# Blog

## 08 Lesson Study in ITE

This Blog is by Rosa Archer who is a senior Lecturer at the University of ~Manchester where she leads the PGCE Secondary Maths programme.

I became interested in Collaborative Lesson Research (CLR) more than 10 years ago when attending a conference. Since then, I have tried to embed it into my work with Initial Teacher Education (ITE)

I lead a team that works with a cohort of roughly 50 PGCE Secondary Mathematics student teachers. As part of the PGCE course the student teachers are directly involved in a lesson study cycle in selected schools that work in partnership with the university. Student teachers visit the local partner schools in groups of 10 accompanied by a university tutor. They visit the schools three times in September but during these initial visits no lesson study cycles take place. In fact, student teachers use these three days to get used to the school and become comfortable with working with each other. They observe a lesson and plan it retrospectively and facilitate a carousel of problem-solving activities. This first experience is very important in allowing the group to build trust in each other. So early in the course the student teachers are not yet ready to take charge of a full lesson. In January, once the student teachers are a little more experienced, two lesson study cycles take place in each school involving a group 5 of student teachers. The student teachers spend a considerable amount of time planning for the lesson in university and teach the lesson to borrowed classes. The class teachers are present during the post lesson discussion and might offer some feedback but are not involved in the planning or in the teaching. The university tutors observe the planning, teaching and act as koshi during the post-lesson discussions. The same lesson is then taught again to a different class the following week.

This model has developed over time. Initially my approach was extremely naïve and my understanding has developed during the years. In particular a visit to Japan in 2015, when I had the privilege to take part to the INPULS immersion program, helped me develop my understanding of Collaborative Lesson Research. Professor Fuiji talks about the misconceptions that arise when Lesson Study is adapted to suit different contexts (Fujii, T. 2014). In particular he analyses the importance of the study of the curriculum which comes before the writing of the lesson plan. This is something I understood by trying the model and making mistakes. Certainly, CLR is not cheap CPD and does not offer a quick fix, in fact in order for it to be effective a significant amount of time needs to be spent studying the curriculum, developing the lesson planned reflecting on expected responses. The advantage of working with student teachers is that they have the advantage of being able to spend a considerable amount of time discussing the lesson plan in university, while experienced teachers often don’t have the luxury of time.

I have set out below some of the advantages of doing CLR with ITE students.

I feel the lesson study experience helps student teachers develop their confidence, since when they arrive at the school ready to teach the lesson, they see themselves as the expert on that lesson since they have spent time and effort planning.

The experience also offers an opportunity to translate theory into practice. Finding a synergy between theory and practice is one of the many difficulties of teacher training and I feel that CLR provides a very good opportunity to do so. In fact, having analysed the theory in university, student teachers can use their understanding to plan lessons and see with their own eyes how the learners respond.

Another advantage of working on Lesson Study with student teachers is that it gives the students the opportunity to construct their pedagogical understanding by working on ‘risky’ lessons. Often, when training to teach in school, student teachers are required follow rigid lesson structures and might not be encouraged (or might not have the confidence) to experiment with emphasising problem-solving, collaboration and allowing an active role for students.

During the post lesson discussion, university tutors, acting as Koshi, encourage student teachers to reflect on learners’ responses deflecting the attention from the teacher to the learners. It is common for beginning teachers to focus more attention on the teacher rather than the learners. CLR in ITE seems to offer a great opportunity to encourage student teachers to move the attention from the teacher to the learners by analysing and reflecting on learners’ responses.

It is my belief, and something I am hoping to analyse in more detail, that student teachers build on their own understanding of mathematics while planning in detail and analysing learners’ responses with others. Subject Matter Content Knowledge, Pedagogical Content Knowledge, and Curricular Knowledge Shulman,L.S.(1986) are developed through open dialogue with colleagues during the lesson study cycle.

Below I have reflected on aspects of CLR that I have developed to better suit ITE

I believe that for student teachers the re-teaching of the lesson is a very significant part of the experience. The re-teaching of the lesson gives inexperienced teachers the ability to reflect on practice. Experienced teachers have rich knowledge about teaching and learning that they have acquired during the years. Given a problem, they can quickly assess the situation and think of a solution that matches the problem, they can also predict learners’ responses while beginners might have difficulties in imagining how the lesson will evolve. Re-teaching the lesson is not common practice in Japan, where it is also very unusual to involve student teachers as active participant in lesson study cycles. Fuiji reflects on the practice of re-teaching the lesson after the post lesson discussion.

…. in [countries other than Japan] there seemed to be no hesitation in re-teaching the research lesson. This practice evaluates the teacher's performance and the feasibility of the lesson plan. The author believes the possible roots of this misconception may stem from the steps in lesson study described in The Teaching Gap (Stigler & Hiebert, 1999, pp. 112–113). These include: Step 3: Teaching the lesson; Step 4: Evaluating the lesson and reflecting on its effect; Step 5: Revising the lesson; and Step 6: Teaching the revised lesson. This suggests a practice of revising a faulty part and replacing it in the revised lesson. An inorganic system, such as a car, is composed of parts that may be easily replaced. However, in organic systems like a lesson or like lesson study, each part is systemic, not systematic. (Fujii, T. 2014)

To achieve an honest reflective dialogue with student teachers we make a conscious effort to ensure that the student teachers do not see the lesson study cycle as a graded activity. As explained, during observations we placed the focus on the learners rather than the teacher, as well as guiding the post-lesson discussion to be mainly focused on what students did, said and wrote in their books. My hope is that by limiting performative anxiety, working in a collaborative, non-threatening climate allows student teachers to experiment with pedagogy.

Despite passionately believing that this is a worthwhile experience for my student teachers there are some aspects of this experience that I would like to continue developing. In particular I would love to be able to involve experienced teachers in CLR working alongside student teachers. When I began including CLR as part of the PGCE course I attempted to do so but unfortunately it didn’t work out. I believe lack of time prevented overworked teachers being fully involved in the lesson study events. On one occasion one teacher invested time planning alongside the student teachers and spoke to me about having gained a lot form the experience. Unfortunately, most teachers were not able to be involved in the planning, due to lack of time, and did not receive any benefit form the experience. I will continue to reflect on how I could develop the model so that host schools also benefit from the experience. Unfortunately to be effective CLR needs a firm commitment in terms of time and effort from participants. My hope is that by my continuing to demonstrate CLR, in school management in schools will recognise its value and make sure that there is time set aside for teachers for this experience.

## References

Fujii, T. (2014). Implementing Japanese lesson study in foreign countries: misconceptions revealed. Mathematics Teacher Education and Development, 16(1), n1.

Shulman,L.S.(1986).Those who Understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.

## 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 ).

Here is the teacher’s bansho work on the chalkboard at the end of the lesson. (Bansho refers to the board work of a lesson: it is developed over the course of the lesson and by the end of the lesson tells the mathematical narrative that has been developed. For further insight into this see for example the writing of Shirley Tan about her research (Tan et al. 2021) into bansho).

Here you can see a number of ways that students carried out their calculations in response to the question posed as the task for the lesson. I’d like to draw attention to these two responses.

Important in each of these is the order in which the pupils’ calculations are expressed. In the case of 4 x 3 + 2 x 3 the heights of the two rectangles the multiplicands in each part of the expression (4 and 2 in the left-hand attempt) with 3 as the multiplier. In the right-hand attempt (2 x 9) the 2 is the multiplicand and the 9 the multiplier. In Japan, the curriculum is consistent in working with the multiplicand as the first term in an expression of the form a x b and the multiplier as the second term. At a later stage than illustrated here this is consistent with a model of direct proportion being expressed as y = k x x.

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.

https://youtube.com/shorts/lCNyK5CRidI?feature=share

2. Quotative division

https://www.youtube.com/watch?v=1bIzZseGAVQ

Here is part of the teacher’s bansho work at the end of the lesson.

Notice here that although the two different problems give rise to the same division calculation of when re-presented as multiplication scenarios they are written as 3 x 2 (two people each have 3 candies) and 2 x 3 (2 candies are given to each of 3 people). You can see here that attaching the units of candies and people to the calculations expressed in words suggests the two different situations (being consistent with ideas highlighted in research lesson 1).

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

The diagrams below show a student’s work with the double number line in response to the problem of finding the cost of 1 metre of tape given that 0.8 metres costs 120 yen.

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.

Each of the illustrations here represents just small moments in time of much more complex lessons. My intention was to highlight how there is an underlying coherence across the intended curriculum in Japan which ensures both pupils and teachers have opportunities to interpret each other’s thinking than a more laissez faire approach might facilitate. For example, there is specific meaning attached to an expression such as 24 x 7, as above. In England we might not be so concerned to differentiate between the expression 24 x 7 and 7 x 24, but in the lessons considered here they would be used to signify very different situations. For example, a rectangle with area 4 x 3, whilst numerically having the same area as one with area 3 x 4, would have a different orientation in elementary school lessons.

The glimpses into lessons I provide here are just that, glimpses. But I hope that they provide some indication of the level of thought that developing curriculum coherence requires and how lesson study allows teachers, and educators more widely, to explore interactions between the intended and implemented curriculum.

Tan, S., Nozaki, S., Fu, H., & Shibata, Y. (2021). The principles of teacher’s decision-making in Japanese board writing (bansho) process. Asia Pacific Journal of Education. https://doi.org/10.1080/02188791.2021.1924119

Wake, G. and Seleznyov, S. (2020) ‘Curriculum design through lesson study’.

London Review of Education, 18 (3), 467–79. https://doi.org/10.14324/LRE.18.3.10

## 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.

What do you think of when you hear the expression “lesson study”? I suspect that this might trigger images of teachers working together, maybe observing a lesson together and reflecting on what they noticed afterwards. Without question, teachers are the prime purpose for whom lesson study exists however many individuals with different roles engage in lesson study. In this blog, I consider who (in the context of mathematics education) lesson study is for and consider what lesson study offers to those who participate. In doing so I hope to convince you that lesson study offers something for everyone.

Lesson Study as a community of inquiry

In Sarah Leakey’s blog she describes some different interpretations of lesson study, including collaborative lesson research (CLR) (Takahashi & McDougal, 2016), Research Lesson Study (RLS) (Dudley, 2014) and the Dutch model (Wolthuis et al., 2022). Other interpretations exist too, some of which I will elaborate on as I come to them later in this blog. In many cases various interpretations of lesson study can be thought of as a community of inquiry (Jaworski, 2019). I like this theoretical model for thinking about collaborative teacher professional activity in mathematics education because it recognises more than just one ‘type’ of participant collaborating. In this model (Figure 1), we see that students, teachers and didacticians (or teacher educators) form the entire community in three nested layers. Using this model, I will consider how each of the participants in these three layers engage in different interpretations of lesson study.

Students as participants in lesson study

Central to a community of inquiry are the students. In fact, it could be argued that students are central to any form of lesson study in that they are the reason that teachers wish to develop their practices. I.e. so that their students’ learning experiences are more meaningful. Jaworski’s model requires the students to also be engaged in some form of mathematical inquiry. This means that they too are working on mathematics that goes beyond routine practice exercises by collaboratively exploring a mathematical problem or constructing ideas from tasks that require them to think mathematically (Goos, 2004). In Japanese Lesson Study (JLS) the focus of the teachers’ inquiry is the students’ mathematical learning provoked by a carefully chosen problem. The research lessons are designed to consider the students’ whole learning experience i.e. not just the mathematical content but also students’ mathematical dispositions (Takahashi et al., 2013). Furthermore, students’ anticipated responses to the problem inform the design of the research lesson. During the research lesson itself, students explore a solution to the problem which is then shared and compared with other students’ solutions. This is done by presenting students’ solutions on a chalkboard known as Bansho (see Figure 2), that gathers the collaborative learning throughout the lesson (Baldry et al., 2023). This shows how central the student is in the whole lesson.

In the post-lesson discussion, the students’ solutions are the focus of the discussion and teachers’ reflect on what they observed and learned from their responses.

In RLS (Dudley, 2014) teachers observe a small group of students within a whole class. By only focusing on a selection of students the teachers gain ‘forensic visibility’ on students’ learning. After the research lesson, and before the post-lesson discussion, students are interviewed to enable further insight into their experience of the research lesson and these reflections then feed into the teachers’ post lesson discussion and the next iteration of the lesson design.

Learning Study (LS) (Pang & Lo, 2012) is a version of lesson study that uses variation theory of learning (Marton & Booth, 1997) to guide the design of the research lesson and frame teachers' observations and reflections on the lesson. In addition to the students’ learning being observed in the research lesson, students are also assessed before and after they participate in a LS. The outcomes of these assessments are used to determine the change in awareness of an ‘object of learning’ that could be attributed to discerning patterns of variation in the critical aspect of that object of learning.

Teachers as participants in lesson study

The middle layer of Jaworski’s diagram includes teacher inquiry. All forms of lesson study offer a rich learning space for teachers at all stages of their professional careers. Some teachers are fortunate enough to participate in lesson studies while preparing to become a teacher. In the US, (Fernández, 2005) developed a model of lesson study called Micro-Teaching Lesson Study (MLS) which enabled the pre-teachers to collaboratively prepare lesson episodes (parts of a lesson) and then teach this to peers in their initial teacher education groups. In MLS, the pre-service teachers are both teachers and students and the focus is on teaching practices.

In China, participation in Teacher Research Groups (TRGs) is part of the professional work of a teacher. TRGs involve several types of activities including Chinese Lesson Study (CLS) (Yang & Ricks, 2012) and can involve novice teachers through to expert teachers. In CLS a team of teachers at different stages of their career might work collaboratively to support a novice teacher to design and teach a lesson on a particular topic. Several iterations of the lesson are explored until the TRG feel that the lesson can no longer be improved. Whilst one teacher is the focus for the lesson, all the participants in the TRG can benefit from the collaborative activity (Han, 2013). To support more experienced teachers, the focus for CLS would be to develop ‘excellent’ lessons which are then showcased as “public lessons” for district wide teacher observation (Han & Paine, 2010) or used for teaching contests (Li & Li, 2013).

In JLS teachers form part of the research lesson design team, collectively exploring research and teaching materials about the mathematical focus for the lesson and producing a detailed lesson plan. This process is called kyouzai kenkyuu. One teacher from the design team is chosen to lead the research lesson. Other teachers may join the research lesson, who jointly observe and reflect on students’ learning as a means to develop teachers’ professional knowledge.

Didacticians/ teacher educators as participants in lesson study

Finally, the outer layer represents a group of participants who also contribute and can benefit from lesson study – didacticians. Jaworski and Huang (2014) refer to didacticians as teacher-educators “who work with teachers to enable development to take place”. When didacticians participate in lesson study, not only do they have a window on student learning as co-partners with the teachers, but they also have a lens on the teachers’ learning that can inform their own practices that support teaching development of teaching practices and knowledge. For some forms of lesson study, didacticians may focus on student learning. For instance, in JLS, a “knowledgeable other” (koshi) contributes a deep reflection in the post-lesson discussion, summarising key points of the lesson study process (Takahashi, 2014) observed three purposes of knowledgeable others summaries – (1) bringing new knowledge from research and the curriculum; (2) showing the connection between the theory and the practice; and (3) helping others learn how to reflect on teaching and learning.

Lesson study has been used to inform teaching approaches. For instance in Japan, teaching mathematics through problem solving (TTP) has evolved from years of exploring practices accompanying mathematical tasks through JLS and this in turn has influenced the national mathematics textbooks that are used by teachers in Japan (Takahashi, 2021). When textbook authors are involved, they are able to use their participation to observe how the textbook tasks are enacted by teachers in the research lessons and, as a result, modify the task and accompanying text teaching manual.

Didacticians use lesson study to gain deeper understanding of theories of learning and teaching. For instance Lo and Marton (2012) describe how learning study is used to explore how well variation theory works in the context of classrooms. This in turn informs design and pedagogical principles to promote pupils’ learning from variation. Researchers can also use lesson study as methodological tool. In my recently completed PhD study, I developed a model of lesson study called ‘Task-Design Lesson Study’ (TDLS) to enable a lens on teachers’ construction of design principles and pedagogical practices to accompany one-problem-multiple-changes procedural variation tasks (Gu et al., 2004; Lai & Murray, 2012) making visible the teachers’ work (rather than their professional learning) whilst they collaborated in the TDLS. This has resulted in new conceptualisations of design principles and pedagogical practices associated with teaching with variation (Jacques, 2023). This model of lesson study was specifically designed as a community of inquiry and is modelled in Figure 3. Where three sets of inquiry questions are reflexively related to one another.

In the above, I have attempted to illustrate that by considering lesson study as a community of inquiry, I have shown that there are many different ‘types’ of individuals in a lesson study community and for whom participating is both relevant and beneficial. So, if you are asking yourself, is lesson study for me? I hope you now see that that it very likely, is.

Baldry, F., Mann, J., Horsman, R., Koiwa, D., & Foster, C. (2023). The use of carefully planned board work to support the productive discussion of multiple student responses in a Japanese problem-solving lesson. Journal of Mathematics Teacher Education, 26(2), 129-153. https://doi.org/10.1007/s10857-021-09511-6

Dudley, P. (2014). Lesson Study: a handbook. Lesson Study UK https://lessonstudy.co.uk/wp-content/uploads/2012/03/new-handbook-revisedMay14.pdf

Fernández, M. L. (2005). Learning through Microteaching Lesson Study in Teacher Preparation. Action in teacher education, 26(4), 37-47. https://doi.org/10.1080/01626620.2005.10463341

Goos, M. (2004). Learning Mathematics in a Classroom Community of Inquiry. Journal for Research in Mathematics Education, 35(4), 258-291. https://doi.org/10.2307/30034810

Gu, L., Huang, R., & Marton, F. (2004). Teaching with variation: A Chinese way of promoting effective mathematics learning. In L. Fan, N. Y. Wong, J. Cai, & S. Li (Eds.), How Chinese learn mathematics: Perspectives from insiders (Vol. 1, pp. 309-347). World Scientific.

Han, X. (2013). Improving classroom instruction with apprenticeship practices and public lesson development as contexts. In Y. Li & R. Huang (Eds.), How Chinese teach mathematics and improve teaching (pp. 171–185.). Routledge.

Han, X., & Paine, L. (2010). Teaching Mathematics as Deliberate Practice through Public Lessons. The Elementary School Journal, 110(4), 519-541. https://doi.org/10.1086/651194

Jacques, L. (2023). Primary Teachers’ Design Principles and Pedagogical Practices for Promoting Mathematical Learning from Procedural Variation Tasks University College London]. London.

Jaworski, B. (2019). Inquiry-Based Practice in University Mathematics Teaching Development. In D. Potari, T. Wood, P. A. Sullivan, & O. Chapman (Eds.), International Handbook of Mathematics Teacher Education: Volume 1: Knowledge, Beliefs, and Identity in Mathematics Teaching and Teaching Development (Second Edition) (Vol. 1, pp. 275-302). Brill. https://doi.org/https://doi.org/10.1163/9789004418875_011

Jaworski, B., & Huang, R. (2014). Teachers and didacticians: key stakeholders in the processes of developing mathematics teaching. ZDM, 46(2), 173-188. https://doi.org/10.1007/s11858-014-0574-2

Lai, M. Y., & Murray, S. (2012). Teaching with Procedural Variation: A Chinese Way of Promoting Deep Understanding of Mathematics. International Journal for Mathematics Teaching and Learning,(April).

Li, J., & Li, Y. (2013). The teaching contest as a professional development activity to promote classroom instruction excellence in China. In Y. ILi & R. Huang (Eds.), How Chinese Teach Mathematics and Improve Teaching (pp. 204-220). Routledge.

Lo, M. L., & Marton, F. (2012). Towards a science of the art of teaching: Using variation theory as a guiding principle of pedagogical design. International Journal for Lesson and Learning Studies, 1(1), 7-22. https://doi.org/10.1108/20468251211179678

Marton, F., & Booth, S. (1997). Learning and awareness. Lawrence Erlbaum Associates.

Pang, M. F., & Lo, L. (2012). Learning study: helping teachers to use theory, develop professionally, and produce new knowledge to be shared. Instructional Science, 40(3), 589-606. http://www.jstor.org.libproxy.ucl.ac.uk/stable/pdf/43574702.pdf

Takahashi, A. (2014). The Role of the Knowledgeable Other in Lesson Study: Examining the Final Comments of Experienced Lesson Study Practitioners. Mathematics Teacher Education and Development, 16, 4-21.

Takahashi, A. (2021). Teaching mathematics through problem-solving: a pedagogical approach from Japan. Routledge.

Takahashi, A., Lewis, C., & Perry, R. (2013). A US lesson study network to spread teaching through problem solving. International Journal for Lesson and Learning Studies, 2(3), 237-255. https://doi.org/10.1108/IJLLS-05-2013-0029

Takahashi, A., & McDougal, T. (2016). Collaborative lesson research: maximizing the impact of lesson study. ZDM, 48(4), 513-526. https://doi.org/10.1007/s11858-015-0752-x

Wolthuis, F., Hubers, M. D., van Veen, K., & de Vries, S. (2022). The hullabaloo of schooling: the influence of school factors on the (dis)continuation of lesson study. Research Papers in Education, 37(6), 1020-1041. https://doi.org/10.1080/02671522.2021.1907776

Yang, Y., & Ricks, T. (2012). Chinese lesson study: Developing classroom instruction through collaborations in school-based teaching research group activities. In Y. Li & R. Huang (Eds.), How Chinese teach mathematics and improve teaching (pp. (pp. 51–65).). Routledge.

## 05 Learning from Lesson Study

Stefanie Burke, Primary Maths Advisor, Devon

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.

Children’s recording

After I had read the lesson proposal, I wondered about how I would know what the children were thinking if I am not there in the live lesson as I would not be able to overhear the children talking to each other. I soon realised that the children’s recordings provided during the video of the lesson were a window to the children’s thinking. As Janine (Blinko) pointed out, the choice to let children record how they liked and to include their recordings as part of the video of the lesson meant that we could see the children thinking and understanding of multiplication and division in the context of packets of doughnuts.

I realised that when I am in a live lesson, I use both what the children say and write in tandem to try to work out what they are thinking and so the planning team’s choice of leaving the children to decide how to record their thinking on a blank piece of paper, not a type of worksheet allowed some of the children’s thinking to be revealed. It made me wonder about what many children are writing/drawing on in lessons and whether what is provided by a scheme or programme could be adapted to make it more open and thus reveal more of children’s thinking. I am starting a collaborative lesson research cycle next month and I will now try to remember to ask the planning group to not only think about what the teacher writes/draws on the board (Bansho) but also about how the children are expected to write/draw.

What is the calculation for the problem?

A difficulty that I have encountered a few times when working both with teachers and children is that I end up disagreeing with them about what the calculation is for a contextualised problem e.g. I think that the calculation for ‘I have £290 in my bank account, but I need £300 to buy the ticket for the festival, so I need to find £10’ is 300 – 290 = 10. However, when I ask teachers and children to write the calculation many of them would write 290 + 10 = 300 and tell me that both our calculations represent the problem. I agree with them that they may have solved the problem by adding on 10 to 290 but if they were to have much more tricky numbers e.g. ‘I have £238.93 in my bank account, but I need £307.72 to buy the ticket for the festival’ and they wanted to use a calculator to work it then they would need to plug in 307.72 – 238.93. It was a similar situation for the context used in this research lesson: The baker sells packs of five doughnuts. He baked 35 doughnuts today. How many packs can he sell? The problem was division, but the children were mostly ‘seeing’ and describing multiplication and so the lesson tried to support the children to notice the division and at times some children were able to articulate why it is a division.

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.

This process and terminology gave me a new way of thinking about the dilemma and confirmed for me that is worth spending time thinking about this when planning and teaching because it will have an impact on children’s understanding in the future. E.g. when they come to divide by fractions

Unitising

Right at the start of the session together it was explained that the research lesson is not and is not intended to be a perfect lesson and the lesson proposal also included post lesson discussion notes summarising the reflections that the planning team had about the lesson. They felt that strips of 5 dots did not allow the children to model the 35 doughnuts as 35 individual doughnuts before they are grouped into 5s by the baker. This prompted me to realise that I need to think carefully when choosing resources to model division and that the same resource might not work for both multiplication and division problems even if they are in the same context. Then my thinking about multiplication was moved on again when Andy (Tynemouth) described Fosnot and Dolk’s research and the progression from counting in ones to skip counting and then on to sophisticated strategies to derive multiplication see Elijah, Richard and Hannah below. The description of this progression prompted me to compare it with my understanding of progression in additive strategies of young children: count all count on and know/derive. I could suddenly see this remarkable change children go through to move on from counting all in both addition and multiplication and I had not thought about this similarity before.

This professional development session allowed me to think more deeply about such a variety of maths and mathematical pedagogies. It showed me how the research lesson can be a great learning opportunity not only for those involved in the planning team or those who are able to observe the live lesson and post lesson discussion and koshi, but, if the lesson is filmed it can then be used as a vehicle to stimulate us to think even more deeply about children’s mathematical learning.

## 04 Leading Lesson Study

This 'long read' is by Stef Edwards, D.Prof and describes her doctoral study focsused on Lesson Study.

This blog is about a doctoral study that has absorbed weekends and holidays for the almost the last decade of my professional and personal life. It’s based on a seminar I presented in January 2023 for CLR about my EdD thesis (Edwards, 2022). I start by explaining the background to the study, and why it felt like a good idea at the time. Next, I briefly explain how I established a conceptual/theoretical framework for Lesson Study (LS) leadership – to inform my own understanding of LS and what might be involved in leading it well, how I might need to go about studying and understanding it as a phenomenon, what kinds of data I should collect and how I might analyse and interpret it. I explain my research design, hopefully enough so that you’ll understand what I did, but not so much as to send you to sleep. Finally, I tell you what I found out about LS leadership practice. Read more....

## 03 Thinking space - for both pupils and teachers

I had the great privilege recently of taking part in the CLR event at University Primary School in Cambridge where I was able to engage in collaborative professional debate around two lessons taught by Japanese teachers. Having thoroughly enjoyed the two days I am now left with many reflections to ponder over.

When I think about the Japanese lessons and the discussions about conceptual understanding and pedagogy, I find myself coming back to a point near the beginning of the Y5 lesson. One child in the class had seen the representation being shared in a different way to the other children – through his gesturing, he indicated that he had seen the change in height of bamboo as a scaling structure. This was a central concept being explored in the lesson, yet at this point in the lesson it was not followed up. The teacher noticed and acknowledged the response but didn’t explore this further with the other children. Although I had noticed this at the time, I didn’t register the significance of this for my thinking until at the very end of the CLR during the discussions when another observer asked the Japanese teacher why he hadn’t followed this up at the time. The teacher replied that he didn’t feel that the children were ready yet.

Ownership of learning

I have since found myself thinking, what would I have done at that point in the lesson if I were teaching my class. I feel pretty sure that I would have been delighted that one of the children had recognised the scaling structure and then I would have proceeded to teach the other children about scaling since that was a central idea of the lesson. The Japanese way was far more focussed around all children owning their learning – to come to the scaling concept when they were ready to make sense of this potentially new way of thinking about the change in height of the bamboo. The more I think about this, the more I think about how both lessons observed were designed with this ownership of learning in mind. The careful choice of context, representation, measurements and questioning guiding children towards potential shifts in thinking. The design of Japanese problem-solving style lessons is something that I would like to research further.

Maths talk and classroom community

In both lessons that we observed, encouraging children to talk was central to the lesson design. A lot of emphasis was placed on the children using their own words to verbalise their thinking about a mathematical idea. For example, children were encouraged to turn and rehearse an explanation of their mathematical thinking with their partner before sharing with the whole class. Children were actively encouraged to come out to the front of the class and share their thinking. Once a child’s thinking was shared, the other children were then encouraged to turn and explain to their partner what had just been said. This process may have involved children verbalising an explanation which differed from their own, a consideration of another viewpoint. Even within the short time of these two lessons, I felt that a sense of collective responsibility for everyone learning, was being fostered by the teacher.

The life of a teacher can be exhilarating but also exhausting and overwhelming. At times it can feel as though the logistics of the day-to-day organisation of school life can take over from conversations about curriculum and pedagogy. The opportunity provided by CLR to observe Japanese style maths lessons and engage in professional debate has been very refreshing. I have come away invigorated, with so much to reflect on within my own practice in the classroom and within my wider Trust and Maths Hub role.

Katie Crozier, Y4 Teacher Jeavons Wood Primary School, Primary Lead Cambridge Maths Hub, Primary Maths Director Cam Academy Trust

## 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.

In this blog I reflect on a Collaborative Lesson Research (CLR) event that took place at the University of Cambridge Primary School in conjunction with the attached Elementary School of the University of Tsukuba, Japan. The on-the-day element of the event included a pre-lesson discussion, a live research lesson and a post-lesson discussion. However, I will structure my reflections around the six stages of the collaborative lesson research (clr) cycle as described by Takahashi and McDougal (2016) and make inferences around any stages that I was not directly part of.

It’s worth noting that the lesson was predominantly conducted in Japanese with a colleague from the University of Cambridge Primary School translating between the students and the teacher. Any reservations about how this would proceed were quickly allayed through the skill of the teachers involved and the positive attitude of the students

For context, the live research lesson centred on developing an understanding of additive and multiplicative reasoning with a Year 5 class by describing the growth of two bamboo shoots (see the diagram below). The students were initially just presented with two shoots that had grown to 6m and 8m over 2 weeks. Only after discussion around which may have grown most were the starting points of 2m and 4m respectively revealed.

## Stage 1: The research purpose

The first stage of the clr cycle is to identify a clear research purpose. I was not part of the planning team but identifying a clear purpose gives structure to the design of the lesson and a focus for observers. The planning team shared their intention of designing a lesson to deepen student reasoning and understanding over the course of the lesson. For me, this purpose linked well with the school’s ethos which includes a desire for students to be ‘engaged purposefully in their learning and able to articulate their views in polite, respectful and positive ways’. It feels to me that having a clear purpose, linked to the aims of the school, is a vital element of the clr cycle. I think that the clearer this link can be, the more it can shape the design decisions and the actions of the teacher during the lesson.

## Stage 2: Kyouzai kenkyuu

For someone who doesn’t speak Japanese I don’t really find the name of this stage particularly helpful! However, I’d summarise it as the study of curriculum materials so that the student learning can be envisioned (Watanabe, Takahashi and Yoshida 2008). Again, I was not present when the research team completed this stage, but it is possible to make inferences from what was seen. It was clear that this lesson was based on Japanese materials that are designed to show how change can be described in terms of both addition and multiplication. However, the research team adjusted the familiar curriculum materials based on their knowledge of the Year 5 class. I think this is important - they didn’t just wheel out a standard lesson but considered what was best for the students. The aim of the clr cycle is not to perfect a lesson, but to develop mathematical thinking in students (Lewis, Perry and Murata 2006) and the collaborative learning of teachers. For example, the original materials required the comparison of three bamboo shoots but in this lesson it was adjusted to two. Similarly, the numbers that students would work with were changed from two-digit numbers to single-digit ones. Underpinning these changes were intelligent decisions made with the purpose of enabling learning for the students in that class.

Stage 3: A written research proposal

As a result of stage 2 a simple research proposal was shared prior to the lesson and provided helpful structure for the pre-lesson discussion. Perhaps the difficulty of translating into English meant it was less detailed than some Japanese plans that I have seen. However, one of the things I really like is the anticipation of student responses which are added to the plan. For example, the research team anticipated that many students would initially think bamboo shoot B had grown the most, because shoot B was taller, without considering the starting points. The result of this careful planning was that the students’ learning remained a priority throughout the design process and in the lesson.

Stage 4: The live research lesson and discussion

Stage 4 of the clr cycle includes both the live research lesson and the subsequent post-lesson discussion. Space is limited so it will be difficult to describe all that took place, but there are some general things that stood out to me during the lesson:

· The choice of numbers (from 2m to 6m and from 4m to 8m) created the opportunity for student discussion that a different set of numbers may not. It may seem obvious, but well-chosen numbers affect the direction of the lesson.

· The careful planning meant that the lesson unfolded in a way that took the students on a journey and gave them opportunities to demonstrate their mathematical thinking.

· Throughout the lesson there was a lovely balance of individual thinking, paired discussion, and whole class interaction.

During the post-lesson discussion the class teacher confirmed that they wanted all students to understand the two ways of reasoning. This meant that students were asked to come to the front of the class to share their explanations, that he checked the clarity of explanations with the rest of the class, and that students were asked to explain what other students might be thinking. These actions illustrate well the research purpose stated in stage 1 and the notion in the English Mathematics National Curriculum that ‘the majority of pupils will move through the programmes of study at broadly the same pace’.

Stage 5: Knowledgeable others

As part of the clr cycle a member of the CLR group gave some final insights and thoughts around the lesson. There were several helpful points here, but I particularly appreciated how attention was drawn to the current Year 4 NCETM mastery PD materials on scaling. In comparison to this lesson, it is noticeable that the NCETM materials only focus on the multiplicative reasoning (perhaps understandably). What was so powerful in this lesson was that students were encouraged to think and explain with both additive and multiplicative thinking so that the comparison between the two ways of thinking and reasoning became clear. It feels that sometimes in the English curriculum we try to move to what we perceive as ‘better ways to think’ without considering the student’s journey in understanding. I would tentatively suggest that encouraging development through comparison of methods could be a helpful addition to the NCETM materials in this unit.

Stage 6: Sharing of results

I think that this is the stage of the clr cycle that is still quite embryonic in England. An online discussion took place a couple of days after the live research lesson but it still feels that there could be more opportunities for findings to be communicated to a wider audience. Without doing this we can risk collaborative lesson research becoming seen as one-off events rather than as ongoing and sustained professional learning. Importantly, ‘lesson study is not just about improving a single lesson. It’s about building pathways for ongoing improvement of instruction’ (Lewis, Perry, and Hurd, 2004, p. 18).

Concluding thought

Finally, it’s worth noting that there was never a sense that our Japanese colleagues had come to show teachers from England how to teach. This was in part thanks to their good humour and humility, but also because of the clr process. The clr cycle is designed to focus on student learning around opportunities that reveal mathematical thinking. A natural consequence of this is that teachers learn through each stage of the clr cycle because they are always considering the learning of the students. This shifts the focus from looking only at the teacher’s actions and on to understanding how the teacher’s actions affect learning. For me this is what distinguishes the clr cycle from so many other lesson study practices and research groups that I have been involved with. If you are interested in learning more about the clr cycle and how it can contribute to ongoing improvement of instruction then please keep an eye on our CLR events page.

References

## 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:

A clear research purpose - This is twofold and involves an overarching research theme that is not specific to a particular subject area or year group. This theme may be explored over a longer time period e.g. three years. Within each lesson study cycle, there is also a specific focus related to a specific topic within a subject area e.g. something specific related to the teaching of fractions.

Kyouzai kenkyuu - literally translated as study or research of teaching materials. This might include study of curriculum materials including the trajectory of learning through different year groups. It might also include addressing common misunderstandings of the area of focus as well as issues around which manipulatives to use and how the tasks might be presented to pupils.

A written research proposal - This will include the findings from kyouzai kenkyuu, as well as the learning goals for the unit as a whole and the specific research lesson within that unit. There will be a detailed lesson plan for the research lesson, including a rationale for the choices made, and this will be linked to the research theme and lesson goals. It will also include anticipated responses from pupils in relation to the task that is the focus of the lesson.

A live research lesson and post-lesson discussion - One member of the planning team teaches the research lesson that has been collaboratively planned by the group. All members of the planning team observe the research lesson. Additional 'observers' may also attend the lesson. The observers are responsible for collecting data on pupil learning relative to key points of evaluation set out in the research proposal that relate to the research theme and the goals of the lesson. After the lesson, the group (and other observers) meet to share what they found and discuss the implications. This knowledge feeds into future lesson study cycles and helps the team to learn more about the issues they were interested in and address their overarching research theme.

Knowledgeable others - This is someone who supports the team to go beyond their current knowledge boundaries. As you can see in the diagram above, in an ideal world there would be two knowledgeable others - one at the planning stage and a second for the research lesson and post-lesson discussion.

Sharing of results - This may be by inviting others to observe the research lesson, sharing the research lesson proposal more widely or disseminating the results by other means.

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).

Initial study phase

Establish the focus for the research.

Determine the research proposal and research questions.

Identify three case study pupils and the level these pupils are working at and what you want their knew knowledge to be at the end of the lesson.

Review and modify teaching materials as you plan.

Conduct iterative cycles of research lesson study

The series of cycles (e.g. three as in the diagram above) are conducted with the same class and on the same concept but each cycle is a different lesson within a broader series of lessons.

Each cycle also consists of planning, teaching the collaboratively planned lesson while the other members of the planning team observe, interviewing case study pupils and having a post-lesson discussion.

The first research lesson enables the group to see gaps between the case study pupils and the object of learning more clearly.

The second research lesson, which is not an adjusted repeat of the first but a different lesson, develops the concept under consideration further and will be a better match between the approach taken and the needs of the pupils.

The third cycle is used to address any remaining issues.

Discuss and share findings of the Research Lesson Study.

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.

Setting Goals - Identifying a research theme which acts as a long-term goal to guide the lesson study cycle. This theme may be the focus of multiple cycles over several years.

Planning the lesson - The planning team works collaboratively to develop a research lesson plan. This includes identifying specific goals, examining teaching materials and considering prior experiences. The plan is very detailed and includes anticipated responses from pupils to the problem posed.

Teaching, Observing and Debriefing - One person teaches the research lesson while the other members observe and collect data. Sometimes knowledgeable others will join this process. After the lesson, those involved in the planning team as well as additional observers take part in a post-lesson discussion sharing the evidence of pupil learning.

Revising and Reteaching - The team makes changes to the lesson based on the post-lesson discussion. The revised lesson is then taught to a new group of pupils. This lesson is also observed and a post-lesson discussion is held. A final version of the lesson may be developed.

Reflecting and Sharing Results - The research lesson is recorded and shared in a report that includes teacher reflections. The results will inform future cycles and other broader professional development.

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:

Picking a research theme

Planning a research lesson

Teaching or observing the research lesson

Discussing the research lesson

Revising, reteaching and rediscussing the research lesson

Reflecting on the lesson study experience.

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.

Summary

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.

Further reading:

If you want to read more about variations to lesson study, the paper by Norwich (2018), 'Making sense of international variations in lesson study and lesson study like practices: An exploratory and conceptual perspective,' is a useful source.

If you want to read more about misconceptions related to lesson study, the paper by Fujii (2014), 'Implementing Japanese Lesson study in Foreign Countries: Misconceptions Revealed,' makes for an interesting read.

If you want to find out more about how lesson study is being used in the US, the following are useful sources for understanding more about lesson study and seeing research proposals:

If you want to see examples of research proposals from Japan (written in English), these can be found in the Lesson Study Library on the IMPULS website.

If you want to access more from a UK perspective, the following might be useful:

If you want an international feel as well as access to some brilliant material from previous conferences and a wealth of journal articles then WALS is a great source of information particularly if you become a member.

References:

De Vries, S., N. Verhoef, and S. L. Goei. (2016). Lesson Study: Een Praktische Gids Voor Het Onderwijs [Lesson Study: A Practical Guide for Education]. Antwerp: Garant.

Dudley, P. (2019). Research Lesson Study: A handbook (Fifth edition)

Fujii, T. (2014). Implementing Japanese lesson study in foreign countries: Misconceptions revelead. Mathematics Teacher Education and Development, 16(1), 2–18.

Norwich, B. (2018). Making sense of international variations in lesson study and lesson study-like practices: An exploratory and conceptual perspective. International Journal for Lesson and Learning Studies, 7(3), 201–216.

Stepanek, J., Appel, G., Leong, M., Mangan., M. T. and Mitchell, M. (2007). Leading lesson study: A practical guide for teachers and facilitators. Thousand Oaks, CA: Corwin Press

Takahashi, A. and McDougal, T. (2016). Collaborative lesson research: maximizing the impact of lesson study. ZDM Mathematics Education, 48, pp. 513–526.

Wolthuis, F., Hubers, M. D., van Veen, K., & de Vries, S. (2021). The hullabaloo of schooling: The influence of school factors on the (dis)continuation of lesson study. Research Papers in Education, 1–22.