Recent scholarly work in mathematics education has included a focus on learning mathematics with understanding (Hiebert & Carpenter, 1992; Hiebert et al., 1997; Fennema & Romberg, 1999; National Council of Teachers of Mathematics, 2000). Hiebert et al. (1997) discussed two processes that they suggested increase understanding and that are central to this study: reflection and communication. Learning mathematics with understanding requires that the students create a deeper knowledge of mathematics through reflection and communication. The environment in which such learning can take place must include patterns of behavior, known as social norms that promote deeper thinking. When the social norms encourage reflection and communication among the members of the classroom community, or supports learning with understanding, it becomes what I term a productive discourse community. The purpose of this study is to find out what a teacher does to create and maintain a productive discourse community where students can reason and learn with understanding. To accomplish this purpose, this research asks the following question: In what ways does the teacher in the study direct mathematical discourse in order to facilitate understanding? To answer this research question, data was gathered from eight class periods. The classroom discourse was analyzed and six discourse generating tools were found to be used by the teacher: (1) using lower-order questions to engage students, (2) persisting in eliciting students' reasoning, (3) encouraging as many student participations as possible, (4) encouraging students to analyze and evaluate each other's comments, (5) encouraging students to share as many strategies as possible and (6) using a focusing discourse pattern. There were also three social norms found to be established in the classroom at the time of the data collection. These norms are: all students are expected to (a) participate (b) share their reasoning when called upon, and (c) listen to, analyze, and evaluate each other's comments. Through further analysis, it was found that the six discourse generating tools reinforced the social norms, while the social norms supported the six discourse generating tools. Thus creating an environment where reflection and communication occurred in a way that promoted learning mathematics with understanding.

[pt] O presente estudo tem por objetivo investigar o processo de reflexão profissional co-construído por um grupo de profissionais de ensino de Inglês que se engajaram em um grupo de discussão on-line inserido no contexto profissional brasileiro no qual eles atuam: em um Instituto de Ensino de Línguas. A investigação deste processo é feita neste estudo interpretativo através da análise do discurso dos 64 enunciados produzidos pelos participantes em um período de um mês e dez dias. Como participante da comunidade discursiva institucional estudada, a professora - pesquisadora ressalta a importância da linguagem e da presença do outro - do interlocutor - no processo reflexivo profissional. A análise da negociação de significado e da construção do conhecimento permitiu mapear quatro processos reflexivos, a saber: a intensificação da observação, a descrição da prática para si e para o outro, a interação com o outro, e o questionamento da prática profissional. Constatou-se também a valiosa contribuição trazida pela Comunicação Mediada por Computador para a prática reflexiva como incentivo à educação continuada do professor. / [en] The aim of this research is to investigate how the process of professional reflection was co-developed by a group of English language teaching professionals who engaged in an On-line Discussion Group designed within a Brazilian professional environment at which those professionals work. The inquiry consists of an interpretative study, which analyzes 64 exchanges produced over the period of one month and ten days. As a participant of the institutional discourse community being focused, the teacher-researcher highlights the presence of the other - the interlocutor - in the process of professional reflection. The analysis of the negotiation of meaning and the construction of knowledge was useful to map four reflective processes, such as: intensification of observation, description of professional practice to oneself and to the other, interaction with the other and questioning of professional practice. The valuable contribution brought by Computer Mediated Communication to the reflective practice, as a way to foster in-service teacher education and professional development as well, was one of the greatest findings.

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