Mathematics at Sedbergh: a conversation with Mr Dafydd Roberts-Harry
From the excitement of “lightbulb moments” in the classroom to the quiet confidence that comes from mastering fundamentals, Mr Dafydd Roberts-Harry, Head of Mathematics, shares what makes maths a powerful subject that has retained its relevance within the curriculum. He gives us a glimpse into the thinking behind the department and how the environment at Sedbergh supercharges the level of support available to pupils.
“Numeracy is fundamental — without it, a vast amount of information in everyday life is simply inaccessible.”
What is it about maths that you find exciting to teach?
Learning maths is not a passive process — it is achieved through the active application of a new idea or method. Because of this, it is a subject with very visible ‘lightbulb’ moments. The moment when something clicks — that is what is exciting about teaching maths.
What does it mean, in your view, to think like a mathematician rather than simply learn maths?
Pupils who love maths love it because they don’t have to memorise everything. Deep understanding allows them to solve problems from first principles, without a script to follow. Yes, procedural fluency through practice is very important, but the word fluency is key — a fluent speaker does not rack their brain for words; the words come to them. For a numerically fluent student, key methods are automatic. This frees them up to give full attention to the problems they encounter — their engagement is outward-facing, rather than turning inward to try to remember steps they have learned.
Do you find that there a moment when pupils realise maths is about ideas, not just answers?
It’s not a specific moment; it’s the culture of the classroom. If answers without explanations are rewarded and praised, then when pupils don’t know the answer, their best bet is to act like a random number generator! If explanations are the expectation, then pupils will strive to understand the ideas.
What does a Sedbergh education allow you to do as a teacher that you might not be able to do elsewhere?
The boarding environment makes a difference — as a department, we can provide extra support to pupils in early morning sessions before school, during additional study periods, informally with Sixth Formers during their free periods, and in house in the evenings. Any extra one-to-one support is always a valuable and rewarding experience.
Many international students join us for a year in the Sixth Form. Often, they are required to study maths but may not wish to take A Level Maths, which is a very demanding course. This year, we have worked with international agents to provide a bespoke class focusing on the maths these pupils will need on returning to their home countries.
How do you help pupils who lack confidence in maths begin to trust their own thinking?
Maths learning inherently builds on itself — when pupils have gaps in their knowledge or prior misconceptions, these become barriers to further learning. We therefore need to meet pupils where they are, and we do that through our assessment and streaming. When a pupil is moving at their pace and encountering new ideas in a way that is appropriate to their current knowledge, that is when they progress, and it is that success and progress which builds confidence.
Why do you believe maths continues to be an important subject for current school leavers?
Numeracy is like literacy — without it, a vast amount of information is inaccessible. From understanding payslips and taxes to comparing mobile phone plans or interpreting statistics in the news, maths allows people to function confidently and independently in everyday life.
Beyond basic numeracy, mathematical concepts develop logical thinking, problem-solving skills and the ability to analyse information critically. These skills are valuable in almost every career path, not just traditionally maths-based fields like engineering or finance. Employers consistently look for people who can interpret data, spot patterns, make reasoned decisions and approach problems methodically — all of which are strengthened through studying maths.
If a prospective parent asked you why maths matters within a broader Sedbergh education, what would you say?
Sedbergh is a haven in which children develop into adults ready to thrive. A Sedbergh education develops the whole child, and acquiring ‘powerful knowledge’ is key to this. Maths is powerful knowledge — it transforms your ability to understand and interact with the world.
If you could change one misconception parents (or pupils) have about maths, what would it be?
I am going to cheat and give two, but they are opposite sides of the same coin. Some tell themselves they, or their children, can’t do maths. Others think they should be able to run before they can walk. Nobody ‘just gets maths’ or ‘just doesn’t get maths’. Learning maths is about getting the fundamentals in place and slowly building from them. Anyone can do that, but it takes time, effort and patience. Something as simple as being really strong on times tables or number bonds might be dismissed in the age of the calculator, but these skills start a virtuous cycle — if they are automatic, then more attention is immediately available for new learning. The more automatic you can make the simple things, the better.