Designing a fully-resourced, research-informed school mathematics curriculum
Written by Colin Foster, Tom Francome, Dave Hewitt and Chris Shore. Please see the MEC website for more information about us and our research: https://www.lboro.ac.uk/departments/mec/staff/
The Loughborough University Mathematics Education Network is now in its second year, providing high-quality research-informed professional development to schools and teachers of mathematics in the East Midlands and London areas, drawing on the wealth of expertise within the Mathematics Education Centre here. In the next phase of this work, we’re embarking on creating and trialling a complete, fully-resourced school mathematics curriculum, which will be available free of charge on the LUMEN website. In this blogpost we outline why we’re doing this and the research-based design principles we’ve established for beginning this project, which we wrote about in our recent paper.
The need for a fully-resourced school mathematics curriculum
Teachers in the LUMEN network have frequently talked about the considerable demands placed on schools to develop and resource their mathematics curricula. Although in England we have a National Curriculum, this only sets out what to teach, and doesn’t provide teaching materials. This means that schools are faced with broadly two options for their curriculum resourcing, both of which present considerable challenges.
On the one hand, schools may buy in to a commercial scheme of textbooks or online learning resources. These are often perceived to be expensive and of poor quality, and they generally take little account of the research literature that exists across mathematics education, cognitive science and educational design. Once purchased, they are hard to adapt or use flexibly. On the other hand, schools can opt to curate their own curriculum resources from the many (often free and online) sources available. While there are some excellent teaching materials on the web, these can be hard to find among the ocean of material that exists (currently over 700,000 resources on the Tes website), and it is an extremely time-consuming and difficult job for each mathematics department to attempt to assemble a coherent curriculum from these diverse materials.
With the recent expansion of the Centre for Mathematical Cognition, and the wealth of different expertise available here, we feel that we are in an ideal position to address the challenge of designing high-quality classroom mathematics resources to cover the entire school mathematics curriculum, initially focusing on key stage 3 (ages 11-14). Clearly, this is a highly ambitious aim, but we believe it would be of enormous benefit to schools and teachers, particularly at a time when there are great challenges around teacher recruitment and retention.
Informed by robust research
Our overarching aim is for the LUMEN mathematics curriculum to take serious account of the best international research evidence available. In recent decades, increasing knowledge has accumulated within mathematics education, cognitive science and educational design, and much of this has important implications for the design of school mathematics resources. It is vital that our design learns from this body of knowledge. As well as basing our design choices on robust research findings, we are also committed to trialling the resources in real classrooms with real students and teachers. Most commercial resources are never tested out in the field before they are published, and this is a serious missed opportunity. By trialling our materials through several cycles, obtaining detailed feedback at each stage about how students respond, and where the difficulties surface for the teacher, we can considerably improve the quality of the resources. Since the materials will be freely available on the LUMEN website, in principle the process of feedback and improvement can continue indefinitely.
Every teacher who has ever tried to curate a curriculum from the best resources they can find from a variety of sources has faced the problem of coherence. A collection of great tasks may not add up to a great collection of tasks. The same problem arises with commercial textbooks, where, even though the superficial page design may be consistent from chapter to chapter, at a deeper level the ideas rarely cohere in mathematically meaningful ways.
We have thought a lot about features of the curriculum that could facilitate conceptual coherence across different topics. One way to do this could be through the use of consistent representations and contexts from topic to topic, such as prioritising number lines wherever possible. This could be more effective than the more haphazard approach which can result when resources are brought together from a variety of different places. Sequencing topics carefully so that concepts diverge and converge in planned ways as the student makes their way through seems to offer ways to enhance their experience. We have found the work of Dr Leslie Dietiker extremely useful in thinking about this, as she writes about the mathematics curriculum as a coherent story. Her metaphor has helped us to draw out a set of initial design principles from the research literature that we hope will enable us to construct a curriculum that makes sense at each stage, while setting up and resolving tensions and surprises along the way.
We give a lot more detail about this in our paper, but our five main principles are that the mathematics curriculum should:
- harness and develop the skills and expertise of teachers;
- balance the teaching of fluency, reasoning and problem solving;
- give explicit attention to important errors and misconceptions;
- allow learners to compare and contrast alternative methods; and
- engineer coherence through strategic use of consistent representations and contexts.
Above all else, the curriculum can only be as successful as the skilled and knowledgeable teachers who draw on their expertise to make use of it with their students. We are utterly reliant on our partnerships with schools and teachers through LUMEN as we work to develop these resources. We are realising that the teacher guidance materials that will accompany the student resources are at least as important as the resources themselves, and are perhaps a more difficult design challenge.
To find out more about the development of this project over the coming years, please visit the LUMEN Curriculum page.
Centre for Mathematical Cognition
We write mostly about mathematics education, numerical cognition and general academic life. Our centre’s research is wide-ranging, so there is something for everyone: teachers, researchers and general interest. Jayne Pickering, a research fellow at the CMC, runs this blog and edits all posts. Please email email@example.com if you have any feedback or if you would like information about being a guest contributor. We hope you enjoy our blog!