An analysis of writing and postwriting group collaboration in middle school pre-algbra

School Science and Mathematics, Mar 2000 by Johanning, Debra I

The current reform effort in mathematics education emphasizes the importance of students' being active in their own development and understanding of mathematical ideas. The reform recommends that students read, write, and discuss mathematics as a way of developing mathematical thinking. This study emphasizes writing as a way to help students learn to think mathematically. Typically, writing has been used as a dialogue between the teacher and the student or as a product for the teacher to examine. However, this study is significant because students wrote as a preparation for discourse with the teacher and other students. Qualitative analysis was used to understand how middle school students think about and approach problems while they wrote descriptions of why and how they solve problems. For this study, students wrote detailed descriptions of their approaches to nonroutine problems and then met in groups to discuss and evaluate their approaches. In order to understand their mathematical thinking, the researcher examined students' writing, participated in and audiotaped group discussions, and interviewed students. The results of the analysis showed that rich learning experiences are possible when writing is used as a way to prepare for small group discussion in mathematics.

In recent years writing has been used as a way to enhance learning in several subject areas. This emphasis has been referred to as the writing to learn movement. Particularly in mathematics, writing to learn emphasizes writing as a way to create conceptual understanding of the subject matter. Through writing, the learners develop the capacity to communicate their ideas and use the language of mathematics fluently. Traditional writing assumes that in order for students to write about something, they must first understand the concepts. Writing to learn takes the opposite stance. This approach uses writing to help students create an understanding of the concepts by learning to communicate their ideas while using the language of the discipline. The traditional approach assumes the use of thought to create words, while writing to learn implies the use of words to create thoughts. This need to represent and convey thoughts in words contributes to the learning process (Borasi & Rose, 1989). When writing is used as part of mathematics instruction, students become active in creating and clarifying their thoughts while they struggle to share them.

Writing has been implemented in the mathematics classroom in a variety of ways and in many forms, including journals, reports, essays, and expository writing. Many researchers have explored using writing as a way to teach problem solving (Bell & Bell, 1985; Countryman, 1992; Kenyon, 1989; Tsuruda, 1994). In these studies, as in the present one, students responded in writing to a problem-solving prompt. Kenyon (1989) explained that when students write out their thinking processes during problem solving, they use higher level thinking skills to explain each step. These explanations allow the reader to understand the reasoning that led to the solution. Bell and Bell (1985) found that mathematical problem solving and writing use the same thought processes. Problem solving involves defining the unknown, determining what you need to know, designing a plan to solve the problem, solving the problem, and looking back at the solution strategy. The writing process involves discovering a topic, deciding what to say about it, organizing how to say it, writing a draft, and then revising the draft. Bell and Bell and Kenyon also pointed out that this thinking process does not come without regular practice. If the writing process is a way to strengthen student problem-solving and develop mathematical thinking, then the teacher must regularly incorporate its use. The use of writing as an enrichment activity does not have the same benefits as does writing as a way of learning.

The literature supports the benefits of writing as a way to learn mathematics (Borasi & Rose, 1989; Buerk, 1990; Countryman, 1992; DiPillo, 1994: Tsuruda, 1994). However, there is little research on the use of writing as a way to prepare for discussion about mathematics. In this study, students wrote in isolation first and then met to share and discuss ideas. It is important that students anchor on a problem in their own way at their own level (Burrill, 1998). Writing, prior to discussion, allows students to explore and understand a problem at their own level before seeing the ideas of others that may be more advanced or different from theirs. When writing is followed by group collaboration, students discuss their views and learn from others. "When children are given the opportunity to talk about their mathematical understandings, problems of genuine communication arise. These problems, as well as the mathematical tasks themselves, constitute occasions for learning mathematics" (Yackel, Cobb, Wood, Wheatly, & Merkel, 1990, p. 12). The process of writing leads to group discussion and provides a foundation in which a community of learners, including the teacher, can create and discuss mathematical knowledge.