Bowland maths: Development steps

(informed by the ‘Lesson Study’ approach of Japan)

Background

Bowland Maths

The Bowland Maths materials now comprise 27 full Case Studies, each requiring 2 to 5 lessons to complete, 35 Assessment Tasks, each requiring 10 to 30 minutes, and seven Professional Development Modules, each requiring about 3 hour’s work for a teacher. All these are, or very shortly will be, available on the Bowland Maths web site ( the earlier ones are also on the Bowland DVD, copies of which weresent to all secondary schools in England about 4 years ago.

We have conducted a surveywhich showed that about 90% of maths teachers had heard of Bowland Maths and about 60% had used one or more Case Studies in the class-room. The feedback has generally been very positive, with teachers and pupils saying how much the materials engaged and enthused pupils and also helped to develop process skills that are so often inadequately tackled in more conventional maths.

One reservation expressed in the feedback was about suitable professional development, despite the PD materials included in the Bowland ‘package’. This may reflect teachers’ desire for a more active approach to professional development, but we also recognise that the current PD materials are not easy to navigate. Our experience suggests that teachers tend to go straight to the Case Studies and/or the Assessment Tasks, with little reference to the PD materials.

As the range of Bowland materials has now been in general use for several years, it istime to consider what improvements can be made in the light of experience – and with the passage of time. The Bowland Trust is therefore planning toundertakea ‘development programme’ to revise some of the materials, resulting in a sort of ‘Bowland II’. The extent of the revisions will depend on the availability of funds, but we know we can make a start – which is what this note is about.

Lesson Study in Japan

The ‘Lesson Study’ (LS) approach of Japan is a form of ‘teacher-led’ PD.It focuses on observingpupils’ class room learning, with the aim of developing teacher skills to support independent learningand toprovide pupils with opportunities to developtheir understanding. The approach is normally built around a ‘Research Lesson’ in which the teacher poses a questionthat requirespupils to apply maths that they have already learned, but to link topics in new ways and in unfamiliar circumstances.

This approach to PD has a resonancewiththe needin the UK to developteaching skills that help pupils to structure unfamiliar and open-ended problems and to develop their process skills more widely. This is also a specific aim ofthe Bowland materials,which thus makes themespecially suitable within the LS approach in Japan.

The principles of Lesson Studyare based on supportive collaboration between a team of teachers,together with an outside expert/advisor, and with a clear recognition that this is indeed Professional Development. The teachers are mainly from one school, but teachers from other schoolsoften join in. The principles most relevant for the UK are:

  • The Lesson Study ‘event’ has three main components, based arounda Research Lesson (RL):
  • the team jointly researches and plans the Research Lesson (exploring available materials, known approaches, typical mistakes etc.); the joint planning means that the lesson itself is viewed as a team responsibility
  • the Research Lesson is then delivered by one team member, with observationin the class room by the other members of the team - and often others too; observations are focussed on the approaches the pupils use to learn and on the ways in which pupilsdevelop the maths concepts (rather than on the teacher)
  • on the same day, a comprehensive post-lesson discussion is held, themain purposes of whichareto discuss what was observed and to identify, and develop responses to, any general ‘difficulties’ that the pupils had with the types of learning involved; all members of the team learn from this discussion as part of their own development; the discussion can also identify improvements for thelesson, although that is not usually the main point
  • It is recognised that PD benefits accrue to all the members of the team (and tothe other observers),not just tothe one doing the teaching; typically a teacher might ‘deliver’ one or two Lesson Studies in a year, but observe 10-20 others
  • Themost effective Lesson Study teamsusually include an external expertin class room observation who: provides advice about what to look for during the lesson - and how to look and listen; attends and observes the lesson itself;structures and contributes to the post lesson discussion; and so also helps maximise the PD benefits for the teachers involved

The structure of the Research Lesson itself clearly varies with the topic, but an essential component is what is referred to as ‘neriage’ which comprises extensive full class discussion in which various approaches to the problem are aired and discussed. The discussion is informed by the teachers’ observations of ways in which pupils tackled the problem. The lesson structure tends to be rather different from what is often considered‘good practice’ for a maths lesson in England, which is a point that might be considered during the proposed project.

These Lesson Study concepts and approaches have been used in Japan for over 100 years – and may go some way to explain the country’s superior performance on most international maths platforms. More recently, about 7 years ago, and based on their researched conviction that teaching quality is the key to success (rather than fiddling with the curriculum), Singapore adopted the LS approach. It is now used in about 70% of Singapore schools and also as a base for many of their text books. There has been sporadic interest in these methods in other countries over the years; recently this interest has grown significantly, especially in the USA. Partly as a response to these initiatives in the West, Japan has now started a project (IMPULS) to promote the conceptoutside Japan.

Links between Bowland Maths and Japan

In Japan, a group of maths experts advising their Government on the curriculum has been developing an interest in Bowland Maths. They are looking to develop lessons in which pupils structure open-ended problems and develop their process skills and so are interested in the Bowland work because it represents a critical aspect of maths teaching which they consider that they are currently missing.

The Japan team visited the UK in the autumn of 2010 to see Bowland maths in action. They subsequently decided to develop Bowland style problem solving lessons for Japan and have already made experimental use of Bowland cases in some schools, they have now developed a web-site called Bowland Japan and have begun to translate some of the Bowland cases for use in Japan. They recognize the critical importance of PD, and would like to develop their own PD learning, partly based on the Bowland PD materials, but using LS as a key mechanism. This is the context in which they look forward to further collaboration with Bowlandto promote Bowland type teaching. Recently theyinvited a four person Bowland team to Japan in February this year to see Lesson Study in action and to discuss forging links with Bowland developments.Two further Bowland nominees have now been invited to Japan in the summer to learn more about the practical application of Lesson Study.

Objectives and outcomes of the proposed Bowland project

The Bowland Trust now intends to fund a project which would use the ‘Lesson Study’ approach to assist with the PD for process skills, with particular reference to the use of Bowland materials. It is hoped that this will be done jointly with the team from Japan. This note outlinesour current thinking about the project and is intended to stimulate interest in participating in the project from practicing teachers and from other maths teaching experts.

There are two main (complementary) purposes for the project:

  • to use the LS experience to revise and develop some of Bowland’s current materials; for example, when using the LS approach, teachers may well find that they wish to refer to the Bowland PD materials so, to facilitate this, one output of the project will be to provide better ‘signposts’ and easier navigation
  • to introduce the Japanese concept of ‘Lesson Study’ into PD for maths teachers, with the benefit of advice from Japan; one result of this would be a small ‘trained’ cadre of maths teachers who can then help to develop networks of maths teachers to promote the LS approach and the use of Bowland maths for it

In summary, the project has two longer term objectives, each with an expected shorter term output:

Objective / Outputs
To help secondary maths teachers to improve pupils’ process skills and increase their interest in maths in general, not least through more active use ofBowland materials / Improvements and simplifications to theteacher guidance and/or lesson plans for at least some of the Bowland materials, by drawing on the Lesson Study experiences
To encourage secondary maths teachers to make active use of Research Lessons within the ‘Lesson Study’ approach to further their professional development / A small cadre of trained teachers who can act as ‘Ambassadors’ to catalyse networks of interested teachers, along with guides on the use of Research Lessons (which might include video material) for PD - as well as for ITE

Roles and tasks in the project

Teachers in schools

It is proposed that the project should be undertaken insix schools, for example arranged as two ‘geographical clusters’ of three schools, with each cluster operating in conjunction with an expert in class room observation(see below). We would select schools which had (at least three) maths teachers who were enthusiastic about taking part in the project – and had a supportive senior management team (both in spirit and logistically). The teachers would be keen to participate not only to help with their own professional development, but alsoto be part of a school team contributing to the wider objectives and outputs of the project; in Japan, such a team is sometimes referred to as the school (or maths) research committee.We would hope to find schools which had good links with ITE, in one or other of its various forms.

It is strongly hoped that, for each school, the team of teachers would be joined by at least one teacher from another school – hence the logistical desirability oftwo geographical clusters. In addition, each team would also be joined by external experts as outlined below.

In each school, the team would research and planat least three Research Lessons (RL),perhaps with one in eachterm. Each teacher would deliver one of the lessons in their school – observed by the others, and all would actively participate in the post-lesson discussions. In addition, the teachers would contribute to developing the LS guides and the revisions of the Bowland supportmaterials.

As part of the project, towards the end, we would askthe teachers toact as ‘Ambassadors’ and ‘cascade’ their experienceto a small number of other local schools to encourage them to see the value ofadoptingthe Lesson Study approach for their PD. One way to start the cascade might be for the‘ambassador’ teachers to offer to lead a ‘demonstration’ LS event in a neighbouring school, with a suitable external expert also involved. We would hope that, in time, networksmight form around groups of local schools and teachers who were interested in using the approach (as now happens in Singapore).

External class room experts

The involvement of external experts is an important aspect of LS which we are keen to replicate. We understand that there is a growing desire within the education community in higher education to work more closely with schools; this project would provide an excellent opportunity for them to do that. We would be looking for twopedagogical experts who had expertise in class room observation of pupils’ learning; they might be based in higher education, but need not be. Each would cover three schools, if the logistics allowed; they would assist with fivetasks:

  • advise on what to look for during the Research Lesson and on the tools that can be used to observe pupils’ learning (see the preparatory work below)
  • assist ‘their’ teacher teams to design the three Research Lessons at each of ‘their’ 3 schoolsand then take part in observing the resulting (9) lessons
  • provide the structure for, advise, and contribute to the post-lesson discussion of the observations made during the RL – in part this would be to help secure professional development for the teachers involved
  • lead the development of a ‘Lesson Study’ guide asone of the outputs of the project; the two expertswould work together on this
  • advise on ways to encourage interest in university education faculties to adopt the Lesson Study concept, not only fortheir CPD provision but also for their ITE

Expert(s) in Bowland maths

This would be aperson (or perhaps two) who would work with the school teams, partly to help design the Research Lessons – and to observethem, but mainly to draw out the implications forrevisions and simplifications to thelesson plans and the teacher guidance in the Bowland materials used for the Lesson Studies. This task couldpossibly be undertaken by one of the external class room experts.

Experts from Japan

The group of maths experts in Japan have kindly agreed to help us with this project, although exactly how has yet to be agreed. We hope that some of them would be available to the Lesson Study teams to provide advice on the work; this might include a researcher, an expert teacher and/or a curriculum expert. Their experience of, and emphasis on, class room observation of pupils’ learning (and NOT of teachers teaching) is extensive and considerably greater than exists in Britain. The involvement of some of the Japan team in this project should also help them with their own task ofadapting aspects of the Bowland materialsin order to incorporate them into future Japanese maths.

The approach to the project

Preparatory work

Although, there has been interest in the UK in Lesson Study for some time, there have been variousinterpretations of it. It should be said that the Japanese think that the concept has been widely misunderstood outside Japan, especially in the USA. Nevertheless, the project should examinewhat has been done so far within the UKto see if there are any lessons for this project.

Preparatory work would be needed to develop advice about what to look for during the Research Lesson and todevelop tools to help teachers focus on observing significant features of pupils’ learning during the lesson; this preparatory workwould need to be undertaken only once in depth at the start of the project. It is for consideration how it might best be done, but as well as drawing on the experience from Japan, it would be useful to examine the reports of the Singapore National Institute which document their experience of implementing Lesson Study. Singapore has also developed four short ‘training’ modules on LS which might be useful.

If at all possible, we would plan to hold a meeting of all those likely to be involved in the project, some time in June or July. This would be to discuss the principles of the project, which Bowland topics might be used for the Lesson Study events, any existing available materials (eg points for lesson observation and for post-lesson discussion), logisticalissues, support needed from schools, etc.– and also for participants to get to know one another.

During the first half of the project,we would also explore the policy context for this initiative. Many of the ‘movers and shakers’ in maths education have changed since Bowland maths was first introduced (eg the growth of the role of the National College and of ‘Teaching Schools’) – and of course, the National Curriculum is now being revised. It would be valuable to ‘map the land’ to assess how best to promote the initiative within the current climate and circumstances. This will be the task of a small central group – which might also act as a form of ‘coordinating group’ for the project, and perhaps later as a ‘marketing’ group.

The conduct of the project

The project will consist of each of the six schools using the LS principles to develop three Lesson Study events (perhaps one per term), with the Research Lessons (RL) delivered, in turn, by each of that school’s teachers. The RL and the post-lesson discussion should be held on the same day. If time allowed, it would be good to repeat the RL within a school, with a different teacher, after having revised it in the light of the post-lesson subsequent discussion.

The RLs would be based on Bowland material (to be agreed) for exampleusing a lesson within one of the Case Studies (perhaps focussed on a specific ‘content’ topic),or one Assessment Task, or an illustrative example taken from the current PD materials. If the budget allows, we would like to video parts of the RLs and use the material in support of the ‘cascade’ and as part of any written guide.