Lesson study and curriculum development

Lesson study is a teacher development process focused on professional practice that is receiving increasing recognition in many countries around the world. Although very popular in mathematics, there are experiences in many other school subjects, both for in-service and pre-service teachers. Originated from Japan, it receives local adaptations regarding the national cultures and conditions and also the agendas of those that promote it. Lesson studies constitute reflexive and collaborative activities as teachers work together, identifying students’ difficulties on a given topic or issue, documenting curriculum objectives and guidelines, analyzing tasks, and planning what those teachers regard as an “exemplary” lesson. This lesson (called “research lesson”) is taught by one member of the group whereas the other participants observe it with a focus on student learning. So, the teachers seek to verify to what extent this lesson achieved the sought objectives and what difficulties arose. We may regard this process as a small investigation of the teachers on their own professional practice. Lesson studies take into account the curricular guidelines and the research results on the topic or issue under study. In this paper our aim is to discuss how teachers consider curriculum guidelines in three lesson study experiences carried out in mathematics, with special attention to teachers’ views on the nature of the tasks, students’ reasoning processes, and classroom communication. The methodology is qualitative, using participant observation, as practitioner research. The participants are three groups of teachers from a cluster of schools in Lisbon, at 1st, 2nd and 3rd cycles of basic education(corresponding to grades 1 to 9), and the four authors of this paper. Three of the authors conducted the lesson studies sessions and one author was responsible for data collection which included research journal, video recording with transcription of the sessions, teachers’ written reflections, and individual interviews. The lesson study at grade 3 focused on representing rational numbers as fractions and on the number line, at grade 5 focused on ordering and comparing rational numbers, and at grade 7 focused on solving first degree equations. The results show that the current Portuguese curriculum documents (Programa de Matemática / Metas de Aprendizagem) were very important to map the development of the topics under study. However, the teachers did not agree with the formalistic orientation of these curriculum documents, and decided to emphasize intuitive elements such as connections with students’ reality and pictorial representations. With their participation in the lesson study, the teachers developed a sense for the importance of the wording of tasks and for possible students’ difficulties in solving them. The teachers recognized that tasks with some degree of challenge were important to stimulate students’ reasoning and that in such cases unforeseen responses could be given by students. The teachers also got a clearer notion of students’ difficulties in reasoning processes (especially generalizing and justifying) and to aspects of classroom communication that promote or inhibit such processes. As teachers did not identify themselves with the curriculum documents, these did not play a significant role, besides the initial planning of the research lesson.