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Enriching mathematics: the NRICH Project in England

Liz Woodham
Primary Coordinator, NRICH Program

England's mathematics curriculum aims to ensure that all students have opportunities to see mathematics as relevant, worthwhile, and enjoyable. It emphasises real-life applications of mathematics, and the relationships between different aspects of the discipline. The curriculum encourages students to collaborate around problem-solving, and explore the use of a range of resources and technologies.

The NRICH Project, staffed by a team of qualified mathematics teachers, provides learning resources for use within this curriculum, including rich mathematics-related tasks that show mathematics in meaningful contexts. NRICH began in 1996 and is based in the Faculty of Education and the Centre for Mathematical Sciences at the University of Cambridge.

The project offers a range of resources, including a website, printed publications, and face-to-face outreach activity in the form of Continuing Professional Development workshops. It also aims to develop valuable partnerships with educators and schools.

This article provides an introduction to the NRICH website, and then describes a major project undertaken by England's Qualifications and Curriculum Development Agency and with significant input from NRICH. This project resulted in the creation of a key resource for secondary mathematics educators, titled Engaging Mathematics for All Learners

The NRICH website

The NRICH Project website provides free mathematics enrichment resources for pupils of all ages, including a discussion forum. The maths problems posted on the website encourage students to find and share different experiences of problems, to think mathematically and to explain their ideas clearly. The site is republished every month with new content that is linked to a particular mathematical theme. Each of the resources is labelled to indicate the stage or level of mathematics involved, and according to three levels of difficulty challenge in the task.

Accompanying each problem are notes for teachers which suggest ways of using it in the classroom, and which at the same time encourage and assist them to explore a more process-oriented approach to teaching. The notes are structured under five headings: 

  • Why do this problem? This gives the teacher some background, explaining the mathematics that it addresses, the process skills that may be drawn out and opportunities for assessing pupils' progress.
  • Possible approach: How the problem is used will depend on the needs of the class or individual but this section offers some suggestions.
  • Key questions: This section provides a list of appropriate prompts and questions that may help guide learning or assist students, particularly those who are struggling with the task.
  • Possible extension: Students might wish to consider variants of each problem, such as seeking different outcomes, or find alternative ways of doing the problem. This section gives suggestions for taking the problem further.
  • Possible support: Here, learners who are struggling to get started are given some ideas. This could include a link to a similar but more straightforward problem.  

Working in groups or individually, students submit solutions to the problems. Students' solutions are then published online and archived. These solutions, which showcase the different approaches taken by different learners, become a rich resource that teachers can draw on for classroom use. They may assist teachers in determining possible methods of approach, or as examples to show their students after completing a problem.

The problems and solutions are supplemented by the Ask NRICH discussion board, where students, teachers and other registered participants can ask mathematics-related questions and discuss issues that are of interest to them. The board is monitored by a team of mathematicians, including university students, who provide assistance as needed.

The For Teachers page summarises the content of the site from a teacher's perspective. It includes links to a variety of resources, including research material, games, and tasks. Of particular interest to teachers is the Curriculum Mapping section, which links to a number of rich tasks on the website that are designed to develop both content knowledge and skills in mathematical thinking and problem-solving for all stages. These documents are based on England's curriculum, but are likely to be transferable to other curricula. The website also includes an explanation of the nature and value of rich tasks.

The Engaging Mathematics for All Learners project

In the past academic year, NRICH has contributed to Engaging Mathematics for All Learners.  This publication guides secondary educators through the use of rich mathematical tasks, which are designed to be engaging, challenging, extendable, and invite learners to explore different ways to solve them. The tasks also encourage students to collaborate, and develop new mathematical understandings. The publication draws on examples of mathematics enrichment and enhancement from the NRICH website.

Engaging Mathematics for All Learners guides educators through issues such as how to use ICT to develop challenging problems, and designing and using games to teach maths. It offers a range of other tips for activities and how to use resources. Other topics include the use of real-life data, the role of maths outside the classroom, how maths is used in society, and how to link maths to other curriculum areas.

It includes case studies to show how different schools have identified aims, processes for achieving them, and ways to measure their progress. Some of these case studies were prepared by schools who were working with staff from NRICH so they reflect the journey each school made as they integrated NRICH tasks into their everyday classroom practice. 

Educators in Australia and elsewhere are welcome to follow the NRICH program as it develops. Interested readers can keep up to date with NRICH developments by signing up for the NRICH mailing list. They can also contact the NRICH Team by emailing enquiries.nrich@maths.org.

Key Learning Areas

Mathematics

Subject Headings

Mathematics teaching
Inquiry based learning
Great Britain
Curriculum planning