Stage 6: post lesson discussion
How does a focus on case pupils help to ensure that the post lesson discussion focuses on learning rather than teaching?
Here, another ground rule for talk comes into play. The flow of the discussion needs to begin with each teacher’s observations of the case pupils, of how closely their observed learning matched the group’s predictions, and their responses to the lesson shared through pupil interviews (see Figure 3.15).
This ground rule discussion process preserves the group’s focus on pupil learning and on the teacher learning that arises from this. It tints reduces any tendency for the discussion to hurt into judgemental feedback on teaching, which so often kills teacher learning before it has begun.
Notes (provided in Table 3.1) from the first postlesson discussion of the lesson study group featured in Example 3 reflect how this ground rule can ensure that the team focuses on the learning from case pupils before they consider any teaching approaches. The prompts to the left of the notes help to ensure that the group considers the learning not only of the case pupils but of all pupils in the group and acts as a guide to analysis of the lesson for the teachers. You can also see how the data collected from the case pupils influenced their subsequent planning of the second research lesson.
How to improve learning for all pupils 23 Table 3.1 Post lesson discussion record RL1 (the LS group’s agreed notes)
What progress did each case pupil make? Was this enough? 
Case pupil A: M really benefited from the use of the manipulatives and the partner talk. In the post lesson discussion, she explained that she likes it when someone her own age explains “stuff because it gets in her head”. M certainly developed her conceptual understanding through the lesson. She explained that before, she didn't understand why thousandths were smaller than hundredths, but that she “gets it now”. Case pupil B: S was initially confused with the difference in relative size. She struggled to articulate why a tenth is a tenth and a hundredth is a hundredth. However, with the help of her partner and through directed questioning from the teacher, her conceptual understanding and confidence grew. She did make progress in this lesson and I think we are clear about S’s next steps. Case Pupil C: The gaps in R’s conceptual understanding were evident in the exploratory talk section of the lesson. He needed the guidance from his partner to understand how to divide the whole into tenths, hundredths and thousandths. However, we did notice that through the manipulation of the resources he was more confident in showing decimal fractions at the end of the lesson. 
What about others in the groups they typify? 
All learners seemed to benefit from the use of the concrete materials. Through the handson manipulation of the resources, the children were better able to understand the relative size of each of the parts of the whole. In the post lesson feedback from the children, all of them seemed to have a more secure understanding of the basics of decimal fractions; in particular the value of each number in a decimal. 
Do we need to revise our assessment of any pupils? 
As this was the first lesson in the sequence, we planned this as a reconnaissance lesson, and I think there were good opportunities to assess the children’s understanding in the lesson we planned. Through our probing questions and listening in to the children’s exploratory talk, we were able to assess the children’s conceptual understanding. In the next lesson we also need to build in some independent activities so we can continue to assess the individual children’s understanding. 
How did the teaching being developed help or hinder the pupils’ learning? (Maybe a bit of both?) 
Case pupil A: M was very clear in the post lesson discussion about the benefits of using the concrete materials and discussion with her partner. M showed increased confidence by the end of this lesson, and we need to build on this in the next lesson. 
What surprises were there? Did we find out anything of note about the way they were learning? 
Case pupil B: S definitely benefitted from the talk and the support of her partner. It was hugely beneficial that the class teacher took the time to think carefitlly about the mixed ability pairings. We were surprised and pleased to see S showing increasing confidence in her discussions with her partner. Case pupil C: R is normally very confident in the procedural side of maths, but it was surprising to see how much he struggled in this lesson. It was interesting to see the gaps in his conceptual understanding of fractional decimals. He certainly benefitted from the use of concrete materials and partner talk. 
What aspect(s) of our teaching could be adjusted next time to improve the progress of our case pupils and all pupils? 
We could have modelled the exploratory talk more explicitly, as some pairs struggled to sustain the conversation themselves. We will need to recap very explicitly on the new/improved understanding of decimal fractions from the first lesson. 
24 Peter Dudley and Jean Lang Table 3.1 (Continued)
We will allow partner talk before asking pupils to demonstrate the understanding using base ten equipment. We will incorporate the use of diagrammatic representation of decimal fractions and symbolic representation alongside the concrete apparatus dining this lesson and hopefully strengthen the visual representation of decimal fractions before moving on to purely symbolic representation. Continue to allow partner talk as all of our focus children have said that they like the opportunity to talk with a partner in maths to help them understand better (either by teaching it to a peer or by having it explained by a peer). 

So, what should we try next time? 
Make sme we have a model of the whole that will break up into tenths and a model of the whole that will break up into hundredths. Get the children to demonstrate the relationship between the tenths, hundredths and thousandths by dividing each of these into ten. Move the children away from the concrete to the visual and finally the symbolic once their understanding is secure, but encourage children to use apparatus or diagrams if they feel they need them. Introduce the decimal parts of length using a meter tape that can be cut up into its decimal parts. 
Sequenced research lessons
How to build on discoveries made in each of a sequence of research lessons about how your teaching has affected your pupils 'learning and how to develop, refine and test these in order to develop new pedagogical content knowledge that others can use.
Table 3.1 also shows how each successive research lesson is dependent upon the findings of its predecessor. In fact, as teachers discuss each case student’s learning in turn, they begin to realize what may be needed in the next research lesson which, thus, has its genesis in the analysis and findings of its predecessor.
Usually the first research lesson reveals more about gaps in teachers’ knowledge of their pupils learning than it does about the content of the research lesson. Sometimes teachers use the first research lesson as a reconnaissance exercise precisely for this reason (as seen earlier in Example 3). The second research lesson is usually an opportunity to recalibrate and retiy ideas in the new lesson on the basis of better knowledge of how pupils actually learned from the previous lesson. Often by the third research lesson there are one or two ideas that you wish to tiy out again for confirmation. But there will still be new approaches to be researched and trialled for those children whose needs you have yet to properly diagnose or meet.
So, these are not iterations of an identical lesson with the same intended learning outcome. They are sequences of different lessons that introduce, develop and embed particular skills and knowledge throughout the sequence. RLS thus combines lesson study, action research and design study. Design study is a science that is used when the safety of participants is paramount. It is used, for example, to improve aircraft engineering in seiies of design, txial and review flights. For this reason, lesson study is a good example of what is now called “improvement science”.