The innovative new website (undergroundmathematics.org
) offers hundreds of free teaching resources to help make A-Level mathematics a richer, more coherent and more stimulating experience for students and teachers alike.
The resources combine problem solving, mathematical reasoning and fluency to stimulate curiosity, introduce students to new ideas, and encourage them to pose questions, reflect and collaborate.
The project’s central aim is to empower students to make connections between different areas of mathematics and thereby develop a deeper understanding.
To achieve this, the new website takes the form of an underground map and arranges its resources around a network of five thematic tube lines: ‘Number’, ‘Geometry’, ‘Algebra’, ‘Functions’, ‘Calculus’.
Each station on the tube map features an overarching question. At the ‘Thinking about Functions’ station teachers and students are asked the question: ‘What are key properties of functions?
’ Additional key questions follow which students should be able to discuss by the time they leave the station, such as ‘What features of functions are visible on a graph?’ and ‘What do we mean by symmetry of a function?’
At each station, teachers will find a range of teaching resources, often with notes to support their use in the classroom. Within the resources, the website also provides additional insight into the problem, suggests alternative approaches and highlights links to other areas of mathematics.
When appropriate resources are selected, students should benefit from tasks that provide the opportunity for deeper understanding to develop. Teachers can also visit the ‘Pervasive Ideas’ wheel to access mathematical ideas which permeate topics throughout A level mathematics, such as transformations
, symmetry and averages.
The project’s Directors are Martin Hyland
, Professor in Mathematical Logic in the Department of Pure Mathematics and Mathematical Statistics; and Lynne McClure, Director of Cambridge Mathematics
, a partnership between four University departments (Cambridge University Press, Cambridge Assessment, and the Faculties of Mathematics and Education).
Professor Hyland said:
“The project aims to help teachers develop the mathematical understanding of all their students. Our resources present students with significant mathematics which enables them to experience the fundamental ideas which pervade the subject.
"Students get the opportunity to question and exchange ideas and become accustomed to tackling unfamiliar problems. We hope that they will appreciate the beauty of mathematics and at the same time acquire the confidence to deploy their skills to meet the challenges of the modern world.”
Lynne McClure said:
“Underground Mathematics offers engaging and thought-provoking tasks which encourage students to communicate, reason and internalise mathematics for themselves. We firmly believe that this will equip students well for the wide range of careers which now also require these more sophisticated skills, as well as preparing them for public examinations.
"And the extensive feedback which we have received shows that both teachers and students really enjoy working in this way. This has always been at the heart of the project.”
Over the last four years, the Underground Mathematics team has worked closely with dozens of partner schools from across England to learn from teacher and student experiences of using the resources, to optimize the website and to discuss wider aspects of the project.
“It was an honour to be invited to try out the resources as the website was being developed, and such fun too! The resources are rich, engaging and enjoyable for both the students and the teachers.
"We love the atmosphere they create in the classroom as students develop their problem solving skills and improve their ability to think, and work, collaboratively: skills which are invaluable for them to be honing as they prepare for further academic study and their future careers.
"We look forward to incorporating the resources more and more into the experience we provide our students with.”