NACE is proud to partner with the NRICH project at the University of Cambridge’s Centre for Mathematical Sciences, which offers free online resources to enrich the mathematics curriculum, provide challenging and meaningful activities, and develop mathematical thinking and problem-solving skills. In this blog post, the project’s director, Ems Lord, explains why and how NRICH is developing resources designed to get GCSE students seriously interested in Further Mathematics…

Entries for the Further Mathematics A-level have tripled in recent years, from around 5,000 students in 2005 to a staggering 15,000 by 2015 (source: JCQ). But one of the greatest recent success stories in mathematics is under threat.

Figure 1: Entries for Further Mathematics up to 2016 (source: JCQ)

The transformation of Further Mathematics has all the ingredients of a great news story, yet the latest figures are alarming. Anecdotal evidence from both schools and colleges indicate a staggering 50% drop in the number of students opting to study Further Mathematics this year.

Recent changes in national policy promoting the study of three A-levels have hit Further Mathematics – often regarded as a fourth option – harder than most subjects. The NRICH team at the University of Cambridge has joined up with colleagues at the University of Oxford to address concerns regarding the current decline in Further Mathematics entries. The realisation that many GCSE students do not appreciate the opportunities offered by Further Mathematics led to our new set of free resources for schools, which we’ve called Adventures with Complex Numbers.

Why focus on complex numbers?

The current GCSE mathematics curriculum offers learners very limited insights into some of the most exciting topics awaiting them with Further Mathematics, such as complex numbers. The topic offers a terrific opportunity to give students interested in a range of different subjects a real taste of Further Mathematics well before they make their A-level choices. Complex numbers is an engaging topic for potential artists, engineers and scientists, as well as future mathematicians.

Figure 2: The Mandlebrot Fractal, a very popular concept with artists, who frequently exploit the level of detail and complexity revealed by zooming in on the original image.

What resources are available?

The key here is remembering that the resources created by NRICH are aimed at GCSE students; they are not intended for A-level teaching, although teachers may recognise their potential for those students too.

The materials adopt two straightforward approaches towards complex numbers. First, they explore the day-to-day applications of complex numbers in the real world. Learners can hear first-hand accounts about the crucial role that complex numbers play in the electricity networks that power our daily lives and how they help engineers keep structures safe and stable – as well as some spectacular examples of what can go wrong!

Figure 3: A dramatic clip from Professor Ahmer Wadee’s video Complex Numbers – Strength 

The second approach encourages learners to explore complex numbers for themselves. The team have devised a range of animations which encourage a very hands-on approach, letting learners ask themselves “What if?” and giving them the tools to explore their ideas:

Figure 4: Screenshot from Vanishing Roots

So, they’re interested… What next?

We very much hope that learners enjoy the interactive resources and first-hand accounts exploring the uses of complex numbers. But the resources go much further than that. Learners can access a range of articles which take the topic much deeper, allowing them to discover how Heron of Alexandria  missed his chance to explore the unknown mathematical land of complex numbers, as well as exploring the role of complex numbers in movie animation. For learners considering signing up for the Further Mathematics A-level, there’s also a live link to the national Further Mathematics Support Programme.

We’re not suggesting that this set of new resources will halt the declining numbers of Further Mathematics entries. Clearly, other agencies need to get involved too to arrest the decline. But we do hope they will offer an excellent starting point for engaging learners with the ideas they’ll encounter when studying Further Mathematics, and that they will be tempted to learn more about the possibilities offered by the subject.

Become an NRICH ambassador…

NRICH is partnering with NACE to pilot its new ambassadors scheme through the NACE Research and Development (R&D) Hubs. Through this partnership, teachers at NACE member schools will have the opportunity to work alongside the NRICH team, exploring ways to share NRICH’s resources with schools at differing stages along the journey of developing confident and competent problem-solvers. Supported by bespoke training from NRICH, ambassadors will share their learning through the NACE R&D Hubs, collaborating to develop approaches for wider dissemination of NRICH’s resources for teachers and learners. 

Want to get involved? Contact NACE to find out more.

Ems Lord has been Director of NRICH since 2015, following a previous role leading one of the country's largest Mathematics Specialist Teacher Programmes. Ems has taught mathematics across the key stages, from early years to A-level Further Mathematics, and has worked in a variety of settings, including a hospital school. She’s supported schools as a leading mathematics teacher, local authority consultant and Chartered Mathematics Teacher, and has taught mathematics education on both BEd and PGCE teacher programmes. She is currently working on her PhD thesis, which explores approaches to improve support for those learning calculation skills, and is President-Elect of the Mathematical Association for 2019-2020.

Wednesday, February 7, 2018