Marisa Quaresma

Exploratory Activity in the Mathematics Classroom

In this chapter, we show that mathematical explorations may be integrated into the core of the daily classroom mathematics activities instead of just being a peripheral activity that is carried out occasionally. Based on two episodes, one on the initial learning of the rational number at grade 5 and the other on the learning of algebraic language at grade 7, we show how teachers may invite students to get involved and interpret such tasks and how they may provide students with significant moments of autonomous work and lead widely participated collective discussions. Thus, we argue that these tasks provide a classroom setting with innovative features in relation to conventional education based on the exposition of concepts and procedures, presentation of examples, and practice of exercises and with much more positive results regarding learning.

Fitting Lesson Study to the Portuguese Context

The adaptation of lesson study to different national contexts raises problems that are attracting the attention of researchers. In this chapter, we show how we have conducted lesson study in Portugal, taking into account the national educational context and our perspective on the teaching of mathematics, the exploratory mathematics curriculum approach, with particular attention on the development of students’ mathematical reasoning. We present two examples of lesson study, one conducted with in-service teachers of grades 5–6 and another in initial teacher education with prospective teachers of grades 7–12. We reflect on what we have identified as the main obstacles to the realization of lesson study in these contexts due to cultural factors and teachers’ concerns. We conclude with a summary of the adaptations that we have made in this teacher education process, with a view to the suitability and potential of lesson study in our country.

Teachers’ involvement and learning in a lesson study

The aim of this study is to analyse the way a group of basic education teachers got involved in a lesson study and their views, as they discuss the features of tasks, students’ expected difficulties and how to conduct exploratory work in the mathematics classroom. The conceptual framework draws on notions of task design and considers the features of lesson study. Data collection was made through a research journal made by one of the authors in the role of observer, video recording with transcription of the sessions, teachers’ written reflections and interviews. The results underscore the value of focusing on students’ reasoning in working in mathematical tasks as well as the need to address affective issues, regarding the way teachers are invited to become involved and participate in lesson studies.