Exploring socially distributed professional knowledge for coherent curriculum design

This proposal seeks to support and develop, in new directions, an existing relationship between researchers in mathematics education based at the Universities of Leicester, Nottingham and Tokyo Gakugei University. The intention is to explore the potential for future collaboration that builds on the expertise of the groups in their design research of learning materials to focus on the social co-construction of knowledge for curriculum coherence in mathematics.
Mathematics education research provides insight into a considerable range of issues important in teaching for effective learning of mathematics. Important in this regard, for example, are studies that explore knowledge for teaching, student understanding and learning, how teachers use, and students respond to, tasks and models of teaching for learning.
Integral to the practice of teachers in Japan is lesson study by which they engage in joint inquiry into teaching and learning in their classrooms. This has been recognised as having the potential to improve teaching and in turn improve learning outcomes. It has been adapted, at a small scale, in a substantial number of countries as a mode of collaborative teacher learning and has been central to the collaboration of the two research groups to this point. In Japan the research group implements lesson study in its work with a number of teachers and to inform the writing of student and teacher texts.
The proposal here is based on our contention that in the UK, and perhaps to a lesser extent in Japan, much mathematics education research is inaccessible to teachers in their day-to-day practice and that the education community more widely lacks insight about how to draw on such research in ways that support the design of a coherent approach to curriculum implementation.
It is our intention to explore how we might better inform teachers' work that lies at the intersection of research and teacher praxis, in ways that can inform coherent curriculum design. In lesson study this important work is known as kyozaikenkyu, a term that has no direct translation into English. As part of our work in this area we will consider how we might identify a range of didactic devices that provide insight into mathematical structure and consequently have the potential to support learning across topic areas and over time. For example, number lines, as didactical devices, can have an important role to play in developing understanding of all aspects of number during early years. These may later be further developed as double number lines to provide insight into the mathematical relationships inherent in situations involving proportionality, can support working with Cartesian graphs and eventually working with complex numbers in the complex plane. Central to our collaborative work, therefore, will be to explore how such understanding might be drawn from, and co-constructed in social interaction in communities that bring together teachers, researchers and other appropriate curriculum experts.
We propose to fund a series of symposia/workshops during 2019 that will explore how we might develop devices such as the double number line to support teaching towards, a mathematically coherent and interconnected curriculum We will draw on a number of theoretical perspectives to inform our discussions.
Outcomes are expected to include enhanced knowledge for curriculum design, understanding of how the process of kyozaikenkyu might be effectively researched more substantially together in future, together with increased research capacity in the two teams and stronger links and connections between the two research groups and their mathematics education communities.
The outcomes of this collaboration will be disseminated to academic, professional and policy stakeholder audiences and will be supported by a web presence and a programme of seminars, workshops, conference attendance in addition to planned academic journal articles and scoping report.

The potential impact of the proposed collaboration is that of developing new insights into an issue of international concern, that is the development of teacher knowledge for the teaching of a coherent curriculum. This is a barely researched area and the proposed agenda has potential significance and interest to inform academic, professional and policy/stakeholder audiences. The outcomes of the work will be to provide insight and knowledge that has the potential to stimulate an important future research agenda.
In the UK the work of the collaborative endeavour will be centred at Leicester but not exclusively based there. For example, this will support further collaboration between PI Foster and Co-I Wake who worked together on the Nuffield funded Lessons for Mathematical Problem Solving project) as well as emerging researchers studying for research degrees (there are three currently under the supervision of PI Wake in Nottingham).
In Tokyo lesson study research and its outcomes to inform design research of curriculum and materials is well-established through a number of teacher research groups and masters courses led by PI Nishimura. The work undertaken has the potential to have impact on future iterations of curriculum design and consequently inform and stimulate both future research and practitioner activity.
To ensure that an outcome of the collaboration makes academic impact the proposal provides for:
1 Nationally
- a planned series of both closed and open seminars organised and hosted by each UK and Japanese research groups
- dissemination of emerging work at regular conferences of the national organisations for research in mathematics education in each country
2 Internationally
- a scoping report of the project work that identifies and informs a future research agenda
- activity in appropriate research communities in the field in which the partners are already networked and that are likely to find the focus of the collaborative work of significance: in particular the World Alliance of Lesson Study and an informal grouping of European education researchers in lesson study both of which will hold conferences in 2019 at which the work of the group may be presented.
3 Publications
The collaboration plans to work towards a future series of collaborative publications including two that situate the work in the national context of each partner and a further publication that synthesises this work to provide a comparative study.
Outcomes of the proposed work have the potential to have impact more widely than academic audiences. It is planned through a number of workshops to be held during bi-national visits of the research teams to engage with professional (teacher) audiences as well as with policy stakeholders (for example, the National Centre for Excellence in Teaching Mathematics and Cambridge Mathematics in the UK and the Ministry of Education in Japan). Partners in their respective countries have well-established relationships with these organisations. In the UK NCETM support provides the potential for dissemination and resulting impact via the Maths Hub network.
The development of a web presence associated with "curriculum coherence for mathematics" allows for dissemination of the work of the collaborative group and will have a structure that supports dissemination to the three main potential areas of impact academic, professional and policy stakeholders. This has the potential to support a level of sustainability of activity in this area.