Our First Lesson
Before your first lesson, I’ll send you a Google Meet link by email. If we decide to continue, you’ll use the same link for all future sessions — simple and consistent.
All you need to bring is a pen and paper, though if you have a device that lets you write on my online whiteboard, that can be helpful. If you have any recent school tests, I’d love to see them — they’re not essential, but they give me a useful snapshot of your current level and how you perform under exam conditions.
We’ll start by discussing your goals — what you’d like to achieve, where you think you are now, and what’s motivating you to improve. Then we’ll do some maths together. It’s not a test, it won’t be done in silence and you don’t need to have prepared for it. It’s simply a way for me to see what you’re confident with and what challenges you. You should expect it to feel uncomfortable at times because I’ll be trying to find the limits of what you know. It also gives you an insight into what lessons with me would be like – lots of conversation and curiosity, focused on understanding why maths works, not just how.
If you’re working towards your GCSE, we’ll probably look at topics like fractions, negative numbers, percentages, area, and algebra. For A-level students, we’ll focus on algebraic manipulation and circles, and we might explore differentiation and integration as well.
Throughout the lesson, I’ll be asking you to explain your reasoning — how you got your answers, how confident you feel, and how you check your results. This helps me understand not only what you know, but how you think.
By the end of the session, I’ll have a clear idea of your strengths, key focus areas, and three to five topics for us to tackle next. It’s a great starting point for your learning journey; I’ll keep reassessing you informally as we go and adjusting our plans accordingly.
Exam vocab revisited.
It all begins with an idea.
In 2015, having completed action research as part of my PGDip in Maths Education at Warwick and early in my teaching career, I wrote an article for the Times Educational Supplement on the value of teaching A-level maths exam vocabulary explicitly.
Ten years later, how has my teaching and thinking about pedagogy evolved? Do I stand by what I wrote then?
100% YES.
The underlying idea was something that I was taught on my PGCE - “make the implicit, explicit” - and the specific idea of teaching maths-specific exam vocabulary is something I work on with all my students. In the article, I wrote about it being needed most for A-level students and that continues to be true but there is no reason why it can’t be taught sooner so that the leap to A-level is less shocking.
The research and the article that led from it have become a integral part of my teaching. I am constantly considering what fundamentals may not have yet been made explicit to my students and I focus on making them explicit. This can mean having conversations about simpler ideas than my students or their parents might expect but if that brick of understanding is missing from their wall of maths, it needs filling in and will give them a stronger foundation for future learning.