How to Make the Most of Your Maths Lessons

Why some students fly and others don't

I've been tutoring maths for over fifteen years, and in that time I've noticed something. The students who make the biggest progress aren't necessarily the cleverest ones. They're the ones who approach their learning in a particular way — and it's a way that any student can adopt, regardless of ability.

If you're investing time and money in maths tutoring, you want to get the most out of it. So here's what I've learned about what actually works.

The rule of thirds

I use a simple framework when I'm planning practice for a student. I call it the rule of thirds, and it goes like this:

• One third of the questions should be easy. These are the confidence builders — the problems a student can do without much thought. They reinforce what's already been learned and keep the basics sharp.
• One third should be fine but with the odd issue. These are the questions where the student mostly knows what to do, but might trip up on a step or make the occasional mistake. This is where the real learning happens — working through small errors and tightening up understanding.
• One third should be really tough. These are the stretch questions that push a student to the edge of what they can do. Not every student will get every one of these right, and that's fine. They're there to build resilience and show the student where their ceiling currently is.

The balance matters. Too many easy questions and the student gets bored — they're not being challenged and they're not making progress. Too many hard questions and they get demoralised — they can't access the work and they start to believe they "just can't do maths." The sweet spot is a mix that keeps them engaged, challenged, and making steady progress.

If your child comes away from every session or practice set feeling like they got everything right with no effort, the work isn't hard enough. If they come away feeling like they couldn't do any of it, the work is too hard. The goal is that feeling of productive struggle — working hard, getting most things right, and learning from the things they got wrong.

The tortoise and the hare

There's an analogy I come back to constantly with my students: the tortoise and the hare.

The hare is the student who wants to skip ahead to exam papers. They've covered the topics in class, they reckon they understand the basics, and they want to start doing past papers straight away. I understand the logic — exams are the goal, so why not practise for them?

The problem is that exam practice only works when you already have a strong foundation. If a student jumps into past papers before they've truly mastered the underlying concepts, they end up wrestling with questions that are out of reach. They can't access the harder marks because the building blocks aren't solid. They get frustrated, they lose confidence, and — ironically — they end up less prepared for the exam than if they'd taken a slower approach.

The tortoise takes a different route. They start at the beginning. They work through each topic methodically, making sure they genuinely understand it before moving on. They don't rush. They don't skip steps. And when they eventually get to past papers — which they will — they're able to access far more of the content, because the foundations are in place.

I believe exam technique is overrated. I know that's a provocative thing for a tutor to say, but I genuinely mean it. A student who is truly fluent in the underlying maths can apply that knowledge in an exam setting without needing weeks of exam technique coaching. The students who struggle in exams are almost always struggling because of gaps in their knowledge, not because they don't know how to read the question or manage their time.

So if your child's tutor is spending most of the sessions on past papers, I'd encourage you to ask whether that's really the best use of time — especially if the exams are more than a few months away. When the time is right for past papers, my free past papers archive has thousands of papers from all the major exam boards.

Start at the beginning

This is the advice that students (and parents) find hardest to accept. If a student has gaps in their understanding — and by Year 10 or 11, most students do — the most effective thing to do is go back and fill those gaps, even if it means revisiting topics from a year or two ago.

I know it can feel like going backwards. But it isn't. It's like a builder discovering that the foundations of a house are cracked. You can keep building upward and hope for the best, or you can go back, fix the foundations, and build something that will actually stand up.

The students who see the most progress with me are the ones who are prepared to slow down and start at the beginning. They trust the process, they put in the work, and the results follow.

Don't wrestle with questions out of reach

This is one of the most common mistakes I see students make during independent practice. They get stuck on a question, and they spend 20 or 30 minutes trying to figure it out on their own. I admire the persistence, but it's usually counterproductive.

If you've been stuck on a question for more than 10 minutes, there's a good chance it's testing a concept you haven't fully understood yet. The answer isn't to keep staring at it — it's to go back to the textbook, find the relevant section, and read through the explanation. If that doesn't help, mark the question and bring it to your next tutoring session. That's exactly what the session is for.

Time spent wrestling with a question that's genuinely out of reach is time that could have been spent practising something at the right level. And practice at the right level is what builds fluency.

Do the work between sessions

I can't stress this enough. A tutoring session is one hour a week. That's roughly 2% of the student's waking hours. If the other 98% doesn't involve any maths, progress is going to be slow.

I recommend that every student does at least two hours of independent maths practice per week, on top of any homework they get from school. I go into more detail on why this matters in my guide on how many tutoring sessions you need per week. That practice should follow the rule of thirds — a mix of easy, moderate, and hard questions — and it should be focused on the topics we're currently covering.

The students who do this consistently are the ones who improve the fastest. It's not complicated, and it doesn't require any special talent. It just requires a routine — and the discipline to stick to it.

Think of it like going to the gym. Your tutor is your personal trainer. They design the programme, coach you on technique, and hold you accountable. But the actual fitness comes from the work you do between sessions. If you only train when the trainer is watching, you're not going to get fit.

Be prepared to slow down

I'll say it one more time, because it's the single most important piece of advice I can give: be prepared to slow down.

The students who make the fastest long-term progress are the ones who are willing to go slowly in the short term. They don't chase grades — they build understanding. They don't jump to exam papers — they master the fundamentals. They don't rush through topics to keep up with their class — they make sure they've genuinely understood each one before moving on.

It takes patience. It takes trust. But it works, every single time. For more on what this looks like in practice, have a read of my guides on how to revise for GCSE maths and how to revise for A-Level maths.

If you'd like to talk about how your child can get more from their maths lessons — or if you're considering tutoring for the first time — I offer a free 30-minute intro session with no strings attached. We'll have a chat, I'll get to know the student, and we'll work out a plan that makes sense.