08 Lesson Study in ITE
07 Curriculum Thoughts from Japan
This blog by Geoff Wake draws on lesson study research lessons observed in Japan. Geoff is Professor of Mathematics Education at the University of Nottingham and Chair of trustees of CLR - UK.
Elsewhere (Wake and Selezynov, 2020) I have written, with Sarah Seleznyov, more substantially about the use of, and further potential, of lesson study as a means of researching and informing the design of the mathematics curriculum. This is indeed central to the work of at least some of the teacher research groups that are facilitated by university researchers in Japan, as is the case of our researcher colleagues at Tokyo Gakugei University. Over many years their knowledge and experience has been important in informing the implemented curriculum scross aspects of curriculum specification, guidance, textbooks and associated tasks. Here, I provide glimpses into four research lessons at different grade levels in Japan. Across these the mathematical concept that informs each of them is that of multiplicative reasoning. For each I post just a picture/video or two that I took in each of these lessons to draw attention to how there is a level of coherence and connectedness. I present them in the order in which I observed the lessons, but I could equally have provided a different order without detracting from the thread that weaves its way through them.
Research lesson 1
The first lesson was based on this task with the intention that the students use the area formula for a of a rectangle when calculating. In an earlier lesson these grade 4 students had worked with the formula which is always presented as "height" x "width". This allows students to "interpret" the thinking of others by examining the expressions they write for areas. These expressions can provide insight into the way their peers were thinking about how to solve the problem. (I've written a blog about the three-dimensional equivalent lesson here: https://educationblog.oup.com/secondary/maths/teaching-for-learning-the-japanese-approach ).
Bringing together the two curriculum issues I have highlighted here allows the teacher and students to interpret the thinking of the author of the left-hand diagram as being consistent with splitting the L shape into two rectangles of height 4 and 2 with each being of width 3. The right-hand diagram is less obvious; it isn’t clear that the author of this attempt is working with a rectangle of height 2 and width 9 (which could be arranged by cutting the L shape horizontally along DE extended), rather than working out the total in nine groups of 2. This raises the question of whether the student whose work we see in the right-hand attempt was sure about how to calculate the area by decomposing the shape.
Research lesson 2
This lesson explored similarities and differences in partitive and quotative division in a Grade 3 lesson. Pupils explored two problem situations:
1. There are six candies. If 2 people share the same number of candies how many candies will each person get?
2. There are six candies. If you share 2 candies to each person how many people can share the candies?
A simple online manipulative tool was available and in the two brief videos linked below you can see how the pupil I observed used this tool to illustrate the two problem situations.
1. Partitive division.
2. Quotative division
Here is part of the teacher’s bansho work at the end of the lesson.
Research lesson 3
In this Grade 4 lesson pupils were working on a problem which required them to divide a three digit number by a two digit number for the first time. The problem resulted in them needing to divide 168 by 24 (to find the number of origami paper cranes each student would need to fold to reach the required number across the school).
The left-hand diagram shows how some students reduced this to a division calculation that they could answer of a two-digit number divided by a single digit (with their fluent understanding of multiplication tables up to 9 x 9). In the right-hand diagram they checked that the fixed number of students 24 in a class would each fold 7 paper cranes. Again consistent in its expression of the fixed multiplicand (24) multiplied by the multiplier (7).
Research lesson 4
Across the three diagrams you can see how the student works with this partitive division situation to determine the cost per metre. Their multiplication and division expressions are consistent with the work we have seen across the grade 3 and 4 lessons.
06 Is lesson study for me?
Laurie Jacques is an independent mathematics teacher educator and research fellow on the Student Grouping Study at IOE, UCL.
05 Learning from Lesson Study
Last week (January 10th 2023) I attended the Learning from Lesson Study online PD event. When I booked onto this session, I was a bit apprehensive as I had experienced a number of collaborative lesson study live research lessons in the UK with face-to-face post lesson discussions and a koshi (knowledgeable other) conclusion. I wondered how this online version could make me think as deeply as a face-to-face session could. It turns out that the reading of the lesson proposal, watching the recorded lesson and listening to the planning team and three further knowledgeable others (Andy, Mike and Janine) reflect on the lesson gave me a number of very varied and thought-provoking ideas to play with in my work as a primary maths advisor.
So having a personal struggle with this dilemma it was great to hear Mike (Askew) explain the difference between a mathematical model and a reshaped mathematical model.
04 Leading Lesson Study
03 Thinking space - for both pupils and teachers
02 Reflections on a Collaborative Lesson Research cycle
This blog from Matt Woodford reflects on one of two lessons CLR facilitated at the University of cambridge Primary School with teachers visiting from the Tsukuba University attached Elementary School in Tokyo. The lesson was held in October 2023.
Matt is a Senior Lecturer at Nottingham Trent University and is researching Lesson Study.
Stage 1: The research purpose
Stage 2: Kyouzai kenkyuu
01 What is lesson study?
This blog first appeared here: https://sarahleakey.wordpress.com/
Sarah Leakey is a teacher, currently working in Highland, Scotland and undertaking PhD studies at the University of Nottingham.
I gave a general outline of what lesson study is in my last blog post along with a timeline of my own experiences. Here, the purpose is to outline a handful of the variations of lesson study to highlight the fact that when people talk about lesson study they are not always talking about the same thing. Variations have arisen out of different interpretations of the available literature at different points in time and out of the need to adapt models to suit cultural differences as well as differences related to education systems in different countries and availability of resources.
The other reason for writing this blog post is to begin to make my use of lesson study transparent to others. One of the factors that I've found quite frustrating when reading about lesson study is that what is being described is sometimes labelled quite generically as 'lesson study' but the finer details of what was actually undertaken are not always obvious. As a result, I have at times found it hard to fully understand the implications of what was done, draw conclusions or attempt to replicate or adapt what others have done in the settings I work in.
Hopefully I have presented a fair account of the variations I have chosen to focus on here but I'm happy to make amendments if anyone thinks I've misinterpreted or misrepresented any aspects.
Collaborative Lesson Research (CLR)
This is the 'type' of lesson study that I have most closely tried to align my own attempts with. This is due to a number of factors including opportunities and experiences related to my own professional development and greater transparency of what is involved e.g. through publications such as that by Takahashi and McDougall (2016). Of all the variations I have come to learn about, for various reasons it also seems to resonate more closely with what I believe to be important in relation to both professional learning for teachers and pupil learning.
Collaborative Lesson Research Cycle (Takahashi and McDougal, 2016)
Takahashi and McDougal (2016) define CLR as having the following essential features:
Future cycles would have the same overarching research theme but might be taught to a different year group with a focus on a different area of mathematics.
Research Lesson Study (RLS)
This model was introduced to the UK by Pete Dudley. More information on this variant can be found here. I believe this is the model that the version of lesson study I was a participant of, back in 2007/8 was based on but in reality it was a diluted version of this.
The Research Lesson Study Process (Dudley, 2019)
The diagram above and the details below have been summarised from the Research Lesson Study Handbook (Dudley, 2019).
You can see many similarities to Collaborative Lesson Research such as establishing a focus for the research theme, reviewing and modifying teaching materials (kyouzai kenkyuu), having a research proposal, live lesson and post-lesson discussion and sharing the findings.
In terms of a 'knowledgeable other' RLS doesn't appear to make this an essential feature but does say that 'it can be key'. This may be in-house expertise or if this is limited, an expert could join the lesson study group for at least one of the three research lessons.
Other key differences to CLR include the explicit use of case study pupils in RLS and the way the cycles are conducted. In RLS, my understanding is that the three cycles would be conducted with the same class and the same 'unit' of learning whereas with CLR just one research lesson is taught from the broader unit that has been planned and subsequent cycles might be on a different topic and potentially with a different year group but with the same overarching research theme.
Adaptations in the USA described by Stepanek et al. (2007)
The book Leading Lesson Study: A practical guide for teachers and facilitators by Stepanek et al. (2007) was one of the first books I purchased when my awareness/interest in lesson study was renewed in 2018/19. The key features are outlined below along with key differences to the two variations I've already described.
A key difference here, as you can see, is the revising and reteaching of the lesson. In Research Lesson Study, the first lesson was discussed and used to influence decisions about a lesson taught to the same class in a second cycle but the same lesson isn't retaught. In Collaborative Lesson Research, while information from one cycle feeds into the next cycle, it would typically be on a different topic (but with the same overarching research theme). In CLR, Takahashi and McDougal (2006) explicitly state that the purpose of the post-lesson discussion is to 'gain insights into teaching and learning and to inform the design of future lessons, not to revise the lesson plan.' They also highlight the purpose of lesson study as gaining new knowledge for teaching and learning - not to perfect a lesson plan.
The Dutch Model
I can't claim to have any in-depth knowledge of the Dutch Model but from what I have read, it makes for a useful comparison to the ones I've outlined so far. De Vries, Verhoef and Goei (2016) have written a guide book related to this model however as I don't have access to this, I'm citing them from Wolthuis et al. (2021).
In the Dutch model there are six phases:
This model recommends 20 hours per cycle. You can see here, an essential feature is repeating the research lesson which appears similar to the model described by Stepanek et al. (2007). From my reading, there appears to be more flexibility in the use of a knowledgeable other and rather than needing to be a physical person, this could be in the form of books, articles, videos etc. Kyouzai kenkyuu is also said to feature less prominently as there is no national curriculum.
Features common to all, although there will undoubtedly be subtle differences even in these common elements, appear to be a research theme, planning, teaching (or observing) a research lesson and engaging in a post-lesson discussion.
Features that appear to either differ or be more flexible/less prominent are the inclusion of a knowledgable other, engagement with kyouzai kenkyuu, the use of case study pupils, the purpose or structure of subsequent cycles including reteaching the research lesson (or not), sharing the findings.
It seems to me that these differences could result in huge variations in the 'outcomes' or 'effectiveness' of lesson study and as such I feel it's important that people are transparent about their implementation of lesson study so it's easier to make sense of which features might be influencing various outcomes.
In the next few posts I intend to outline in more detail how I've used lesson study in schools in Highland including some of the benefits and challenges we've encountered along the way and adaptations we're exploring.