathematics problems and the English language. We were curious about what kinds of interactions might be helpful (or not helpful) to the problem-solving process. Previous research had identified certain aspects of group interaction that seem to affect individual student achievement. For example, summarizing seventeen studies of small-group interaction in mathematics classes, Webb (1 991) stated that "(1) giving explanations to teammates is positively related to achievement, and (2) receiving non-responsive feedback from teammates is negatively related to achievement" (p. 382).
We decided to use problems designed for collaborative groups, drawn from the books Get It Together: Math Problems for Groups (Erickson 1989) and United We Solve (Erickson 1996). Each student in the group has one or two "clues," which are combined with other students' clues to find a solution to the problem. Figure 1 shows an example of one of the problems. Each box contains a different clue.
A total of one hundred twenty-two students, ages ten to twelve, participated in the study. The group consisted of twenty-three students from one fifth-grade class and ninety-nine students from four sixth-grade classes. Slightly more than one half of the students were native English speakers; the rest were native Spanish speakers. Each teacher assigned the students in his or her classes to mixed-language, mixed-ability groups of three or four students. The groups engaged in twenty minutes of collaborative problem solving for four days a week over a period of four weeks. During the collaborative problem solving, the students were instructed to read their own clues, listen to their teammates' ideas, and work together until they reached a solution that they all agreed on. When a group agreed on a solution, the teacher would ask them to justify their solution by stating how it satisfied all the clues. Students were allowed to use any classroom materials to solve the problems, including manipulatives, paper and pen cil, and calculators. The students had access to Spanish translations of the clues.
We collected two kinds of data: written measures of individual problem solving and videotapes of selected small groups. The primary written measure was an individual pre-test and post-test composed of problems similar to those that the small groups solved. …