In a recent short-lived but productive panic about money (I have them occasionally, since trading in my smattering of unsuccessful careers for life as a full-time home-maker and freelance child-wrangler), I reactivated my old tutoring profiles on a couple of websites. Within days one of them bore fruit, and last week I trundled off to the same seaside town in which I recently spent a week babysitting an adorable toddler, to conduct my first tutoring class for some years.

My student is 9 years old, a bright boy who I’ll call Livewire. His brother is 13 and his moniker can be Steadfast. I’m officially only tutoring Livewire, but Steadfast has hung around for at least part of the two lessons we’ve had so far, and has joined in our end-of-session chats. I think this is probably going to be a very useful thing, because it means the two boys can discuss what we’ve covered in the lesson and work together on figuring things out.

I was tasked by the parents to get Livewire ready for transitioning to secondary school in just under two years. They were concerned because Livewire is less quiet and studious than his older brother (hence the nicknames) and worried that he wouldn’t achieve his full potential when he did his GCSEs. I spent twenty minutes after the first lesson reassuring his mum that Livewire is a bright boy who is clearly motivated to learn, and that the fact he learns in a different way to Steadfast doesn’t mean he’ll be any less successful. She admitted that she was heavily influenced by the fact that she was taught using the head-down, textbook-open, memorise-and-repeat method and anxious about the unproven record of any other approach.

Point of interest: all my tutoring students to date have been from Asian families, their parents either first or second generation immigrants to the UK, and very eager for their offspring to achieve highly in exams. They’ve also, oddly enough, all been boys, but that’s beside the point. I did once turn down a job tutoring a 5 year old for four hours a week on the basis that the poor little mite shouldn’t have to endure extra classes after fighting his way through a full day of school when he’s very probably still in nappies at night, but on the whole I admire my employer parents’ desire to give their children a good education and am quite willing to work with their children towards their goals of academic excellence, but using my own methods.

My own methods are essentially based around three premises: that the student will get enough rote-learning and fact-instilling at school, that learning is most successful when enjoyable, and that knowledge is worthless without understanding. With Livewire, I’m tutoring both maths and English, although really we’re just discussing philosophy and the mysteries of the universe under different headings.

In our first session I got Livewire to spend 15 minutes on each of two practice maths SATs tests, to get a baseline for his knowledge at present. He didn’t complete both papers or get all the answers right, which is precisely what I expected since he won’t take the tests for real until the end of next year, and will get three times as long to do them, but he did enough for me to tell that he is intelligent and has been taught well. I identified some basic gaps in his understanding though, so that’s what we’re targeting first.

On Friday we spent nearly 45 minutes trying to figure out why the order of operations does, and doesn’t, work. He didn’t know the concept, but that didn’t stop him discovering, within minutes, that the claim I had been taught at school and parroted on to him, that you can do multiplication and division in any order and get the same answer, was wrong. You have to do it left to right, and we couldn’t figure out why that was the case.

I came home determined to ensure that I understood the underlying mathematics to the rule so that I could explain them to Livewire and Steadfast, who was also baffled by the discovery that his teachers had mislead him. I’ve spent quite a few hours on it over the weekend and have figured out how to explain addition, subtraction and multiplication in real-world terms (represented by marbles and a number line), but I’m still wrestling with division. *Why* is 8 divided by 4 the same as 8 times 0.25? I can dimly recognise that it is logical that division is inverse multiplication, but I’ve not managed to grasp it with the same certainty that I now have regarding subtraction being inverse addition (or rather, addition of a negative number).

I’m really enjoying this new tutoring venture, but I’m not convinced that it would be true to say that I’m teaching and Livewire is learning. Rather, we’re both rooting around to figure out why things are true, and he’s leading the discoveries at least as much as I am. I always preferred to understand the mathematical reasoning rather than simply learning the formula, but my GCSE teacher was so dismissive and critical of my questions that he completely put me off the whole thing for nearly a decade, so it’s fun to come back to it and start again from the very basics. Who knows? This time next year we might both be moving onto the sort of advanced maths I never studied at school!