The team of four teachers were participants of an inservice course. The meetings with myself were on 5 May, 23 May, and 27 May. In the first meeting, which was attended by the Principal and Head of Mathematics and Science, we focused on developing the research theme and helping teachers understand the lesson-study process better. Although they had attended some workshops, they still felt that they needed to have an opportunity to clarify some questions.
The team met on their own to plan the research lesson. I met them once to discuss the lesson plan. As their research theme is on students developing conceptual understanding in mathematics, I kept on asking the team if the steps in the lesson plans and the examples selection can help students develop conceptual understanding.
The team had to do a bit of modification to the research lesson as the students were going to m missed a lesson due to a school outing. Also, our discussion went off tangent for a few moments as some members brought up an interesting observation from a lesson on equivalent fraction.
The research lesson was on comparing two fractions with the same numerator but different denominators.
At the end of the lesson planning sessions, team members were asked to share a learning point. I started the ball rolling. One teacher noted that she realized how important the selection of examples was. In the discussion, I asked teachers several times why the tasks selected were so and if the selection or its alternative would lead to better conceptual understanding. For example when these three were put up: compare 1/2 and 1/8, compare 2/3 and 2/5 and compare 5/12 and 5/8, I pressed the team to explain the wisdom of having 1/2 and 1/8 as the first example. One member gave an illuminating answer that 1/2 and 1/8 are obviously different. Students would be able to say that 1/2 is larger without having to change both 1/2 and 1/8 to a common denominator. The discussion ended with the point that using an obvious case where students can use prior knowledge to validate the 'new' method would enhance conceptual understanding.
Two others said they learnt from the case of the unusual pattern students raised during a lesson on equivalent fraction other members shared (see photo). One of them mentioned that sometimes as teachers we tended to "focus on what is in the textbook (and) too quick to discount" students' responses.
Finally, another member realized how important the concept of trigger and source is. In the discussion, I discussed in the context of preparing for the research lesson, to be on a look out for conceptual understanding (I summarized some indicators of conceptual understanding which the teachers gave - if they can use correct terms, if they can recognize a pattern, if they are able to use diagrams to explain and if they are able to resolve apparent conflicts) and the triggers and sources of these conceptual understanding.
The team met on their own to finalize the lesson plan and to prepare the resources for the research lesson...