# Lesson Study practice and research

Between 2013 and 2016 (across the end of Phase 1 and the beginning of Phase 2) we explored a model of Lesson Study (LS) at school but after school hours in small collaborating groups of teachers with teachers from three clusters of the schools in Phase 1. In our LS work with teachers we use the MTF as a structuring device to guide lesson planning and reflection illustrated in Figure 1. The MTF is thus an observation/reflection tool on the ‘quality’ of mathematics offered in their teaching in LS.

Figure 2 shows one cycle in doing LS in the WMCS. While the cycle follows mainstream practice of LS, constraints on time and teachers are planned for. Our LS cycle takes place one afternoon a week for three weeks. Between 2013 and 2016 over 25 LS cycles were carried out.

In the first week, the LS group plan a lesson, the topic of which is agreed by the teachers sometimes in advance, otherwise during in the first meeting. The plan usually includes a short pre-test to be given the learners at the start and then again as a post-test at the end of the lesson. In the second week, one teacher teaches the lesson to a class of learners who agree to remain after school for a one hour lesson. The learners then leave and the LS group spend the following hour reflecting on the enacted lesson and planning the second lesson which is taught in the third week, to a different class, but the same grade. A Lesson Study cycle thus involves six hours of face to face collaborations, an evolving lesson plan, and reflection on both taught lessons. Between 2013 and 2016 we conducted over 25 LS cycles across the three clusters.

In 2016 we systematically studied the work of our most participative and sustained LS study group. We found that it opened up opportunities for teachers and researchers together to learn about teaching, particularly exemplifying. We found that the qualitative changes occurred in the example set over a cycle were a collective accomplishment of teachers’ attention to their learners’ activity in the lesson enactment, and the resources researchers bring; a function of the MTF framework and so theoretically informed; and each change is an opportunity for learning mathematics and mathematics teaching.

What I have learned from these lesson studies, it is not only about my teaching and the strategies I use, but it is about giving them [learners] the mathematics that is behind each and every topic so that they understand what we are doing. The reflection has helped a lot. We can reflect on what language are the learners using …

And most of all looking at the examples, that is one where we have grown a lot, what examples we use and why we use such examples.

Prior to starting the lesson study cycles, a doctoral study (Vasen Pillay) was carried out with four teachers in two of our schools exploring the possibilities for teachers learning together from collaborative lesson study. It was the success of this study that provided the impetus for the intervention that followed.