Development of mathematical communication in problem solving groups by language minority students

Bilingual Research Journal, Spring 1998 by Brenner, Mary E

Abstract

This article is an examination of mathematical communication in two algebra classes with ESL students. Using videotaped data, the author found that students in one classroom engaged in very little mathematical communication, most of which was oriented toward simple answers and fragmented procedural descriptions. This is attributed to instructional decisions that minimized the authority and use of small groups, and students' difficulties with the mathematical register in both English and Spanish. This contrasted with the other classroom in which students engaged in extensive mathematical communication in small and large group formats. The paper discusses how small groups facilitate the development of communicative competence and the potential value of computers for stimulating discussion.

With the adoption of a constructivist philosophy, mathematics educators now advocate more active learning on the part of students and a more facilitative role for teachers. A key component of most new instructional programs is that students are expected to discuss mathematics with their peers and their teachers. This new emphasis upon mathematical communication is a challenge for teachers and students in classrooms everywhere. For the 1.2 million Limited English Proficiency (LEP) students in California and their counterparts in other states, the challenge is even greater. As recently reported by the California Department of Education, most of these students receive no content instruction in their native language (Macias, 1995). These students are given the double challenge of learning new ways to talk about mathematics while learning a second language.

There is an urgent need for researchers and teachers to work together to find effective ways of including LEP students in the new mathematics programs, using the resources that are currently available, so that linguistic minority students are not left behind as mathematics education is transformed. This study addresses that need by examining how two teachers who were implementing an innovative algebra program called College Preparatory Mathematics: A Change from Within (CPM) structured classroom discussions in classes with substantial numbers of second language learners. One teacher, Miss G, taught a class composed totally of native speakers of Spanish; Miss G was not a native Spanish speaker, had a very low level of proficiency in Spanish, and used only English as a medium of instruction. The teacher consciously used the principles of sheltered instruction (Snow, 1990) and made other adaptations to her teaching style. The school also assigned Spanish-speaking aides to help in this class. The second class, taught by Miss Y, was at the same school and used the same curriculum. A majority of students in the class were native speakers of English, but with a substantial minority having similar language skills to Miss G's students. Miss G's class is of particular interest because it represents one school's attempt to meet the needs of students with limited English proficiency while carrying out a major change in the mathematics curriculum. All names mentioned in this article are pseudonyms.

The goal of this article is to describe what kinds of mathematical communication took place under what instructional conditions in each classroom. In particular, I want to analyze why the students in Miss G's class engaged in almost no mathematical communication in either large group discussions or in their cooperative groups, despite the school's efforts to provide extra resources in support of the class. I will argue that the changes made to accommodate the language differences between the teacher and students in fact undermined the CPM program's intended cooperative group structure. In addition, despite the extra use of Spanish-speaking aides in the class, the students did not receive enough comprehensible language input to develop their communication skills in either English or Spanish. In contrast, the students in Miss Y's class had more opportunities to practice their mathematical communication because of Miss Y's more extensive reliance upon small group instructional formats.

Educational Reform in Mathematics and Linguistic Minority Students

Improving students' ability to communicate mathematics is one of the major goals of the mathematics reform movement. The Curriculum and Evaluation Standards for School Mathematics published by the National Council of Teachers of Mathematics (1989) states:

In grades 9-12, the mathematics curriculum should include the continued development of language and symbolism to communicate mathematical ideas so that all students can: reflect upon and clarify their thinking about mathematical ideas and relationships; formulate mathematical definitions and express generalizations discovered through investigations; express mathematical ideas orally and in writing; read written presentations of mathematics with understanding; ask clarifying and extending questions related to mathematics they have read or heard about; (and) appreciate the economy, power, and elegance of mathematical notation and its role in the development of mathematical ideas.(p.140)