INTRODUCTION TO MODULE 4

Module 4 focuses on whole class discussion. Whole class discussion constitutes an important part of the lesson in different forms of mathematics teaching. It is rather demanding for the teacher who attempts to engage all his students with challenging mathematical tasks. The challenge the teacher faces is to honour all students’ thinking and follow the rich mathematical agenda these tasks impose to students. In this context, a rich whole class discussion serves a number of important purposes such as to foster a community of learners; to build student confidence; to facilitate students’ thinking and reasoning skills; and to improve all students’ mathematical understanding. The fact that many aspects of the above cannot be foreseen by the teachers while planning his lesson adds to the challenges he has to face while enacting whole class discussion in his classroom.

Stein et al. (1996) analyse challenging mathematical tasks (a) as they are presented in the curriculum materials, (b) as they are set up by the teacher in the classroom and (c) as they are implemented by the students in the classroom. Whole class discussion takes place before and after students’ exploration with the task. It is mainly related to the launching and the synthesizing part of the lesson. In the launching phase, the teacher has to make the task accessible to the students. Important practices in this phase are to anticipate how students may interpret the task and the difficulties they may face, to monitor students’ queries or ideas and to provide feedback and tools that give students space to work on the task themselves. While students are solving the task, the teacher usually circulates around the classroom monitoring students’ autonomous work, and plans for her concluding whole class discussion (the synthesizing phase of the lesson). In this phase, students are more likely to learn from the discussion if they have been able to engage productively in the task and the teacher has to take certain decisions on how to handle that by taking into consideration all students’ needs.

This module aims to introduce issues related to whole class discussion in mathematics lessons and support teachers to facilitate classroom discussions that balance differentiation and mathematical challenge. It consists of four cases of practice for the primary and secondary level of education. The first two cases of practices, case of practice 1 and case of practice 2, relate to the launching phase of the lesson where the teacher sets up the task and last two cases (case of practice 3 and case of practice 4) relate to the synthesizing phase of a lesson. Focusing on the practices of launching and synthesizing, the teachers are expected to inquire their own practice related to whole class discussion while enacting mathematical challenging tasks to all their students.

In particular, teachers are going to reflect on classroom incidents offered in the module, and discuss and interpret them in collaboration with the other teachers in the group. Moreover, the teachers are expected to produce video clips from their own teaching, share them in the group and reflect on their actions and decisions taken in advance or on the spot.

The four cases of practice are the following:
Case of practice 1: Launching the task: Making the task accessible to the students
Case of practice 2: Launching the task: Discussing key mathematical ideas.
Case of practice 3: Sharing students’ solutions in whole class discussion.
Case of practice 4: Synthesizing: Reflections and mathematical extensions.

These cases of practice are presented in two separate sections for the primary and the secondary level of education. Before the four cases of practice in the primary and the secondary level there is an introductory activity that aims to initialize teachers with the key aspects of the module.